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1. 8 10 4 The weight Hessians of the ellipsoid 8 10 5 The correlation times of the ellipsoid 50 50 53 55 vi CONTENTS 8 10 6 The correlation time gradients of the ellipsoid 102 8 10 7 The correlation time Hessians of the ellipsoid 104 8 11 Spheroidal diffusion tensor s lt e is s roeas s edok mo ea Gue E e E 106 8 11 1 The diffusion equation of the spheroid 106 8 11 2 The weights of the spheroid coser ana ee A 106 8 11 3 The weight gradients of the spheroid 107 8 11 4 The weight Hessians of the spheroid 107 8 11 5 The correlation times of the spheroid 108 8 11 6 The correlation time gradients of the spheroid 108 8 11 7 The correlation time Hessians of the spheroid 108 12 Spheneal QUISO Tensor oo a fe ew s Ro doom eee Boe ae A 110 8 12 1 The diffusion equation of the sphere 110 8 12 2 The weight of the sphere o llle 110 8 12 3 The weight gradient of the sphere 110 8 12 4 The weight Hessian of the sphere o 111 8 12 5 The correlation time of the sphere 111 8 12 6 The correlation time gradient of the sphere 111 8 12 7 The correlation time Hessian of the sphere 111 8 13 Ellipsoidal dot product derivatives 2
2. lt Match any character xx Match the character x any number of times for example x will match as will XXXXX Match any sequence of characters of any length Importantly do not supply a string for the data type containing regular expression The regular expression is implemented so that various strings can be supplied which all match the same data type Diffusion tensor parameter string matching patterns 10 2 THE LIST OF FUNCTIONS Data type Global correlation time Tin Isotropic component of the diffusion tensor Diso Anisotropic component of the diffusion tensor Da Rhombic component of the diffusion tensor D Eigenvalue associated with the x axis of the diffusion diffusion tensor Dy Eigenvalue associated with the y axis of the diffusion diffusion tensor D Eigenvalue associated with the z axis of the diffusion diffusion tensor D Diffusion coefficient parallel to the major axis of the spheroid diffusion tensor D Diffusion coefficient perpendicular to the major axis of the spheroid diffusion tensor D Ratio of the parallel and perpendicular components of the spheroid diffusion tensor Dratio The first Euler angle of the ellipsoid diffusion tensor The second Euler angle of the ellipsoid diffusion tensor 3 The third Euler angle of the ellipsoid diffusion tensor y The polar angle defining the major axis of the spheroid diffusion tensor
3. Match the end of the string For example 8s 2 will match s2 but not S2f or s2s lt Match any character xx Match the character x any number of times for example x will match as will XXXXX Match any sequence of characters of any length Importantly do not supply a string for the data type containing regular expression The regular expression is implemented so that various strings can be supplied which all match the same data type 10 2 THE LIST OF FUNCTIONS 367 Model free set details Setting a parameter value may have no effect depending on which model free model is chosen for example if S values and 5 values are set but the run corresponds to model free model m4 then because these data values are not parameters of the model they will have no effect Note that the Rex values are scaled quadratically with field strength and should be supplied as a field strength independent value Use the following formula to get the correct value value Rex 2 0 m frequency 2 where Rex is the chemical exchange value for the current frequency 7 is in the namespace of relax ie just type pi frequency is the proton frequency corresponding to the data Model free data type string matching patterns 368 Data type Object name Local Tm local_tm Order parameter S s2 Order parameter S s2f Order parameter S2 s2s
4. probs alpha peta gamma ep heteronuc_type proton_type Patterns pO pl p2 PN alphaO alphatl beta0 betal gamma0 gammal r or Bb ond _ L1 ength Hh eteronucleus Pp roton The objects corresponding to the object names are lists or arrays with each element corrsponding to each state 10 2 THE LIST OF FUNCTIONS 309 10 2 145 value read Synopsis Function for reading residue specific data values from a file Defaults value read self run None param None scaling 1 0 file None num_col 0 name_col 1 data_col 2 error_col 3 sep None Keyword Arguments run The name of the run param The parameter scaling The factor to scale parameters by file The name of the file containing the relaxation data num_col The residue number column the default is 0 ie the first column name_col The residue name column the default is 1 data_col The relaxation data column the default is 2 error_col The experimental error column the default is 3 sep The column separator the default is white space Description Only one parameter may be selected therefore the param argument should be a string If the file only contains values and no errors set the error column argument to None If this function is used to change values of previously minim
5. relax gt grace view file s2 agr dir grace 180 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 30 grace write Synopsis Function for creating a grace agr file Defaults grace write self x data type spin y_data_type None spin_id None plot_data value file None dir grace force False norm False Keyword Arguments x data type The data type for the X axis no regular expression is allowed y data type The data type for the Y axis no regular expression is allowed spin_id The spin identification string plot_data The data to use for the plot norm Flag for the normalisation of series type data file The name of the file dir The directory name force A flag which if set to True will cause the file to be overwritten Description This function is designed to be as flexible as possible so that any combination of data can be plotted The output is in the format of a Grace plot also known as ACE gr Xmgr and xmgrace which only supports two dimensional plots Three types of keyword arguments can be used to create various types of plot These include the X axis and Y axis data types the spin identification string and an argument for selecting what to actually plot The X axis and Y axis data type arguments should be plain strings regular expression is not allowed If the X axis data type argument is not given the plot will default to having the spin sequence along the
6. 8 185 1 0 where c is the weight of the single exponential term and 7 is the correlation time of the single exponential term 8 12 2 The weight of the sphere Definitions The entire diffusion parameter set consists of a single geometric parameter and is D rm 8 186 Summation terms The summation indices of the correlation function of the Brownian rotational diffusion of a sphere 8 171 range from k 0 to k 0 therefore i 0 8 187 The weights The single weight c in the correlation function of the Brownian rotational diffusion of a sphere 8 171 is co 1 8 188 8 12 3 The weight gradient of the sphere Tm partial derivative The partial derivative with respect to the geometric parameter Tm is Oco OTm 0 8 189 8 12 SPHERICAL DIFFUSION TENSOR 111 8 12 4 The weight Hessian of the sphere Tm Tm partial derivative The second partial derivatives with respect to the geometric parameter Tm twice is 2 Co 2 OTm i 8 190 8 12 5 The correlation time of the sphere The single correlation time 7 of the correlation function of the Brownian rotational diffu sion of a sphere 8 171 is f em Tin 8 191 8 12 6 The correlation time gradient of the sphere Tm partial derivative The partial derivative with respect to the geometric parameter Tm is OTO 8 12 7 The correlation time Hessian of the sphere Tm Tm partial derivative The second partial derivative with r
7. H2 H98 10 2 THE LIST OF FUNCTIONS 335 10 2 132 spin number Synopsis Function for numbering spins Defaults spin number self spinid None number None Keyword Arguments spin_id The spin identification string corresponding to a single spin number The new spin number Description This function simply allows spins to be numbered The new number cannot correspond to an existing spin number Examples The following sequence of commands will renumber the sequence 1 C1 2 C2 3 C3 to C128 2 lt 4 03 relax gt spin number 1 1 relax gt spin number 2 2 relax gt spin number 3 3 Identification string documentation The identification string is composed of three components the molecule id token begin ning with the character the residue id token beginning with the character and the atom or spin system id token beginning with the character Each token can be composed of multiple elements separated by the character and each individual element can either be a number which must be an integer in string format a name or a range of numbers separated by the character Negative numbers are supported The full id string specification is jmol_namej jres_idj jres_idj jres_idj Qjatom_idj jatom_idj jatom_idj where the token elements are 336 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS mol_namej the name o
8. Parameter initialisation methods 10 2 THE LIST OF FUNCTIONS 193 Minimisation algorithm Patterns Grid search Gg rid Unconstrained line search methods Minimisation algorithm Patterns Back and forth coordinate descent Cc Dd or Cc oordinate _ Dd escent Steepest descent Ss Dd or Ss teepest _ Dd escent Quasi Newton BFGS gt Bb Ff Gg Ss Newton Nn ewton Newton CG gt NnJewton _ Cc Gg or Nn Cc Gg Unconstrained trust region methods Minimisation algorithm Patterns Cauchy point Cc auchy Dogleg Dd ogleg CG Steihaug gt Cc Gg _ Ss teihaug or Ss teihaug Exact trust region Ee xact Unconstrained conjugate gradient methods Minimisation algorithm Patterns Fletcher Reeves IFE RrIS or Fflletcher Rrleeves _ Polak Ribi re Pp Rr or Pp olak _ Rr ibiere Polak Ribi re Pp Rr or Pplolak Rr ibiere Hestenes Stiefel Hh Ss or Hh estenes _ Ss tiefel Miscellaneous unconstrained methods Minimisation algorithm Patterns Simplex 7 Ss implex Levenberg Marquardt L1 Mm or L1 evenburg Mm arquardt 194 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Constrained methods Minimisation algorithm Patterns Method of Multipliers Mm
9. 10 2 THE LIST OF FUNCTIONS Data type a Amplitude of fast motions Amplitude of slow motions Te Tf Ts Timescale of fast motions Timescale of slow motions String tag S2f 2s amp_fast amp_slow tf time_fast time_slow 225 Description The standard model free order parameter equal to 57 S2s for the two timescale models The default colour gradient starts at yellow and ends at red The order parameter of the faster of two internal motions Residues which are described by model free models m1 to m4 the single timescale models are illustrated as white neon bonds The default colour gradient is the same as that for the 9 data type The order parameter of the slower of two internal motions This functions exactly as S except that S2 is plotted instead Model independent display of the amplite of fast motions For residues described by model free models m5 to m8 the value plotted is that of S2 However for residues described by models m1 to m4 what is shown is dependent on the timescale of the motions This is because these single timescale models can at times be perfect approximations to the more complex two timescale models Hence if 7 is less than 200 ps S is plotted Otherwise the peptide bond is coloured white The default colour gradient is the same as that for S Model independent display of the amplite of slow moti
10. ED El 6 11c 34 CHAPTER 6 MODEL FREE ANALYSIS The orientational parameters a 8 y are the Euler angles using the z y z rotation notation The five weights c are defined as c l1 d e 6 12a e 80 6 6 12b co 30282 6 12c c 30207 6 12d co 4 d e 6 12e where d 3 6 6 62 1 6 13 F 1 3D 62 20702 1 3D 6 26262 2 02 20202 6 14 and where R 1 322 6 15 The five correlation times 7 are 1 T_2 6Diso 20491 6 16a 1 T 1 69 55 Dall 3D 6 16b 1 70 6Diso Dall 3D 6 16c 1 11 6D s0 2Da 6 16d 1 7 6945 29 9 6 16e Diffusion as a spheroid The variable k is equal to one in the case of the spheroid defined by the parameter set Diso Da 9 Q hence 1 0 1 The geometric parameters D so Da are defined as Diso 1 9 29 6 17a and are constrained by 0 lt Diso lt oo 6 18a Diso lt Da lt 3Diso 6 18b The orientational parameters 0 are the spherical angles defining the orientation of the major axis of the diffusion frame within the lab frame 6 1 THEORY 35 The three weights c are c 1 362 1 6 192 co 382 1 63 6 19b c 62 1 6 19c The five correlation times 7 are 1473 056 2D a 6 20a 1 7 0D Da 6 20b Diffusion as a sphere In the situation of a molecule diffusing as a sphere either described by the single para
11. gamma0 gammal Bond length T r or Bb ond _ L1 ength Heteronucleus type heteronuc_type Hh eteronucleus Proton type proton_type Pp roton The objects corresponding to the object names are lists or arrays with each element corrsponding to each state N state model default values Data type Object name Value Probabilities pO p1 p2 pr 1 N Euler angle a alpha0 alphai c 1 a N 1 Euler angle O beta0 betal c 1 m N 1 Euler angle y gamma0 gammal c 1 a N 1 In this table N is the total number of states and c is the index of a given state ranging from 0 to N 1 The default probabilities are all set to be equal whereas the angles are given a range of values so that no 2 states are equal at the start of optimisation Note that setting the probability for state N will do nothing as it is equal to one minus all the other probabilities 10 2 THE LIST OF FUNCTIONS 375 10 2 147 value write Synopsis Function for writing residue specific data values to a file Defaults value write self run None param None file None dir None force False Keyword Arguments run The name of the run param The parameter file The name of the file dir The directory name force A flag which if set to True will cause the file to be overwritten Description If no directory name
12. relax gt minimise newton mt gmw relax gt minimise newton func_tol 1e 25 relax gt minimise newton func tol 1e 25 grad_tol None relax gt minimise newton max_iter 1e7 relax gt minimise newton constraints True max_iter 1e7 relax gt minimise newton verbosity 1 To use constrained Simplex minimisation with a maximum of 5000 iterations type relax gt minimise simplex constraints True max_iter 5000 Note All the text which follows is a reproduction of the docstring of the generic_minimise function from the minfx python package Only take note of the minimisation algorithms and minimisation options sections the other sections are not relevant for this function The Grid search and Method of Multipliers algorithms CANNOT be selected as minimisation algorithms for this function 10 2 THE LIST OF FUNCTIONS 191 The section entitled Keyword Arguments is also completely inaccessible therefore please ignore that text Generic minimisation function This is a generic function which can be used to access all minimisers using the same set of function arguments These are the function tolerance value for convergence tests the maximum number of iterations a flag specifying which data structures should be returned and a flag specifying the amount of detail to print to screen Keyword Arguments func The function which returns the value dfunc The function which re
13. usu ulw s y and yin An example which shows most of these conventions is 124 CHAPTER 9 RELAX DEVELOPMENT class Scientific_data Base_struct_API uuu The Scientific Python specific data jobject uuuutt Identification string uuuuidi scientific uuuudef _find_bonded_atom self attached_atom mol_type res uuuuuuuu Find the atom named attached_atom directly bonded to the desired atom vuuuuuuu param attached_atom u The name of uthe attached atom to return vuuuuuuu type attached_atom Wy str vuuuuuuu param mol type uuuuuuuu The typeof the molecule This can jbe jone of protein nucleic acid LILILILILILILILILILILILILILILILIL IL ILI IL ILI IL IL ICI I inii nOT uj other LiLiLiL inii iu type mol type uunuuuouustr Lini i param res ouuu The Scientific Python residue object vuuuuuuu type yres uuuuuuuuuuuuuuscientific Python residue instance vuuuuuuu retura vuuuuuuuuuuuuuuuAjtuple of information about the bonded atom Li niin r type uuuuvuvuouuuuuuuutuple consisting jof jthe atom mumber int atom jname str element LILILILILILILILILILILIL III ICILICIC IL IL I I ILI nuin uname str and atomic position Numeric jarray oflen 3 n LILILILILILILILI uuu Init uuuuuuuubonded_found False uuuuuuuu u The attached atom is in the residue uuuuuuuuif attached_atom in res atoms uvuuuuuuuuuuntt The bonded
14. 00 Mm or Mm ethod of Mm ultipliers Minimisation options The minimisation options can be given in any order Line search algorithms These are used in the line search methods and the conjugate gradient methods The default is the Backtracking line search Line search algorithm Patterns Backtracking line search Bb ack Nocedal and Wright interpolation Nn Ww Ti or based line search gt NnJoceda1 _ Ww right _ Ti nt Nocedal and Wright line search Nn Ww Ww or for the Wolfe conditions Nn ocedal _ Ww right Ww lolfe More and Thuente line search Mm Tt or Mm ore _ Tt huente No line search Nn o L1 ine Ss earch Hessian modifications These are used in the Newton Dogleg and Exact trust region algorithms Hessian modification Patterns Unmodified Hessian tNn o Hh essian Mm od Eigenvalue modification 7 Ee igen Cholesky with added multiple of Cc hol the identity The Gill Murray and Wright Gg Mm Ww modified Cholesky algorithm The Schnabel and Eskow 1999 Ss Ee 99 algorithm Hessian type these are used in a few of the trust region methods including the Dogleg and Exact trust region algorithms In these cases when the Hessian type is set to Newton a Hessian modification can also be supplied as above The default Hessian type is Newton and the default Hessian modification when Newton is
15. 2 n 8 54a 2 xd zi 8 54b 2 O cwos _ y 8 54c gs 72 CHAPTER 8 VALUES GRADIENTS AND HESSIANS Pex Ao partial derivative The second partial derivatives of the relaxation equations with respect to the chemical exchange parameter pex and the CSA parameter Ac are R 0 Open OA rere OR aUo dd O owont Aon Oke eee Pex r partial derivative The second partial derivatives of the relaxation equations with respect to the chemical exchange parameter Pez and the bond length parameter r are Ry 0 aD O 8 56a Ro 0 er o 8 56b 3 onorl0 Ao Ao partial derivative The second partial derivatives of the relaxation equations with respect to the CSA param eter Ac twice are PR1 0 A 8 57a 0Ra 0 c Ra E 57b 2 Ponost i 8 570 OAa Ao r partial derivative The second partial derivatives of the relaxation equations with respect to the CSA param eter Ao and the bond length parameter r are PRO Do Bom PRO DAovoP s 2 D onol _ y 8 58 JA Or 8 8 Ri 6 VALUES GRADIENTS AND HESSIANS 73 r r partial derivative The second partial derivatives of the relaxation equations with respect to the bond length parameter r twice are O R4 0 3 2 eee 8 59a PR2 0 d Ra aa z 8 59b O cuog 0 d JONOE 8 59c Or 74 CHAPTER 8 VALUES GRADIENTS AND HESSIANS 8 9 Mlodel free analysis 8 9 1 The model free equations In
16. 6Dn Da 1 39 3 6Diso Dall 30 8 aD aD X 8 169c Or E 8 169d 09 09 Om ADD 6Diso 2949 6LE 6Diso 20 494 2 8 169 09 0D a T So a R 1S0 a D D partial derivative The second partial derivatives with respect to the geometric parameter D twice are E 72 23 2i 6Diso 29 91 3 655 Diao 29 98 8 1702 1892 6Diso Dall 3D 8 170b Ll 1802 65 Da 1 BD 8 170c s La 8 170d a 72 23 2 Dis 2D R 63 0 iso 29491 8 1700 106 CHAPTER 8 VALUES GRADIENTS AND HESSIANS 8 11 Spheroidal diffusion tensor 8 11 1 The diffusion equation of the spheroid The correlation function of the Brownian rotational diffusion of a spheroid is 1 1 a Col 5 J ce Ti 8 171 i 1 where c are the weights of the three exponential terms which are dependent on the ori entation of the XH bond vector and 7 are the correlation times of the three exponential terms 8 11 2 The weights of the spheroid Definitions The direction cosine defining the XH bond vector within the spheroidal diffusion frame is pi XH 8 172 Let the set of geometric parameters be B T0 ss 8 173 and the set of orientational parameters be the spherical angles O 0 0 8 174 The weights The three spheroid weights c in the correlation function of the Brownian rotational diffu sion of a spheroid 8
17. J wg uh J31w Hh or J3 VG Hh Bond length T r or Bb ond _ Ll ength CSA cea gt Cc Ss Aa Heteronucleus type heteronuc_type Hhl eteronucleus Proton type proton_type gt Pp roton Reduced spectral density mapping default values Data type Object name Bond length Y CSA csa Heteronucleus type heteronuc_type Proton type proton_type Diffusion tensor set details Value 1 02 1e 10 172 1e 6 15N 4H If the diffusion tensor has not been setup use the more powerful function diffusion_tensor init to initialise the tensor parameters This function cannot be used to initialise a diffusion tensor The units of the parameters are Inverse seconds for Tm Seconds for Diso Da Dz Dy Dz Dy Da 370 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Unitless for Dratio and D Radians for all angles a 3 y 0 When setting a diffusion tensor parameter the residue number has no effect As the internal parameters of spherical diffusion are tm spheroidal diffusion are Tm Da 0 9 and ellipsoidal diffusion are 7 4 Da Dr a B y supplying geometric parameters must be done in the following way If a single geometric parameter is supplied it must be one of Tm Diso Da Dr or Dratio For the parameters 2j D1 Dz Dy and Dz it is not possible to determine how to use the current
18. Keyword Arguments model The name of the preset N state model Description Prior to optimisation the N state model type should be selected The preset models are 2 domain The N state model for a system of two domains where one domain experiences a a reduced tensor population The N state model whereby only populations are optimised The structures loaded into relax are assumed to be fixed Le if two domains are present the Euler angles for each state are fixed The parameters of the model include the weight or probability for each state and the alignment tensor pO pl pN Axx Ayy Axy Axz Ayz fixed The N state model whereby all motions are fixed and all populations are fixed to the set probabilities The parameters of the model are simply the alignment tensor Axx Ayy Axy Axz Ayz Examples To analyse populations of states type relax n_state_model select_model model populations 248 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 64 n state model set domain Synopsis Set the domain label for the alignment tensor Defaults n state model set domain self tensor None domain None Keyword Arguments tensor The alignment tensor to assign the domain label to domain The domain label Description Prior to optimisation of the N state model the domain to which each alignment tensor belongs must be specified Examples To link the alignment tensor
19. Match the character x any number of times for example x will match as will Xxxxx 6 Match any sequence of characters of any length Importantly do not supply a string for the data type containing regular expression The regular expression is implemented so that various strings can be supplied which all match the same data type Model free set details Setting a parameter value may have no effect depending on which model free model is chosen for example if S values and S2 values are set but the run corresponds to model free model m4 then because these data values are not parameters of the model they will have no effect Note that the Rex values are scaled quadratically with field strength and should be supplied as a field strength independent value Use the following formula to get the correct value value Reg 2 0 m frequency 2 where Rex is the chemical exchange value for the current frequency 7 is in the namespace of relax ie just type pi frequency is the proton frequency corresponding to the data 10 2 THE LIST OF FUNCTIONS 361 Model free data type string matching patterns Data type Local Tm Order parameter 9 Order parameter S Order parameter S2 Correlation time Te Correlation time Tf Correlation time 7 Chemical exchange Bond length CSA Heteronucleus type Proton type Object name local_tm heteronuc_type proton_type
20. le 6 param csa To set the NH bond length of all spins to 1 02 A type relax value set 1 02 1e 10 bond length relax value set val 1 02 1e 10 param r To set both the bond length and the CSA value to the default values type relax value set param bond length csa To set both 7f and 7 to 100 ps type relax value set 100e 12 tf ts relax value set val 100e 12 param tf ts To set the S and 7 parameter values of residue 126 Ca spins to 0 56 and 13 ps type relax value set 0 56 13e 12 S2 te 126 Ca relax value set val 0 56 13e 12 param S2 te spin id 1260Ca relax value set val 0 56 13e 12 param S2 te spin id 1260Ca Regular expression The python function match which uses regular expression is used to determine which data type to set values to therefore various data type strings can be used to select the same data type Patterns used for matching for specific data types are listed below This is a short description of python regular expression for more information see the regular expression syntax section of the Python Library Reference Some of the regular expression syntax used in this function is A sequence or set of characters to match to a single character For example Ss 2 will match both S2 and s2 Match the start of the string
21. rp m wrrr S2 SD 7 Ti Ts eere em Oj S partial derivative The second partial derivative of 8 65 with respect to the orientational parameter D and the order parameter S is k PH 25 2a 1 tis 8 93 0D 05 5 4 8D NIFUN Cs n wn De S partial derivative The second partial derivative of 8 65 with respect to the orientational parameter D and the order parameter S is o J E Tg Ta TF Ts Ti Ts 5 _ gt 94 Oo rs p D inl TEHTI wre Ta Ti WTaTi id D Tf partial derivative The second partial derivative of 8 65 with respect to the orientational parameter D and the correlation time ry is PI 24 y E On tp 74 rin T Eo VIL IA OD Or 5C 5p E Oj 7g 74 org 8 95 Dj Ts partial derivative The second partial derivative of 8 65 with respect to the orientational parameter D and the correlation time Ts is Os Iw 2 OG 2 Ts Ti wrsTiY ie 5 a a IDEAE TDI DO Or 5 E 995 Ts T wreri 8 96 84 CHAPTER 8 VALUES GRADIENTS AND HESSIANS S S partial derivative The second partial derivative of 8 65 with respect to the order parameter 5 twice is 9 J w 952 0 8 97 S S partial derivative The second partial derivative of 8 65 with respect to the order parameters 5 and S is 8 J w S Tf partial derivative The second partial derivative
22. viii CONTENTS JO 28 C HOO A Y asd oa eo ew Sok 179 TR AU EFSOGONPIG oe Eno tgo 9o IR Rome koe Ree pee eee OY X 180 TS ol eri sensOh 24 22e kom deo Ecke RR E a a a 185 DO 2 P A te RS a s EROR chow m x om e hx d de Be 186 VAIO ASG cc 187 102 4 pe mapping SLE doe ee ee Poe Bb ew A 188 e A a a a a D E A e E E a a e L e A 189 10 2 36 model free create_model 196 10 2 37 model free delete a 198 10 2 38 model_free removettm 2 0 s 199 10 2 39 model free select_model 1 2 ee a 200 10 2 40 model_selection 2 1 a a 205 IE AT mo epp insu ee rd RO RUMOR ce es Evo ee a ee A 207 10 2 42 melecul ped uuo Rus A E ox Kr be X ue 209 10 2 43 molecnledlelede gt 2o Beas me bee X m dae de Rn d 210 A dl molecule display l2 ug d eR Eos om hs RR me Ra aa 212 10 2 45 meleoulenasn 2221222 2 bee oboe bee es 213 10 2 46 molmolclear history 2 E 2 215 10 2 47 molmol command 2 222xc o rasa 216 10 248 molmol Macro cke oo oy EUER sona s Rk GA 217 102 49 moelioL AN 219 10 2 50 molmoltensor pdb onu beo Rok eR b Rx xo 9o 3 RO 3 e o 220 10 2 51 molmolview 22 2 uud und Re E OR Kwane ken waaa 222 10 2 53 molinoL HE oia oed yoke dew wem Rx de xo es 223 10 2 53 monte carlo create data ss 228 10 2 54 monte carlo erroranalysis o o 231 10 2 50 monte carlo wal values occur a os 234 A de o A 236 IO YE dn ET it cacas dia a a 238 10 2 58 monbe carl
23. 0 The azimuthal angle defining the major axis of the spheroid diffusion tensor Model free data type string matching patterns Object name Dpar Dper Dratio alpha beta gamma theta phi 173 Patterns tm Dd iso Da a Da r Da x Dd y Da z Dd par Dd per Dd ratio a or alpha b or beta g or gamma theta 6 phi 174 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Data type Local Tin Order parameter S Order parameter S Order parameter S Correlation time Te Correlation time Ty Correlation time Ts Chemical exchange Bond length CSA Heteronucleus type Proton type Object name local_tm s2 s2f heteronuc_type proton_type Patterns L1 ocal _ tm Ss 2 Ss 2 Ss 2s roy ey ces Rr ex or Cc emical Eelxchange r or Bblond _ LlJength Cc Ss Aa Hh eteronucleus Pp roton 10 2 THE LIST OF FUNCTIONS 175 10 2 26 eliminate Synopsis Function for model elimination Defaults eliminate self function None args None Keyword arguments function A user supplied function for model elimination args A tuple of arguments for model elimination Description T
24. 10 2 THE LIST OF FUNCTIONS 281 10 2 93 pymol write Synopsis Function for creating PyMOL macros Defaults pymol write self data type None style classic colour_start None colour_end None colour_list None file None dir pymol force False Keyword Arguments data_type The data type to map to the structure style The style of the macro colour_start The starting colour either an array or string of the linear colour gradient colour_end The ending colour either an array or string of the linear colour gradient colour_list The list of colours to match the start and end strings file The name of the file dir The directory name force A flag which if set to True will cause the file to be overwritten Description This function allows residues specific values to be mapped to a structure through the creation of a PyMOL macro which can be executed in PyMOL by clicking on File Macro Execute User Currently only the classic style which is described below is available Colour The values are coloured based on a linear colour gradient which is specified through the colour_start and colour_end arguments These arguments can either be a string to identify one of the RGB red green blue colour arrays listed in the tables below or you can give the RGB vector itself For example colour_start white and colour_start 1 0 1 0 1 0 both select the same colour Leaving both a
25. 132 Unix 130 user functions 5 6 7 139 user manual HTML compilation 130 PDF compilation 130 web site 15 write 181 263 290 297 315 325 347 375 395
26. 2 C2 3 C3 to 1 C11 2 C12 3 C13 relax gt spin name 1 C11 relax gt spin name 2 C12 relax spin name 3 C13 Identification string documentation The identification string is composed of three components the molecule id token begin ning with the character the residue id token beginning with the character and the atom or spin system id token beginning with the character Each token can be composed of multiple elements separated by the character and each individual element can either be a number which must be an integer in string format a name or a range of numbers separated by the character Negative numbers are supported The full id string specification is jmol_namej ires id jres id jres_idj Gjatom id jatom id jatom_idj where the token elements are 334 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS jmol_name j the name of the molecule res_id the residue identifier which can be a number name or range of numbers atom_id the atom or spin system identifier which can be a number name or range of numbers If one of the tokens is left out then all elements will be assumed to match For example if the string does not contain the character then all molecules will match the string Regular expression can be used to select spins For example the string H will select the protons H
27. 8 2 2 32 32 00n 001 004 009 t 00 2 As the order in which the partial derivatives are calculated is inconsequential the Hessian is symmetric The most powerful minimisation algorithm for model free analysis Newton optimisation requires the value gradient and Hessian at the current parameter values 8 3 The four parameter combinations In model free analysis four different combinations of parameters can be optimised each of which requires a different approach to the construction of the chi squared value gradient and Hessian These categories depend on whether the model free parameter set the diffusion tensor parameter set D or both sets are simultaneously optimised The addition of the local Tm parameter to the model free set creates a fourth parameter combination 8 3 1 Optimisation of the model free models This is the simplest category as it involves solely the optimisation of the model free pa rameters of an individual residue while the diffusion tensor parameters are held constant The model free parameters belong to the set of the residue i The models include m0 to m9 and the dimensionality is low with dim k lt 5 8 3 8 3 THE FOUR PARAMETER COMBINATIONS 59 for the most complex model m8 8 rg S Ts Ren The relaxation data of a single residue is used to build the chi squared value gradient and Hessian 8 3 2 Optimisation of the local 7 models The addition of the local 7 parameter
28. Defaults relax_fit select_model self model exp Keyword Arguments model The type of relaxation curve to fit The preset models The supported relaxation experiments include the default two parameter exponential fit selected by setting the fit_type argument to exp and the three parameter inversion recovery experiment in which the peak intensity limit is a non zero value selected by setting the argument to inv The parameters of these two models are exp Rx 10 inv Rx IO linf 302 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 109 reset Synopsis Reset relax Defaults reset self All of the data of the relax data storage object will be erased and hence relax will return to its initial state 10 2 THE LIST OF FUNCTIONS 303 10 2 110 residue copy Synopsis Function for copying all data associated with a residue Defaults residue copy self pipe_from None res_from None pipe to None res_to None Keyword Arguments pipe_from The data pipe containing the residue from which the data will be copied This defaults to the current data pipe res_from The residue identifier string of the residue to copy the data from pipe_to The data pipe to copy the data to This defaults to the current data pipe res_to The residue identifier string of the residue to copy the data to Description This function will copy all the data associated with th
29. If the planned changes have the potential to introduce problems the creation of a private branch may be suggested 9 4 6 Branches Branch creation If a change is likely to be disruptive or cause breakages in the program the use of your own temporary branch is recommended This private branch is a complete copy of one of the main development lines wherein you can make changes without disrupting the other developers Although called a private branch every change is visible to all other developers and each commit will result in an automatic email to the relax commits mailing list Other developers are even able to check out your branch and make modifications to it Private branches can also be used for testing ideas If the idea does not work the branch can be deleted from the repository in reality the branch will always exist between the revision numbers of its creation and deletion and can always be resurrected For example to create a branch from the main 1 2 development line called molmol_macros whereby new Molmol macros are to be written type svn cp svntssh xxxxx svn gna org svn relax 1 3 svn ssh xxxxx0svn gna org svn relax branches molmol_macros replacing xxxxx with your login name You can then check out your private branch by typing svn co svn ssh xxxxx0svn gna org svn relax branches molmol_macros which will create a directory called molmol_macros containing all the relax source files To have the files placed into a diff
30. Patterns L1 ocal _ tm gt Ss 2 Ss 2f Ss 2s teg try cts Rr ex or Cc emical _ Ee xchange r or Bb ond L1 ength Cc Ss Aa Hh eteronucleus Pp roton Reduced spectral density mapping set details In reduced spectral density mapping three values must be set prior to the calculation of spectral density values the bond length CSA and heteronucleus type 362 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Reduced spectral density mapping data type string matching patterns Data type Object name Patterns J 0 jo Jj 0 or Jj CO J wx jwx J31w EXx1 or 2j VG Xx D J wg wh J31w EHh 1 or Jj w Hh D Bond length E r or Bb ond L1 ength CSA csa Cc Ss Aa Heteronucleus type heteronuc_type Hhleteronucleus Proton type proton_type gt Pp roton Relaxation curve fitting set details Only three parameters can be set the relaxation rate Rx the initial intensity 10 and the intensity at infinity Iinf Setting the parameter Tinf has no effect if the chosen model is that of the exponential curve which decays to zero Relaxation curve fitting data type string matching patterns Data type Object name Patterns Relaxation rate rx Rr x Average peak intensities series ave_intensities Aa
31. S 1 S2 e t SF S e 7 7 8 63 where the faster of the motions is defined by the order parameter S and the correlation time ry the slower by the parameters S and Ts and the two order parameter are related by the equation 9 5 S2 The relaxation equations of Abragam 1961 are composed of a sum of power spectral density functions J w at five frequencies The spectral density function is related to the correlation function as the two are a Fourier pair Applying the Fourier transform to the correlation function composed of the generic diffusion equation and the original model free correlation function results in the equation irn o s OSEE Bd nes 1 04 Te T ur 8 9 MODEL FREE ANALYSIS T5 The Fourier transform using the extended model free correlation function is k S2 rs Ti T 2 S9 yr Ti T Ho 2 anf AU sper Dry f eu 8 65 re WP 1 wn TEHTE wren Ts 7 w7s7 8 9 2 The original model free gradient The model free gradient of the original spectral density function 8 64 is the vector of partial derivatives of the function with respect to the geometric parameter 6 the orien tational parameter O the order parameter 7 and the internal correlation time Te The positions in the vector correspond to the model parameters which are being optimised 6 partial derivative The partial derivative of 8 64 with respect to the ge
32. The distance travelled along pz is the step length a and the parameter values for the next iteration are Ok 1 Ok ALP 6 28 The line search algorithm determines the search direction p whereas the value of a is found using an auxiliary step length selection algorithm One of the simplest line search methods is the steepest descent algorithm The search direction is simply the negative gradient pj V fk and hence the direction of maximal descent is always followed This method is inefficient the linear rate of convergence requires many iterations of the algorithm to reach the minimum and it is susceptible to being trapped on saddle points within the space The coordinate descent algorithms are a simplistic group of line search methods whereby the search directions alternate between vectors parallel to the parameter axes For the back and forth coordinate descent the search directions cycle in one direction and then back again For example for a three parameter model the search directions cycle 01 02 03 02 01 05 which means that each parameter of the model is optimised one by one The method becomes less efficient when approaching the minimum as the step length oj continually decreases ibid The quasi Newton methods begin with an initial guess of the Hessian and update it at each iteration using the function value and gradient Therefore the benefits of using the quadratic model of 6 27 are obtained without calcul
33. This function will copy the alignment tensor data to a new tensor or a new data pipe The destination data pipe must not contain any alignment tensor data corresponding to the tensor_to label If the pipe_from or pipe_to arguments are not supplied then both will default to the current data pipe Both the tensor_from and tensor_to arguments must be supplied Examples To copy the alignment tensor data corresponding to Pf1 from the data pipe old to the current data pipe type one of relax align_tensor copy Pf1 old relax align_tensor copy tensor_from Pf1 pipe_from old To copy the alignment tensor data corresponding to Otting from the current data pipe to the data pipe new type one of relax align_tensor copy Otting pipe_to new relax align_tensor copy tensor_from Otting pipe to new To copy the alignment tensor data of Otting to that of Otting new type one of relax align_tensor copy Otting tensor_to Otting new relax align tensor copy tensor from Pf1 tensor to Otting new 142 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 5 align_tensor delete Synopsis Function for deleting alignment tensor data Defaults align_tensor delete self tensor None Keyword Arguments tensor The alignment tensor identification string Description This function will delete the specified alignment tensor data from the current dat
34. Z Shapiro Y E Freed J H and Meirovitch E 2001 A structural mode coupling approach to 15N NMR relaxation in proteins J Am Chem Soc 123 13 3055 3063 Zhuravleva A V Korzhnev D M Kupce E Arseniev A S Billeter M and Orekhov V Y 2004 Gated electron transfers and electron pathways in azurin a NMR dynamic study at multiple fields and temperatures J Mol Biol 342 5 1599 1611 Index angles 144 146 149 149 163 167 173 diff 17 244 247 341 353 358 362 363 diffusion 33 370 371 373 374 378 anisotropic 165 167 173 371 API documentation 131 Brownian 33 220 277 340 argument 5 ellipsoid asymmetric 33 46 93 149 keyword 5 166 166 168 173 340 370 371 sphere isotropic 35 110 149 163 163 166 168 170 173 243 244 341 371 spheroid axially symmetric 34 45 46 106 149 163 164 164 165 168 bond length 174 183 184 197 201 203 352 353 356 358 361 363 366 368 369 374 377 378 branches 128 od 173 340 370 371 esign tensor 149 160 168 172 173 177 220 search 17 268 277 340 342 365 369 369 370 370 371 372 direction cosine 93 106 bug report 124 bug tracker 11 12 16 18 124 127 131 C module compilation 11 130 display 143 162 170 212 220 225 252 camel case 121 261 274 277 279 288 294 299 chemical exchange 174 184 197 225 351 308 313 322 332 355 352 356 360 361
35. back_calc Step 4 relax gt monte_carlo initial_values Step 5 relax gt minimise newton Step 6 relax gt eliminate Step 7 relax gt monte_carlo error_analysis Step 8 An example for reduced spectral density mapping is relax gt calc Step 2 relax gt monte_carlo setup number 500 Step 3 10 2 THE LIST OF FUNCTIONS 233 relax gt monte_carlo create_data method back_calc Step 4 relax gt calc Step 6 relax gt monte_carlo error_analysis Step 8 234 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 55 monte carlo initial values Synopsis Function for setting the initial simulation parameter values Defaults monte carlo initial values self Description This function only effects where minimisation occurs and can therefore be skipped if the values or parameters are calculated rather than minimised However if accidentally run in this case the results will be unaffected It should only be called after the model or run is fully minimised Once called the functions grid_search and minimise will only effect the simulations and not the model parameters The initial values of the parameters for each simulation is set to the minimised parameters of the model A grid search can be undertaken for each simulation instead although this is computationally expensive and unnecessary The minimisation function should be executed for a second time after running
36. is equivalent to Equation 8 15 when the index 7 ranges over the relaxation data of all selected residues 8 4 2 Construction of the gradient The construction of the gradient is significantly different for the models D and G In Figure 8 1 the construction of the chi squared gradient Vx for the global model 6 is demonstrated In this case l Vx my V 8 11 i l where Vx is the vector of partial derivatives of the chi squared equation x for the residue 1 The length of this vector is IVx dim 6 8 12 Ox where each 0 is a parameter of the model J with each position of the vector j equal to The construction of the gradient Vx for the model 9 is simply a subset of that of G This is demonstrated in Figure 8 1 by simply taking the component of the gradient Vx 8 4 CONSTRUCTION OF THE VALUES GRADIENTS AND HESSIANS 61 Jaquinu INPISIN 90D os o OS OF Os OS Figure 8 1 The construction of the model free gradient Vx for the global model 6 For each residue i a different vector Vx is constructed The first element of the vector represented by the symbol 0D the orange block is the sub vector of chi squared partial derivatives with respect to each of the diffusion tensor parameters Dj The rest of the elements grouped into blocks for each residue denoted by the symbol 03 are the sub vectors of chi squared partial derivatives with respect to each of the model free parameters 87 For the re
37. tf cry Correlation time 7 ts ts Chemical exchange rex Rr ex or Cc emical _ Ee xchange Bond length T r or Bb ond _ L1 ength CSA csa Cc Ss Aa Heteronucleus type heteronuc_type Hh eteronucleus Proton type proton_type Pp roton 10 2 THE LIST OF FUNCTIONS 307 Reduced spectral density mapping data type string matching patterns Data type Object name Patterns J 0 jo Jj10 or LIZ CO J wx jwx Jj w Xx or E31 VQ Xx D J wg jwh J31w Hh or EJj1 VG Hh D Bond length Y r or Bb ond _ L1 ength CSA csa Cc Ss Aa Heteronucleus type heteronuc_type Hh eteronucleus Proton type proton_type Pp roton Relaxation curve fitting data type string matching patterns Data type Object name Patterns Relaxation rate rx Rr x Average peak intensities series ave intensities Aa ve Iilnt Initial intensity 10 Ti 0 Intensity at infinity iinf Iilinf Relaxation period times series relax times Rr elax Tt imes 358 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS N state model data type string matching patterns Data type Probabilities Euler angle a Euler angle 8 Euler angle y Bond length Heteronucleus type Proton type Object name
38. whereas a value of 1 0 excludes all data In almost all cases prune must be set to zero any value greater than zero will result in an underestimation of the error values If a value is supplied the lower and upper tails of the distribution of chi squared values will be excluded from the error calculation Monte Carlo Simulation Overview For proper error analysis using Monte Carlo simulations a sequence of function calls is required for running the various simulation components The steps necessary for imple menting Monte Carlo simulations are 1 The measured data set together with the corresponding error set should be loaded into relax 232 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 2 Either minimisation is used to optimise the parameters of the chosen model or a calculation is run 3 To initialise and turn on Monte Carlo simulations the number of simulations n needs to be set 4 The simulation data needs to be created either by back calculation from the fully minimised model parameters from step 2 or by direct calculation when values are calcu lated rather than minimised The error set is used to randomise each simulation data set by assuming Gaussian errors This creates a synthetic data set for each Monte Carlo simulation 5 Prior to minimisation of the parameters of each simulation initial parameter estimates are required These are taken as the optimised model parameters An alternative is to use a grid searc
39. 113 sa Se 6 O partial derivative The second partial derivative of 8 65 with respect to the geometric parameter 6 and the orientational parameter 9 is Jw _ 2 3 Ori Oc foz co 1 wn 06 00 5 H 6 90K I 14 wr Tg Ta wr pti ry Ti wrgi y gny2 s ti wet ts Ti wrsTi 2 e z Sj B 1 S ry Ti Tf S SCR sr ee 8 114 96 DOL 114 Ton TEHTI wren Ts T wT cC 1 S2 77 97 1 8 9 MODEL FREE ANALYSIS 89 Di S partial derivative The second partial derivative of 8 65 with respect to the geometric parameter 6 and the order parameter 8 is k Jw 2 Ori f a2 1 wi Tp ri wrgri 2 6 ang s CHW rg n Gorg 08 057 5 Ts Ti UTT k 1 usu l rs 74 w7 7 2 Oc B8 T Jn 1 06 tj i r m wtp 8 Ts T Ti Ts been 8 115 6 S partial derivative The second partial derivative of 8 65 with respect to the geometric parameter 6 and the order parameter S is PI _2 25 On ea 2 n wren 56 95 7 57 2 96 jaz 78 32 22 j 5 Cr j 1 wr rs Ti wT57 Oc 1 Ts Ti Ts caia a PO E 11 i 06 5 E wm Ts 7 m P 6 Tf partial derivative The second partial derivative of 8 65 with respect to the geometric parameter 6 and the correlation time Ty is 8 J w 2 2 d 07 ry 7 3 wrpry e
40. 255 235 205 bisque 255 228 196 peach puff 255 218 185 navajo white 255 222 173 moccasin 255 228 181 cornsilk 255 248 220 ivory 255 255 240 lemon chiffon 255 250 205 seashell 255 245 238 honeydew 240 255 240 mint cream 245 255 250 azure 240 255 255 alice blue 240 248 255 lavender 230 230 250 lavender blush 255 240 245 misty rose 255 228 225 white 255 255 255 black 0 0 0 dark slate grey 4T 79 79 dim grey 105 105 105 slate grey 112 128 144 light slate grey 119 136 153 grey 190 190 190 light grey 211 211 211 midnight blue 25 25 112 navy 0 0 128 cornflower blue 100 149 237 dark slate blue 72 61 139 slate blue 106 90 205 medium slate blue 123 104 238 light slate blue 132 112 255 medium blue 0 0 205 royal blue 65 105 225 blue 0 0 255 dodger blue 30 144 255 deep sky blue 0 191 255 sky blue 135 206 235 light sky blue 135 206 250 steel blue 70 130 180 light steel blue 176 196 222 light blue 173 216 230 powder blue 176 224 230 pale turquoise 175 238 238 dark turquoise 0 206 209 228 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 53 monte_carlo create_data Synopsis Function for creating simulation data Defaults monte_carlo create_data self method back_calc Keyword Arguments method The simulation method Description The method argument can either be set to back_calc or direct the choice of which determines the simulation type If the values or parameters are calculated rather than minimi
41. 367 368 377 distribution archive 12 17 119 131 chi squared 31 36 36 37 38 42 46 182 doc string 120 231 chi squared gradient 46 chi squared Hessian 46 clean up 131 commit access 125 commit log 125 126 compression 315 338 eigenvalues 144 163 164 166 173 194 341 371 Euler angles 93 163 166 167 173 247 353 358 302 363 371 373 374 378 exponential curve fitting 2 bzip2 314 315 337 338 floating point number 4 144 163 165 168 gzip 314 315 337 338 2492 uncompressed 314 337 function class 5 6 constraint 165 176 185 189 191 253 copy 141 160 205 207 259 264 286 292 Gna 15 126 303 321 326 350 GNU Linux 12 130 correlation time 163 166 168 173 176 176 Google 15 184 196 197 225 340 341 352 GPG 356 361 368 371 377 key 18 ctypes 12 signature 18 GPL 1 381 data pipa 6 GUI 8 134 delete 142 161 198 210 260 287 293 306 330 help system 5 5 139 392 INDEX indentation 120 installation 11 integer 4 134 keyword argument 5 licence 381 linking 136 list 4 134 Mac OS X 13 130 mailing list 15 15 119 127 135 archive 15 archives 15 16 relax announce 15 119 relax commits 15 16 119 128 relax devel 15 16 18 21 27 119 125 127 128 131 relax users 15 17 119 make 130 manual HTML 15 map 170 171 171 181 183 188 217 218 223 224 229 232 235 237 239 241 265 275 276 2
42. Alternative parameters can be used by changing the param_types flag to the following integers 164 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 0 tm Default 1 Diso where 1 Tm 6Dis0 The spheroid axially symmetric diffusion When two of the three eigenvalues of the diffusion tensor are equal the molecule diffuses as a spheroid Four pieces of information are required to specify this tensor the two geometric parameters Diso and Da and the two orientational parameters the polar angle 0 and the azimuthal angle describing the orientation of the axis of symmetry The correlation function of the global diffusion is 1 tau tau_i C tau gt ci e n 5 i 1 where c 1 1 4 3 6 2 1 2 c0 36 72 1 6 72 el 3 4 5 72 1 2 and 1 7 1 69i 29 1 70 695 Da 1 11 6Diso 29 10 2 THE LIST OF FUNCTIONS 165 The direction cosine 6 is defined as the cosine of the angle between the XH bond vector and the unique axis of the diffusion tensor To select axially symmetric anisotropic diffusion the parameters argument should be a tuple of floating point numbers of length four A tuple is a type of data structure enclosed in round brackets the elements of which are separated by commas Alternative sets of parameters param_types are 0 74 Da 0 gt Default i Diso Da 0 o 2 oe Dratio 0 o 3 Di Di 0 ot A eds JD rati
43. Correlation time Te te Correlation time tf tf Correlation time 7 ts Chemical exchange rex Bond length bad CSA csa Heteronucleus type heteronuc type Proton type proton_type Model free default values Data type Local Tm Order parameters 7 S5 and S Correlation time Te Correlation time Tf Correlation time Ts Chemical exchange relaxation Bond length CSA Heteronucleus type Proton type Patterns L1 ocal tm Ss 2 Ss 2f Ss 2s tep arg ts CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Rr ex or Cc emical _ Ee xchange r or Bb ond _ L1 ength Cc Ss Aa Hh eteronucleus Pp roton Object name local_tm s2 s2f s2s heteronuc_type proton_type Value 10 1e 9 0 8 100 1e 12 10 1e 12 1000 1e 12 0 0 1 02 1e 10 172 1e 6 15N 4H 10 2 THE LIST OF FUNCTIONS Reduced spectral density mapping set details 369 In reduced spectral density mapping three values must be set prior to the calculation of spectral density values the bond length CSA and heteronucleus type Reduced spectral density mapping data type string matching patterns Data type Object name Patterns J 0 jo 53 0 or J31 V CO J wx jux J31w EXx1 or 2j VG Xx D
44. Cw EHh V y r or Bb ond L1 ength csa Cc Ss Aa heteronuc_type Hh eteronucleus proton_type Pp roton 378 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS NOE calculation data type string matching patterns Data type Reference intensity Saturated intensity NOE Object name Patterns ref gt Rr ef or Rr ef Iilnt sat Sslat or Ss at Iilnt noe Nn 00 Ee Relaxation curve fitting data type string matching patterns Data type Relaxation rate Average peak intensities series Initial intensity Intensity at infinity Relaxation period times series Object name Patterns rx Rr x ave_intensities Aa ve Ii nt 10 Ii 0 tint Iilinf relax_times Rr elax _ Tt imes N state model data type string matching patterns Data type Probabilities Euler angle a Euler angle 8 Euler angle y Bond length Heteronucleus type Proton type Object name probs alpha beta gamma r heteronuc_type proton_type Patterns 6 p0 pi p2 pn alpha0 alphatl beta0 betal gamma0 gammal r or Bb ond _ L1 ength Hh eteronucleus Pp roton The objects corr
45. J uw rs Ti 3w T3 Ts Ts Tj WT age CINE ME jy ap tn rn uri Ts j _k Urs 7 wTsTi 86 CHAPTER 8 VALUES GRADIENTS AND HESSIANS 8 9 6 The alternative extended model free gradient Because of the equation S S S2 and the form of the extended spectral density function 8 65 a convolution of the model free space occurs if the model free parameters 57 S2 Tf Ts are optimised rather than the parameters 5 S5 Tf Ts This convolution increases the complexity of the gradient For completeness the first partial derivatives are presented below 6 partial derivative The partial derivative of 8 65 with respect to the geometric parameter 6 is 8J 24 Or 1 wri 06 4x 06 s Sr os 1 Te ny wr pti rg 7 wrpti Te Ti wrsTiy rs Ti wrsri Sen 825 1 S9 rg m S21 582 n24 oe emi 06 Vl c wn TET HWT Te T lwr J J 1 S2 77 S 1 527 O partial derivative The partial derivative of 8 65 with respect to the orientational parameter 0 is J u 24 00 1 8 1 S2 rp 7 79 de ete UD 5 4200 l wn rpm erp n Ten 8 108 S partial derivative The partial derivative of 8 65 with respect to the order parameter S is Y E Te Ty 1 S2 7 74 Ts 8 109 Ast wT TF den wre tee HUT S partial derivative The partial derivative of 8 65 with respect to the order p
46. Numeric 11 Optik 11 optimise 163 228 229 232 234 236 238 240 247 268 order parameter 174 184 196 197 218 224 225 242 276 282 352 356 361 368 377 parameter bounds 165 170 185 191 limit 175 176 180 190 231 301 394 parameter convolution 86 patch 124 diff 125 Subversion 125 PDB 20 26 165 167 219 220 222 242 244 255 258 274 277 279 280 340 344 346 347 379 peak height 21 intensity 21 25 27 volume 21 plot 170 180 181 225 prompt 4 134 pyreadline 12 Python 1 4 4 5 8 9 11 134 171 181 182 189 192 250 344 350 355 360 366 376 QT 134 read 220 243 251 252 262 274 277 279 289 295 296 299 314 315 323 324 340 342 344 359 reduced spectral density mapping 2 55 regular expression 171 171 172 180 181 181 182 192 208 211 212 214 250 304 307 308 310 312 327 329 331 332 334 336 345 346 350 350 351 355 355 356 360 360 366 366 376 376 relaxation 151 157 163 181 183 183 188 197 202 265 291 297 299 301 318 353 353 357 357 359 362 362 368 372 372 373 373 378 378 relaxation curve fitting 25 relaxation dispersion 2 relaxation rate cross rate 32 cross relaxation 32 spin lattice 32 spin spin 32 repository 17 119 127 back up 17 branch creation 128 branches 128 keeping up to date 128 merging branch back 129 svnmerge py 128 RMSD 21 INDEX r
47. OD 0D co OD OD 3c OD 0D 0 c u Ore D D 00 0D 0 8 152b 0 8 152c 0 8 152d 8 152e where ee 1 x 05 aby TA 9 s Bap ae eget 08 05 08 2 9 TM Luz z 1 9 s bbe 6 x 78 86 06 00 DO E or 2 422 E ap tv ag 05 3 8 153 8 10 ELLIPSOIDAL DIFFUSION TENSOR 99 Tm Tm partial derivative The second partial derivatives with respect to the geometric parameter Tm twice are E 0 8 1542 d 0 8 154b E 0 8 154c d 8 154d 8 154e Tm Da partial derivative The second partial derivatives with respect to the geometric parameters Tm and Da are 0 c 5 355 8 155a e 0 8 155b 8 155c e 0 8 155d x 0 8 155e Tm D partial derivative The second partial derivatives with respect to the geometric parameters Tm and D are a TR 0 8 156a 2 0 8 156b 0 8 156c x 0 8 156d v i 8 1560 OTm OD 100 Da Da partial derivative CHAPTER 8 VALUES GRADIENTS AND HESSIANS The second partial derivatives with respect to the geometric parameter Da twice are Da D partial derivative O0 c Dant o 0 c 4 u D A co m DD i e 2270 co aD 2 0 8 157a 8 157b 8 157c 8 157d 8 157e The second partial derivatives with respect to the geometric parameters Da and D are D D partial d
48. OF FUNCTIONS 211 If one of the tokens is left out then all elements will be assumed to match For example if the string does not contain the character then all molecules will match the string Regular expression can be used to select spins For example the string H will select the protons H H2 H98 212 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 44 molecule display Synopsis Function for displaying the molecule information Defaults molecule display self mol_id None Keyword Arguments mol_id The molecule identifier string Identification string documentation The identification string is composed of three components the molecule id token begin ning with the character the residue id token beginning with the character and the atom or spin system id token beginning with the character Each token can be composed of multiple elements separated by the character and each individual element can either be a number which must be an integer in string format a name or a range of numbers separated by the character Negative numbers are supported The full id string specification is jmol_namej res_id ires id jres_idj Qjatom_idj jatom id jatom_idj where the token elements are jmol_name the name of the molecule res_id the residue identifier which can be a number name or range of numbers atom_id t
49. OTs s 2 E IO rp n wrr 8 122 8 9 MODEL FREE ANALYSIS 91 Oj Ts partial derivative The second partial derivative of 8 65 with respect to the orientational parameter D and the correlation time T is 2 k 2 A2 O J w 2g g Oci o Ts t mi WTsTi AN 8 123 00 0r 5 2 995 ts T wrsi ns S2 S partial derivative The second partial derivative of 8 65 with respect to the order parameter S twice is 9 J w 0 8 124 S S2 partial derivative The second partial derivative of 8 65 with respect to the order parameters S and 57 is 9 J Ts Ti Ts M M s 8 125 882 852 am 5 D EE ori Ts mi wrsti pe S Tf partial derivative The second partial derivative of 8 65 with respect to the order parameter S and corre lation time Ty is oO dt Te TY wr pti i e DU TT 8 126 F OTF rg T wrrri S 7 partial derivative The second partial derivative of 8 65 with respect to the order parameter S and corre lation time 7 is 0 J w 24 82 y or Us m7 rsny 8 127 08 Ors OTs 5 i k m Ts T n wrsT 2 S S partial derivative The second partial derivative of 8 65 with respect to the order parameter S2 twice is 9 J w 052 0 8 128 92 CHAPTER 8 VALUES GRADIENTS AND HESSIANS S rp partial derivative The second partial derivative of 8 65 wi
50. S2 The square of the generalised order parameter 9 5 T5 ts The effective correlation time of the slower motion 10 2 THE LIST OF FUNCTIONS 197 The following parameters are accepted for the extended 2 model free equation S2f The square of the generalised order parameter of the faster motion tf The effective correlation time of the faster motion S2s The square of the generalised order parameter of the slower motion ts The effective correlation time of the slower motion The following parameters are accepted for all equations Rex The chemical exchange relaxation r The average bond length lt r gt CSA The chemical shift anisotropy Spin identification string If spin_id is supplied then the model will only be created for the corresponding spins Otherwise the model will be created for all spins Examples The following commands will create the model free model m1 which is based on the original model free equation and contains the single parameter S2 relax model_free create_model m1 mf_orig S2 relax model_free create_model model m1 params S2 equation mf_orig The following commands will create the model free model large_model which is based on the extended model free equation and contains the seven parameters S2f tf S2 ts Rex C
51. The model parameter errors are calculated from the distribution of simulation param eters Monte Carlo simulations can be turned on or off using functions within this class Once the function for setting up simulations has been called simulations will be turned on The effect of having simulations turned on is that the functions used for minimisation grid search minimise etc or calculation will only affect the simulation parameters and not the model parameters By subsequently turning simulations off using the appropriate function the functions used in minimisation will affect the model parameters and not the simulation parameters An example for model free analysis which includes only the functions required for imple menting the above steps is relax gt grid_search inc 11 Step 2 relax gt minimise newton Step 2 relax gt monte_carlo setup number 500 Step 3 relax gt monte_carlo create_data method back_calc Step 4 relax gt monte_carlo initial_values Step 5 relax gt minimise newton Step 6 relax gt eliminate Step 7 relax gt monte_carlo error_analysis Step 8 An example for reduced spectral density mapping is relax gt calc Step 2 relax gt monte_carlo setup number 500 Step 3 relax gt monte_carlo create_data method back_calc Step 4 relax gt calc Step 6 relax gt monte_carlo error_analysis Step 8 242 CHAPTER 10 ALPHABETICAL LISTING OF
52. The name of the preset model The preset models The standard preset model free models are m0 y m1 S2 n S Teh no 9 Rer mg 94 Te Rer ub ers RB mG 87 ry E Teh du ee 55 6 7 Bard mg S Ti Si Ta Ha m9 Rex The preset model free models with optimisation of the CSA value are m10 CSA mid CSA S mi 4 CSA S Te m13 CSA S Rer 10 2 THE LIST OF FUNCTIONS 201 m14 CSA Se Te Rest m15 CSA S2 S Ts mi6 CSA 57 Tf Sr Te mi7 CSA B B Ts fils mis CSA 52 Tf S Ts Reg m19 CSA Rez The preset model free models with optimisation of the bond length are m20 r mat le EU m22 r 8 Te m23 r 82 Rer m24 r B Te Rex m25 fr 87 SS ou m26 r S5 PR tah uo e D EL o m28 17 87 ful ds fia m29 Ir CSA Rer The preset model free models with both optimisation of the bond length and CSA are m30 r CSA m31 r CSA 7 m32 fr CSA S Tet m33 r OSA 82 Res usq edu CSA ST m dba m35 Tr CSA 55 97 Ts m36 r CSA S5 6557 Teh m37 r CSA S2 S2 Ts Reg 202 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS m38 r CSA 52 05 57 Rer mao r CSA Rer Warning
53. a charge no more than your cost of physically performing source distribution a complete machine readable copy of the corresponding source code to be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange or c Accompany it with the information you received as to the offer to distribute correspond ing source code This alternative is allowed only for noncommercial distribution and only if you received the program in object code or executable form with such an offer in accord with Subsection b above The source code for a work means the preferred form of the work for making modifications to it For an executable work complete source code means all the source code for all modules it contains plus any associated interface definition files plus the scripts used to control compilation and installation of the executable However as a special exception the source code distributed need not include anything that is normally distributed in either source or binary form with the major components compiler kernel and so on of the operating system on which the executable runs unless that component itself accompanies the executable If distribution of executable or object code is made by offering access to copy from a designated place then offering equivalent access to copy the source code from the same place counts as distribution of the source code even though third parties are not compelled
54. a number which must be an integer in string format a name or a range of numbers separated by the character Negative numbers are supported The full id string specification is jmol_namej jres_idj jres_idj jres_idj Qjatom_idj atom id jatom_idj where the token elements are jmol_name j the name of the molecule 214 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS res_id the residue identifier which can be a number name or range of numbers atom_id the atom or spin system identifier which can be a number name or range of numbers If one of the tokens is left out then all elements will be assumed to match For example if the string does not contain the character then all molecules will match the string Regular expression can be used to select spins For example the string H will select the protons F H2 H98 10 2 THE LIST OF FUNCTIONS 10 2 46 molmol clear_history Synopsis Function for clearing the Molmol command history Defaults molmol clear_history self 215 216 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 47 molmol command Synopsis Function for executing a user supplied Molmol command Defaults molmol command self command None Keyword Arguments command The Molmol command to execute Description This user function allows you to pass Molmol commands to the program This can be useful for automat
55. analysis relaxation curve fitting reduced spectral density mapping and the NOE calculation Each type is located in a separate file in the directory specific_fns Mathematical functions This is reserved for CPU intensive code involved in calcula tions The code may be written in Python however C code can be used to significantly increase the speed of the calculations For optimisation the code can include function evaluations calculation of gradients and calculation of Hessians These functions are located in the directory maths_fns Data The program state stored in the class self relax data This class contains all the program data and is accessed by the generic and specific code The mathematical functions may also access this data but this is not recommended The structure is initialised by the file data py and the data is modified solely by the generic and specific code 9 7 THE MAILING LISTS 135 9 7 The mailing lists 9 7 1 Private vs public messages If you would like to start a private discussion please label your email as such Private messages are however strongly discouraged only start a private conversation if you really must If you receive a reply to a message you have sent a bug report you have filed etc which has not been sent to the mailing list and has not been labelled as private then the most likely explanation is that reply to all has not been used and hence the mailing list has not been included o
56. and is executed by passing the command dx to the command line with various options The program is designed for visualising multidimensional data and can be found at http www opendx org 14 CHAPTER 2 INSTALLATION INSTRUCTIONS 2 3 3 Molmol Molmol is used for viewing the PDB structures loaded into the program and to display parameter values mapped onto the structure 2 3 4 PyMOL PDB structures can also be viewed using PyMOL Although the mapping of parameter values onto the structure is not yet supported this program can be used to display geo metric objects generated by relax for representing physical concepts such as the diffusion tensor 2 3 5 Dasha Dasha is a program used for model free analysis of NMR relaxation data It can be used as an optimisation engine to replace the minimisation algorithms implemented within relax 2 3 6 Modelfree4 Art Palmer s Modelfree4 program is also designed for model free analysis and can be used as an optimisation engine to replace relax s high precision minimisation algorithms Chapter 3 Open source infrastructure 3 1 The relax web sites The main web site for relax is http nmr relax com From these pages general information about the program links to the latest documentation links to the most current software releases and information about the mailing lists are available There are also Google search capabilities built into the pages for searching both the HTML version of the
57. and not the simulation parameters An example for model free analysis which includes only the functions required for imple menting the above steps is relax gt grid_search inc 11 Step 2 relax gt minimise newton Step 2 relax gt monte_carlo setup number 500 Step 3 relax gt monte_carlo create_data method back_calc Step 4 relax gt monte_carlo initial_values Step 5 relax gt minimise newton Step 6 relax gt eliminate Step 7 relax gt monte_carlo error_analysis Step 8 An example for reduced spectral density mapping is relax gt calc Step 2 relax gt monte_carlo setup number 500 Step 3 relax gt monte_carlo create_data method back_calc Step 4 relax gt calc Step 6 relax gt monte_carlo error_analysis Step 8 240 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 58 monte_carlo setup Synopsis Function for setting up Monte Carlo simulations Defaults monte_carlo setup self number 500 Keyword Arguments number The number of Monte Carlo simulations Description This function must be called prior to any of the other Monte Carlo functions The effect is that the number of simulations will be set and that simulations will be turned on Monte Carlo Simulation Overview For proper error analysis using Monte Carlo simulations a sequence of function calls is required for running the various simulation components The steps neces
58. azure 240 255 255 alice blue 240 248 255 lavender 230 230 250 lavender blush 255 240 245 misty rose 255 228 225 white 255 255 255 black 0 0 0 dark slate grey 4T 79 79 dim grey 105 105 105 slate grey 112 128 144 light slate grey 119 136 153 grey 190 190 190 light grey 211 211 9 midnight blue 25 25 112 navy 0 0 128 cornflower blue 100 149 237 dark slate blue 72 61 139 slate blue 106 90 205 medium slate blue 123 104 238 light slate blue 132 112 255 medium blue 0 0 205 royal blue 65 105 225 blue 0 0 255 dodger blue 30 144 255 deep sky blue 0 191 255 sky blue 135 206 235 light sky blue 135 206 250 steel blue 70 130 180 light steel blue 176 196 222 light blue 173 216 230 powder blue 176 224 230 pale turquoise 175 238 238 dark turquoise 0 206 209 10 2 THE LIST OF FUNCTIONS 10 2 94 rdc back calc Synopsis Back calculate RDCs Defaults rdc back calc self id None Keyword Arguments id The alignment identification string 285 286 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 95 rdc copy Synopsis Copy RDC data from pipe from to pipe_to Defaults rdc copy self pipe_from None pipe_to None id None Keyword Arguments pipe_from The name of the pipe to copy the RDC data from pipe_to The name of the pipe to copy the RDC data to id The alignment identification string Description This function will copy RDC data from pipe_from to pipe_to If id is not given then all RDC
59. calculated The user function 22 calc will calculate both the NOE and the errors The NOE value will be calculated using the formula where Isat is the intensity of the peak in the saturated spectrum and l y is that of the CHAPTER 4 CALCULATING THE NOE Isat NOE Tref reference spectrum The error is calculated by where Osat and o ef are the peak intensity errors in the saturated and reference spectra ONOE Osat Dref ref lnr Iref respectively To create a file of the NOEs the command value write param noe file noe out force True will create a file called noe out with the NOE values and errors The force flag will cause any file with the same name to be overwritten An example of the format of noe out is Num Name Value Error 1 GLY None None 2 PRO None None 3 LEU None None 4 GLY 0 12479588727508535 0 020551827436105764 5 SER 0 42240815792914105 0 02016346825976852 6 MET 0 45281703194372114 0 026272719841642134 7 ASP 0 60727570079478255 0 032369427242382849 8 SER 0 63871921623680161 0 024695665815261791 9 PRO None None 10 PRO None None 11 GLU None None 12 GLY 0 92927160307645906 0 059569089743604184 13 TYR 0 88832516377296256 0 044119641308479306 14 ARG 0 84945042565860407 0 060533543601110441 4 8 Viewing the results Any two dimensional data set can be plotted in relax in conjunction with the program Grace The program is also known as Xmgrace and was previousl
60. calculated using Equations 6 3a 6 3b 6 3c and 6 6 Finally the chi squared value is calculated using Equation 6 25 6 1 THEORY 37 Topology of the space The problem of finding the minimum is complicated by the fact that optimisation algo rithms are blind to the curvature of the complete space Instead they rely on topological information about the current and sometimes the previous parameter positions in the space The techniques use this information to walk iteratively downhill to the minimum Very few optimisation algorithms rely solely on the function value conceptually the height of the space at the current position Most techniques also utilise the gradient at the current position Although symbolically complex in the case of model free analysis the gradient can simply be calculated as the vector of first partial derivatives of the chi squared equa tion with respect to each model free parameter The gradient is supplied as a second function to the algorithm which is then utilised in diverse ways by different optimisation techniques The function value together with the gradient can be combined to construct a linear or planar description of the space at the current parameter position by first order Taylor series approximation f 01 2 amp fy 4 xT V fr 6 26 where f is the function value at the current parameter position 0 V fj is the gradient at the same position and x is an arbitrary vector By accumulating in
61. column the default is 0 i e the first column res_name_col The residue name column this defaults to no column spin num col The spin number column this defaults to no column spin_ name_col The spin name column this defaults to no column sep The column separator the default is white space change all A flag specifying if all other spins should be changed Description Empty lines and lines beginning with a hash are ignored The change al1 flag argument default is False meaning that all spins currently either selected or deselected will remain that way Setting the argument to True will cause all spins not specified in the file to be selected Examples To deselect all overlapped residues listed with residue numbers in the first column of the file unresolved type relax deselect read unresolved relax deselect read file unresolved 10 2 THE LIST OF FUNCTIONS 157 To deselect the spins in the second column of the relaxation data file r1 600 while selecting all other spins for example type relax deselect read r1 600 res num col None spin num col 1 change_all True relax deselect read file r1 600 res_num_col None spin num col 1 change all True 158 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 18 deselect reverse Synopsis Function for the reversal of the spin selection Defaults deselect reverse self spin id None Keyword Argum
62. cos 0 sin o 25 cos 211 20 06 cos d 8 211b IS sin cos Y AT sin6sin 8 211c 0 118 CHAPTER 8 VALUES GRADIENTS AND HESSIANS Chapter 9 relax development This chapter is for developers or those who would like to extend the functionality of relax It is not required for using relax If you would like to make modifications to the relax source code please subscribe to all the relax mailing lists see the open source infrastructure chapter for more details Announcements are sent to relax announce at gna org whereas relax users at gna org is the list where discussions about the usage of relax should be posted relax devel at gna org is where all discussions about the development of relax including feature requests program design or any other discussions relating to relax s structure or code should be posted Finally relax commits at gna org is where all changes to relax s code and documentation as well as changes to the web pages are automatically sent to Anyone interested in joining the project should subscribe to all four lists 9 1 Version control using Subversion The development of relax requires the use of the Subversion SVN version control software downloadable from http subversion tigris org The source code to relax is stored in an SVN repository located at http svn gna org svn relax Every single change which has ever made to the program is recorded within this reposi
63. data set by assuming Gaussian errors This creates a synthetic data set for each Monte Carlo simulation 5 Prior to minimisation of the parameters of each simulation initial parameter estimates are required These are taken as the optimised model parameters An alternative is to use a grid search for each simulation to generate initial estimates however this is extremely computationally expensive For the case where values are calculated rather than minimised this step should be skipped although the results will be unaffected if this is accidentally run 6 Each simulation requires minimisation or calculation The same techniques as used in step 2 excluding the grid search when minimising should be used for the simulations 7 Failed simulations are removed using the techniques of model elimination 8 The model parameter errors are calculated from the distribution of simulation param eters Monte Carlo simulations can be turned on or off using functions within this class Once the function for setting up simulations has been called simulations will be turned on The effect of having simulations turned on is that the functions used for minimisation grid search minimise etc or calculation will only affect the simulation parameters and 10 2 THE LIST OF FUNCTIONS 239 not the model parameters By subsequently turning simulations off using the appropriate function the functions used in minimisation will affect the model parameters
64. data will be copied otherwise only a specific data set will be Examples To copy all RDC data from pipe m1 to pipe m9 type one of relax rdc copy m1 m9 relax rdc copy pipe from m1 pipe to m9 relax rdc copy m1 m9 None relax rdc copy pipe_from m1 pipe_to m9 id None To copy only the Th RDC data from m3 to m6 type one of relax gt rdc copy m3 m6 Th relax rdc copy pipe from m3 pipe_to m6 id Th 10 2 THE LIST OF FUNCTIONS 10 2 96 rdc delete Synopsis Delete the RDC data corresponding to the alignment id Defaults rdc delete self id None Keyword Arguments id The alignment identification string Examples To delete the RDC data corresponding to id PH_gel type relax gt rdc delete PH_gel 287 288 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 97 rdc display Synopsis Display the RDC data corresponding to the alignment id Defaults rdc display self id None Keyword Arguments id The alignment identification string Examples To display the phage RDC data type relax gt rdc display phage 10 2 THE LIST OF FUNCTIONS 289 10 2 98 rdc read Synopsis Read the RDC data from file Defaults rdc read self id None file None dir None mol_name_col None res num col 0 res name_col 1 spin_ num_col None spin_name_col None da
65. diffusion tensor init params 1 698e7 1 417e7 67 174 83 718 param types 3 relax diffusion tensor init 1 698e 1 1 417e 1 67 174 83 718 param types 3 d_scale 1e8 relax gt diffusion tensor init params 1 698e 1 1 417e 1 67 174 83 718 param_types 3 d_scale 1e8 relax gt diffusion_tensor init 1 698e 1 1 417e 1 1 1724 1 4612 param_types 3 d scale 1e8 angle units rad relax diffusion tensor init params 1 698e 1 1 417e 1 1 1724 1 4612 param types 3 d scale 1e8 angle units rad fixed True To select ellipsoidal diffusion type relax diffusion tensor init 1 340e7 1 516e7 1 691e7 82 027 80 573 65 568 param types 2 10 2 THE LIST OF FUNCTIONS 169 10 2 24 dx execute Synopsis Function for running OpenDX Defaults dx execute self file map dir dx dx exe dx vp exec True Keyword Arguments file The file name prefix For example if file is set to temp then the OpenDX program temp net will be loaded dir The directory to change to for running OpenDX If this is set to None OpenDX will be run in the current directory 0 exe The OpenDX executable file vp_exec A flag specifying whether to execute the visual program automatically at start up The default of True causes the program to be executed 170 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 25 dx map Synopsis Function for creating a map of the given space in OpenDX format Def
66. e The standard Python convention of a one line description separated from a detailed description by an empty line should be adhered to This line must start with a capital letter and end in a period This convention is required for certain docstring parsers see the Python docs e All functions should have a docstring describing in detail the function structure and organisation of the code e A docstring should be followed by an empty line Indentation of the docstring should be the same as that of the first line of code excluding indented lists etc An example of a single line docstring is def delete self Function for deleting all model free data An example of a multiline docstring is def aic chi2 k n Akaike s Information Criteria AIC The formula is AIC chi2 2k param chi2 The minimised chi squared value Ctype chi2 float Cparam k The number of parameters in the model type k int Oparam n The dimension of the relaxation data set Ctype n int return The AIC value Ortype float return chi2 2 0 k 9 2 3 Variable function and class names In relax a mixture of both camel case eg CamelCase and lower case with underscores is used Despite the variability there are fixed rules which should be adhered to These naming conventions should be observed at all times Variables and functions For both variables and functions lower case with underscores between words is always use
67. eS ciz TETTE 7 3 58 0r 5 pe A tor Br 2 pee AP 8 117 06 ry 4 m wrr 90 CHAPTER 8 VALUES GRADIENTS AND HESSIANS 6 7 partial derivative The second partial derivative of 8 65 with respect to the geometric parameter 6 and the correlation time Ts is k 9 J w 2 42 2 On 57 5i gt SETS Tata Ts Ti Ta 7 3 wr47 06 OTs 5 oe rs 74 w77 2 3 2 26 E al OA 8 118 08 r 75 wrsTi Oj O partial derivative The second partial derivative of 8 65 with respect to the orientational parameters Oj and Oy is 9 J Se S2 1 S T Ti TF 00 00 5 X 35 35 258 jo T rp lr S 1 S2 t riy Caer eu Bo S partial derivative The second partial derivative of 8 65 with respect to the orientational parameter D and the order parameter Sj is 02J J w 7 2 k a S2 7 TF TT 1 S2 Ts Ti Ts 00 00 057 5 E OO 14 wri TE T WTH gt rs wrsTi 8 120 Oj S partial derivative The second partial derivative of 8 65 with respect to the orientational parameter D and the order parameter 2 is 8 J w k dc 1 Ts Ti e i A 121 D 08 5 2 morem S my D Tf partial derivative The second partial derivative of 8 65 with respect to the orientational parameter D and the correlation time Ty is 9 J w 2 2 i Oc 2 Ty 7 wr pti ecl 0
68. file dir The directory where the file is located model The PDB model number parser The PDB parser used to read the file Description To load a specific model from the PDB file set the model flag to an integer i The structure beginning with the line MODEL in the PDB file will be loaded Otherwise all structures will be loaded starting from the model number 1 A few different PDB parsers can be used to read the structural data These are selected by setting the parser argument to one of scientific the Scientific Python PDB parser internal a lower quality and less reliable although faster PDB parser built into relax Example To load all structures from the PDB file test pdb in the directory pdb type one of relax gt structure read_pdb test pdb pdb relax gt structure read_pdb file test pdb dir pdb To load the 10 model from the file test pdb using the internal relax parser use one of relax structure read_pdb test pdb model 10 parser internal relax gt structure read pdb file test pdb model 10 parser internal 10 2 THE LIST OF FUNCTIONS 345 10 2 139 structure vectors Synopsis Extract unit bond vectors from the structure Defaults structure vectors self attached H spin_id None struct_index None verbosity 1 ave True unit True Keyword arguments attached The type of atom attached to the spi
69. file net and the OpenDX import file will be called file general dir The directory to output files to Set this to None if you do not want the files to be placed in subdirectory If the directory does not exist it will be created point An array of parameter values where a point in the map shown as a red sphere will be placed The length must be equal to the number of parameters point_file The name of that the point output files will be prefixed with 10 2 THE LIST OF FUNCTIONS 171 remap A user supplied remapping function This function will receive the parameter array and must return an array of equal length Map type The map type can be changed by supplying the map_type keyword argument Here is a list of currently supported map types Surface type Pattern 3D isosurface Iso3D This argument is case insensitive Examples The following commands will generate a map of the extended model free space for model m5 consisting of the parameters S S Ts Files will be output into the directory dx and will be prefixed by map In this case the system is a protein and residue number 6 will be mapped relax dx map S2 S2f ts 6 relax dx map S2 S2f ts 6 20 map dx relax dx map S2 S2f ts spin_id 6 file map dir dx relax gt dx map params S2 S2f ts s
70. for NMR spectroscopists 9 2 1 Indentation Indentation should be set to four spaces rather than a tab character This is the recommendation given in the Python style guide found at http www python org doc essays styleguide html Emacs should automatically set the tabstop correctly For vi add the following lines to the vimrc file set tabstop 4 set shiftwidth 4 set expandtab For UNIX systems including Linux and Mac OS X the vimrc file is vimrc whereas in MS Windows the file is VIM _vimrc which is usually C Program Files vim _vimrc Certain versions of vim those within the 6 2 series contain a bug where the tabstop value cannot be changed using the vimrc file although typing set tabstop 4 in vim will fix it One solution is to edit the file python vim which on GNU Linux systems is located in the path usr share vim ftplugin It contains the two lines Python always uses a tabstop of 8 setlocal ts 8 If these lines are deleted the bug will be removed Another way to fix the problem is to install newer versions of the run time files which will do the same thing 9 2 2 Doc strings The following are relax s conventions for docstrings Many of these are Python conventions e Each line of the should be set to no more than 100 characters long this includes all leading white space For one line docstrings the trailing double quotes are ignored 9 2 CODING CONVENTIONS 121
71. functions within this class Once the function for setting up simulations has been called simulations will be turned on The effect of having simulations turned on is that the functions used for minimisation grid search minimise etc or calculation will only affect the simulation parameters and not the model parameters By subsequently turning simulations off using the appropriate function the functions used in minimisation will affect the model parameters and not the simulation parameters An example for model free analysis which includes only the functions required for imple menting the above steps is relax gt grid_search inc 11 Step 2 relax gt minimise newton Step 2 relax gt monte_carlo setup number 500 Step 3 relax gt monte_carlo create_data method back_calc Step 4 relax gt monte_carlo initial_values Step 5 relax gt minimise newton Step 6 relax gt eliminate Step 7 relax gt monte_carlo error_analysis Step 8 An example for reduced spectral density mapping is relax gt calc Step 2 relax gt monte_carlo setup number 500 Step 3 relax monte_carlo create_data method back_calc Step 4 relax gt calc Step 6 230 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS relax gt monte_carlo error_analysis Step 8 10 2 THE LIST OF FUNCTIONS 231 10 2 54 monte carlo error analysis Synopsis Function for calculating parameter errors from th
72. identification string boolean The boolean operator specifying how spins should be selected change all A flag specifying if all other spins should be changed Description The change_all flag argument default is False meaning that all spins currently either selected or deselected will remain that way Setting the argument to True will cause all spins not specified by spin_id to be selected Examples To select only glycines and alanines assuming they have been loaded with the names GLY and ALA type one of relax select spin spin id GLY ALA To select residue 5 CYS in addition to the currently selected residues type one of relax select spin 5 relax select spin 5 amp CYS relax select spin spin_id 5 amp CYS 10 2 THE LIST OF FUNCTIONS 321 10 2 123 sequence copy Synopsis Copy the molecule residue and spin sequence data from one data pipe to another Defaults sequence copy self pipe from None pipe to None Keyword Arguments pipe_from The name of the data pipe to copy the sequence data from pipe to The name of the data pipe to copy the sequence data to Description This function will copy the sequence data between data pipes The destination data pipe must not contain any sequence data If the pipe from or pipe to arguments are not supplied then both will default to the current data pipe hence giving one argument is essential Examples To copy the sequen
73. ijle if PE Lg es MR VAL ages 06 OG 1 wm Te 71 WTeT 6 O partial derivative The second partial derivative of 8 64 with respect to the geometric parameter 6 and the orientational parameter Dz is 8 J w 2 E OT Oc 2 1 wi 2 2 Te T n wren lt a aa SS Si H 1 S ri 06 OD 2 06 OO 14 w7 2 5 re n wrer 2 Fe s 1 5 Te Ti Te T I6 0D gt T pose eh 8 71 Of S partial derivative The second partial derivative of 8 64 with respect to the geometric parameter 6 and the order parameter S is PI w ay 9n Al a ret ren 06 082 5 21 9G 1 wr 2 re n wreri2 Oc 1 Te Ti Te 96 m mittee ug 8 9 MODEL FREE ANALYSIS 77 6 Te partial derivative The second partial derivative of 8 64 with respect to the geometric parameter 6 and the correlation time Te is Te Ti 3 wreT OT w 2 a Or 86 Or 7 Bes Hs 68 PE Pea rere Ti Gr n P wr 7 2 i k y ete 2 pla a eth lr 8 73 06 i Te TE Ti p wreTi 2y D O partial derivative The second partial derivative of 8 64 with respect to the orientational parameters 0 and Oy is 82J E Pe B RO A E PS DN A is 74 D Dk Q Dra 0D OD do E mE Tet Ti oret Said Oj S partial derivative The second partial derivative of 8 64 with respect to the orientational par
74. is computation ally expensive Conjugate gradient methods The conjugate gradient algorithm CG was originally designed as a mathematical tech nique for solving a large system of linear equations Hestenes and Stiefel 1952 but was later adapted to solving nonlinear optimisation problems Fletcher and Reeves 1964 The technique loops over a set of directions po P1 Pn Which are all conjugate to the Hessian Nocedal and Wright 1999 a property defined as pi V7 fep 0 forallizj 6 31 By performing line searches over all directions p the solution to the quadratic model 6 27 of the position 0 will be found in n or less iterations of the CG algorithm where n is the total number of parameters in the model The technique performs well on large problems with many parameters as no matrices are calculated or stored The al gorithms perform better than the steepest descent method and preconditioning of the system is used to improve optimisation A number of preconditioned techniques will be investigated including the Fletcher Reeves algorithm which was the original conjugate 6 1 THEORY Al gradient optimisation technique Fletcher and Reeves 1964 the Polak Ribi re method Polak and Ribi re 1969 a modified Polak Ribi re method called the Polak Ribi re method Nocedal and Wright 1999 and the Hestenes Stiefel algorithm which originates from a formula in Hestenes and Stiefel 1952 As a line search is performed to f
75. is repeated for each of the Brownian diffusion models Finally AIC model selection is used to determine the best description of the dynamics of the molecule by selecting between the global models G including the sphere oblate spheroid prolate spheroid and ellipsoid Once the solution has been found Monte Carlo simulations can be utilised for error analysis 6 7 THE NEW MODEL FREE OPTIMISATION PROTOCOL 53 6 7 The new model free optimisation protocol Please write me Until this section is written please look at the sample script full_analysis py A description of the protocol is given at the top of the script The protocol is summarised in Figure 6 3 54 CHAPTER 6 MODEL FREE ANALYSIS Failure Failure Failure Failure Failure CR CR Ge coreemerer Oblate Prolate Hybrid global 3 Figure 6 3 A schematic of the new model free optimisation protocol Initially models tm0 to tm9 6 23 0 6 23 9 of the set T for each spin system i are optimised model elimination used to remove failed models and AIC model selection used to pick the best model Once all the have been determined for the system the the local Tm parameter is removed the model free parameters are held fixed and the global diffusion parameters of 4 are optimised These parameters are used as input for the central part of the schematic which follows the same procedure as that of Figure 6 2 Convergence is however precisely defined as iden
76. length of the vectors in the PDB representation meters file The name of the PDB file dir The directory to place the file into symmetry A flag which if True will create a second chain with reversed XH bond orien tations force A flag which if True will overwrite the file if it already exists Description This function creates a PDB file containing an artificial vectors the length of which default to the length argument of 20 A A structure must have previously been read into relax The origin of the vector distribution is located at the centre of mass of the selected residues This vector distribution PDB file can subsequently be read into any molecular viewer Because of the symmetry of the diffusion tensor reversing the orientation of the XH bond vector has no effect Therefore by setting the symmetry flag two chains A and B will be added to the PDB file whereby chain B is chain A with the XH bonds reversed 10 2 THE LIST OF FUNCTIONS 343 10 2 137 structure load spins Synopsis Load spins from the structure into the relax data store Defaults structure load spins self spin id None ave_pos True Keyword Arguments spin id The spin identification string ave pos A flag specifying if the position of the atom is to be averaged Description This function allows a sequence to be generated within the relax data store using the atomic information from the structure already associa
77. loaded as chi3 C dom to the C terminal domain C type relax n_state_model set_domain tensor chi3 C dom domain C 10 2 THE LIST OF FUNCTIONS 249 10 2 65 n state model set type Synopsis Set whether the alignment tensor is the full or reduced tensor Defaults n state model set type self tensor None red False Keyword Arguments tensor T he alignment tensor identification string red The state of the alignment tensor If True then it is labelled as the full tensor If False then it is labelled as the tensor reduced because of domain motions Description Prior to optimisation of the N state model the state of alignment tensor whether it is the full or reduced tensor must be set using this user function Examples To state that the alignment tensor loaded as chi3 C dom is the reduced tensor type relax n_state_model set_type tensor chi3 C dom red True 250 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 66 noe error Synopsis Function for setting the errors in the reference or saturated NOE spectra Defaults noe error self error 0 0 spectrum_type None res num None res_name None Keyword Arguments error The error spectrum_type The type of spectrum res_num The residue number res_name The residue name Description The spectrum_type argument can have the following values ref The NOE reference spectrum sat The NOE spe
78. matching the string will be set to the default value The parameter matching the string will be set to the supplied number Invalid combination Each parameter matching the strings will be set to the default values Each parameter matching the strings will be set to the supplied number Each parameter matching the strings will be set to the corresponding number Both arrays must be of equal length Spin identification If the spin_id argument is left as the default of None then the function will be applied to all spins If the data is global non residue specific data such as diffusion tensor parameters supplying the spin identifier will terminate the program with an error Examples To set the parameter values for the current data pipe to the default values for all spins type relax value set To set the parameter values of residue 10 which is in the current model free data pipe m4 and has the parameters 159 Te Rex the following can be used Rey term is the value for the first given field strength relax value set 0 97 2 048 1e 9 0 149 spin_id 10 relax value set val 0 97 2 048 1e 9 0 149 spin id 10 To set the CSA value of all spins to the default value type relax value set param csa To set the CSA value of all spins to 172 ppm type 366 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS relax value set 172 1e 6 csa relax gt value set val 172
79. not coded the most mature and least desta bilising widget set to use would be QT The GUI should be relatively easy to tie into relax The design is such that the GUI can be dropped straight into relax without effecting the normal prompt and script based operation of the program Other interfaces Any number of interfaces for example other GUIs an ncurses inter face a web based interface or an MPI interface could be added to relax without modification of the current sources Generic code This code includes classes and functions which are independent of the UI and not specific to a certain data pipe type for example not being involved in model free analysis relaxation curve fitting the NOE calculation and reduced spectral density mapping All this code is located in the directory generic_fns Specific setup This code implements the internal interface between the generic and specific code The generic code calls the specific setup asking for a specific function for the given data pipe type For example by asking for the minimise function when the data pipe type is model free analysis the function self relax specif ic model_free minimise is returned Although the generic code accesses the specific code solely through this interface the specific code can access the generic code directly The code is located in the file specific_fns specific_setup py Specific code This is the code which is specific to the data pipe type model free
80. of 8 65 with respect to the order parameter S and corre lation time Ty is 8 J uw S 7 partial derivative The second partial derivative of 8 65 with respect to the order parameter S and corre lation time 7 is Iw _ 2 Da Ts Ti wrsTi 5 8 100 0S Ors p v n wts7 2 l S S partial derivative The second partial derivative of 8 65 with respect to the order parameter S twice is 0 8 101 S Tf partial derivative The second partial derivative of 8 65 with respect to the order parameter S and corre lation time Ty is PI 2X rtm wrn acd A RE iTi 8 102 E Orn py 8 9 MODEL FREE ANALYSIS 85 S 7 partial derivative The second partial derivative of 8 65 with respect to the order parameter S and corre lation time 7 is k 8 J w Nu 2 y ee rs Ti WTsTi 8 103 1 092 00 5 r ri wrr Tf Tf partial derivative The second partial derivative of 8 64 with respect to the correlation time T twice is ui za Sf 2 CiT aren 807 Ty T wri r 8 104 orp gu rg Ti wrer Tf Ts partial derivative The second partial derivative of 8 64 with respect to the correlation times Tf and 7 is 9 J w md ll n n PS Ts Ts partial derivative The second partial derivative of 8 64 with respect to the correlation time Ts twice is 8 106 0
81. of the relax project Go to the Gna website https gna org and login Click on My Groups to go to https gna org my groups php In the section Request for inclusion type relax and hit enter Select relax and write something in the comments If you have been approved see section 9 4 1 you will be added to the project committers list 9 4 4 Format of the commit logs If you are a relax developer and you have commit access to the repository the following conventions should be followed for all commit messages e The length of all lines in the commit log should never exceed 100 characters This is so that the log message viewed in either emails or by the command prompt command svn log is legible 9 4 COMMITTERS 127 The first line of the commit log should be a short description or synopsis of the changes If the change relates to a bug or a task include the bug and task number using the notation type num where type is either bug task or support and num is the id number for example bug 6503 This terminology is important because the Gna infrastructure knows how to translate this into a link to the issue Also include a link to the issue e The second line should be blank e If the commit is a bug fix reported by a non committer or if the commit originates from a patch posted by a non committer the next lines should be reserved for credit ing The name of the person and their obfuscated email address for example e
82. parameter are c Da partial derivative Tm 0 Oc_ OTm Oco Em dc pM Oca T 0 0 0 The partial derivatives with respect to the D geometric parameter are partial derivative kana aio The partial derivatives with respect to the D geometric parameter are where e 1 as 1 Dr 62 26202 1 Dr 07 26262 2D 0 26207 0D R c oD c 0D Oc 0D dci 0D Oca 0D __3 0e 49D de 0D Co 95 8 144a 8 144b 8 144c 8 144d 8 144e 8 145a 8 145b 8 145c 8 145d 8 145 8 146a 8 146b 8 146c 8 146d 8 146e 8 147 96 CHAPTER 8 VALUES GRADIENTS AND HESSIANS 8 10 4 The weight Hessians of the ellipsoid D Oj partial derivative The second partial derivatives with respect to the orientational parameters D and O are Peo s a Pos 3 Or 2 D D 9D D 00 00 6 ty Mx xt 52 6 235 Mu 35 xum 8 1482 126 6 zt x a x 602 Ooms EN x 8 148b 2 2 Peo ag PG 82 08 D D 09 09 09 09 126 5 UR 00 00 Or D 00 O09 09 8 5 00 00 20 00 E 9D s x 8 148c 692 s Poa e e 0 0y 00V 8D 0D CN VEO 0D OD 0D 125 25 5 06 m 09 00 D 09 825 00 00 9D 0D 0D 4 8 148 2 05 s 00 00 09 a9 RC T
83. partial derivative The partial derivatives with respect to the geometric parameter D are OT_1 2 2 iso 2Da i 70 169 Da 8 180a To 2 6Diso Da 8 180b oa 8 180 aT 2 2 i50 ea 4 wl 25 6Diso 2Da 8 180c 8 11 7 The correlation time Hessians of the spheroid Tm Tm partial derivative The second partial derivatives with respect to the geometric parameter Tm twice are Pr TL 2 4 6Diso 29 3 27m 3 6Diso 2 94 gt 8 181a Tm rm A 3 3 2 ar 9 2T Diso E Da DT 6555 Da 8 181b Pr 4 3 3 9 A Dy Oa 8 181c OTm 8 11 SPHEROIDAL DIFFUSION TENSOR 109 Tm Da partial derivative The second partial derivatives with respect to the geometric parameters Tm and Da are Ec CU BEL a 8 1822 OT 09 mE m 250 a gt rm 2 3 27 6D 50 Da 8 182b arn 0D 2m 62 e 2 6Diso 2D 3 8 182c Tm R 09 m m so a Da Da partial derivative The second partial derivatives with respect to the geometric parameter Da twice are Mei 8 6Diso 2D 8 183a EE iso a gt 2 6Diso Da 8 183b sx 8 183b 0 7l 8 6Diso 29 3 8 183c 0m 110 CHAPTER 8 VALUES GRADIENTS AND HESSIANS 8 12 Spherical diffusion tensor 8 12 1 The diffusion equation of the sphere The correlation function of the Brownian rotational diffusion of a sphere is 1 Col E m 8 184 i z Ge
84. pdb use one of relax gt structure write_pdb test pdb struct_index 3 relax gt structure write_pdb file test pdb struct_index 3 348 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 141 system Synopsis Function which executes the user supplied shell command Defaults system command 10 2 THE LIST OF FUNCTIONS 349 10 2 142 temperature Synopsis Specify the temperature of an experiment Defaults temperature self id None temp None Keyword arguments id The experiment identification string temp The temperature of the experiment Description This function allows the temperature of an experiment to be set In certain analyses for example those which use pseudocontact shift data knowledge of the temperature is essential 350 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 143 value copy Synopsis Function for copying residue specific data values from runl to run2 Defaults value copy self runl None run2 None param None Keyword Arguments runl The name of the run to copy from run2 The name of the run to copy to param The parameter to copy Description Only one parameter may be selected therefore the param argument should be a string If this function is used to change values of previously minimised runs then the minimisation statistics chi squared value iteration count function count gradient count and Hessian count will be reset to N
85. separated by the character and each individual element can either be a number which must be an integer in string format a name or a range of numbers separated by the character Negative numbers are supported The full id string specification is jmol_namej jres id jres_idj jres_idj Qjatom_idj atom id jatom_idj where the token elements are jmol_name j the name of the molecule res_id the residue identifier which can be a number name or range of numbers atom_id the atom or spin system identifier which can be a number name or range of numbers 10 2 THE LIST OF FUNCTIONS 331 If one of the tokens is left out then all elements will be assumed to match For example if the string does not contain the character then all molecules will match the string Regular expression can be used to select spins For example the string H will select the protons H H2 H98 332 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 130 spin display Synopsis Function for displaying information about the spin s Defaults spin display self spin_id None Keyword Arguments spin_id The spin identification string Identification string documentation The identification string is composed of three components the molecule id token begin ning with the character the residue id token beginning with the character and the atom or s
86. the default is 2 error_col The experimental error column the default is 3 sep The column separator the default is white space Examples The following commands will read the PCS data out of the file Tb txt where the columns are separated by the symbol and store the PCSs under the identifier Tb relax pcs read Tb Tb txt sep 10 2 THE LIST OF FUNCTIONS 263 10 2 77 pcs write Synopsis Write the PCS data to file Defaults pcs write self id None file None dir None force False Keyword Arguments id The alignment identification string file The name of the file dir The directory name force A flag which if True will cause the file to be overwritten Description If no directory name is given the file will be placed in the current working directory The id argument are required for selecting which PCS data set will be written to file 264 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 78 pipe copy Synopsis Function for copying a data pipe Defaults pipe copy self pipe from None pipe to None Keyword Arguments pipe_from The name of the source data pipe to copy the data from pipe to The name of the target data pipe to copy the data to Description This user function allows the contents of a data pipe to be copied If the pipe_from keyword argument is set to None the current data pipe is assumed The data pipe cor
87. the original model free analysis of Lipari and Szabo 1982a the correlation function C r of the XH bond vector is approximated by decoupling the internal fluctuations of the bond vector Ci T from the correlation function of the overall Brownian rotational diffusion Co 7 by the equation C r Co 7 7 8 60 The overall correlation functions of the diffusion of a sphere spheroid and ellipsoid are presented respectively in section 8 10 1 on page 93 section 8 11 1 on page 106 and sec tion 8 12 1 on page 110 These three different equations can be combined into one generic correlation function which is independent of the type of diffusion This generic correlation function is k 1 z gt ee tlt 8 61 i k where c are the weights and 7 are correlation times of the exponential terms In the orig inal model free analysis of Lipari and Szabo 1982a b the internal motions are modelled by the correlation function Cy r S 1 82 e77 7e 8 62 where S is the generalised Lipari and Szabo order parameter which is related to the amplitude of the motion and 7 is the effective correlation time which is an indicator of the timescale of the motion albeit being dependent on the value of the order parameter The order parameter ranges from one for complete rigidity to zero for unrestricted motions Model free theory was extended by Clore et al 1990 to include motions on two timescales by the correlation function C t
88. the residue identifier which can be a number name or range of numbers atom_id the atom or spin system identifier which can be a number name or range of numbers If one of the tokens is left out then all elements will be assumed to match For example if the string does not contain the character then all molecules will match the string Regular expression can be used to select spins For example the string H will select the protons F H2 H98 10 2 THE LIST OF FUNCTIONS 309 10 2 114 residue name Synopsis Function for naming residues Defaults residue name self res_id None name None Keyword Arguments res_id The residue identification string corresponding to one or more residues name The new name Description This function simply allows residues to be named or renamed Examples The following sequence of commands will rename the sequence 1 ALA 2 GLY 3 LYS to 1 XXX 2 XXX 3 XXX relax residue name 1 XXX relax gt residue name 2 XXX relax gt residue name 3 XXX Alternatively relax gt residue name 1 2 3 XXX Identification string documentation The identification string is composed of three components the molecule id token begin ning with the character the residue id token beginning with the character and the atom or spin system id token beginning with the character Eac
89. this function Monte Carlo Simulation Overview For proper error analysis using Monte Carlo simulations a sequence of function calls is required for running the various simulation components The steps necessary for imple menting Monte Carlo simulations are 1 The measured data set together with the corresponding error set should be loaded into relax 2 Either minimisation is used to optimise the parameters of the chosen model or a calculation is run 3 To initialise and turn on Monte Carlo simulations the number of simulations n needs to be set 4 The simulation data needs to be created either by back calculation from the fully minimised model parameters from step 2 or by direct calculation when values are calcu lated rather than minimised The error set is used to randomise each simulation data set by assuming Gaussian errors This creates a synthetic data set for each Monte Carlo simulation 5 Prior to minimisation of the parameters of each simulation initial parameter estimates are required These are taken as the optimised model parameters An alternative is to use a grid search for each simulation to generate initial estimates however this is extremely computationally expensive For the case where values are calculated rather 10 2 THE LIST OF FUNCTIONS 235 than minimised this step should be skipped although the results will be unaffected if this is accidentally run 6 Each simulation requires minimisation or
90. tion disassemble param vector and the RelaxError class RelaxNoSequenceError While this is not normal for coding it is an important component of relax as it facilitates the reading of the source code by a non coder or someone not familiar with the codebase Iteration counters can be single letter variables such as i j k etc however for all other variables functions and classes please attempt to use descriptive names which are instantly identifiable Please minimise the amount of abbreviations used and only use those which are obvious For example naming the parameter vector self param vector the relaxation data relax data the model selection class class Model selection the type of spheroidal diffusion spheroid_type etc 9 2 4 Whitespace The following conventions are for general code cleanliness and readability e Trailing whitespace should be avoided although this is not very important e All functions should be preceded by two empty lines The only exception is the first function of the class definition e Function arguments should be separated by a comma followed by a single space e The assignment operator should be surrounded by spaces for example tm 7 1e 8 The exception is function arguments where for example self classic_colour res_num None width 0 3 e The comparison operators should also be surrounded by spaces e g u lt u ouw mmy us u ue
91. to copy the source along with the object code 4 You may not copy modify sublicense or distribute the Program except as expressly pro vided under this License Any attempt otherwise to copy modify sublicense or distribute the Program is void and will automatically terminate your rights under this License However parties who have received copies or rights from you under this License will not have their licenses terminated so long as such parties remain in full compliance 11 2 THE GPL 385 5 You are not required to accept this License since you have not signed it However nothing else grants you permission to modify or distribute the Program or its derivative works These actions are prohibited by law if you do not accept this License Therefore by modifying or distributing the Program or any work based on the Program you indicate your acceptance of this License to do so and all its terms and conditions for copying distributing or modifying the Program or works based on it 6 Each time you redistribute the Program or any work based on the Program the recipient automatically receives a license from the original licensor to copy distribute or modify the Program subject to these terms and conditions You may not impose any further restrictions on the recipients exercise of the rights granted herein You are not responsible for enforcing compliance by third parties to this License 7 If as a consequence of a court judgment
92. to the set creates a new set of models which will be labelled These include models tm0 to tm9 The local Tm parameter is the single member of the set D and in set notation E D USK 8 4 Although the Brownian rotational diffusion parameter local Tm is optimised this category is residue specific As such the complexity of the optimisation is lower than the next two categories It is slightly greater than the optimisation of the set as dim 1 k lt 6 8 5 where k is the number of model free parameters 8 3 3 Optimisation of the diffusion tensor parameters The parameters of the Brownian rotational diffusion tensor belong to the set D This set is the union of the geometric parameters 6 Diso Da Dr and the orientational parameters D D 6U0 8 6 When diffusion is spherical solely the geometric parameter Diso is optimised When the molecule diffuses as a spheroid the geometric parameters Diso and Da and the orientational parameters 0 the polar angle and the azimuthal angle are optimised If the molecule diffuses as an ellipsoid the geometric parameters Diso Da and D are optimised together with the Euler angles a 3 and y This category is defined as the optimisation of solely the parameters of D The model free parameters of are held constant As all selected residues of the macromolecule are involved in the optimisation this category is global and can be more complex than the optimisation of or
93. truncated Newton algorithm finds an approximate solution to Equation 6 29 by using a conjugate gradient CG sub algorithm Retaining the performance of the pure Newton algorithm the CG sub algorithm guarantees that the search direction is always downhill as the method terminates when negative curvature is encountered This algorithm is similar to the Newton Raphson CG algorithm implemented within Dasha Newton optimisation is sometimes also known as the Newton Raphson algorithm and as documented in the source code the Newton algorithm in Dasha is coupled to a conjugate gradient algorithm The auxiliary step length selection algorithm in Dasha is undocumented and may not be employed Once the search direction has been determined by the above algorithms the minimum along that direction needs to be determined Not to be confused with the methodology for determining the search direction pz the line search itself is performed by an auxiliary step length selection algorithm to find the value o A number of step length selection methods can be used to find a minimum along the line 0k api although only two will be investigated The first is the backtracking line search of Nocedal and Wright 1999 This method is inexact it takes a starting step length a and decreases the value until a sufficient decrease in the function is found The second is the line search method of Mor and Thuente 1994 Designed to be robust the MT algorithm finds the exa
94. ve Iilnt Initial intensity 10 Ti 0 Intensity at infinity iinf Iilinf Relaxation period times series relax times Rr elax Tt imes N state model set details Setting parameters for the N state model is a little different from the other type of analyses as each state has a set of parameters with the same names as the other states To set the parameters for a specific state c ranging from 0 for the first to N 1 for the last the number c should be added to the end of the parameter name So the Euler angle y of the third state is specified using the string gamma2 10 2 THE LIST OF FUNCTIONS 363 N state model data type string matching patterns Data type Probabilities Euler angle a Euler angle 8 Euler angle y Bond length Heteronucleus type Proton type Object name probs alpha peta gamma i heteronuc_type proton_type Patterns pO pl p2 PN alphaO alphatl beta0 betal gamma0 gammal r or Bb ond _ L1 ength Hh eteronucleus Pp roton The objects corresponding to the object names are lists or arrays with each element corrsponding to each state 364 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 146 value set Synopsis Function for setting spin specific data values Defaults value set sel
95. with the given minimisation algorithm if the keyword argument constraints is set to 1 The grid search algorithm should also not be selected as this is accessed using the grid function instead The first argument passed will be set to the minimisation algorithm while all other arguments will be set to the minimisation options Keyword arguments differ from normal arguments having the form keyword value All arguments must precede keyword arguments in python For more information see the examples section below or the python tutorial Keyword Arguments func_tol The function tolerance This is used to terminate minimisation once the function value between iterations is less than the tolerance The default value is 1e 25 grad_tol The gradient tolerance Minimisation is terminated if the current gradient value is less than the tolerance The default value is None max_iterations The maximum number of iterations The default value is le constraints A boolean flag specifying whether the parameters should be constrained The default is to turn constraints on constraints True scaling The diagonal scaling boolean flag The default that scaling is on scaling True verbosity The amount of information to print to screen Zero corresponds to minimal output while higher values increase the amount of output The default value is 1 190 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Diagonal scaling Diagonal
96. work which contains a notice placed by the copyright holder saying it may be distributed under the terms of this General Public License The Program below refers to any such program or work and a work based on the Program means either the Program or any derivative work under copyright law that is to say a work containing the Program or a portion of it either verbatim or with modifications and or translated into another language Hereinafter translation is included without limitation in the term modification Each licensee is addressed as you Activities other than copying distribution and modification are not covered by this Li cense they are outside its scope The act of running the Program is not restricted and the output from the Program is covered only if its contents constitute a work based on the Program independent of having been made by running the Program Whether that is true depends on what the Program does 1 You may copy and distribute verbatim copies of the Program s source code as you receive it in any medium provided that you conspicuously and appropriately publish on each copy an appropriate copyright notice and disclaimer of warranty keep intact all the notices that refer to this License and to the absence of any warranty and give any other recipients of the Program a copy of this License along with the Program You may charge a fee for the physical act of transferring a copy and you may at
97. your option offer warranty protection in exchange for a fee 2 You may modify your copy or copies of the Program or any portion of it thus forming a work based on the Program and copy and distribute such modifications or work under the terms of Section 1 above provided that you also meet all of these conditions a You must cause the modified files to carry prominent notices stating that you changed the files and the date of any change b You must cause any work that you distribute or publish that in whole or in part contains or is derived from the Program or any part thereof to be licensed as a whole at no charge to all third parties under the terms of this License c If the modified program normally reads commands interactively when run you must cause it when started running for such interactive use in the most ordinary way to print or display an announcement including an appropriate copyright notice and a notice that there is no warranty or else saying that you provide a warranty and that users may redistribute the program under these conditions and telling the user how to view a copy of this License Exception if the Program itself is interactive but does not normally print such an announcement your work based on the Program is not required to print an announcement These requirements apply to the modified work as a whole If identifiable sections of that work are not derived from the Program and can be reasonably consider
98. 0 dark green 0 000 0 392 0 000 green 0 000 1 000 0 000 cyan 0 000 1 000 1 000 turquoise 0 251 0 878 0 816 royal blue 0 255 0 412 0 882 aquamarine 0 498 1 000 0 831 sky green 0 529 0 808 0 922 dark violet 0 580 0 000 0 827 pale green 0 596 0 984 0 596 purple 0 627 0 125 0 941 brown 0 647 0 165 0 165 light blue 0 678 0 847 0 902 grey 0 745 0 745 0 745 light grey 0 827 0 827 0 827 violet 0 933 0 510 0 933 light coral 0 941 0 502 0 502 khaki 0 941 0 902 0 549 beige 0 961 0 961 0 863 red 1 000 0 000 0 000 magenta 1 000 0 000 1 000 deep pink 1 000 0 078 0 576 orange red 1 000 0 271 0 000 hot pink 1 000 0 412 0 706 coral 1 000 0 498 0 314 dark orange 1 000 0 549 0 000 orange 1 000 0 647 0 000 pink 1 000 0 753 0 796 gold 1 000 0 843 0 000 yellow 1 000 1 000 0 000 light yellow 1 000 1 000 0 878 ivory 1 000 1 000 0 941 white 1 000 1 000 1 000 X11 RGB colour arrays The following table is the list of X11 colour names and their corresponding RGB colour values ranging from 0 to 255 10 2 THE LIST OF FUNCTIONS 227 Name Red Green Blue snow 255 250 250 ghost white 248 248 255 white smoke 245 245 245 gainsboro 220 220 220 floral white 255 250 240 old lace 253 245 230 linen 250 240 230 antique white 250 235 215 papaya whip 255 239 213 blanched almond
99. 0 6 2a R2 0 Ra 0 6 2b YH Onon NOR 14 Te erm 6 2c whereas the relaxation equations are the R4 0 R2 0 exox 0 6 1 3 The relaxation equations R 0 The relaxation values of the set R 0 include the spin lattice spin spin and cross relaxation rates at all field strengths These rates are respectively Abragam 1961 Rad e a Jon ap taor eo wx eu 6 3a Ro 6 S 4100 weon tol dde d wx d 5 440 3J wx FR 6 3b as d 6J wn diccns es wx 6 3c where J w is the power spectral density function and Re is the relaxation due to chemical exchange The dipolar and CSA constants are defined in SI units as 1 2 yay R n 2 um 64 pp ondo 6 5 3 where uo is the permeability of free space yy and yx are the gyromagnetic ratios of the H and X spins respectively h is Plank s constant divided by 27 r is the bond length and Ao is the chemical shift anisotropy measured in ppm The cross relaxation rate Oxog is related to the steady state NOE by the equation Va O non O NOE 0 1 2 RO 6 6 6 1 4 The spectral density functions J w The relaxation equations are themselves dependent on the calculation of the spectral density values J w Within model free analysis these are modelled by the original model free formula Lipari and Szabo 1982a b Dn gt s SEES 6 7 ne 1 wri Te 7 wren 6 1 THEORY 33 where S is the square of the Lipari and Sza
100. 0 00 00 8 31 The second partial derivative with respect to the spectral density function parameters 0 and 6 is Ry EJP Pioy wx PI wx Jwg wx Ji 3 mc c A uu c ppc E 8 32 00 00 80 00 80 00 00 00 502 Spectral density terms of the R CSA component For the CSA component of the R4 equation 6 3a on page 32 the spectral density terms are JB J wx 8 33 The partial derivative of these terms with respect to the spectral density function param eter 0 is OJ AT wx JPY atc l 8 34 7 00 00 The second partial derivative with respect to the spectral density function parameters 0 and 6j is n LI u 9 J wx id 00 00 00 00 7 8 35 68 CHAPTER 8 VALUES GRADIENTS AND HESSIANS Spectral density terms of the Raz dipolar component For the dipolar component of the Ra equation 6 3b on page 32 the spectral density terms are JT 4J 0 J ug wx 3J ux 6F we 6J wy wx 8 36 The partial derivative of these terms with respect to the spectral density function param eter 0 is ay d 402 i OJ wH wx 397 ex 69 05 097 9n wx 00 00 80 00 80 mp o en Ro Jia The second partial derivative with respect to the spectral density function parameters 0 and 6 is jR 2 BI i PINO 8 J wg uwx O J wx 4 00 00 80 20 80 80 80 80 0 J wg iy wx a 96 80 38 Spectral density terms of the Rg C
101. 0 6 40 0 0 0 0 1 00 0 0 Ts 0 0 0 0 0 0 10 0 0 Rez 0 0 0 0 0 L 10 0 0 r 0 0 0 00001 0 0 CSA 0 0 0 00000 1 0 0 9e 10 0 0 0 0 0 0 0 1 0 20718 0 0 0 0 0 00 0 1 300e 0 0 0 0 0 00 0 1 0 Through the isolation of each individual element the constraints can be see to be equivalent 6 1 THEORY 45 to Qu S lt 1 6 41a 0x 97 lt 1 6 41b 0 lt 1 6 41c S Si 6 41d aede 6 41e Te 2 0 6 41f Tf 2 0 6 41g Ts 2 0 6 41h Ts 2 0 6 41i Tf STs 6 413 Rg gt 0 6 41k 0 9e7 lt r lt 2671 6 411 300e 5 lt CSA lt 0 6 41m To prevent the computationally expensive optimisation of failed models in which the inter nal correlation times minimise to infinity d Auvergne and Gooley 2006 the constraint Te Tf Ts 2Tm was implemented When the global correlation time is fixed the constraints in the matrix notation of 6 39 are 0 0 Te 2Tm 1 0 gt 2 6 42 0 0 1 Ts 2Tm However when the global correlation time Tm is one of the parameters being optimised the constraints become 2 1 0 0 i 0 2 0 1 0 T qe 10 6 43 2 0 xp 2 QU 0 Ts For the parameters of the diffusion tensor the constraints utilised are 0 lt Tm lt 200 0e 6 44a Da 2 0 6 44b 0 lt lt 1 6 44c which in the matrix notation of 6 39 become 1 0 0 0 10 0 Tus 200 0e 0 1 0 Da 2 0 6 45 0 0 1 D 0 0 0 1 1 46 CHAPTER 6 MODEL FREE ANALYSIS T
102. 112 8 13 1 The dot product of the ellipsoid 112 8 13 2 The dot product gradient of the ellipsoid 112 8 13 3 The dot product Hessian of the ellipsoid 114 8 14 Spheroidal dot product derivatives 2 0 0 eee ee 116 8 14 1 The dot product of the spheroid 116 8 14 2 The dot product gradient of the spheroid 116 8 14 3 The dot product Hessian of the spheroid 116 relax development 119 9 1 Version control using Subversion 0 0000 o 119 8 2 Coding conventions 0 Rum ROI SOROR SOR UR RR n a 120 mE o Zouk eu deu FR Ry T ROR 3e E Poe eee RUE RW A 120 922 DOO RIES l3 3 9 Re RS E e e Rc eU CR EUR m BS Se ee 120 9 2 8 Variable function and class names 2 121 92 4 WILGSEBEE o ios ow ok ohm ok Roe Red a Se Ron 3 do 123 O25 Comme ts coo sas b RR o eee ROS X xoa p A dom a 124 9 3 Submitting changes to the relax project o 124 9 3 1 Submitting changes as a patch coss eeose d esi r eaor Er e ae 124 9 3 2 Modification of official releases creating patches with diff 125 9 3 8 Modification of the latest sources creating patches with Subversion 125 Mal a AA eae T 125 94 1 Becoming committer 2223 be eee ee x 9 b RR E RR 125 94 2 Joining Gna 2222s 126 94 3 Joining the relax project cesc cessare kn 126 9 4 4 Format of the commit logs cc esoo 2s 126 9 4 5 Discussing majo
103. 171 are 1 302 1 8 1752 co 362 1 62 8 175b 2 82 1 8 175c 8 11 SPHEROIDAL DIFFUSION TENSOR 8 11 3 The weight gradients of the spheroid D partial derivative The partial derivatives with respect to the orientational parameter D are Oc_1 2 06 ial 36 362 Dao aco m 2 00 95 66 1 207 0 ci ES 2 00 5 36 62 Uso 8 11 4 The weight Hessians of the spheroid D Oj partial derivative 107 8 1762 8 176b 8 176c The second partial derivatives with respect to the orientational parameters O and O are 06 06 gt 2 A D D s os DD DD 06 00 2 D D e a 65 30 20 00 00 E 2 D D 3 aus DD 35 382 1 1 282 F 6 1 8 177a 8 177b 8 177c 108 CHAPTER 8 VALUES GRADIENTS AND HESSIANS 8 11 5 The correlation times of the spheroid The three spheroid correlation times 7 in the correlation function of the Brownian rota tional diffusion of a spheroid 8 171 are Lal OD ize 2Da T 8 178a TQ 60D ias n SE 8 178b Ti 6Diso 29 8 178c 8 11 6 The correlation time gradients of the spheroid Tm partial derivative The partial derivatives with respect to the geometric parameter Tm are OT Tm De 294 8 179a Tm Puy Tm 6Diso Da 8 179b Otis on Tm 6Diso d 9 A 8 179c Da
104. 1981 Practical Optimization Academic Press Goldfarb D 1970 A family of variable metric methods derived by variational means Math Comp 24 109 23 26 Hestenes M R and Stiefel E 1952 Methods of conjugate gradients for solving linear systems J Res Natn Bur Stand 49 6 409 436 Horne J d Auvergne E Coles M Velkov T Chin Y Charman W Prankerd R Gooley P and Scanlon M 2007 Probing the flexibility of the DsbA oxidoreductase from Vibrio cholerae a 15N 1H heteronuclear NMR relaxation analysis of oxidized and reduced forms of DsbA J Mol Biol 371 3 703 716 Korzhnev D M Billeter M Arseniev A S and Orekhov V Y 2001 NMR studies of Brownian tumbling and internal motions in proteins Prog NMR Spectrosc 38 3 197 266 Lefevre J Dayie K Peng J and Wagner G 1996 Internal mobility in the partially folded DNA binding and dimerization domains of GAL4 NMR analysis of the N H spectral density functions Biochemistry 35 8 2674 2686 Levenberg K 1944 A method for the solution of certain non linear problems in least squares Quarterly of Applied Mathematics 2 164 168 Lipari G and Szabo A 1982a Model free approach to the interpretation of nuclear magnetic resonance relaxation in macromolecules I Theory and range of validity J Am Chem Soc 104 17 4546 4559 Lipari G and Szabo A 1982b Model free approach to the interpretation of n
105. 2 compressed file save bz2 relax gt state save save relax gt state save state save relax gt state save save bz2 relax gt state save state save bz2 10 2 THE LIST OF FUNCTIONS 339 If the file save already exists the following commands will save the current program state by overwriting the file relax gt state save save True relax gt state save state save force True 340 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 135 structure create diff tensor pdb Synopsis Create a PDB file to represent the diffusion tensor Defaults structure create diff tensor pdb self scale 1 7999999999999999e 06 file tensor pdb dir None force False Keyword Arguments scale Value for scaling the diffusion rates file The name of the PDB file dir The directory where the file is located force A flag which if set to True will overwrite the any pre existing file Description This function creates a PDB file containing an artificial geometric structure to represent the diffusion tensor A structure must have previously been read into relax The diffusion tensor is represented by an ellipsoidal spheroidal or spherical geometric object with its origin located at the centre of mass of the selected residues This diffusion tensor PDB file can subsequently read into any molecular viewer There are four different types of residue within the PDB The centre of mas
106. 5 RELAXATION CURVE FITTING relax_fit read file T2_ncyci1 list relax time 0 1936 relax fit read file T2 ncyciib list relax time 0 1936 Calculate the peak intensity averages and the standard deviation of all spectra relax fit mean and error Deselect unresolved residues deselect read file unresolved Set the relaxation curve type relax_fit select_model exp Grid search grid_search inc 11 Minimise minimise simplex scaling False constraints False Monte Carlo simulations monte_carlo setup number 500 monte_carlo create_data monte_carlo initial_values minimise simplex scaling False constraints False monte_carlo error_analysis Save the relaxation rates value write param rx file rx out force True Grace plots of the relaxation rate grace write y_data_type rx file rx agr force True grace view file rx agr Save the program state state save file rx save force True 5 3 Initialisation of the data pipe and loading of the data The start of this sample script is very similar to that of the NOE calculation on page 20 The command pipe create rx relax_fit initialises the data pipe labelled rx The data pipe type is set to relaxation curve fitting by the argument relax_fit The backbone amide nitrogen sequence is extracted from a PDB file using the same commands as the NO
107. 50 ns although this can be overridden by supplying the value in seconds as the first element of the args tuple Internal correlation times 7 Tf Ts model elimination rules These parameters may experience the same problem as the local Tm in that the model fails and the parameter value is stuck at the upper limit These parameters are constrained using the formula re Tf Ts 27m These failed models are eliminated using the rule Te Tf Ts C Tm The default value of c is 1 5 Because of round off errors and the constraint algorithm setting c to 2 will result in no models being eliminated as the minimised parameters will always be less than 27 The value can be changed by supplying the value as the second element of the tuple Arguments The args argument must be a tuple of length 2 the elements of which must be numbers For example to eliminate models which have a local Tm value greater than 25 ns and models with internal correlation times greater than 1 5 times Tm set args to 25 1e 9 1 5 10 2 THE LIST OF FUNCTIONS 177 10 2 27 fix Synopsis Function for either fixing or allowing parameter values to change during optimisation Defaults fix self element None fixed True Keyword Arguments element Which element to fix fixed A flag specifying if the parameters should be fixed or allowed to change Description The keyword argument element can be any of the following di
108. 580 0 000 0 827 pale green 0 596 0 984 0 596 purple 0 627 0 125 0 941 brown 0 647 0 165 0 165 light blue 0 678 0 847 0 902 grey 0 745 0 745 0 745 light grey 0 827 0 827 0 827 violet 0 933 0 510 0 933 light coral 0 941 0 502 0 502 khaki 0 941 0 902 0 549 beige 0 961 0 961 0 863 red 1 000 0 000 0 000 magenta 1 000 0 000 1 000 deep pink 1 000 0 078 0 576 orange red 1 000 0 271 0 000 hot pink 1 000 0 412 0 706 coral 1 000 0 498 0 314 dark orange 1 000 0 549 0 000 orange 1 000 0 647 0 000 pink 1 000 0 753 0 796 gold 1 000 0 843 0 000 yellow 1 000 1 000 0 000 light yellow 1 000 1 000 0 878 ivory 1 000 1 000 0 941 white 1 000 1 000 1 000 X11 RGB colour arrays The following table is the list of X11 colour names and their corresponding RGB colour values ranging from 0 to 255 284 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Name Red Green Blue snow 255 250 250 ghost white 248 248 255 white smoke 245 245 245 gainsboro 220 220 220 floral white 255 250 240 old lace 253 245 230 linen 250 240 230 antique white 250 235 215 papaya whip 255 239 213 blanched almond 255 235 205 bisque 255 228 196 peach puff 255 218 185 navajo white 255 222 173 moccasin 255 228 181 cornsilk 255 248 220 ivory 255 255 240 lemon chiffon 255 250 205 seashell 255 245 238 honeydew 240 255 240 mint cream 245 255 250
109. 81 282 352 352 357 361 361 362 369 369 377 minimisation 4 31 57 152 165 175 176 182 189 189 190 192 192 193 194 194 195 206 228 229 231 232 234 241 350 359 364 365 minimisation algorithm BFGS 38 39 Cauchy point 40 CG Steihaug 40 coordinate descent 38 dogleg 40 exact trust region 40 Fletcher Reeves 40 Hestenes Stiefel 40 Levenberg Marquardt 42 Newton 38 42 Newton CG 39 41 Polak Ribi re 40 Polak Ribi re 40 simplex 41 steepest descent 38 40 41 minimisation techniques BFGS 58 193 195 Cauchy point 193 393 CG Steihaug 193 conjugate gradient 193 194 dogleg 193 194 exact trust region 193 194 Fletcher Reeves 193 Hestenes Stiefel 193 Levenberg Marquardt 152 193 Method of Multipliers 189 194 Newton 58 152 190 193 195 Newton conjugate gradient 193 Polak Ribi re 193 Polak Ribi re 193 simplex 57 190 193 steepest descent 193 minisation 2 model elimination 2 3 175 175 176 229 232 235 236 238 241 model selection 2 AIC 2 205 206 AICc 2 205 ANOVA 3 BIC 2 205 bootstrap 2 205 cross validation 2 205 hypothesis testing 3 model free analysis 31 modelling 175 molecule 156 163 164 166 207 207 208 209 209 210 210 211 212 212 213 213 214 222 262 268 280 289 295 303 312 317 321 323 325 336 340 341 343 379 Monte Carlo simulation 3 25 28 MS Windows 12 130 news 17 NMR 345 NOE 2 19
110. Da OTO ODa OT m DU 2R 6Diso 20 9 aD AR OD 20 90 1 3D 6Diso Dall 39 1 3D 6Diso Da 1 39 2 6Diso 204 8 161a 8 161b 8 161c 8 161d 8 161e Pm Eo om PER 8 1622 8 162b 8 162c 8 162d 8 162e 8 163a 8 163b 8 163c 8 163d 8 1636 8 10 ELLIPSOIDAL DIFFUSION TENSOR partial derivative The partial derivatives with respect to the geometric parameter D are T2 0D OT_1 OD OT 09 OT 0D OT OD DD 6 6Diso 2D R 3D TO Dall 39 39a 6D Dall 3D 0 DaDr 6 R 6D AA A 103 8 164a 8 164b 8 164c 8 164d 8 164e 104 CHAPTER 8 VALUES GRADIENTS AND HESSIANS 8 10 7 The correlation time Hessians of the ellipsoid Tm Tm partial derivative The second partial derivatives with respect to the geometric parameter Tm twice are 2 72 20 6Diss 20 9 2m 3 6Diso 20491 7 8 1652 Tm Ora 4 3 3 2 p 27m 06945 Dall 3D 27m 6D so Dall 3Dy 8 165b Tm 070 4 3 3 2 PE 27m 6Diso Dall 3D 27m 6Diso Dall 3Dy 8 165c Tm Or E 8 8 2 51 3 2054 Di 294 2 5 amp 6Diso 295 8 165d Tm 077 4 3 3 2 Tm Tm Da partial derivative The second partial derivatives with respect to the g
111. E calculation script structure read_pdb name Ap4Aase_new_3 pdb structure load_spins spin_id ON 5 4 THE REST OF THE SETUP 27 To load the peak intensities into relax the user function relax_fit read is executed Two important keyword arguments to this command are the file name and the relaxation time period of the experiment in seconds It is assumed that the file format is that of a Sparky peak list Using the format argument this can be changed to XEasy text window output format To be able to import any other type of format please send an email to the relax development mailing list with the details of the format Adding support for new formats is trivial The following series of commands will load peak intensities from six different relaxation periods four of which have been duplicated relax_fit read file T2_ncyc1 list relax time 0 0176 relax fit read file T2 ncycib list relax time 0 0176 relax fit read file T2 ncyc2 list relax time 0 0352 relax fit read file T2 ncyc4 list relax time 0 0704 relax fit read file T2 ncyc4b list relax time 0 0704 relax fit read file T2 ncyc6 list relax time 0 1056 relax fit read file T2 ncyc9 list relax time 0 1584 relax fit read file T2 ncyc9b list relax time 0 1584 relax fit read file T2 ncycii list relax time 0 1936 relax fit read file T2 ncyciib list relax time 0 1936 5 4 The rest of the setup Once all the peak intensity data has been loade
112. EING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES END OF TERMS AND CONDITIONS How to Apply These Terms to Your New Programs If you develop a new program and you want it to be of the greatest possible use to the public the best way to achieve this is to make it free software which everyone can redistribute and change under these terms To do so attach the following notices to the program It is safest to attach them to the start of each source file to most effectively convey the exclusion of warranty and each file should have at least the copyright line and a pointer to where the full notice is found lt one line to give the program s name and a brief idea of what it does gt 11 2 THE GPL 387 Copyright C lt year gt lt name of author gt This program is free software you can redistribute it and or modify it under the terms of the GNU General Public License as published by the Free Software Foundation either version 2 of the License or at your option any later version This program is distributed in the hope that it will be useful but WITHOUT ANY WARRANTY without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE See the GNU General Public License for more details You should have received a copy of the GNU Gener
113. GLY 3 LYS relax residue create 1 ALA relax residue create 2 GLY relax residue create 3 LYS 306 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 112 residue delete Synopsis Function for deleting residues Defaults residue delete self res_id None Keyword Arguments res_id The residue identifier string Description This function can be used to delete a single or sets of residues See the identification string documentation below for more information If spin system atom ids are included a RelaxError will be raised Identification string documentation The identification string is composed of three components the molecule id token begin ning with the character the residue id token beginning with the character and the atom or spin system id token beginning with the character Each token can be composed of multiple elements separated by the character and each individual element can either be a number which must be an integer in string format a name or a range of numbers separated by the character Negative numbers are supported The full id string specification is jmol_namej jres id jres_idj jres_idj Qjatom_idj jatom_idj jatom_idj where the token elements are jmol_name the name of the molecule res_id the residue identifier which can be a number name or range of numbers atom_id the atom or spin system ide
114. MITTERS 125 the Unix command diff or the Subversion program The resultant file patch of either the diff or svn command described below can be posted to the relax devel at gna org mailing list Please label within your post which version of relax you modified or which revision the patch is for Also try to create a commit log message according to the format described in section 9 4 4 on page 126 for one of the relax committers to use as a template for committing the change 9 3 2 Modification of official releases creating patches with diff If your modifications have been made to the source code of one of the official relax releases for example 1 2 2 then the Unix command diff can be used to create a patch A patch file is simply the output of the diff command run with the recursive flag and presented in the unified format Therefore two directories need to be compared If the original sources are located in the directory relax_orig and the modified sources in relax_mod then the patch can be created by typing diff ur relax_orig relax_mod gt patch 9 3 3 Modification of the latest sources creating patches with Subver sion If possible changes to the latest sources is preferred Using the most up to date sources from the relax SVN repository will significantly aid the relax developers to incorporate your changes back into the main development line To check out the current development line see section 9 1 on page 119
115. N Other literature related to the improved model free analysis used within relax which can nevertheless be applied to other techniques such as SRLS include model free model se lection d Auvergne and Gooley 2003 Chen et al 2004 model free model elimination d Auvergne and Gooley 2006 the theory d Auvergne and Gooley 2007 behind the new model free optimisation protocol d Auvergne and Gooley 2008b and the hybridi sation of different models Horne et al 2007 d Auvergne and Gooley 2008b Most of these details can be found in the PhD thesis of d Auvergne 2006 1 1 2 Supported NMR theories The following relaxation data analysis techniques are currently supported by relax e Model free analysis Lipari and Szabo 1982a b Clore et al 1990 e Reduced spectral density mapping Farrow et al 1995 Lefevre et al 1996 e Exponential curve fitting to find the Ri and Ra relaxation rates e Steady state NOE calculation The future At some time in the future the following techniques are planned to be implemented within relax e Relaxation dispersion e SRLS Slowly relaxing local structure Tugarinov et al 2001 Because relax is free software if you would like to contribute addition features functions or modules which you have written for your own publications for the benefit of the field almost anything relating to molecular dynamics may be accepted Please see the Open Source chapter for more
116. O 2 SG pymelclear Hist Py ul lo ei eR ee a TW 272 10 287 pemol command 2 2 sho doe ee aa ev Q9 o Rom o go 273 10 2 88 pymoLeone pdb sse oto hehe GES ASR ER oL 274 10 2 89 pymol macro_exec ls 215 1032 pymolienBOr Dd cox RR oS RR Ms ues X Rec 277 10 2 91 pyri vector digb usu ns o RG ee Re et 279 MA eei ea RE RR pom m 9 OR Pee oe be ee Sox Sa es 280 a TTS o a ca ets ee Se a RO ee Ro m 281 I 94rdeBackale 2 socor bh be ae roe a ee a Oe es 285 MPA eon o Rom eb Ae ERR RU eee RD REE SE S S 286 DN IGI CCP 287 BEST PAG AISI uo kw ek dea UR BA aoe a ben Be xU es 288 10 2 ORO a we ae a Rum A a eo CS Eee ae Ga 289 ID 2O0Tde WHS oe ws RO eR Remo s ead Bae ee be ee oe Sages 290 10 2 10061ax data badk eale 2 22 doses lE REG RR EG 291 A e s son nog os Roms do roe Row Ro 9 y er oom Roy oo gos 292 10 2 102e ax data delete llle 293 10 2 10961ax data display so 22x Rc x RR a a ao e a 294 A sa i2 gn coge ese 37x RS Gow DR Fas ve NUR 295 10 2 TU elax ae solus ome E PR Ox RE RR de ROW Rs 297 10 2 10 elax_fit mean_and_error gt co lees 298 UWLATU Tela IE Sea E ee be RR Ree BoP ee a y ed 299 10 2 10 elax_tit select model 2 ee o o oso RR 301 102 1096960 socios or m ok Rom Ro RR Ree eed E ede eR ESTEE 302 A a CC 303 I 2 or A TT 305 102 Li tesiiegelte 2d 19 moa Low ew eee e Bee ae 306 10 2 1 Reside display o e so sra RR m s RR Sx GA 308 WS TIPS ARE uou luec o ke eR n Red ee E e RT Ros e 309 10 21 sesiduea mbef 2s
117. PDB file Defaults molmol view self Example relax gt molmol view relax gt molmol view 10 2 THE LIST OF FUNCTIONS 223 10 2 52 molmol write Synopsis Function for creating Molmol macros Defaults molmol write self data type None style classic colour_start None colour_end None colour_list None file None dir molmol force False Keyword Arguments data_type The data type to map to the structure style The style of the macro colour_start The starting colour either an array or string of the linear colour gradient colour_end The ending colour either an array or string of the linear colour gradient colour_list The list of colours to match the start and end strings file The name of the file dir The directory name force A flag which if set to True will cause the file to be overwritten Description This function allows residues specific values to be mapped to a structure through the creation of a Molmol mac macro which can be executed in Molmol by clicking on File Macro Execute User Currently only the classic style which is described below is available Colour The values are coloured based on a linear colour gradient which is specified through the colour_start and colour_end arguments These arguments can either be a string to identify one of the RGB red green blue colour arrays listed in the tables below or you can give the RGB vect
118. PUBLIC LICENSE Version 2 June 1991 Copyright C 1989 1991 Free Software Foundation Inc 59 Temple Place Suite 330 Boston MA 02111 1307 USA Everyone is permitted to copy and distribute verbatim copies of this license document but changing it is not allowed Preamble The licenses for most software are designed to take away your freedom to share and change it By contrast the GNU General Public License is intended to guarantee your freedom to share and change free software to make sure the software is free for all its users This General Public License applies to most of the Free Software Foundation s software and to any other program whose authors commit to using it Some other Free Software Foundation software is covered by the GNU Library General Public License instead You can apply it to your programs too When we speak of free software we are referring to freedom not price Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software and charge for this service if you wish that you receive source code or can get it if you want it that you can change the software or use pieces of it in new free programs and that you know you can do these things To protect your rights we need to make restrictions that forbid anyone to deny you these rights or to ask you to surrender the rights These restrictions translate to certain responsibilities for you if you distribute copi
119. S2 vs te for all spins type one of relax gt grace write S2 te file s2_te agr relax gt grace write x_data_type S2 y_data_type te file s2_te agr relax gt grace write x_data_type S2 y_data_type te file s2_te agr force True To create a Grace file of the Monte Carlo simulation values of Rex vs te for residue 123 type one of relax grace write Rex te spin_id 123 plot_data sims file s2_te agr relax gt grace write x_data_type Rex y_data_type te spin_id 123 plot_data sims file s2_te agr By plotting the peak intensities the integrity of exponential relaxation curves can be checked and anomalies searched for prior to model free analysis or reduced spectral density mapping For example the normalised average peak intensities can be plotted verses the relaxation time periods for the relaxation curves of all residues of a protein The normalisation whereby the initial peak intensity of each residue I 0 is set to 1 emphasises any problems To produce this Grace file type relax gt grace write x_data_type relax_times y_data_type ave_int g yP y yP file intensities_norm agr force True norm True Regular expression The python function match which uses regular expression is used to determine which data type to set values to therefore various data_type strin
120. SA r relax gt model_free create_model large_model mf_ext S2f tf S2 ts Rex CSA r relax model free create model model large model params S2f tf S2 ts Rex CSA r equation mf ext 198 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 37 model free delete Synopsis Function for deleting all model free data from the current data pipe Defaults model_free delete self Examples To delete all model free data type relax gt model_free delete 10 2 THE LIST OF FUNCTIONS 199 10 2 38 model free remove_tm Synopsis Function for removing the local Tm parameter from a model Defaults model_free remove_tm self spin_id None Keyword Arguments spin id The spin identification string Description This function will remove the local 7 parameter from the model free parameter set If there is no local Tm parameter within the set nothing will happen If no spin identification string is given then the function will apply to all spins Examples The following command will remove the parameter tm relax gt model_free remove_tm 200 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 39 model_free select_model Synopsis Function for the selection of a preset model free model Defaults model_free select_model self model None spin_id None Keyword Arguments model
121. SA component For the CSA component of the Ra equation 6 3b on page 32 the spectral density terms are JP 4J 0 3J wx 8 39 The partial derivative of these terms with respect to the spectral density function param eter 0 is 9JP2 0J 0 OJ wx JE 4s A IZ 8 40 7786 80 86 9 The second partial derivative with respect to the spectral density function parameters 0 and 6 is Pu J 0 9 wx pre 3 88 06 005 00 00 00 PAD Spectral density terms of the oxo dipolar component For the dipolar component of the onos equation 6 3c on page 32 the spectral density terms are JNO 6J ug wx J w wx 8 42 The partial derivative of these terms with respect to the spectral density function param eter 0 is OT NO OJ wH wx OJ wH wx JONOE d 6 _ 8 43 8 00 00 00 Bos 8 8 Rj 0 VALUES GRADIENTS AND HESSIANS 69 The second partial derivative with respect to the spectral density function parameters 0 and 6 is cae NOE u 0 J wg wx B 0 J wy wx 8 44 00 00 00 00 00 00 i ONOE Jra 8 8 2 R 0 values Using the components of the relaxation equations defined above the three relaxation equa tions can be re expressed as R1 0 dJ 2 cJ 8 45a d Ra 0 ZJ SDN 8 45b Owox 8 gu eee 8 45c 8 8 3 R gradients A different partial derivative exists for the spec
122. TER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 32 intro_off Synopsis Function for turning the function introductions off Defaults intro off self 10 2 THE LIST OF FUNCTIONS 10 2 33 intro_on Synopsis Function for turning the function introductions on Defaults intro_on self 187 188 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 34 jw_mapping set_frq Synopsis Function for selecting which relaxation data to use in the J w mapping Defaults jw_mapping set_frq self frq None Keyword Arguments frq The spectrometer frequency in Hz Description This function will select the relaxation data to use in the reduced spectral density mapping corresponding to the given frequency Examples relax jw mapping set frq 600 0 1e6 relax jw mapping set frq frq 600 0 1e6 10 2 THE LIST OF FUNCTIONS 189 10 2 35 minimise Synopsis Minimisation function Defaults minimise self args keywords Arguments The arguments which should all be strings specify the minimiser as well as its options A minimum of one argument is required As this calls the minfx function generic_minimise the full list of allowed arguments is shown below in the reproduced generic_minimise docstring Ignore all sections except those labelled as minimisation algorithms and min imisation options Also do not select the Method of Multipliers constraint algorithm as this is used in combination
123. The models in the thirties range fail when using standard R4 R and NOE relaxation data This is due to the extreme flexibly of these models where a change in the parameter r is compensated by a corresponding change in the parameter CSA and vice versa Additional preset model free models which are simply extensions of the above models with the addition of a local Tm parameter are tm0 tm tmt es Deu 9 tmp Tus BP uL ta t Hl gm Tm S Te Rex bmb Dp S BA nb Dn S Th Ves imn ms S Se Ta Reh tm 7m S2 Tp 82 Ta Res ED a Res The preset model free models with optimisation of the CSA value are tm10 Tm CSA tm11 Tm CSA 52 mo Tm CSA S Te emis De CSA D Ret mid n CSA S5 Te Rex tm15 Tm CSA 5 S te tm16 tm CSA 5 ry S Te tm17 os CSA S S2 Ts Rez 10 2 THE LIST OF FUNCTIONS 203 tm18 n OSA S Tn 58 qu fos mni9 Tm CSA Rer The preset model free models with optimisation of the bond length are 020 Eras r tm21 Tm r S tm22 n r 9 Te tm28 Tm r 82 Res ena eus r SP Te Rer m25 Imus S Bow m25 m m S Ti S Teh bmOT Tm T S5 Bt Fink Ebm28 IT S re ss 029 Tm r CSA Rez The preset model free models with both optimisation of th
124. Ti The dimensionality of the problem nevertheless low with dmD 1 dimD 4 dimD 6 8 7 for the diffusion as a sphere spheroid and ellipsoid respectively 8 3 4 Optimisation of the global model 6 The global model is defined as l s 2u Us 8 8 i l 60 CHAPTER 8 VALUES GRADIENTS AND HESSIANS where 7 is the residue index and is the total number of residues used in the analysis This is the most complex of the four categories as both diffusion tensor parameters and model free parameters of all selected residues are optimised simultaneously The dimensionality of the model G is much greater than the other categories and is equal to l dim 6 dimD k lt 6 51 8 9 i l where k is the number of model free parameters for the residue 7 and is equal to dim the number six corresponds to the maximum dimensionality of D and the number five corresponds to the maximum dimensionality of 8 4 Construction of the values gradients and Hessians 8 4 1 The sum of chi squared values For the single residue models of and the chi squared value x which is optimised is simply Equation 8 15 on page 62 in which the relaxation data is that of residue i However for the global models 9 and G in which all selected residues are involved the optimised chi squared value is the sum of those for each residue l D a 8 10 jl where 7 is the residue index and is the total number of residues used in the analysis This
125. US 00 00 00 09 925 06 06 oe ls 2 Z ili zZ zZ z 6 00 i 00 359 OO E 00 8 148e Pez x a o Po RE j 8 10 ELLIPSOIDAL DIFFUSION TENSOR where x 14 39 16 6 x taie ui 6 uum A m Os o 26 6 5 1 39 s gt 62 OS 423 4 a T EC 6 3E a6 05 2 y Ody e a 80 00 0D Po 85 2 E es ee e he OD D 0D Dy Dy 08 Di Tm partial derivative The second partial derivatives with respect to geometric parameter Tm are 0 c 9 Si ODi OTm 0 c 4 _ 0 OO Tm co 0 oDi Or 3c _ 0 Di Tm 97 e S a y S5 x us Q amp Q Bla Slov 33 E Dl EE O a UA ON Ne Nn a Nae ON Na al a ss NZ e a x Q amp Q 9 D S 8 S Q S y x uw Qj amp e amp Q S 8 S D S 8 S 8 149 the orientational parameter 9 and the 8 150a 8 150b 8 150c 8 150d 98 CHAPTER 8 VALUES GRADIENTS AND HESSIANS 9 C2 TS 8 1500 Di Da partial derivative The second partial derivatives with respect to the orientational parameter 0 and the geometric parameter D are gt Li i 8 1512 as exi 8 151b mos 8 151c X 8 151d ts 0 8 1510 Di D partial derivative The second partial derivatives with respect to the orientational parameter and the geometric parameter D are O0 c 9 e 0D 09 0D OD J 8c
126. USER FUNCTIONS 10 2 59 n_state_model CoM Synopsis Centre of mass CoM analysis Defaults n_state_model CoM self pivot_point 0 0 0 0 0 0 centre None Keyword Arguments pivot_point The pivot point of the motions between the two domains centre The optional argument for manually specifying the CoM of the initial position prior to the N rotations to the positions of the N states Description This function is used for analysing the domain motion information content of the N states from the N state model The states do not correspond to physical states hence nothing can be extracted from the individual states This analysis involves the calculation of the pivot to centre of mass pivot CoM order parameter and subsequent cone of motions For the analysis both the pivot point and centre of mass must be specified The supplied pivot point must be a vector of floating point numbers of length 3 If the centre keyword argument is supplied it must also be a vector of floating point numbers of length 3 If the centre argument is not supplied then the CoM will be calulcated from the selected parts of a previously loaded structure Examples To perform an analysis where the pivot is at the origin and the CoM is set to the N terminal domain of a previously loaded PDB file the C terminal domain has been deselected type relax gt n_state_model CoM To perform an analysis where the pivot is at the origin because the real piv
127. a ee es e E 139 10 2 1 Thesynopsis 2021 ssai tao ee we a a aa 139 12 2 Deilie gt lt aw meom m Ru 3m pea da E E eee ae Eos 139 10 2 8 Docstring sectioning 26x29 T E km RR hok ee a 140 HESaL uen DeHBORODIU dee eeu be kg kt 9 Sm Roe ee ee SUUS A RR 141 10 2 5 align tensor delel amp 2 2022 142 10 96 als tensor displasia a ee cea UR RR eme 143 12 7 ASOC eo noce pe koe ds Boe quem Ron 144 10 2 8 align tensor matrixangles llle 146 10 29 alisndensoeBwd o uic a ke we km eo ROSE Nox mer RU A de 147 TES Danse cM rae oom msn Roe Kemp Y x XR Ros Rc DEC E Elm EORR ee 149 WO 2 LEGAS Leu acne sod en hr Roe ke x eO Saw X SE ae ee E e 150 10 2 12 consistency Leste Set Dp ullo lE x VOR EG on Rok RR 151 a 2 doux Rogo koe RR OR ee ee RE mos Pos Re 152 10 2 14 dashia execute o sc ooo oo m m m R9 AR 153 HYS IS5dasha sU H6 uuo Ecko a 3 X mox dox oe A 154 10 2 16 deseleet all cocinar Ge Ro ROSTER a WORD 155 10 2 17 deseleckgesd oos RR RR omm OR Pe ee RU ROBUR EO Sas 156 10 2 18 deselect teverSe 2 RO RR RR Rom mo Rm mo 158 10 2 18 deselect spi soo clo os om sow ro RR ee a ee a 159 10 2 20 diffusion tensor copy es 160 10 2 21 diffusion tensor delete 2o ee ms 161 10 2 22 diffusion tensor display 22r 162 10 2 23 diffusion tensor Mb zo RR o 9 ee 9 E RR B EE ER 163 IAM bes coi C wm 169 JR Eu cur M 170 10 2 26 eliminate 242 546 42 hok RR t eee CRI SAGA 175 WO ee C CCP 177 isse ID P I ee hae ee ee eo de ee ee 178
128. a pipe 10 2 THE LIST OF FUNCTIONS 10 2 6 align tensor display Synopsis Function for displaying the alignment tensor information Defaults align tensor display self tensor None Keyword Arguments tensor The alignment tensor identification string 143 144 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 7 align tensor init Synopsis Function for initialising the alignment tensor Defaults align tensor init self tensor None params None scale 1 0 angle units deg param_types 0 errors False Keyword Arguments tensor The alignment tensor identification string params The alignment tensor data scale The alignment tensor eigenvalue scaling value angle_units The units for the angle parameters param_types A flag to select different parameter combinations errors A flag which determines if the alignment tensor data or its errors are being input Description Using this function the alignment tensor data can be set up The params argument should be a tuple of floating point numbers a list surrounded by round brakets These correspond to the parameters of the tensor which can be specified by the param_types argument where the values correspond to 0 Sxx Syy Sxy Sxz Syz unitless 1 Szz Sxx yy Sxy Sxz Syz Pales default format 2 Axx Ayy Axy Axz Ayz unitless 3 Azz Axx yy Axy Axz Ayz unitless 4 Axx Ayy Axy Axz Ayz unit
129. ad file sat list spectrum_type sat Set the errors noe error error 3600 spectrum_type ref noe error error 3000 spectrum_type sat Individual residue errors noe error error 122000 spectrum_type ref res_num 114 noe error error 8500 spectrum_type sat res_num 114 Deselect unresolved residues deselect read file unresolved 19 20 CHAPTER 4 CALCULATING THE NOE Calculate the NOEs calc Save the NOEs value write param noe file noe out force True Create grace files grace write y_data_type ref file ref agr force True grace write y_data_type sat file sat agr force True grace write y_data_type noe file noe agr force True View the grace files grace view file ref agr grace view file sat agr grace view file noe agr Write the results results write file results dir None force True Save the program state state save save force True 4 3 Initialisation of the data pipe The data pipe is simply created by the command pipe create NOE noe This user function will then create a NOE calculation specific data pipe labelled NOE The second argument sets the pipe type to that of the NOE calculation Setting the pipe type is important so that the program knows which user functions are compatible with the data pipe for example the function minim
130. al Public License along with this program if not write to the Free Software Foundation Inc 59 Temple Place Suite 330 Boston MA 02111 1307 USA Also add information on how to contact you by electronic and paper mail If the program is interactive make it output a short notice like this when it starts in an interactive mode Gnomovision version 69 Copyright C year name of author Gnomovision comes with ABSOLUTELY NO WARRANTY for details type show w This is free software and you are welcome to redistribute it under certain conditions type show c for details The hypothetical commands show w and show c should show the appropriate parts of the General Public License Of course the commands you use may be called something other than show w and show c they could even be mouse clicks or menu items whatever suits your program You should also get your employer if you work as a programmer or your school if any to sign a copyright disclaimer for the program if necessary Here is a sample alter the names 2 Yoyodyne Inc hereby disclaims all copyright interest in the program Gnomovision which makes passes at compilers written by James Hacker lt signature of Ty Coon gt 1 April 1989 Ty Coon President of Vice This General Public License does not permit incorporating your program into proprietary programs If your program is a subroutine library you may consider it more usefu
131. all the data pipes is the same and that no spin system is allowed to be selected in two or more data pipes The selections must not overlap to allow for rigorous statistical comparisons 10 2 THE LIST OF FUNCTIONS 10 2 83 pipe list Synopsis Print a list of all the data pipes Defaults pipe list self Examples To run the user function type relax gt pipe list 269 270 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 84 pipe switch Synopsis Function for switching between data pipes Defaults pipe switch self pipe_name None Keyword Arguments pipe_name The name of the data pipe Description This function will switch from the current data pipe to the given data pipe Examples To switch to the ellipsoid data pipe type relax pipe switch ellipsoid relax pipe switch pipe_name ellipsoid 10 2 THE LIST OF FUNCTIONS 271 10 2 85 pymol cartoon Synopsis Apply the PyMOL cartoon style and colour by secondary structure Defaults pymol cartoon self Description This function applies the PyMOL cartoon style which is equivalent to hiding everything and clicking on show cartoon It also colours the cartoon with red helices yellow strands and green loops The following commands are executed cmd hide everything file cmd show cartoon file util cbss file red yellow green where file is the file name without the pdb e
132. ameter D and the order parameter S is k JW _ 2 Oc 1 7 Te Ti Te 8 75 00 082 B 00 Vl wn mtn wrens J l Dj Te partial derivative The second partial derivative of 8 64 with respect to the orientational parameter D and the correlation time Te is Sw a gh OG o Te T wreri 0D OTe OTe 5 E 00 te Ti wrer 2 8 76 S S partial derivative The second partial derivative of 8 64 with respect to the order parameter S twice is 9 J w Bs t 8 77 78 CHAPTER 8 VALUES GRADIENTS AND HESSIANS S Te partial derivative The second partial derivative of 8 64 with respect to the order parameter S and corre lation time Te is 8 J PE Te i wreri a ar 8 78 OS OTe 5 te Ti wrer 2 8 78 Te Te partial derivative The second partial derivative of 8 64 with respect to the correlation time Te twice is k PT w ia _ gh Y di Te Ti 3 73 Te i wr 8 79 r 5 re Ti wre 8 9 MODEL FREE ANALYSIS 79 8 9 4 The extended model free gradient The model free gradient of the extended spectral density function 8 65 is the vector of partial derivatives of the function with respect to the geometric parameter 6 the orientational parameter O the order parameters S and S and the internal correlation times Tf and Ts The positions in the vector correspond to the model parameters which are b
133. amless and extremely flexible environment able to accept input in any format produced by other NMR software able to faultlessly create input files control and read output from various programs including Modelfree and Dasha output results in many formats and visualise the data by controlling programs such as Grace OpenDX MOLMOL and PyMOL All data analysis tools from optimisation to model selection to Monte Carlo simulations are inbuilt into relax Therefore the use of additional programs is optional The flexibility of relax arises from the choice of either relax s scripting capabilities or its Python prompt interface Extremely complex scripts can be created from simple building blocks to fully automate data analysis A number of sample scripts have been provided to help understand script construction In addition any of Python s powerful features or functions can be incorporated as the script is executed as an arbitrary Python source file within relax s environment The modules of relax can also used as a vast library of dynamics related functions by your own software relax is free software free as in freedom which is licenced under the GNU General Public Licence GPL You are free to copy modify or redistribute relax under the terms of the GPL 1 1 Program features 1 1 1 Literature The primary references for the program relax are d Auvergne and Gooley 2008a and d Auvergne and Gooley 2008b 2 CHAPTER 1 INTRODUCTIO
134. anch all changes which have occurred in the main line have been merged using svnmerge py and the changes have been approved for merging back into the main line then your branch can be merged First check out a copy of the main line svn co svntssh xxxxx svn gna org svn relax 1 3 relax 1 3 or update a previously checked out version svn up Then svnmerge py can be utilised again First initialise the merging process by typing from within the checked out copy of the main line svnmerge py init svntssh xxxxx svn gna org svn relax branches molmol_macros Then commit the change svn ci F svnmerge commit message txt To merge the branch and commit the changes type svnmerge py merge bidirectional svn ci F svnmerge commit message txt Finally the merge properties need to be removed svnmerge py uninit S svn tssh xxxxx0svn gna org svn relax branches molmol macros the changes commited svn ci F svnmerge commit message txt 130 CHAPTER 9 RELAX DEVELOPMENT and your private branch deleted svn rm svn ssh xxxxxOsvn gna org svn relax branches molmol macros 9 5 The SCons build system The SCons build system was chosen over other build systems including make as it is a cross platform build system which can be used in Unix GNU Linux Mac OS X and even MS Windows the correct compilers are nevertheless required Various components of the program relax can be created using the SCons utility Th
135. arameter S2 is Ou So 1 Ts Ti Ts m o AECE NA 110 08 5 2 ny Get ny wren os 8 9 MODEL FREE ANALYSIS 87 Tf partial derivative The partial derivative of 8 65 with respect to the correlation time Ty is 910 2 0 Lua ro m wry a pe a 8 111 Ts partial derivative The partial derivative of 8 65 with respect to the correlation time 7 is 9J w B 2 Ts F ar WTsTi 2 6 1 8 CiT Ons f rs 71 war 8 112 88 CHAPTER 8 VALUES GRADIENTS AND HESSIANS 8 9 7 The alternative extended model free Hessian The model free Hessian of the extended spectral density function 8 65 is also complicated by the convolution resulting from the use of the parameters S7 S2 Tf Ts The second partial derivatives with respect to these parameters are presented below 6 6 partial derivative The second partial derivative of 8 65 with respect to the geometric parameters 6 and 6 is 8 J uw a OT OT 2 a 9 3 wt 55 08 5 2 7556 96 pyre al 233 un sy T 3w 27 TF 75 wrp 7 3 rg Ti rpm Ts Ti 3o Tr 7 Ti wTs 47 2 ts 7 w57 2 27 _ 2 Se ES dc ed se enr 1 937 S7 1 cus us 06 064 V 7 14 wr 1 rt nY rr j rg Ti wrpri 2 Te Ti wrsTi rs Ti wrs7 2 e 3 82 82 1 5 lr n 821 521 2 0G OG 1 wn TEHTE wre Ts 4 WET 8
136. at the bug has not already been submitted to the bug tracker You can search the bugs from the page https gna org project search php group relax Once the bug has been confirmed by one of the relax developers you may speed up the resolution of the problem by trying to fixing the bug yourself If you do wish to play with the source code and try to fix the issue see the relax development chapter of this manual on how to check out the latest sources how to generate a patch which is just the output of diff in the unified format and the guidelines for the format of the code 3 4 Latest sources the relax repositories relax s source code is kept within a version control system called Subversion http subversion tigris org Subversion or SVN allows fine control over the develop ment of the program The repository contains all information about every change ever made to the program To learn more about the system the Subversion book located at http svnbook red bean com is a good place to start The contents of the relax repos itory can be viewed on line at http svn gna org viewcvs relax The current sources assuming that the most recent minor version number is 1 2 can be downloaded using the SVN protocol by typing svn co svn svn gna org svn relax 1 2 relax however if this does not work try the command svn co http svn gna org svn relax 1 2 relax to download using the HTTP protocol The entire relax repository
137. ate c ranging from 0 for the first to N 1 for the last the number c should be added to the end of the parameter name So the Euler angle y of the third state is specified using the string gamma2 N state model data type string matching patterns Data type Object name Patterns Probabilities probs pO PL p2 PN Euler angle a alpha alpha0 alphat Euler angle 8 beta beta0 betal Euler angle y gamma gamma0 gamma1 Bond length T r or Bb ond _ L1 ength ti Heteronucleus type heteronuc_type Hh eteronucleus Proton type proton_type Pp roton 354 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS The objects corresponding to the object names are lists or arrays with each element corrsponding to each state 10 2 THE LIST OF FUNCTIONS 355 10 2 144 value display Synopsis Function for displaying residue specific data values Defaults value display self runc None param None Keyword Arguments run The name of the run param The parameter to display Description Only one parameter may be selected therefore the param argument should be a string Examples To show all CSA values for the run m1 type relax value display m1 CSA Regular expression The python function match which uses regular expression is used to determine wh
138. ating the computationally expensive Hessian The Hessian approximation Bj is updated using various formulae the most common being the BFGS formula Broyden 1970 Fletcher 1970 Goldfarb 1970 Shanno 1970 The search direction is given by the equation p B lv fi The quasi Newton algorithms can attain a superlinear rate of convergence being superior to the steepest descent or coordinate descent methods 6 1 THEORY 39 The most powerful line search method when close to the minimum is the Newton search direction py V fg V fr 6 29 This direction is obtained from the derivative of 6 27 which is assumed to be zero at the minimum of the quadratic model The vector pz points from the current position to the exact minimum of the quadratic model of the space The rate of convergence is quadratic being superior to both linear and superlinear convergence The technique is computationally expensive due to the calculation of the Hessian It is also susceptible to failure when optimisation commences from distant positions in the space as the Hessian may not be positive definite and hence not convex a condition required for the search direction both to point downhill and to be reasonably oriented In these cases the quadratic model is a poor description of the space A practical Newton algorithm which is robust for distant starting points is the Newton conjugate gradient method Newton CG This line search method which is also called the
139. ation data type ie R1 R2 or NOE frq_label The field strength label Examples To display the NOE relaxation data at 600 MHz type relax gt relax data display NOE 600 10 2 THE LIST OF FUNCTIONS 295 10 2 104 relax_data read Synopsis Function for reading R4 R4 or NOE relaxation data from a file Defaults relax_data read self ri_label None frq_label None frq None file None dir None mol_name_col None res_num_col 0 res_name_col 1 spin_num_col None spin_name_col None data_col 2 error_col 3 sep None Keyword Arguments ri_label The relaxation data type ie R1 R2 or NOE frq_label The field strength label frq The spectrometer frequency in Hz file The name of the file containing the relaxation data dir The directory where the file is located mol_name_col The molecule name column this defaults to no column res num col The residue number column the default is 0 i e the first column res_name_col The residue name column the default is 1 i e the second column spin_num_col The spin number column this defaults to no column spin name col The spin name column this defaults to no column data_col The relaxation data column the default is 2 error_col The experimental error column the default is 3 sep The column separator the default is white space Description The frequency label argument can be anything as long as data co
140. ation theory The model free space The optimisation of the parameters of an arbitrary model is dependent on a function f which takes the current parameter values 0 R and returns a single real value f 0 R corresponding to position 0 in the n dimensional space For it is that single value which is minimised as arg min f 0 6 24 where 6 is the parameter vector which is equal to the argument which minimises the function f 0 In model free analysis f 0 is the chi squared equation TL x 0 y Ri ER RO 6 25 where 7 is the summation index R is the experimental relaxation data which belongs to the data set R and includes the R1 Ra and NOE values at all field strengths R 0 is the back calculated relaxation data belonging to the set R 0 and c is the experimental error For the optimisation of the model free parameters while the diffusion tensor is held fixed the summation index ranges over the relaxation data of an individual residue If the diffusion parameters are optimised simultaneously with the model free parameters the summation index ranges over all relaxation data of all selected residues of the macromolecule Given the current parameter values the model free function provided to the algorithm will calculate the value of the model free spectral density function J w at the five frequencies which induce NMR relaxation by using Equations 6 7 and 6 8 The theoretical R1 Ra and NOE values are then back
141. atom jobject uuuuuuuuuuuubonded res lattached_atom 9 2 5 Comments Comments are a very important component within relax In the current source code the percentage of comment lines relative to lines of code ranges from 15 to over 30 for different files The average comment density would be close to 25 The purpose of having so many comment lines much more than you would expect from source code is so that the relax s code is fully self documented It allows someone who is not familiar with the codebase to read the code and quickly understand what is happening It simplifies the process of learning and allows NMR spectroscopists who are not coders to dive into the code If writing code for relax please attempt to maintain the tradition by aiming towards a 25 comment ratio The comment should be descriptive of what the code below it is supposed to do Most importantly the comment explains why that code exists The script http nmr relax com scripts code_validator can be used to check the comment density 9 3 Submitting changes to the relax project 9 3 1 Submitting changes as a patch The preferred method for submitting fixes and improvements to the relax source code is by the creation of a patch If your changes are a fix make sure you have submitted a bug report to the bug tracker located at https gna org bugs group relax first See section 3 3 on page 16 for more details Two methods can be used to generate the patch 9 4 COM
142. aults dx map self params None map type lso3D spin_id None inc 20 lower None upper None axis_incs 5 file prefix map dir dx point None point_file point remap None Keyword Arguments params The parameters to be mapped This argument should be an array of strings the meanings of which are described below map type The type of map to create For example the default a 3D isosurface the type is Iso3D See below for more details spin_id The spin identification numbe inc The number of increments to map in each dimension This value controls the resolu tion of the map lower The lower bounds of the space If you wish to change the lower bounds of the map then supply an array of length equal to the number of parameters in the model A lower bound for each parameter must be supplied If nothing is supplied then the defaults will be used upper The upper bounds of the space If you wish to change the upper bounds of the map then supply an array of length equal to the number of parameters in the model A upper bound for each parameter must be supplied If nothing is supplied then the defaults will be used axis_incs The number of increments or ticks displaying parameter values along the axes of the OpenDX plot file_prefix The file name All the output files are prefixed with this name The main file containing the data points will be called the value of file The OpenDX program will be called
143. ax 2 Either minimisation is used to optimise the parameters of the chosen model or a calculation is run 10 2 THE LIST OF FUNCTIONS 229 3 To initialise and turn on Monte Carlo simulations the number of simulations n needs to be set 4 The simulation data needs to be created either by back calculation from the fully minimised model parameters from step 2 or by direct calculation when values are calcu lated rather than minimised The error set is used to randomise each simulation data set by assuming Gaussian errors This creates a synthetic data set for each Monte Carlo simulation 5 Prior to minimisation of the parameters of each simulation initial parameter estimates are required These are taken as the optimised model parameters An alternative is to use a grid search for each simulation to generate initial estimates however this is extremely computationally expensive For the case where values are calculated rather than minimised this step should be skipped although the results will be unaffected if this is accidentally run 6 Each simulation requires minimisation or calculation The same techniques as used in step 2 excluding the grid search when minimising should be used for the simulations 7 Failed simulations are removed using the techniques of model elimination 8 The model parameter errors are calculated from the distribution of simulation param eters Monte Carlo simulations can be turned on or off using
144. ay first be reported on the relax users mailing list then placed within the bug tracker discussed on relax devel a fix committed to the repository and finally the bug report closed To be able to follow this chain links are very important email message ids are also important When the bug is first added to the bug tracker a link to the relax users mailing list archive message and the message id should be included If you start a discussion on relax devel try to include links to the bug tracker entry and the relax users message When committing a fix to the repository include links to the bug 9 9 LINKS LINKS AND MORE LINKS 137 report to the start of the thread in the mailing list archive and the original message to relax users Then when the bug report is closed include the revision number of the fix and a link to the relax commits archive message and message id By having all these links it is then very easy for someone else to jump between the systems and follow the progression of the bug fix If you send a message referring to an old post which was sent the relax mailing lists an old bug report or any other archived information please take the time to find that original information in the archives and include a link to it including the message id if relevant It is much more efficient for a single person to hunt down that message than for the many recipients of your post to search for the message themselves By including the li
145. be sent to the relax mailing list please resend the message hitting reply to all or making sure that the mailing list is in the CC field Please do not forward your message for thread consistency in the mailing list archives sending a new message in response to the original post with the text of the old is best 9 8 The bug task and support request trackers relax s infrastructure includes three different issue trackers These are the bug tracker the task tracker and the support request tracker 9 8 1 Submitting a bug report If someone reports a bug to one of the relax mailing lists ask that person if they would like to create a bug report for that problem pointing them to the submission web page This is a good starting point to allow the person to become more involved in the relax project 136 CHAPTER 9 RELAX DEVELOPMENT If they do not respond or say that they would prefer not to then you can create bug report for the issue linking to the original message and crediting the person for reporting the issue 9 8 2 Assigning an issue to yourself If you are a relax committer and see an issue which you would like to solve please assign that issue to yourself before you start work on it The assignment will prevent duplicated efforts If you can see an area where relax needs work feel free to create a report within task tracker and then assign the task to yourself 9 8 3 Closing an issue When closing an issue whether a
146. bo generalised order parameter and Te is the effective correlation time The order parameter reflects the amplitude of the motion and the correlation time in an indication of the time scale of that motion The theory was extended by Clore et al 1990 by the modelling of two independent internal motions using the equation 9 Jw z5 cmn 9 1 S NTE Ti TF i k 1 wr 9 rp 74 wrer SF S Ts Ti Ts 4 eS Ps where S and r are the amplitude and timescale of the faster of the two motions whereas f f S and 7 are those of the slower motion S and S2 are related by the formula S 5585 6 1 5 Brownian rotational diffusion In equations 6 7 and 6 8 the generic Brownian diffusion NMR correlation function presented in d Auvergne 2006 has been used This function is k 1 T T C r 5 2 eeu 6 9 where the summation index 7 ranges over the number of exponential terms within the correlation function This equation is generic in that it can describe the diffusion of an ellipsoid a spheroid or a sphere Diffusion as an ellipsoid For the ellipsoid defined by the parameter set Diso Da Dr a B y the variable k is equal to two and therefore the index i 2 1 0 1 2 The geometric parameters Diso Da Dr are defined as Diso Dz Dy Dz 6 10a Da D 45 De Dy 6 10b D Dz T E E a D 25 6 10c and are constrained by dad OU 6 11a Diso NED E 6 11b 3 9
147. bug report a task or a support request a number of steps need to be taken The tracker status should be changed to Done and the issue Closed In addition a message should be included which states the repository revision and the relax commits mailing list archive link with the message id in which the issue was solved If multiple commits were required then include all the revisions and as many links as possible if a task required many commits the relax commits links could be skipped An example is bug 7402 where the closing comment was This documentation bug was fixed in r2641 The commit message is located at https mail gna org public relax commits 2006 10 msg00073 html Message id lt E1GYG41 0002kK Jx subversion gna org gt 9 9 Links links and more links Creating links throughout the relax infrastructure is important for two major reasons navigation and search engine indexing When including a link to a post within the mailing list archives please include the message id email header This enables subscribers to the mailing lists to search for the specific message within their local copy of the email messages 9 9 1 Navigation To be able to easily navigate between the relax infrastructure components the bug tracker the task tracker the support request tracker the relax devel mailing list the commit logs and the SVN and CVS repositories try to include as many links as possible For example a bug m
148. byte compiled Python pyc files to speed up the start time of relax by typing relax test Alternatively if the Sconstruct system is installed typing scons install in the relax base directory will create a directory in usr local called relax copy all the uncompressed and untarred files into this directory create a symbolic link in usr local bin to the file usr local relax relax and then finally run relax to cre ate the byte compiled Python pyc To change the installation path to a non standard location the Sconstruct script sconstruct in the base relax directory should be modified by changing the variable INSTALL_PATH to point to the desired location 2 2 3 Installation on MS Windows In addition to the above dependencies running relax on MS Windows requires a number of additional programs These include pyreadline Version 1 3 or higher download ctypes The pyreadline package requires ctypes download To install simply download the pre compiled binary distribution relax x x x Win32 zip or the source distribution relax x x x src zip and extract the files to C Program Files relax x x x Then add this directory to the system environment path in Win dows XP right click on My Computer go to Properties click on the Advanced tab and click on the Envirnment Variables button Then double click on the Path system vari able and add the text C Program Files relax x x x to the end o
149. cal diffusion if cdp diff_tensor type sphere param_vector append cdp diff_tensor tm Classes For classes relax uses a mix of camel case for example all the RelaxError objects and underscores for example Model_free The first letter in all cases is always capitalised Generally the camel case is reserved for very low level classes which are involved in the program s infrastructure Examples include the RelaxError code the threading code and the self relax data code All the data analysis specific code generic code interface code etc uses underscores between the words with only the first letter capitalised One exception is the space mapping class OpenDX the reason being that the program is called OpenDX An example is class Model free main Class containing functions specific to model free analysis 9 2 CODING CONVENTIONS 123 def are_mf_params_set self spin Test if the model free parameter values are set Cparam spin The spin container object type spin SpinContainer instance return The name of the first parameter in the parameter list in which the corresponding parameter value is None If all parameters are set then None is returned Ortype str or None nium Deselected residue if spin select return Long names If you have a look at a few relax source files you will notice that the variable function and class names can be quite long For example the model free func
150. cal diffusion tensors and the combination of the diffusion tensor and the model free models 8 2 Minimisation concepts 8 2 1 The function value At the simplest level all minimisation techniques require at least a function which will supply a single value for different parameter values 0 For the modelling of NMR relaxation data this function is the chi squared equation 6 1 on page 31 For certain algorithms such a simplex minimisation this single value suffices 8 2 2 The gradient The majority of minimisation algorithms also require the gradient at the point in the space represented by the parameter values 0 The gradient is a vector of partial derivatives and 57 58 CHAPTER 8 VALUES GRADIENTS AND HESSIANS is defined as Yelo N 8 1 2 065 where n is the total number of parameters in the model An example of a powerful algorithm which requires both the value and gradient at current parameter values is the BFGS quasi Newton minimisation The gradient is also essen tial for the use of the Method of Multipliers constraints algorithm also known as the Augmented Lagrangian algorithm 8 2 3 The Hessian A few optimisation algorithms which are among the most reliable for model free analysis additionally require the Hessian at current parameter values 0 The Hessian is the matrix of second partial derivatives and is defined as 9 0 9 00 2 001 005 Ut 904 004 a a 9 005 00 2 005 005 v z 1 s sd
151. cal_tm s2 s2f heteronuc_type proton_type Patterns L1 ocal _ tm Ss 2 Ss 2 Ss 2s roy ey ces Rr ex or Cc emical Eelxchange r or Bblond _ LlJength Cc Ss Aa Hh eteronucleus Pp roton 10 2 THE LIST OF FUNCTIONS 185 10 2 31 grid_search Synopsis The grid search function Defaults grid_search self lower None upper None inc 21 constraints True verbosity 1 Keyword Arguments lower An array of the lower bound parameter values for the grid search The length of the array should be equal to the number of parameters in the model upper An array of the upper bound parameter values for the grid search The length of the array should be equal to the number of parameters in the model inc The number of increments to search over If a single integer is given then the number of increments will be equal in all dimensions Different numbers of increments in each direction can be set if inc is set to an array of integers of length equal to the number of parameters constraints A boolean flag specifying whether the parameters should be constrained The default is to turn constraints on constraints True verbosity The amount of information to print to screen Zero corresponds to minimal output while higher values increase the amount of output The default value is 1 186 CHAP
152. calculation The same techniques as used in step 2 excluding the grid search when minimising should be used for the simulations 7 Failed simulations are removed using the techniques of model elimination 8 The model parameter errors are calculated from the distribution of simulation param eters Monte Carlo simulations can be turned on or off using functions within this class Once the function for setting up simulations has been called simulations will be turned on The effect of having simulations turned on is that the functions used for minimisation grid search minimise etc or calculation will only affect the simulation parameters and not the model parameters By subsequently turning simulations off using the appropriate function the functions used in minimisation will affect the model parameters and not the simulation parameters An example for model free analysis which includes only the functions required for imple menting the above steps is relax gt grid_search inc 11 Step 2 relax gt minimise newton Step 2 relax gt monte_carlo setup number 500 Step 3 relax gt monte_carlo create_data method back_calc Step 4 relax gt monte_carlo initial_values Step 5 relax gt minimise newton Step 6 relax gt eliminate Step 7 relax gt monte_carlo error_analysis Step 8 An example for reduced spectral density mapping is relax gt calc Step 2 relax gt monte_carlo setu
153. can be used to select spins For example the string H will select the protons H H2 H98 10 2 THE LIST OF FUNCTIONS 10 2 116 results display Synopsis Function for displaying the results Defaults results display self format xml Keyword Arguments format The format of the output 313 314 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 117 results read Synopsis Function for reading results from a file Defaults results read self file results dir None Keyword Arguments file The name of the file to read results from dir The directory where the file is located Description To search for the results file in the current working directory set dir to None This function is able to handle uncompressed bzip2 compressed files or gzip compressed files automatically The full file name including extension can be supplied however if the file cannot be found this function will search for the file name with bz2 appended followed by the file name with gz appended 10 2 THE LIST OF FUNCTIONS 315 10 2 118 results write Synopsis Function for writing results to a file Defaults results write self file results dir pipe_name force False format xml com press_type 1 Keyword Arguments file The name of the file to output results to The default is results Optionally this can be a file object or any object with a wri
154. cantly improved Errors across multiple time points If all spectra are collected in duplicate triplicate or higher number of spectra are sup ported the each time point will have its own error estimate However if there are time points in the series which only consist of a single spectrum then the standard deviations of replicated time points will be averaged Hence for the entire experiment there will be a single error value for all residues and for all time points A better approach rather than averaging across all time points would be to use a form of interpolation as the errors across time points generally decreases for longer time periods This is currently not implemented 10 2 THE LIST OF FUNCTIONS 299 10 2 107 relax_fit read Synopsis Function for reading peak intensities from a file Defaults relax_fit read self file None dir None relax_time 0 0 format sparky heteronuc N proton HN int_col None Keyword Arguments file The name of the file containing the sequence data dir The directory where the file is located relax_time The time in seconds of the relaxation period format The type of file containing peak intensities heteronuc The name of the heteronucleus as specified in the peak intensity file proton The name of the proton as specified in the peak intensity file int_col The column containing the peak intensity data for a non standard formatted file Description The peak in
155. ce False Keyword Arguments ri_label The relaxation data type ie R1 R2 or NOE frq_label The field strength label file The name of the file dir The directory name force A flag which if True will cause the file to be overwritten Description If no directory name is given the file will be placed in the current working directory The ri_label and frq label arguments are required for selecting which relaxation data to write to file 298 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 106 relax_fit mean_and_error Synopsis Function for calculating the average intensity and standard deviation of all spectra Defaults relax_fit mean_and_error self Errors of individual residues at a single time point The standard deviation for a single residue at a single time point is calculated by the formula sd V sum Ii Iav 2 n 1 where n is the total number of collected spectra for the time point and i is the corresponding index li is the peak intensity for spectrum i lav is the mean over all spectra ie the sum of all peak intensities divided by n Averaging of the errors As the value of n in the above equation is always very low normally only a couple of spectra are collected per time point the standard deviation of all residues is averaged for a single time point Although this results in all residues having the same error the accuracy of the error estimate is signifi
156. ce from the data pipe m1 to the current data pipe type relax sequence copy m1 relax sequence copy pipe from mi To copy the sequence from the current data pipe to the data pipe m9 type relax sequence copy pipe to m9 To copy the sequence from the data pipe m1 to m2 type relax sequence copy mi m2 relax sequence copy pipe from mi pipe to m2 322 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 124 sequence display Synopsis Function for displaying sequences of molecules residues and or spins Defaults sequence display self sep None mol_name_flag True res num flag True res name flag True spin num flag True spin name flag True Keyword Arguments sep The column separator the default of None corresponds to white space mol name flag A flag whic if True will cause the molecule name column to be shown res num flag A flag whic if True will cause the residue number column to be shown res name flag A flag whic if True will cause the residue name column to be shown spin num flag A flag whic if True will cause the spin number column to be shown spin name flag A flag whic if True will cause the spin name column to be shown 10 2 THE LIST OF FUNCTIONS 323 10 2 125 sequence read Synopsis Function for reading sequences of molecules residues and spins Defaults sequence read self file None dir None mol_name_col None
157. ch model free model is chosen for example if S values and S values are set but the run corresponds to model free model m4 then because these data values are not parameters of the model they will have no effect Note that the Rex values are scaled quadratically with field strength and should be supplied as a field strength independent value Use the following formula to get the correct value value Rex 2 0 m frequency 2 where Rex is the chemical exchange value for the current frequency 7 is in the namespace of relax ie just type pi frequency is the proton frequency corresponding to the data Model free data type string matching patterns 352 Data type Local Tin Order parameter S Order parameter S Order parameter S Correlation time Te Correlation time Ty Correlation time Ts Chemical exchange Bond length CSA Heteronucleus type Proton type Object name local_tm s2 s2f heteronuc_type proton_type CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Patterns L1 ocal _ tm gt Ss 2 Ss 2 Ss 2s roy ey ces Rr ex or Cc emical Eelxchange r or Bblond _ LlJength Cc Ss Aa Hh eteronucleus Pp roton Reduced spectral density mapping set details In reduced spectral density mapping three values must be set prior to the calculation of
158. cifying that pipe through the pipe argument Examples If the paramagnetic centre is the lanthanide Dysprosium which is labelled as D in a loaded PDB file then type one of relax pcs centre Dy relax pcs centre atom id Dy If the carbon atom C1 of residue 4 in the PDB file is to be used as the paramagnetic centre then type relax pcs centre 40C1 10 2 THE LIST OF FUNCTIONS 259 10 2 73 pcs copy Synopsis Copy PCS data from pipe_from to pipe_to Defaults pcs copy self pipe_from None pipe to None id None Keyword Arguments pipe_from The name of the pipe to copy the PCS data from pipe_to The name of the pipe to copy the PCS data to id The alignment identification string Description This function will copy PCS data from pipe_from to pipe_to If id is not given then all PCS data will be copied otherwise only a specific data set will be Examples To copy all PCS data from pipe m1 to pipe m9 type one of relax gt pcs copy m1 m9 relax pcs copy pipe from mi pipe to m9 relax pcs copy m1 m9 None relax pcs copy pipe from mi pipe_to m9 id None To copy only the Th PCS data from m3 to m6 type one of relax pcs copy m3 m6 Th relax pcs copy pipe from m3 pipe to m6 id Th 260 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 74 pcs delete Synop
159. correlation function is Eo N tau tau i gt ci e l i 2 C tau ale where the weights on the exponentials are c 2 1 4 d e c123 256 2 c0 3 6 2 6 2 cl 3 6 2 6 2 c2 1 4 d e Let A sqrt 1 3D then d 3 67 4 6 4 9 4 1 e 1 5A 1 39 6 4 2672 672 1 39 8 4 26 72 6 72 2 6 4 26 72 6 2 The correlation times are 1 7 2 6Diso 29 R 10 2 THE LIST OF FUNCTIONS 167 pTl e69055 5 0 39 1 T0 6Diso Da 1 39D 1 T 1 6Diso 2Da 1 T1 6Diso 2D R The three direction cosines 6 y and 0 are the coordinates of a unit vector parallel to the XH bond vector Hence the unit vector is dz dy 2 To select fully anisotropic diffusion the parameters argument should be a tuple of length six A tuple is a type of data structure enclosed in round brackets the elements of which are separated by commas Alternative sets of parameters param_types are 0 m itm Da De Q p y Default 1 iso Da Dr Q B y 2 125 Dy Dz Q p yh where Tm 1 6Diso Diso 1 3 Dz Dy Dz Da D Da Dy 2 Dr Dy DD The angles o 8 and y are the Euler angles describing the diffusion tensor within the PDB frame These angles are defined using the z y z axis rotation notation where a is the initial rotation angle around the z axis is the rotation angle around the y axis and y i
160. cos B a sina cos y cos a cos p sin y DN 5 sinasiny cos a cos Bcosy 8 198c y 0 8 13 ELLIPSOIDAL DOT PRODUCT DERIVATIVES 113 The Dy gradient The partial derivatives of the unit vector Di with respect to the Euler angles are aD sina sin y cos a cos D cos y We sina cos y cosa cos B sin y 8 1992 cos asin 3 89 sin q sin P cos y 2 sinasin siny 8 199b OB sin a cos 3 9 COS a COS y sina cos f sin y cosa sin y sin q cos B cos y 8 199c Oy 0 The 9 gradient The partial derivatives of the unit vector D with respect to the Euler angles are cc 0 gt Ses DL 8 200a n 0 zs cos D cos y o cosfsiny 8 200b B sin B a sin B sin y a sinfcosy 8 200c 0 114 CHAPTER 8 VALUES GRADIENTS AND HESSIANS 8 13 3 The dot product Hessian of the ellipsoid The second partial derivative of the dot product 6 with respect to the orientational pa rameters D and Oy is 9 8 da XH 9 yg 2a 8 201 00 00 09 dD DOK The D Hessian The second partial derivatives of the unit vector D with respect to the Euler angles are LT sin q sin y cos a cos f cos y Au sinacos y cosacos sin y 8 202a de cos a sin fg PO sina sin 3 cos y sinasin Bsiny 8 202b da OG sina cos B pes cos a COS y sin a cos p sin y OD cosasiny si
161. ct minimum along the search direction and guarantees sufficient decrease Trust region methods In the trust region class of algorithms the curvature of the space is modelled quadratically by 6 27 This model is assumed to be reliable only within a region of trust defined by the inequality p Az where p is the step taken by the algorithm and Az is the radius of the n dimensional sphere of trust Nocedal and Wright 1999 The solution sought for each iteration of the algorithm is puc milo fk p Vf amp ip Bp st pl lt Az 6 30 where mz p is the quadratic model B is a positive definite matrix which can be the true Hessian as in the Newton model or an approximation such as the BFGS matrix and p 40 CHAPTER 6 MODEL FREE ANALYSIS is the Euclidean norm of p The trust region radius Az is modified dynamically during optimisation if the quadratic model is found to be a poor representation of the space the radius is decreased whereas if the quadratic model is found to be reasonable the radius is increased to allow larger more efficient steps to be taken The Cauchy point algorithm is similar in concept to the steepest descent line search algo rithm The Cauchy point is the point lying on the gradient which minimises the quadratic model subject to the step being within the trust region By iteratively finding the Cauchy point the local minimum can be found The convergence of the technique is inefficient being s
162. cted by specifying the structural index struct_index where 0 corresponds to the first structure model Secondly the bond vectors from all structures models can be extracted if struct index is None and ave is set to False Thirdly if struct_index is None and ave is set to True then a single vector which is the average of all structures models will be calculated 346 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Example To extract the XH vectors of the backbone amide nitrogens where in the PDB file the backbone nitrogen is called N and the attached proton is called H assuming multiple types of spin have already been loaded type one of relax structure vectors spin id QN relax structure vectors H spin_id N relax structure vectors proton H spin_id N If the attached proton is called HN type relax structure vectors proton HN spin id QN For the CA spin bonded to the HA proton type relax gt structure vectors proton HA spin_id CA If you are working with RNA you can use the residue name identifier to calculate the vectors for each residue separately For example to calculate the vectors for all possible spins in the bases type relax structure vectors H2 spin_id A relax gt structure vectors H8 spin_id A relax gt structure vectors H1 spin_id G relax gt structure vecto
163. ction and all other features of relax will be fully functional without compilation If relaxation curve fitting is required but no precompiled version of relax exists for your operating system or architecture then if a C compiler is present the C code can be compiled into the shared objects files so which are loaded as modules into relax To build these modules the Sconstruct system from http scons org is required This software only depends on Python which is essential for running relax anyway Once Sconstruct is installed type scons 11 12 CHAPTER 2 INSTALLATION INSTRUCTIONS in the base directory where relax has been installed and the C modules should hopefully compile without any problems Otherwise please submit a bug report to the bug tracker at https gna org bugs group relax 2 2 2 Installation on GNU Linux To install the program relax on a GNU Linux system download either the precompiled distribution labelled relax x x x GNU Linux arch tar bz2 matching your machine ar chitecture or the source distribution relax x x x src tar bz2 A number of installation methods are possible The simplest way is to switch to the user root unpack and de compress the archive within the usr local directory by typing for instance tar jxvf relax x x x GNU Linux i686 tar bz2 then create a symbolic link in usr local bin by moving to that directory and typing ln s relax relax and finally running relax to create the
164. ctors defining the coordinate system of the space Four simple rules are used to move the simplex through the space 42 CHAPTER 6 MODEL FREE ANALYSIS reflection extension contraction and a shrinkage of the entire simplex The result of these movements is that the simplex moves in an ameoboid like fashion downhill shrinking to pass through tight gaps and expanding to quickly move through non convoluted space eventually finding the minimum Key to these four movements is the pivot point the centre of the face created by the n vertices with the lowest function values The first movement is a reflection the vertex with the greatest function value is reflected through the pivot point on the opposite face of the simplex If the function value at this new position is less than all others the simplex is allowed to extend the point is moved along the line to twice the distance between the current position and the pivot point Otherwise if the function value is greater than the second highest value but less than the highest value the reflected simplex is contracted The reflected point is moved to be closer to the simplex its position being half way between the reflected position and the pivot point Otherwise if the function value at the reflected point is greater than all other vertices then the original simplex is contracted the highest vertex is moved to a position half way between the current position and the pivot point Finally if no
165. ctrum with proton saturation turned on If the res_num and res_name arguments are left as the defaults of None then the error value for all residues will be set to the supplied value Otherwise the residue number can be set to either an integer for selecting a single residue or a python regular expression string for selecting multiple residues The residue name argument must be a string and can use regular expression as well 10 2 THE LIST OF FUNCTIONS 251 10 2 67 noe read Synopsis Function for reading peak intensities from a file for NOE calculations Defaults noe read self file None dir None spectrum_type None format sparky heteronuc N proton HN int_col None Keyword Arguments file The name of the file containing the sequence data dir The directory where the file is located spectrum_type The type of spectrum format The type of file containing peak intensities heteronuc The name of the heteronucleus as specified in the peak intensity file proton The name of the proton as specified in the peak intensity file int_col The column containing the peak intensity data for a non standard formatted file Description The peak intensity can either be from peak heights or peak volumes The spectrum_type argument can have the following values ref The NOE reference spectrum sat The NOE spectrum with proton saturation turned on The format argument can c
166. culation data type string matching patterns Data type Object name Patterns Reference intensity ref Rr ef or Rr ef _ Ii nt 6 Saturated intensity sat Sslat or Sslat _ Ii nt NOE noe Nn 00 Ee 10 2 THE LIST OF FUNCTIONS 183 Relaxation curve fitting data type string matching patterns Data type Object name Patterns Relaxation rate rx Rr x Average peak intensities series ave intensities Aa ve _ Ii nt Initial intensity 10 Ii 0 Intensity at infinity iinf Iilinf Relaxation period times series relax times Rr elax Tt imes Reduced spectral density mapping data type string matching patterns Data type Object name Patterns J 0 jo alos ar E4313 CO J wx jux J31w Xx1 or E31 VQ Xx D J wg jwh Jj w Hh or Jj Cv Hh V Bond length T r or Bb ond _ L1 ength CSA csa Cc Ss Aa Heteronucleus type heteronuc_type Hh eteronucleus Proton type proton_type Pp roton Model free data type string matching patterns 184 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Data type Local Tin Order parameter S Order parameter S Order parameter S Correlation time Te Correlation time Ty Correlation time Ts Chemical exchange Bond length CSA Heteronucleus type Proton type Object name lo
167. d Auvergne E J and Gooley P R 2006 Model free model elimination A new step in the model free dynamic analysis of NMR relaxation data J Biomol NMR 35 2 117 135 d Auvergne E J and Gooley P R 2007 Set theory formulation of the model free problem and the diffusion seeded model free paradigm 3 7 483 494 d Auvergne E J and Gooley P R 2008a Optimisation of NMR dynamic models I Minimisation algorithms and their performance within the model free and Brownian rotational diffusion spaces J Biomol NMR 40 2 107 109 d Auvergne E J and Gooley P R 2008b Optimisation of nmr dynamic models ii a new methodology for the dual optimisation of the model free parameters and the brownian rotational diffusion tensor J Biomol NMR 40 2 121 123 Farrow N A Zhang O W Szabo A Torchia D A and Kay L E 1995 Spectral density function mapping using N 15 relaxation data exclusively J Biomol NMR 6 2 153 162 Fletcher R 1970 A new approach to variable metric algorithms 13 3 317 322 389 390 BIBLIOGRAPHY Fletcher R and Reeves C M 1964 Function minimization by conjugate gradients 7 2 149 154 Fushman D Cahill S and Cowburn D 1997 The main chain dynamics of the dy namin pleckstrin homology PH domain in solution analysis of 15N relaxation with monomer dimer equilibration J Mol Biol 266 1 173 194 Gill P E Murray W and Wright M H
168. d This is for readability as the convention is much more fluent than camel case A few rare 122 CHAPTER 9 RELAX DEVELOPMENT exceptions exist an example is the Brownian diffusion tensor parameter of anisotropy Da which is referenced as cdp diff_tensor Da As a rule though all new variable or function names should be kept as lower case An example of this convention for both the variable name and function name is def assemble_param_vector self spin None spin_id None sim_index None model_type None Assemble the model free parameter vector as numpy array If the spin argument is supplied then the spin id argument will be ignored Okeyword spin The spin data container Ctype spin SpinContainer instance Okeyword spin id The spin identification string Otype spin id str Okeyword sim index The optional MC simulation index Otype sim index int Okeyword model type The optional parameter set one of all diff mf or local tm Otype model type str or None Oreturn An array of the parameter values of the model free model QOrtype numpy array Initialise param vector 1 Determine the model type if not model type model type self determine param set type O Alias the current data pipe cdp relax data store relax data store current pipe Diffusion tensor parameters if model type diff or model_type all Normal parameters if sim_index None Spheri
169. d Arguments file The name of the PDB file containing the tensor geometric object Description In executing this user function a PDB file must have previously been loaded a geometric object or polygon representing the Brownian rotational diffusion tensor will be overlain with the loaded PDB file and displayed within Molmol The PDB file containing the geo metric object must be created using the complementary pdb create_diff_tensor_pdb user function To display the diffusion tensor the multiple commands will be executed To overlay the structure with the diffusion tensor everything will be selected and reoriented and moved to their original PDB frame positions Select Atom SelectBond Select Angle SelectDist SelectPrim Rotatelnit Movelnit Next the tensor PDB file is read in selected and the covalent bonds of the PDB CONECT records calculated ReadPdb file 10 2 THE LIST OF FUNCTIONS 221 SelectMol file CalcBond 1 1 1 Then only the atoms and bonds of the geometric object are selected and the bal1 stick style applied Select Atom 0 SelectBond 0 SelectAtom TNS SelectBond TNS XMacStand ball_stick mac The appearance is finally touched up RadiusAtom 1 SelectAtom TNSOC RadiusAtom 1 5 222 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 51 molmol view Synopsis Function for viewing the collection of molecules extracted from the
170. d a few calculations are required prior to optimisation Firstly the peak intensities for individual residues needs to be averaged across replicated spectra The peak intensity errors also have to be calculated using the standard deviation formula These two operations are executed by the user function relax fit mean and error Any residues which cannot be resolved due to peak overlap were included in a file called unresolved This file consists solely of one residue number per line These residues are excluded from the analysis by the user function deselect read file unresolved Finally the experiment type is specified by the command relax fit select model exp The argument exp sets the relaxation curve to a two parameter R4 Jo exponential which decays to zero The formula of this function is I t Ine 5 1 where I t is the peak intensity at any time point t Jp is the initial intensity and R is the relaxation rate either the R4 or R2 Changing the user function argument to inv will select the inversion recovery experiment This curve consists of three paremeters Ra Io loo and does not decay to zero The formula is I t I ie 5 2 28 CHAPTER 5 RELAXATION CURVE FITTING 5 5 Optimisation Now that everything has been setup minimision can be used to optimise the parameter values Firstly a grid search is applied to find a rough starting position for the subsequent optimisation alg
171. d at the position of this vector plus the centre of mass Finally a uniform distribution of vectors on a sphere is generated using spherical coordinates By incrementing the polar angle using an arccos distribution a radial array of vectors representing latitude are created while incrementing the azimuthal angle evenly creates the longitudinal vectors These unit vectors which are distributed within the PDB frame and are of 1 Ain length are first rotated into the diffusion frame using a rotation matrix the spherical diffusion tensor is not rotated Then they are multiplied by the diffusion tensor matrix to extend the vector out to the correct length and finally multiplied by the scale value so that the vectors reasonably superimpose onto the macromolecular structure The last set of algorithms place all this information into a PDB file The distribution of vectors are represented by H atoms and are all connected using PDB CONECT records Each H atom is connected to its two neighbours on the both the longitude and latitude This creates a geometric PDB object with longitudinal and latitudinal lines 342 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 136 structure create_vector_dist Synopsis Create a PDB file representation of the distribution of XH bond vectors Defaults structure create vector dist self length 2 0000000000000001e 09 file XH_dist pdb dir None symmetry True force False Keyword Arguments length The
172. d second partial derivatives with respect to the diffusion parameter Dj and the model free parameter 7 The yellow blocks are the sub matrices of chi squared second partial derivatives with respect to the model free parameters i and a For the residue dependent matrix V x the second partial derivatives with respect to the model free pa rameters a and kii where i l are zero In addition the second partial derivatives with respect to the model free parameters i and FE where i l are also zero These blocks of sub matrices are left uncoloured The complete Hessian of 6 is the sum of the matrices Vd 64 CHAPTER 8 VALUES GRADIENTS AND HESSIANS x 8 9 R 0 gt R40 Ape pe Figure 8 3 Dependencies between the x transformed relaxation relaxation and spectral density equations gradients and Hessians 8 6 2 The X gradient The x gradient in vector notation is Vx2 0 2 Y Ri Ri OR 6 8 16 8 6 3 The x Hessian The x Hessian in vector notation is viv 9 25 4 UR VR Ri R 8 VR0 847 8 7 THE R 0 VALUES GRADIENTS AND HESSIANS 8 7 The R 0 values gradients and Hessians 8 7 1 The R 0 values The R 0 values are given by Ri 0 Ri 0 R2 0 Ra 0 YH Yy Onon NOE 9 1 2 HOR 8 7 2 The R 0 gradients The R 0 gradients in vector notation are m i VNOE 0 2 1 5 Rr 0 Voor 9 oos 8 VRa 6 Yx Ri 6 8 7 3 The R 0 Hessian
173. del free models pipes mO m1 m2 m3 m4 m5 m6 m7 m8 m9 Loop over the pipes for name in pipes Create the data pipe pipe create name mf Load the sequence sequence read noe 500 out Load the relaxation data relax_data read R1 600 600 0 1e6 r1 600 out 6 4 MODEL FREE MODEL SELECTION 49 relax_data read R2 600 600 0 1e6 r2 600 out relax_data read NOE 600 600 0 1e6 noe 600 out relax_data read Ri 500 500 0 1e6 ri 500 0ut relax_data read R2 500 500 0 1e6 r2 500 out relax_data read NOE 500 500 0 1e6 noe 500 out Setup other values diffusion_tensor init le 8 fixed True value set 1 02 1e 10 bond length value set 160 1e 6 csa value set 15N heteronucleus value set 1H proton Select the model free model model_free select_model model name Minimise grid_search inc 11 minimise newton Write the results results write file results force True Save the program state state save save force True 6 3 2 The rest Please write me Until this section is completed please look at the sample script mf multimodel py 6 4 Model free model selection 6 4 1 The sample script The sample script which demonstrates both
174. details 1 1 3 Data analysis tools The following tools are implemented as modular components to be used by any data analysis technique e Numerous high precision optimisation algorithms e Model selection d Auvergne and Gooley 2003 Chen et al 2004 Akaike s Information Criteria AIC Small sample size corrected AIC AICc Bayesian or Schwarz Information Criteria BIC 1 1 PROGRAM FEATURES 3 Bootstrap model selection Single item out cross validation CV Hypothesis testing ANOVA model selection only the model free specific tech nique of Mandel et al 1995 is supported e Monte Carlo simulations error analysis for all data analysis techniques e Model elimination the removal of failed models prior to model selection d Auvergne 2006 1 1 4 Data visualisation The results of an analysis or any data input into relax can be visualised using a number of programs MOLMOL 1D data can be mapped onto a structure either by the creation of MOLMOL macros or by direct control of the program PyMOL 3D objects such as the diffusion tensor representation can be displayed with the structure Grace any 2D data can be plotted OpenDX The chi squared space of models with three parameters can be mapped and 3D images of the space produced 1 1 5 Interfacing with other programs relax can create the input files execute in line and then read the output of the following programs Thes
175. developers can propose that you receive commit access If a number of developers agree while no one says no then commit access will be offered One area where coding ability can be demonstrated is within the relax test suite The addi tion of tests especially those where the relax internal data structures of self relax data are scrutinised can be a good starting point for learning the structure of relax This is because the introduction of bugs has no effect on normal program execution The relax test suite is an ideal proving ground If skills in only certain areas of relax development for example in creation of the docu mentation an understanding of C but not python an understanding of solely the code of the user interface or an understanding of the code specific to a certain type of data analysis methodology then partial commit access may be granted Although you will have the ability to make modifications to any part of the repository please make modifications only those areas for which you have permission 9 4 2 Joining Gna The first step in becoming a committer is to create a Gna account Go to https gna org account register php and type in a login name password real name and the email address you would like to use You will then get an automatic email from Gna which will contain a link to activate your registration 9 4 3 Joining the relax project The second step in becoming a committer is to register to become a member
176. ding the data into relax The function is called read and the class is called relax_data To execute the function type something like relax gt relax_data read R1 600 600 0 1e6 r1 600 out On first usage the relax prompt can be quite daunting Two features exist to increase the usability of the prompt the help system and tab completion 1 2 4 The help system For assistance in using a function simply type help function In addition to functions if help object is typed the help for the python object is returned This system is similar to the help function built into the python interpreter which has been renamed to help python with the interactive component removed For the standard interactive python help system type help_python 6 CHAPTER 1 INTRODUCTION 1 2 5 Tab completion Tab completion is implemented to prevent insanity as the function names can be quite long a deliberate feature to improve usability The behaviour of the tab completion is very similar to that of the bash prompt Not only is tab completion useful for preventing RSI but it can also be used for listing all available functions To begin with if you hit the TAB key without typing any text all available functions will be listed along with function classes and other python objects This extends to the exploration of user functions within a function class For example to list the user functions within the funct
177. dology as the original exponential curves These randomised curves are created by back calculation from the fitted model parameter values and then each point on the curve randomised using the error values set earlier in the script monte_carlo create_data As a grid search for each simulation would be too computationally expensive the starting point for optimisation for each simulation can be set to the position of the optimised parameter values of the model monte_carlo initial_values Then exactly the same optimisation as was used for the model can be performed minimise simplex constraints False The parameter errors are then determined as the standard deviation of the optimised parameter values of the simulations monte_carlo error_analysis 5 7 FINISHING OFF 29 5 7 Finishing off To finish off the script first saves the relaxation rates together with their errors in a simple text file value write param rx file rx out force True Grace plots are created and viewed grace write y_data_type rx file rx agr force True grace view file rx agr and finally the program state is saved for future reference state save file rx save force True 30 CHAPTER 5 RELAXATION CURVE FITTING Chapter 6 Model free analysis 6 1 Theory 6 1 1 The chi squared function x 0 For the minimisation of the model free models a chain of calculations each based on a different theor
178. dward at_ nmr relax dot com should be included in the message Next should be another blank line e If the commit relates to an entry in the bug tracker or to a discussion on the mailing lists then the web address of either the bug report or the mailing list archive message should be cited in the next section separated from the synopsis or credit section by a blank line All relevant links should be included to allow easy navigation between the repository mailing lists bug tracker etc An example is bug 5559 which is located at https gna org bugs func detailitem amp item_id 5559 and the post to relax devel at gna org describing the fix to that bug which is located at https mail gna org public relax devel 2006 03 msg00013 html e A full description with all the details can follow This description should follow a blank line can itself be sectioned using blank lines and finally the log is terminated by one blank line at the end of the message An example of a commit message for the closure of a bug is Fixing the rest of bug 7241 https gna org bugs 7241 Bug 7241 was thought to be fixed in in r2591 and r2593 the commit messages describing the solution being located at https mail gna org public relax commits 2006 09 msg00064 html Message id lt E1GTgBi 0000R6 4h subversion gna org gt for r2591 and https mail gna org public relax commits 2006 10 msg00001 html Message id lt E1GTt6C 0005rk 8q subversion g
179. e Monte Carlo simulations Defaults monte carlo error analysis self prune 0 0 Keyword Arguments prune Legacy argument corresponding to trim in Art Palmer s Modelfree program Description Parameter errors are calculated as the standard deviation of the distribution of parameter values This function should never be used if parameter values are obtained by minimi sation and the simulation data are generated using the method direct The reason is because only true Monte Carlo simulations can give the true parameter errors The prune argument is legacy code which corresponds to the trim option in Art Palmer s Modelfree program To remove failed simulations the eliminate function should be used prior to this function Eliminating the simulations specifically identifies and removes the failed simulations whereas the prune argument will only in a few cases positively identify failed simulations but only if severe parameter limits have been imposed Most failed models will pass through the pruning process and hence cause a catastrophic increase in the parameter errors If the argument must be used the following must be taken into account If the values or parameters are calculated rather than minimised the prune argument must be set to zero The value of this argument is proportional to the number of simulations removed prior to error calculation If prune is set to 0 0 all simulations are used for calculating errors
180. e appropriate file name If the file is not located within the environment s path include the full path in front of the binary file name 256 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 70 palmer extract Synopsis Function for extracting data from the Modelfree4 mfout star formatted file Defaults palmer extract self dir None Keyword Arguments dir The directory where the file mfout is found 10 2 THE LIST OF FUNCTIONS 10 2 71 pcs back_calc Synopsis Back calculate the pseudocontact shifts Defaults pcs back_calc self id None Keyword Arguments id The alignment identification string 207 258 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 72 pcs centre Synopsis Specify which atom is the paramagnetic centre Defaults pcs centre self atom id None pipe None Keyword Arguments atom id The atom identification string pipe The data pipe containing the structures to extract the centre from Description This function is required for specifying where the paramagnetic centre is located in the loaded structure file If no structure number is given then the average atom position will be calculated if multiple structures are loaded A different set of structures than those loaded into the current data pipe can also be used to determine the position or its average This can be achieved by loading the alternative structures into another data pipe and then spe
181. e bond length and CSA are tm3O Ins r CSA tm31 Tm r CSA SL tm32 ra r CSA S2 Te tm33 A Tri ps CSA B Rat nod c Tas T CSAS ty Renh tm35 Tm r OSA S7 82 rs tm36 Tm r CSA S TiD s Tah tm37 Dos T CSA S m Ts Rez tm38 s T CSA S TF se Ts Rer bugs Eras t CSA Rork 204 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Spin identification string If spin_id is supplied then the model will only be selected for the corresponding spins Otherwise the model will be selected for all spins Examples To pick model m1 for all selected spins type relax gt model_free select_model m1 relax gt model_free select_model model m1 10 2 THE LIST OF FUNCTIONS 205 10 2 40 model_selection Synopsis Function for model selection Defaults model_selection self method None modsel_pipe None pipes None Keyword arguments method The model selection technique see below modsel_pipe The name of the new data pipe which will be created by this user function by the copying of the selected data pipe pipes An array containing the names of all data pipes to include in model selection Description The following model selection methods are supported AIC Akaike s Information Criteria AICc Small sample size corrected AIC BIC Bayesian or Schwarz Information Criteria Bootstrap B
182. e ellipsoid diffusion tensor 3 The third Euler angle of the ellipsoid diffusion tensor y The polar angle defining the major axis of the spheroid diffusion tensor 0 The azimuthal angle defining the major axis of the spheroid diffusion tensor Object name Dpar Dper Dratio alpha beta gamma theta phi 371 Patterns tm Dd iso Da a Da r Da x Dd y Da z Dd par Dd per Dd ratio a or alpha b or beta g or gamma theta 6 phi 372 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Diffusion tensor parameter default values Data type Object name Value Tm tm 10 1e 9 Duo Diso 1 666 1e7 Da Da 0 0 Dr Dr 0 0 Da Dx 1 666 1e7 Dy Dy 1 666 1e7 D Dz 1 666 1e7 i Dpar 1 666 1e7 Di Dper 1 666 1e7 O ratio Dratio 1 0 a alpha 0 0 8 beta 0 0 y gamma 0 0 0 theta 0 0 P phi 0 0 Relaxation curve fitting set details Only three parameters can be set the relaxation rate Rx the initial intensity 10 and the intensity at infinity Iinf Setting the parameter Tinf has no effect if the chosen model is that of the exponential curve which decays to zero 10 2 THE LIST OF FUNCTIONS 373 Relaxation curve fitting data type s
183. e end of the string For example Ss 2 will match s2 but not S2f or s2s Match any character xx Match the character x any number of times for example x will match as will XXXXX Match any sequence of characters of any length Importantly do not supply a string for the data type containing regular expression The regular expression is implemented so that various strings can be supplied which all match the same data type Model free data type string matching patterns 10 2 THE LIST OF FUNCTIONS Data type Local Tm Order parameter S Order parameter S Order parameter S2 Correlation time Te Correlation time Tf Correlation time 7 Chemical exchange Bond length CSA Heteronucleus type Proton type Object name local_tm tag S2f heteronuc type proton type 377 Patterns Llloca1 tm Ss 2 Ss 2 Ss 2s teg try ces Rr ex or Cc emical Eelxchange r or Bb ond _ Ll ength Cc Ss Aa Hh eteronucleus Pp roton Reduced spectral density mapping data type string matching patterns Data type J 0 J wx J wn Bond length CSA Heteronucleus type Proton type Object name Patterns jo 351 09 or LT41X CO wx Jj w Xx or EJ VG EXx D juh Jj w Hh or Jj
184. e identified residue to the new non existent residue The new residue must not already exist Examples To copy the residue data from residue 1 to the new residue 2 type relax gt residue copy res_from 1 res_to 2 To copy residue 1 of the molecule Old mol to residue 5 of the molecule New mol type relax gt residue copy res_from 01d mol 1 res_to New mol 5 To copy the residue data of residue 1 from the data pipe m1 to m2 assuming the current data pipe is m1 type relax residue copy res_from 1 pipe_to m2 relax residue copy pipe_from m1 res from 1 pipe_to m2 res_to 1 304 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Identification string documentation The identification string is composed of three components the molecule id token begin ning with the character the residue id token beginning with the character and the atom or spin system id token beginning with the character Each token can be composed of multiple elements separated by the character and each individual element can either be a number which must be an integer in string format a name or a range of numbers separated by the character Negative numbers are supported The full id string specification is jmol_namej res_id res_id jres_idj Qjatom_idj jatom_idj jatom_idj where the token elemen
185. e model free model m4 after loading six relaxation data sets is Create the data pipe name m4 pipe create name mf Nuclei type nuclei N Load the sequence sequence read noe 500 out Load the relaxation data relax_data read Ri 600 600 0 1e6 r1 600 out relax_data read R2 600 600 0 1e6 r2 600 out relax_data read NOE 600 600 0 1e6 noe 600 out relax_data read Ri 500 500 0 1e6 r1i 500 out relax_data read R2 500 500 0 1e6 r2 500 out 8 CHAPTER 1 INTRODUCTION relax_data read NOE 500 500 0 1e6 noe 500 out Setup other values diffusion_tensor init 2e 8 1 3 60 290 param_types 1 axial_type prolate fixed True value set 1 02 1e 10 bond_length value set 160 1e 6 csa value set 15N heteronucleus value set 1H proton Select a preset model free model model_free select_model model name Grid search grid search inc 11 Minimise minimise newton Finish results write file results force True state save save force True Scripting is much more powerful than the prompt as advanced Python programming can be employed see the file full_analysis py in the sample_scripts directory for an example 1 2 8 Sample scripts A few sample
186. e programs can be used as optimisation engines replacing the minimisation algorithms built into relax e Dasha model free analysis e Modelfree model free analysis 1 1 6 The user interfaces UI relax can be used through the following UIs The prompt this is the primary interface of relax Rather than reinventing a new com mand language relax s interface is the powerful Python prompt This gives the power user full access to a proven programming language Scripting this provides a more powerful and flexible framework for controlling the pro gram The script will be executed as Python code enabling advanced programming for automating data analysis All the features available within the prompt environ ment are accessible to the script and Gooley 4 CHAPTER 1 INTRODUCTION 1 2 How to use relax 1 2 1 The prompt The primary interface of relax is the prompt After typing relax within a terminal you will be presented with relax gt This is the Python prompt which has been tailored specifically for relax You will hence have full access if desired to the power of the Python programing language to manipulate your data You can for instance type relax gt print Hello World the result being relax gt print Hello World Hello World relax gt Or using relax as a calculator relax gt 1 0 2 3 10 0 69999999999999996 relax gt 1 2 2 Python relax has been designed such that knowledge about P
187. e_data method back_calc Step 4 relax gt monte_carlo initial_values Step 5 relax gt minimise newton Step 6 relax gt eliminate Step 7 relax gt monte_carlo error_analysis Step 8 An example for reduced spectral density mapping is relax gt calc Step 2 relax gt monte_carlo setup number 500 Step 3 relax gt monte_carlo create_data method back_calc Step 4 relax gt calc Step 6 relax gt monte_carlo error_analysis Step 8 238 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 57 monte_carlo on Synopsis Function for turning simulations on Defaults monte_carlo on self Monte Carlo Simulation Overview For proper error analysis using Monte Carlo simulations a sequence of function calls is required for running the various simulation components The steps necessary for imple menting Monte Carlo simulations are 1 The measured data set together with the corresponding error set should be loaded into relax 2 Either minimisation is used to optimise the parameters of the chosen model or a calculation is run 3 To initialise and turn on Monte Carlo simulations the number of simulations n needs to be set 4 The simulation data needs to be created either by back calculation from the fully minimised model parameters from step 2 or by direct calculation when values are calcu lated rather than minimised The error set is used to randomise each simulation
188. ecide if he or she is willing to distribute software through any other system and a licensee cannot impose that choice This section is intended to make thoroughly clear what is believed to be a consequence of the rest of this License 8 If the distribution and or use of the Program is restricted in certain countries either by patents or by copyrighted interfaces the original copyright holder who places the Program under this License may add an explicit geographical distribution limitation excluding those countries so that distribution is permitted only in or among countries not thus excluded In such case this License incorporates the limitation as if written in the body of this License 9 The Free Software Foundation may publish revised and or new versions of the General Public License from time to time Such new versions will be similar in spirit to the present version but may differ in detail to address new problems or concerns Each version is given a distinguishing version number If the Program specifies a version number of this License which applies to it and any later version you have the option of following the terms and conditions either of that version or of any later version published 386 CHAPTER 11 LICENCE by the Free Software Foundation If the Program does not specify a version number of this License you may choose any version ever published by the Free Software Foundation 10 If you wish to incorporate parts o
189. ed independent and separate works in themselves then this License and its terms do not apply to those 384 CHAPTER 11 LICENCE sections when you distribute them as separate works But when you distribute the same sections as part of a whole which is a work based on the Program the distribution of the whole must be on the terms of this License whose permissions for other licensees extend to the entire whole and thus to each and every part regardless of who wrote it Thus it is not the intent of this section to claim rights or contest your rights to work written entirely by you rather the intent is to exercise the right to control the distribution of derivative or collective works based on the Program In addition mere aggregation of another work not based on the Program with the Program or with a work based on the Program on a volume of a storage or distribution medium does not bring the other work under the scope of this License 3 You may copy and distribute the Program or a work based on it under Section 2 in object code or executable form under the terms of Sections 1 and 2 above provided that you also do one of the following a Accompany it with the complete corresponding machine readable source code which must be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange or b Accompany it with a written offer valid for at least three years to give any third party for
190. ed require a starting position within the model free space This initial parameter vector is found by employing a coarse grid search chi squared values at regular positions spanning the space are calculated and the grid point with the lowest value becomes the starting position The grid search 38 CHAPTER 6 MODEL FREE ANALYSIS itself is an optimisation technique As it is computationally expensive the number of grid points needs to be kept to a minimum Hence the initial parameter values are a rough and imprecise approximation of the local minimum Due to the complexity of the curvature of the model free space the grid point with the lowest chi squared value may in fact be on the opposite side of the space to the local minimum Once the starting position has been determined by the grid search the optimisation al gorithm can be executed The number of algorithms developed within the mathematical field of optimisation is considerable They can nevertheless be grouped into one of a small number of major categories based on the fundamental principles of the technique These include the line search methods the trust region methods and the conjugate gradient methods For more details on the algorithms described below see Nocedal and Wright 1999 Line search methods The defining characteristic of a line search algorithm is to choose a search direction p and then to find the minimum along that vector starting from 0 Nocedal and Wright 1999
191. ed using the commands select resn CON hide sele show sticks sele color white sele 10 2 THE LIST OF FUNCTIONS 275 10 2 89 pymol macro_exec Synopsis Function for executing PyMOL macros Defaults pymol macro_exec self data_type None style classic colour start None colour end None colour_list None Keyword Arguments data type The data type to map to the structure style The style of the macro colour start The starting colour either an array or string of the linear colour gradient colour_end The ending colour either an array or string of the linear colour gradient colour list The list of colours to match the start and end strings Description This function allows residues specific values to be mapped to a structure through PyMOL macros Currently only the classic style which is described below is available Colour The values are coloured based on a linear colour gradient which is specified through the colour_start and colour_end arguments These arguments can either be a string to identify one of the RGB red green blue colour arrays listed in the tables below or you can give the RGB vector itself For example colour_start white and colour_start 1 0 1 0 1 0 both select the same colour Leaving both arguments at None will select the default colour gradient which for each type of analysis is described below When supplying the colours as s
192. eing optimised 6 partial derivative The partial derivative of 8 65 with respect to the geometric parameter 6 is k 0 2 r 1 wri w P y e Ti 92 wri 06 9 06 1 wri 1 Te n wr pti rg Ti wrpri 2_ 9272 Ts Ti wrsri e Ve mia enr Dc S2 1 SFT TF 5 3 rs Ti Ts 8 80 06 ANTE wri rp 74 wrpti Ts T wr f t 1 52 D partial derivative The partial derivative of 8 65 with respect to the orientational parameter 0 is 0J 2X da f P A Spire try S Ste tn UD 5 2 00 it ene Gp tne tern s n t OTT 8 81 S partial derivative The partial derivative of 8 65 with respect to the order parameter S is k OJ w 2 1 Ts Ti Ts ANA E LS EN UN 8 82 082 5 2 ae 1 07 Ta 74 WTaTi PM S partial derivative The partial derivative of 8 65 with respect to the order parameter S is 846 2 eerie to tts s Ti wrrTi Ts mU Tie e 8 83 80 CHAPTER 8 VALUES GRADIENTS AND HESSIANS Tf partial derivative The partial derivative of 8 65 with respect to the correlation time Ty is T 910 24 gay NS uua ro TO err on M pe ANY 8 84 Ts partial derivative The partial derivative of 8 65 with respect to the correlation time 7 is 9J 2 ga 97 uua T 70 oran Bu IA P on EUN 8 9 MODEL FREE ANALYSIS 8l 8 9 5 The extended model free He
193. elf pipe_name None Keyword Arguments pipe_name The name of the data pipe Description This function will permanently remove the data pipe and all of its contents 267 268 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 82 pipe hybridise Synopsis Create a hybrid data pipe by fusing a number of other data pipes Defaults pipe hybridise self hybrid None pipes None Keyword Arguments hybrid The name of the hybrid data pipe to create pipes An array containing the names of all data pipes to hybridise Description This user function can be used to construct hybrid models An example of the use of a hybrid model could be if the protein consists of two independent domains These two domains could be analysed separately each having their own optimised diffusion tensors The N terminal domain data pipe could be called N_sphere while the C terminal domain could be called C_ellipsoid These two data pipes could then be hybridised into a single data pipe called mixed model by typing relax pipe hybridise mixed model N sphere C_ellipsoid relax pipe hybridise hybrid mixed model pipes N sphere C_ellipsoid This hybrid data pipe can then be compared via model selection to a data pipe whereby the entire protein is assumed to have a single diffusion tensor The requirements for data pipes to be hybridised is that the molecules sequences and spin systems for
194. en premultiplied with a diagonal matrix in which the diagonal elements are the scaling factors For the model free analysis the scaling factor of one was used for the order parameter and a scaling factor of le was used for the correlation times The Rex parameter was scaled to be the chemical exchange rate of the first field strength The scaling matrix for the parameters 5 S7 S2 Te Tf Ts Rex r CSA of individual residues is 100 0 0 0 0 0 0 10 0 0 0 0 0 0 001 0 0 0 0 0 0 000 le o 0 0 0 0 00 0 0 ite 1 0 0 0 6 48 000 0 O te 0 0 0 000 0 0 0 2 vg 0 0 000 0 0 0 0 ie 000 0 0 0 0 ie 6 2 OPTIMISATION OF A SINGLE MODEL FREE MODEL 47 For the ellipsoidal diffusion parameters Tm Da Dr a B y the scaling matrix is le 0 0000 0 1 00 0 0 0 0 10 0 0 0 0 0100 6 49 0 0 00 1 0 0 0 00 0 1 For the spheroidal diffusion parameters Tm Da 0 6 the scaling matrix is le 0 00 0 1 00 0 0 10 6 50 0 0 0 1 6 2 Optimisation of a single model free model 6 2 1 The sample script The sample script which demonstrates the optimisation of model free model m4 which consists of the parameters 97 Te Rex is model free py The text of the script is Script for model free analysis Create the data pipe name m4 pipe create name mf Load the sequence sequence read noe 500 out Load the relaxation data relax_data read Ri 600 600 0 1e6 r1 600 ou
195. ents spin id The spin identification string Description By supplying the spin id argument a subset of spin can have their selection status reversed Examples To deselect all currently selected spins and select those which are deselected type relax deselect reverse 10 2 THE LIST OF FUNCTIONS 159 10 2 19 deselect spin Synopsis Function for deselecting specific spins Defaults deselect spin self spin id None change all False Keyword Arguments spin id The spin identification string change all A flag specifying if all other spins should be changed Description The change_all flag argument default is False meaning that all spins currently either selected or deselected will remain that way Setting the argument to True will cause all spins not specified by spin_id to be selected Examples To deselect all glycines and alanines type relax deselect spin spin id GLY ALA To deselect residue 12 MET type relax deselect spin 12 relax deselect spin spin_id 12 relax deselect spin spin id 12 amp MET 160 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 20 diffusion_tensor copy Synopsis Function for copying diffusion tensor data from one data pipe to another Defaults diffusion_tensor copy self pipe_from None pipe to None Keyword Arguments pipe_from The name of the data pipe to copy the diffusion tensor data from pipe_to The
196. eometric parameters Tm and Da are 2 ART 2 6Diso 2 0498 3 8 166a EE os MAA O 8 166b OTm ODa oO 11D s Dall 39 8 166c OT i 02 T m VSO a T 2 PC PA 2 6Diso 204 3 8 166d OTm 09 m VSO a NU 48 74 6Diso 29 91 8 166e OTm 09 m 1SO a z Tm D partial derivative The second partial derivatives with respect to the geometric parameters Tm and D are O Tm OD O4 Tm OD nm OTm OD Or OT OD Or OTm OD 1222 de Oey 2D R 8 167a 6DaTm 6Diso Dall 3D 3 8 167b 6DaTm 6Diso Dall 39 3 8 167c 8 167d p2 na 1 69 5 20498 5 8 1676 8 10 ELLIPSOIDAL DIFFUSION TENSOR 105 Da Da partial derivative The second partial derivatives with respect to the geometric parameter Da twice are 3T 2 3 3p 3 ROD iso 20 2 8 168a O r i 2 3 507 10 39 69 Dall 39 8 168b nm 2 3 ag3 20 39 69 Dall 3D 8 168c 2 T 8 6Diso 2Da 8 168d Or 2 3 Da Dr partial derivative The second partial derivatives with respect to the geometric parameters Da and D are O r D am 24 avr iso 220a E iso 2D HR 4 8 169 3D 0D DaD 6D D A TES 6D a 3T 3 2 sem 3D 6Diso Dall 13D 30095 Dall a dD OD 6D_ 1 39 1 39 3 1 39 8 169b mn 6Da 1 3D
197. erent directory type the name of that directory at the end of the last command Modifications can be made to this copy while normal development continues on the main line Keeping the branch up to date using svnmerge py As you develop your branch changes will be occurring simultaneously within the main line These changes should be merged into your branch on a regular basis to avoid large 9 4 COMMITTERS 129 incompatible changes from forming between the two branches To simplify this process the svnmerge py script located at http www orcaware com svn wiki Svnmerge py can be used It is best to download the trunk version from that page unless that version is non functional Once you have this script the merging from the main line to your private branch must be initialised by typing from within the checked out copy of your branch svnmerge py init This then needs to be committed using the automatically generated log svn ci F svnmerge commit message txt To keep up to date simply type svnmerge py merge If conflicts have occurred please refer to the Subversion book at http svnbook red bean com for information on how to resolve the problem Otherwise or once fixed the main line revisions merged into your branch can be committed using the automatically generated log file svn ci F svnmerge commit message txt Merging the branch back into the main line Once you have completed the modifications desired for your br
198. erivative 0 c 9 i OD 021 8c zs j 09502 i co f OD 0D f ce 0 OO OD ca 0 OD OD l 8 158a 8 158b 8 158c 8 158d 8 158 The second partial derivatives with respect to the geometric parameter D twice are 0 c_9 3 0 e 00 2 40D 0 c 4 ap co E 029 2 o ec 092 T Pc 3 e D 4092 8 159a 8 159b 8 159c 8 159d 8 159e 8 10 ELLIPSOIDAL DIFFUSION TENSOR where 9 e _ 1 sp _ 99 1 64 26262 592 ll To x qo y z 6D7 9D 1 6 26262 2 6D 1 62 20267 101 8 160 102 CHAPTER 8 VALUES GRADIENTS AND HESSIANS 8 10 5 The correlation times of the ellipsoid The five correlation times 7 in the correlation function of the Brownian rotational diffusion of an ellipsoid 8 134 on page 93 are Ty Dis 2D R T 1 6Diso Dall 39 695 9 1 39 Diso 29 7 6Diso 2D a where A is defined in Equation 8 141 on page 94 8 10 6 The correlation time gradients of the ellipsoid Tm partial derivative The partial derivatives with respect to the geometric parameter Tm are A _ 69s 29 8 OTm oT TL _ Tm 6Diso 1 4 39 Tm hay iso a 1 r Pr T 6D Dal 25 On Tm 6Diso T o OTm On s Tm 3 69 iso 2 0488 Tm Da partial derivative The partial derivatives with respect to the geometric parameter Da are T 9 Og OT_1 O
199. es of the software or if you modify it For example if you distribute copies of such a program whether gratis or for a fee you must give the recipients all the rights that you have You must make sure that they too receive or can get the source code And you must show them these terms so they know their rights We protect your rights with two steps 1 copyright the software and 2 offer you this license which gives you legal permission to copy distribute and or modify the software Also for each author s protection and ours we want to make certain that everyone un derstands that there is no warranty for this free software If the software is modified by someone else and passed on we want its recipients to know that what they have is not the original so that any problems introduced by others will not reflect on the original authors reputations Finally any free program is threatened constantly by software patents We wish to avoid the danger that redistributors of a free program will individually obtain patent licenses in effect making the program proprietary To prevent this we have made it clear that any patent must be licensed for everyone s free use or not licensed at all The precise terms and conditions for copying distribution and modification follow 11 2 THE GPL 383 GNU GENERAL PUBLIC LICENSE TERMS AND CONDITIONS FOR COPYING DISTRIBUTION AND MODIFICATION 0 This License applies to any program or other
200. espect to the geometric parameter Tm twice is rm OT 0 8 193 112 CHAPTER 8 VALUES GRADIENTS AND HESSIANS 8 13 Ellipsoidal dot product derivatives 8 13 1 The dot product of the ellipsoid The dot product is defined as i XH 9 8 194 where i is one of x y z XH is a unit vector parallel to the XH bond vector and D is one of the unit vectors defining the diffusion frame The three diffusion frame unit vectors can be expressed using the Euler angles a 8 and y as sin a sin y cos a cos 3 cos y Da sin a cos y cosacos B sin y 8 195a cos a sin 8 cos asin y sina cos f cos y Dy cosacos y sin a cos B sin 8 195b sin a sin 8 pa sin f cos y sinfsiny 8 195c cos 3 8 13 2 The dot product gradient of the ellipsoid The partial derivative of the dot product 6 with respect to the orientational parameter Dj is 00 o E 09 0XH 00 89 c unm 1 5D BD D 8 196 XH 9 XH Because XH is constant and not dependent on the Euler angles its derivative is zero Therefore M 00 09 XH i 00 00 8 197 The 2 gradient The partial derivatives of the unit vector D with respect to the Euler angles are 09 cos a sin y sin a cos 3 cos y Z cosa cos y sina cos Bsiny 8 198a Oa sin asin 8 aD cos asin 3 cos y cosasin siny 8 198b op cos Q
201. esponding to the object names are lists or arrays with each element corrsponding to each state 10 2 THE LIST OF FUNCTIONS 379 10 2 148 vmd view Synopsis Function for viewing the collection of molecules extracted from the PDB file Defaults vmd view self Example relax gt vmd view 380 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Chapter 11 Licence 11 1 Copying modification sublicencing and distribution of relax To ensure that the program relax including all future versions will remain legally available for perpetuity to anyone who wishes to use the program the code has been released under the GNU General Public Licence The freedom of relax is guaranteed by the GPL This is a licence which has been very carefully crafted to protect both the developers of the program as well as the users by means of copyright law If the licence is violated by improper copying modification sublicencing or distribution then the licence terminates hence the violator is copying modifying sublicencing or distributing the program illegally in full violation of copyright law For a better understanding of the protections afforded by the GPL the licence is reprinted in whole within the next section 11 2 The GPL The following is a verbatim copy of the GNU General Public Licence A text version is available in the relax docs directory within the file COPYING 381 382 CHAPTER 11 LICENCE GNU GENERAL
202. eter Ac Therefore the partial and second partial derivatives with respect to these parameters is zero Only the derivative with respect to the bond length r is non zero being dd 3 Ho vay h lE CER um s 8 22 d dr 2 Ce lt ri gt eee The second derivative with respect to the bond length is d d _ 21 uo V yw xh d a B Ser 8 23 dr 2 4r lt r gt d CSA constant The CSA constant is defined as B iem B 8 24 The partial derivative of this component with respect to all parameters but the CSA parameter Ac is zero This derivative is dc u 202 Ao 8 25 dAc 3 The CSA constant second derivative with respect to Aq is 2 2 2 gi ee 8 26 dAo 3 8 8 Rj 0 VALUES GRADIENTS AND HESSIANS 67 Rex constant The Re constant is defined as Reg pea 21wg 8 27 The partial derivative of this component with respect to all parameters but the chemical exchange parameter pex is zero This derivative is Rer eq dpex 2nwg 8 28 The Rex constant second derivative with respect to pex is II d Rex E doy 0 8 29 Spectral density terms of the R dipolar component For the dipolar component of the Ri equation 6 3a on page 32 the spectral density terms are JR J wg wx 3d wx 6S we wx 8 30 The partial derivative of these terms with respect to the spectral density function param eter 0 is R7 OJ OJ wH wx OJ wx OJ wH wx os E A ad cee 00 0
203. f val None param None spin_id None Keyword arguments val The value s param The parameter s spin_id The spin identifier Description If this function is used to change values of previously minimised results then the minimi sation statistics chi squared value iteration count function count gradient count and Hessian count will be reset to None The val argument can be None a single value or an array of values while the parameter argument can be None a string or array of strings The choice of which combination de termines the behaviour of this function The following table describes what occurs in each instance The Value column refers to the val argument while the Param column refers to the param argument In these columns None corresponds to None 1 corresponds to either a single value or single string and n corresponds to either an array of values or an array of strings 10 2 THE LIST OF FUNCTIONS 365 Value None None Param Description None None None This case is used to set the model parameters prior to minimisation or calculation The model parameters are set to the default values Invalid combination This case is used to set the model parameters prior to minimisation or calculation The length of the val array must be equal to the number of model parameters for an individual residue The parameters will be set to the corresponding number The parameter
204. f the Program into other free programs whose dis tribution conditions are different write to the author to ask for permission For software which is copyrighted by the Free Software Foundation write to the Free Software Foun dation we sometimes make exceptions for this Our decision will be guided by the two goals of preserving the free status of all derivatives of our free software and of promoting the sharing and reuse of software generally NO WARRANTY 11 BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE THERE IS NO WARRANTY FOR THE PROGRAM TO THE EXTENT PERMITTED BY APPLICA BLE LAW EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND OR OTHER PARTIES PROVIDE THE PROGRAM AS IS WITH OUT WARRANTY OF ANY KIND EITHER EXPRESSED OR IMPLIED INCLUD ING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF MERCHANTABIL ITY AND FITNESS FOR A PARTICULAR PURPOSE THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU SHOULD THE PROGRAM PROVE DEFECTIVE YOU ASSUME THE COST OF ALL NECES SARY SERVICING REPAIR OR CORRECTION 12 INNO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER OR ANY OTHER PARTY WHO MAY MODIFY AND OR REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE BE LIABLE TO YOU FOR DAMAGES INCLUDING ANY GENERAL SPECIAL INCL DENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR IN ABILITY TO USE THE PROGRAM INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA B
205. f the molecule res_id the residue identifier which can be a number name or range of numbers atom_id the atom or spin system identifier which can be a number name or range of numbers If one of the tokens is left out then all elements will be assumed to match For example if the string does not contain the character then all molecules will match the string Regular expression can be used to select spins For example the string H will select the protons H H2 H98 10 2 THE LIST OF FUNCTIONS 337 10 2 133 state load Synopsis Function for loading a saved program state Defaults state load self state None dir_name None Keyword Arguments state The file name which can be a string or a file descriptor object of a saved program state dir name The name of the directory in which the file is found Description This function is able to handle uncompressed bzip2 compressed files or gzip compressed files automatically The full file name including extension can be supplied however if the file cannot be found this function will search for the file name with bz2 appended followed by the file name with gz appended For more advanced users file descriptor objects are also supported Examples The following commands will load the state saved in the file save relax gt state load save relax gt state load state save The following commands
206. f variable value field The Python installation must also be located on the path add the text C Program 2 3 OPTIONAL PROGRAMS 13 Files Python24 changing the text to point to the correct directory to the field To run the program from any directory inside the Windows command prompt or dos prompt type C gt relax 2 2 4 Installation on Mac OS X Please write me if you know how to do this 2 2 5 Installation on your OS Please write me if you know how to do this 2 2 6 Running a non compiled version Compilation of the C code is not essential for running relax however certain features of the program will be disabled Currently only the exponential curve fitting for determining the R and Ra relaxation rates requires compilation To run relax without compilation install the dependencies detailed above download the source distribution which should be named relax x x x src tar bz2 extract the files and then run the file called relax in the base directory 2 3 Optional programs The following is a list of programs which can be used by relax although they are not essential for normal use 2 3 1 Grace Grace is a program for plotting two dimensional data sets in a professional look ing manner It is used to visualise parameter values It can be downloaded from http plasma gate weizmann ac il Grace 2 3 2 OpenDX Version 4 1 3 or compatible OpenDX is used for viewing the output of the space mapping function
207. ff the diffusion tensor parameters This will allow all diffusion tensor parameters to be toggled all_spins using this keyword all parameters from all spins will be toggled all all parameter will be toggled This is equivalent to combining both diff and all_spins The flag fixed if set to True will fix parameters during optimisation whereas a value of False will allow parameters to vary 178 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 28 frq set Synopsis Set the spectrometer frequency of the experiment Defaults frq set self id None frq None Keyword arguments id The experiment identification string frq The spectrometer frequency in Hertz Description This user function allows the spectrometer frequency of a given experiment to be set 10 2 THE LIST OF FUNCTIONS 179 10 2 29 grace view Synopsis Function for running Grace Defaults grace view self file None dir grace grace_exe xmgrace Keyword Arguments file The name of the file dir The directory name grace_exe The Grace executable file Description This function can be used to execute Grace to view the specified file the Grace agr file and the execute Grace If the directory name is set to None the file will be assumed to be in the current working directory Examples To view the file s2 agr in the directory grace type relax gt grace view file s2 agr
208. fic protocol is for single field strength data The initial diffusion tensor estimate is calculated using the R2 R4 ratio The diffusion parameters of D are held constant while model free models m1 to m5 6 22 1 6 22 5 of the set for each residue i are optimised and 500 Monte Carlo simulations executed Using a web of ANOVA statistical tests specifically X and F tests a step up hypothesis testing model selection procedure is used to choose the best model free model These steps are repeated for all residues of the protein The global model G the union of D and all is then optimised These steps are repeated until convergence of the global model The iterative process is repeated for both isotropic diffusion sphere and anisotropic diffusion spheroid 52 CHAPTER 6 MODEL FREE ANALYSIS No Convergence S Oblate Prolate Y Figure 6 2 A schematic of model free analysis using the diffusion seeded paradigm the initial diffusion tensor estimate together with AIC model selection and model elimination The initial estimates of the parameters of 9 are held constant while model free models m0 to m9 6 22 0 6 22 9 of the set for each spin system i are optimised model elimination applied to remove failed models and AIC model selection used to determine the best model The global model 6 the union of 9 and all is then optimised These steps are repeated until convergence of the global model The entire iterative process
209. for details Prior to submitting a patch to the mailing list your sources should be updated to include the most recent changes To do this type svn up and note the revision number to include in your post The update may cause a conflict if changes added to the repository clash with your modifications If this occurs see the Subversion book at http svnbook red bean com for details on how to resolve the conflict or submit a message to the relax devel list Once the sources are up to date your changes can be can be converted into the patch text file Using SVN creating a patch is easy Just type svn diff gt patch in the base relax directory 9 4 Committers 9 4 1 Becoming a committer Anyone can become a relax developer and obtain commit access to the relax repository The main criteria for selection by the relax developers is to show good judgement compe tence in producing good patches compliance with the coding and commit log conventions 126 CHAPTER 9 RELAX DEVELOPMENT comportment on the mailing lists not producing too many bugs only taking on challenges which can be handled and the skill in judging your own abilities You will also need to have an understanding of the concepts of version control specifically those relating to Sub version The SVN book at http svnbook red bean com contains all the version control information you will need After a number of patches have been submitted and accepted any of the relax
210. formation from previous parameter positions a more comprehensive geometric description of the curvature of the space can be exploited by the algorithm for more efficient optimisation The best and most comprehensive description of the space is given by the quadratic ap proximation of the topology which is generated from the combination of the function value the gradient and the Hessian From the second order Taylor series expansion the quadratic model of the space is f 0 2 amp feta V fy ia T V fkr 6 27 2 where V fy is the Hessian which is the symmetric matrix of second partial derivatives of the function at the position 0 As the Hessian is computationally expensive a number of optimisation algorithms try to approximate it To produce the gradient and Hessian required for model free optimisation a large chain of first and second partial derivatives needs to be calculated Firstly the partial derivatives of the spectral density functions 6 7 and 6 8 are necessary Then the partial derivatives of the relaxation equations 6 3a to 6 3c followed by the NOE equation 6 6 are needed Finally the partial derivative of the chi squared formula 6 25 is required These first and second partial derivatives as well as those of the components of the Brownian diffusion correlation function for non isotropic tumbling are presented in Chapter 8 Optimisation algorithms Prior to minimisation all optimisation algorithms investigat
211. gle yellow block for that residue The Hessian for the model free model is simply the sub matrix for the residue 7 coloured yellow 8 5 The value gradient and Hessian dependency chain The dependency chain which was outlined in the model free chapter that the chi squared function is dependent on the transformed relaxation equations which are dependent on the relaxation equations which themselves are dependent on the spectral density functions combine with the values gradients and Hessians to create a complex web of dependencies The relationship between all the values gradients and Hessians are outlined in Figure 8 3 8 6 The y value gradient and Hessian 8 6 1 The x value As was presented in Equation 6 1 on page 31 the x value is i QR 2 e SOY 8 15 i 1 t where the summation index 7 ranges over all the relaxation data of all residues used in the analysis 8 6 THE x VALUE GRADIENT AND HESSIAN 63 oD OF 05 IAT 03 Residue number Figure 8 2 The model free Hessian kite a demonstration of the construction of the model free Hessian V x for the global model For each residue i a different matrix Vx is constructed The first element of the matrix represented by the two symbols 0D the red block is the sub matrix of chi squared second partial derivatives with respect to the diffusion tensor parameters 2 and Dg The orange blocks are the sub matrices of chi square
212. gs can be used to select the same data type Patterns used for matching for specific data types are listed below 182 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS This is a short description of python regular expression for more information see the regular expression syntax section of the Python Library Reference Some of the regular expression syntax used in this function is A sequence or set of characters to match to a single character For example Ss 2 will match both S2 and s2 7 Match the start of the string Match the end of the string For example Ss 2 will match s2 but not S2f or s2s Match any character xx Match the character x any number of times for example x will match as will XXXXX 6 Match any sequence of characters of any length Importantly do not supply a string for the data type containing regular expression The regular expression is implemented so that various strings can be supplied which all match the same data type Minimisation statistic data type string matching patterns Chi squared statistic chi Cc hi2 or Cc hi Ss quare Iteration count iter Ii ter Function call count f count F _ Cc ount Gradient call count g_count Ggl L _ Cc ount Hessian call count h_count Hh _ Cc ount NOE cal
213. gt cese co m eR RR RR 12 2 2 8 Installation on MS Windows 12 2 24 Installation on Mac OS X co2o oooooooconsr s ss 13 22 5 Installation am your ES o e eas s iie eek ged we Ro Rog wae 13 2 2 6 Running a non compiled version o 00005 13 me Optional programi lt es s sa sby s pa x kom ER ee es 13 Lol SPACE CC 13 uae APSO N o he ee el EU a OE ee 13 oe or oora ea eae Ge gt eB ee ie oe oa ae ed 14 2 MEI CL 14 o a ack a a ee SO ee og WO eh ee ee es eee Taari 14 230 Modeled 0 22 auo oom ew ee RE RR Rer we a 14 ii Open source infrastructure 3 1 The relax web sites 3 2 The mailing lists 3 2 1 relax announce 3 2 2 relax users 3 2 8 relax devel 3 2 4 relax commits 3 2 5 Replying to a message Reporting bugs Latest sources the relax repositories BIER ee te ea xb ae Sa The relax distribution archives 3 3 3 4 3 5 3 6 Calculating the NOE MEDIO s uude mono Rom es The sample script Initialisation of the data pipe Loading the data Setting the errors Unresolved residues The NOR coo taaa Rz Viewing the results 4 1 4 2 4 3 4 4 4 5 4 6 AT 4 8 Relaxation curve fitting Dubroduecbeon s g d oes kk The sample script Initialisation of the data pipe and loading of the data The rest of the setup 5 1 5 2 5 3 5 4 5 5 5 6 5 7 Model free analysis TREO MDC 6 1 1 The chi squared function x 0 6 1 2 The transformed relaxation equations R 0 6 1 3 The relaxation equation
214. h for each simulation to generate initial estimates however this is extremely computationally expensive For the case where values are calculated rather than minimised this step should be skipped although the results will be unaffected if this is accidentally run 6 Each simulation requires minimisation or calculation The same techniques as used in step 2 excluding the grid search when minimising should be used for the simulations 7 Failed simulations are removed using the techniques of model elimination 8 The model parameter errors are calculated from the distribution of simulation param eters Monte Carlo simulations can be turned on or off using functions within this class Once the function for setting up simulations has been called simulations will be turned on The effect of having simulations turned on is that the functions used for minimisation grid search minimise etc or calculation will only affect the simulation parameters and not the model parameters By subsequently turning simulations off using the appropriate function the functions used in minimisation will affect the model parameters and not the simulation parameters An example for model free analysis which includes only the functions required for imple menting the above steps is relax gt grid_search inc 11 Step 2 relax gt minimise newton Step 2 relax gt monte_carlo setup number 500 Step 3 relax gt monte_carlo create_data method
215. h token can be composed of multiple elements separated by the character and each individual element can either be a number which must be an integer in string format a name or a range of numbers separated by the character Negative numbers are supported The full id string specification is jmol_namej jres_idj jres_idj jres_idj Qjatom_idj jatom_idj jatom_idj 310 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS where the token elements are jmol_name the name of the molecule res_id the residue identifier which can be a number name or range of numbers atom_id the atom or spin system identifier which can be a number name or range of numbers If one of the tokens is left out then all elements will be assumed to match For example if the string does not contain the character then all molecules will match the string Regular expression can be used to select spins For example the string H will select the protons F H2 H98 10 2 THE LIST OF FUNCTIONS 311 10 2 115 residue number Synopsis Function for numbering residues Defaults residue number self res id None number None Keyword Arguments res_id The residue identification string corresponding to a single residue number The new residue number Description This function simply allows residues to be numbered The new number cannot correspond to an existing residue Exa
216. he atom or spin system identifier which can be a number name or range of numbers If one of the tokens is left out then all elements will be assumed to match For example if the string does not contain the character then all molecules will match the string Regular expression can be used to select spins For example the string H will select the protons F H2 H98 10 2 THE LIST OF FUNCTIONS 213 10 2 45 molecule name Synopsis Function for naming a molecule Defaults molecule name self mol_id None name None Keyword Arguments mol_id The molecule identification string corresponding to one or more molecules name The new molecule name Description This function simply allows molecules to be named or renamed Examples To rename the molecule Ap4Aase to Inhib Ap4Aase type relax gt molecule name Ap4Aase Inhib Ap4Aase relax molecule name mol_id Ap4Aase name Inhib Ap4Aase This assumes the molecule Ap4Aase already exists Identification string documentation The identification string is composed of three components the molecule id token begin ning with the character the residue id token beginning with the character and the atom or spin system id token beginning with the character Each token can be composed of multiple elements separated by the character and each individual element can either be
217. he spheroid The single dot product of the spheroid is defined as 6 XH 9D 8 205 where XH is a unit vector parallel to the XH vector i is a unit vector parallel to the unique axis of the diffusion tensor and can be expressed using the spherical angles where 0 is the polar angle and is the azimuthal angle as m sin cos D sindsing 8 206 cos 0 8 14 2 The dot product gradient of the spheroid The partial derivative of the dot product with respect to the orientational parameter O is 06 cum lt gt 0D OX H lt 9 XH 9 XAL 9 2p l a0 00 8 207 Because the XH bond vector is constant and not dependent on the spherical angles its derivative is zero Therefore E 06 gt 0D y XH OD OD 8 208 The D gradient The partial derivatives of the unit vector D with respect to the spherical angles are aD cos cos Y ag 95 O sin pl 8 209a sind ae sin 0 sin Y Et sin8cos 8 209b Og 0 8 14 3 The dot product Hessian of the spheroid The second partial derivative of the single spheroidal dot product 6 with respect to the orientational parameters D and O is eae 9 00 00 09 09 8 210 X38 A 8 14 SPHEROIDAL DOT PRODUCT DERIVATIVES 117 The i Hessian The second partial derivatives of the unit vector D with respect to the spherical angles are IS sin cos Y E sin sing 8 211a cos 0 a
218. he upper limit of 200 ns on Tm prevents the parameter from heading towards infinity when model failure occurs see Chapter This can significantly decrease the computation time To isolate the prolate spheroid the constraint 1 Da gt 0 6 46 1 Da 2 0 6 47 Dependent on the model optimised the matrix A and vector b are constructed from combinations of the above linear constraints Diagonal scaling Model scaling can have a significant effect on the optimisation algorithm a poorly scaled model can cause certain techniques to fail When two parameters of the model lie on very different numeric scales the model is said to be poorly scaled For example in model free analysis the order of magnitude of the order parameters is one whereas for the internal correlation times the order of magnitude is between le to 1e78 Most effected are the trust region algorithms the multidimensional sphere of trust will either be completely ineffective against the correlation time parameters or severely restrict optimisation in the order parameter dimensions In model free analysis the significant scaling disparity can even cause failure of optimisation due to amplified effects of machine precision Therefore the model parameters need to be scaled This can be done by supplying the optimisation algorithm with the scaled rather than unscaled parameters When the chi squared function gradient and Hessian are called the vector is th
219. he value you would like to supply is R1 out Various methods exist for supplying this argument Firstly you could simply type R1 out into the correct position in the argument list Secondly you can type file R1 out The power of this second option is that argument order is unimportant Therefore if you would like to change the default value of the very last argument you don t have to supply values for all other arguments The only catch is that standard arguments must come before the keyword arguments 1 2 3 User functions For standard data analysis a large number of specially tailored functions called user func tions have been implemented These are accessible from the relax prompt by simply typing the name of the function An example is help An alphabetical listing of all accessible user functions together with full descriptions is presented later in this manual A few special objects which are available within the prompt are not actually functions These objects do not require brackets at their end for them to function For example to exit relax type relax gt exit Another special object is that of the function class This object is simply a container which holds a number of user functions You can access the user function within the class by typing the name of the class then a dot followed by the name of the user function An example is the user function for reading relaxation data out of a file and loa
220. herwise 009 V c 0 AF ui In 6 32 0 is the parameter vector 4 is the Augmented Lagrangian function k is the current iteration of the Method of Multipliers A are the Lagrange multipliers which are positive factors such that at the minimum 6 Vf 0 A Vc 8 uy gt 0 is the penalty parameter which decreases to zero as k oo J is the set of inequality constraints and c 0 is an individual constraint value The Lagrange multipliers are updated using the formula AFA mex e 8 15 0 for all i J 6 34 The gradient of the Augmented Lagrangian is veGu vi A vey 635 k ie2te 0 uA e and the Hessian is a V3e4 0 A ur V24 0 O at k i 3 c 0 uy AF Hk v 6 36 The Augmented Lagrangian algorithm can accept any set of three arbitrary constraint functions c 0 Vc 0 and V c 0 When given the current parameter values c 0 returns a vector of constraint values whereby each position corresponds to one of the model pa rameters The constraint is defined as c gt 0 The function Vc 0 returns the matrix of constraint gradients and V c 0 is the constraint Hessian function which should return the 3D matrix of constraint Hessians A more specific set of constraints accepted by the Method of Multipliers are bound con straints These are defined by the function lt 0 lt u 6 37 where and u are the vectors of lower and upper bounds respectively and 0 i
221. his function is used for model validation to eliminate or reject models prior to model selection Model validation is a part of mathematical modelling whereby models are either accepted or rejected Empirical rules are used for model rejection and are listed below However these can be overridden by supplying a function The function should accept five arguments a string defining a certain parameter the value of the parameter the minimisation instance ie the residue index if the model is residue specific and the function arguments If the model is rejected the function should return True otherwise it should return False The function will be executed multiple times once for each parameter of the model The args keyword argument should be a tuple a list enclosed in round brackets and will be passed to the user supplied function or the inbuilt function For a description of the arguments accepted by the inbuilt functions see below Once a model is rejected the select flag corresponding to that model will be set to False so that model selection or any other function will then skip the model Local 7 model elimination rule The local Tm in some cases may exceed the value expected for a global correlation time Generally the Tm value will be stuck at the upper limit defined for the parameter These models are eliminated using the rule Tm ZC 176 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS The default value of c is
222. ich data type to set values to therefore various data_type strings can be used to select the same data type Patterns used for matching for specific data types are listed below This is a short description of python regular expression for more information see the regular expression syntax section of the Python Library Reference Some of the regular expression syntax used in this function is A sequence or set of characters to match to a single character For example Ss 2 will match both S2 and s2 7 Match the start of the string Match the end of the string For example Ss 2 will match s2 but not S2f or s2s Match any character 356 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS xx Match the character x any number of times for example x will match as will xxxxx Match any sequence of characters of any length Importantly do not supply a string for the data type containing regular expression The regular expression is implemented so that various strings can be supplied which all match the same data type Model free data type string matching patterns Data type Object name Patterns Local Tin local_tm L1 ocal tm Order parameter S s2 Ss 2 Order parameter 8 s2f Ss 2 Order parameter S s2s 7 Ss 2s Correlation time 7 te tef Correlation time Tf
223. imilar to that of the steepest descent algorithm In changing the trust region radius the exact solutions to 6 30 map out a curved trajectory which starts parallel to the gradient for small radii The end of the trajectory which occurs for radii greater than the step length is the bottom of the quadratic model The dogleg algorithm attempts to follow a similar path by first finding the minimum along the gradient and then finding the minimum along a trajectory from the current point to the bottom of the quadratic model The minimum along the second path is either the trust region boundary or the quadratic solution The matrix By of 6 30 can be the BFGS matrix the unmodified Hessian or a Hessian modified to be positive definite Another trust region algorithm is Steihaug s modified conjugate gradient approach Steihaug 1983 For each step k an iterative technique is used which is almost iden tical to the standard conjugate gradient procedure except for two additional termination conditions The first is if the next step is outside the trust region the second is if a direction of zero or negative curvature is encountered An almost exact solution to 6 30 can be found using an algorithm described in Nocedal and Wright 1999 This exact trust region algorithm aims to precisely find the minimum of the quadratic model mz of the space within the trust region Aj Any matrix By can be used to construct the quadratic model However the technique
224. in by using the pipe switch user function to jump between pipes The flow of data through relax can be thought of as travelling through these pipes User functions exist to transfer data between these pipes and other functions combine data from multiple pipes into one or vice versa The simplest invocation of relax would be the 1 2 HOW TO USE RELAX 7 creation of a single data pipe and with the data being processed as it is passing through this pipe The primary method for creating a data pipe is through the user function pipe create For example relax pipe create m1 mf will create a model free data pipe labelled mi The following is a table of all the types which can be assigned to a data pipe Data pipe type Description jw Reduced spectral density mapping mf Model free data analysis N state N state model of domain motions noe Steady state NOE calculation relax fit Relaxation curve fitting srls SRLS analysis Currently the NOE calculation relaxation curve fitting model free analysis and reduced spectral density mapping features of relax are implemented if this documentation is out of date then you may be able to do a lot more 1 2 7 Scripting What ever is done within the prompt is also accessible through scripting Just type your commands into a text file and then at the terminal type relax your_script An example of a simple script which will minimise th
225. in the character then all molecules will match the string Regular expression can be used to select spins For example the string H will select the protons H H2 H98 328 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 128 spin create Synopsis Function for creating a new spin Defaults spin create self spin num None spin_ name None res_id None Keyword Arguments spin num The spin number spin name The name of the spin res id The residue ID string identifying the residue to add the spin to Description This function will add a new spin data container to the relax data storage object The same spin number cannot be used more than once Examples The following sequence of commands will generate the sequence 1 C4 2 C9 3 C15 relax spin create 1 C4 relax spin create 2 C9 relax spin create 3 C15 Identification string documentation The identification string is composed of three components the molecule id token begin ning with the character the residue id token beginning with the character and the atom or spin system id token beginning with the character Each token can be composed of multiple elements separated by the character and each individual element can either be a number which must be an integer in string format a name or a range of numbers separated by the character Negative numbers are su
226. in the pdb file spin_id The spin identification string Description The following files are created dir mfin dir mfdata 254 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS dir mfpar dir mfmodel dir run sh The file dir run sh contains the single command modelfree4 i mfin d m data p mfpar m mfmodel o mfout e out which can be used to execute modelfree4 If you would like to use a different Modelfree executable file change the keyword argument binary to the appropriate file name If the file is not located within the environment s path include the full path infront of the binary file name 10 2 THE LIST OF FUNCTIONS 255 10 2 69 palmer execute Synopsis Function for executing Modelfree4 Defaults palmer execute self dir None force False binary modelfree4 Keyword Arguments dir T he directory to place the files force A flag which if set to True will cause the results file to be overwritten if it already exists binary The name of the executable Modelfree program file Description Modelfree 4 will be executed as modelfree4 i mfin d mfdata p mfpar m mfmodel o mfout e out If a PDB file is loaded and non isotropic diffusion is selected then the file name will be placed on the command line as s pdb_file_name If you would like to use a different Modelfree executable file change the keyword argument binary to th
227. ind the minimum along each conjugate direction both the backtracking and Mor and Thuente auxiliary step length selection algorithms will be tested with the CG algorithms Hessian modifications The Newton search direction used in both the line search and trust region methods is dependent on the Hessian being positive definite for the quadratic model to be convex so that the search direction points sufficiently downhill This is not always the case as saddle points and other non quadratic features of the space can be problematic Two classes of algorithms can be used to handle this situation The first involves using the conjugate gradient method as a sub algorithm for solving the Newton problem for the step k The Newton CG line search algorithm described above is one such example The second class involves modifying the Hessian prior to or at the same time as finding the Newton step to guarantee that the replacement matrix Bj is positive definite The convexity of Dj is ensured by its eigenvalues all being positive The performance of two of these methods within the model free space will be investigated The first modification uses the Cholesky factorisation of the matrix By initialised to the true Hessian to test for convexity Algorithm 6 3 of Nocedal and Wright 1999 If fac torisation fails the matrix is not positive definite and a constant 7j times the identity matrix J is then added to Bj The constant originates from the Robbins norm
228. ing the command load file The centre of mass residue COM is displayed using the commands select resn COM show dots sele color blue sele The axes of the diffusion tensor the residue AXS is displayed using the commands select resn AXS hide sele show sticks sele 278 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS color cyan sele label sele name The simulation axes the residues SIM are displayed using the commands select resn SIM colour cyan sele 10 2 THE LIST OF FUNCTIONS 279 10 2 91 pymol vector_dist Synopsis Function displaying the PDB file representation of the XH vector distribution Defaults pymol vector_dist self file XH_dist pdb Keyword Arguments file The name of the PDB file containing the vector distribution Description A PDB file of the macromolecule must have previously been loaded as the vec tor distribution will be overlain with the macromolecule within PyMOL The PDB file containing the vector distribution must be created using the complementary pdb create_vector_dist user function The vector distribution PDB file is read in using the command load file 280 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 92 pymol view Synopsis Function for viewing the collection of molecules extracted from the PDB file Defaults pymol view self Example relax gt pymol view
229. ing with the character Each token can be composed of multiple elements separated by the character and each individual element can either be a number which must be an integer in string format a name or a range 208 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS of numbers separated by the character Negative numbers are supported The full id string specification is jmol_namej res id jres_idj jres_idj Qjatom_idj atom id jatom_idj where the token elements are jmol_name j the name of the molecule res_id the residue identifier which can be a number name or range of numbers atom_id the atom or spin system identifier which can be a number name or range of numbers If one of the tokens is left out then all elements will be assumed to match For example if the string does not contain the character then all molecules will match the string Regular expression can be used to select spins For example the string H will select the protons H H2 H98 10 2 THE LIST OF FUNCTIONS 209 10 2 42 molecule create Synopsis Function for creating a new molecule Defaults molecule create self mol_name None Keyword Arguments mol_name The name of the molecule Description This function will add a new molecule data container to the relax data storage object The same molecule name cannot be used more than once Examples T
230. into any molecular viewer There are four different types of residue within the PDB The pivot point is represented as as a single carbon atom of the residue PIV The cone consists of numerous H atoms of the residue CON The average pivot CoM vector is presented as the residue AVE with one carbon atom positioned at the pivot and the other at the head of the vector after scaling by the scale argument Finally if Monte Carlo have been performed there will be multiple MCC residues representing the cone for each simulation and multiple MCA residues representing the varying average pivot CoM vector for each simulation 244 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS To create the diffusion in a cone PDB representation a uniform distribution of vectors on a sphere is generated using spherical coordinates with the polar angle defined from the average pivot CoM vector By incrementing the polar angle using an arccos distribution a radial array of vectors representing latitude are created while incrementing the azimuthal angle evenly creates the longitudinal vectors These are all placed into the PDB file as H atoms and are all connected using PDB CONECT records Each H atom is connected to its two neighbours on the both the longitude and latitude This creates a geometric PDB object with longitudinal and latitudinal lines representing the filled cone 10 2 THE LIST OF FUNCTIONS 245 10 2 61 n state model number
231. ion The code belonging to this section initialises the program processes the command line arguments and determines what mode the program will be run in including the choice of the UI UI The user interface Currently the prompt and the script are the only user interfaces into relax There are other program modes which are not part of a user interface These include the test mode in which the program instantly exits and threading mode which is spawned by a parent process and waits for commands In the future a graphical user interface GUI a web based interface or any other type of interface may be added Functional code This code is the main part of the program It includes anything which does not fit into the other sections and comprises the generic code the specific code and the specific setup code used as an interface between the two Number crunching The computationally expensive code belongs in this section Program state The state of the program is contained within the data structure self relax data which is accessible from all parts of the program It should only be read by the generic specific and number crunching code Only the generic and specific code should change its contents 9 6 2 The major components of relax Each of the boxes in Figure 9 1 represents a different grouping of code relax The top level module This initialises the entire program tests the dependencies places the custom errors into the module buil
232. ion class model_free type relax gt model_free The dot character at the end is essential After hitting the TAB key you should see something like relax gt model_free model_free _class__ model_free _doc__ model_free __init__ model_free __module__ model_free _relax__ model_free __relax_help _ model_free create_model model_free delete model_free remove_tm model_free select_model relax gt model_free All the objects beginning with an underscore are hidden they contain information about the function class and should be ignored From the listing the user functions copy create_model delete remove_tm and select_model contained within model_free are all visible 1 2 6 The data pipe Within relax all user functions operate on data stored within the current data pipe This pipe stores data is input processed or output as user functions are called There are different types of data pipe for different analyses e g a reduced spectral density mapping pipe a model free pipe an exponential curve fitting pipe etc Multiple data pipes can be created within relax and various operations performed in sequence on these pipes This is useful for operations such as model selection whereby the function model selection can operate on a number of pipes corresponding to different models and then assign the results to a newly created pipe When running relax you choose which pipe you are currently
233. ion or scripting Example To reinitialise the Molmol instance relax gt molmol command InitAll yes 10 2 THE LIST OF FUNCTIONS 217 10 2 48 molmol macro_exec Synopsis Function for executing Molmol macros Defaults molmol macro_exec self data_type None style classic colour start None colour end None colour_list None Keyword Arguments data type The data type to map to the structure style The style of the macro colour start The starting colour either an array or string of the linear colour gradient colour_end The ending colour either an array or string of the linear colour gradient colour list The list of colours to match the start and end strings Description This function allows residues specific values to be mapped to a structure through Molmol macros Currently only the classic style which is described below is available Colour The values are coloured based on a linear colour gradient which is specified through the colour_start and colour_end arguments These arguments can either be a string to identify one of the RGB red green blue colour arrays listed in the tables below or you can give the RGB vector itself For example colour_start white and colour_start 1 0 1 0 1 0 both select the same colour Leaving both arguments at None will select the default colour gradient which for each type of analysis is described below When supplying the colours a
234. is backed up daily to http svn gna org daily relax dump gz 3 5 News Summaries of the latest news on relax can be found on the relax web site https gna org projects relax However more information can be found at the dedicated news page https gna org news group relax 3 6 The relax distribution archives The relax distribution archives the files to download to install relax can be found at http download gna org relax If a compiled binary distribution for your architecture 18 CHAPTER 3 OPEN SOURCE INFRASTRUCTURE does not exist you are welcome to create this distribution yourself and submit it for in clusion in the relax project To do this a number of steps are required Firstly the code to each relax release or version resides in the tags directory of the relax repository To check out version 1 2 0 for example type svn co svn svn gna org svn relax tags 1 2 0 relax Again the sources are available through HTTP by typing svn co http svn gna org svn relax tags 1 2 0 relax The binary distribution can then be created for your architecture by shifting to the main directory of the checked out sources and typing cd relax scons binary dist At the end SCons will attempt to make a GPG signature for the newly created archive However this will fail as the current relax private GPG key is not available for secu rity reasons If the SCons command fails excluding the GPG signing please submit a bug repor
235. is given the file will be placed in the current working directory The parameter argument should be a string Examples To write the CSA values for the run m1 to the file csa txt type relax gt value write mi CSA csa txt relax gt value write run m1 param CSA file csa txt To write the NOE values from the run noe to the file noe type relax gt value write noe noe noe out relax gt value write noe param noe file noe out relax gt value write run noe param noe file noe out relax gt value write run noe param noe file noe out force True 376 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Regular expression The python function match which uses regular expression is used to determine which data type to set values to therefore various data_type strings can be used to select the same data type Patterns used for matching for specific data types are listed below This is a short description of python regular expression for more information see the regular expression syntax section of the Python Library Reference Some of the regular expression syntax used in this function is A sequence or set of characters to match to a single character For example Ss 2 will match both S2 and s2 7 Match the start of the string Match th
236. is includes C module compilation manual creation distribution creation and cleaning up and removing certain files The file sconstruct in the base relax directory which consists of python code directs the operation of SCons for the various functions 9 5 1 SCons help Multiple functions have been built into the sconstruct script and the modules of the scons directory Each of these can be selected by specifying different targets when running SCons A description of each target is given by the SCons help system which is accessible by typing scons help in the base relax directory 9 5 2 C module compilation As described in the installation chapter typing scons in the base directory will create the shared objects or dll files which are imported into Python as modules 9 5 3 Compilation of the user manual PDF version To create the PDF version of the relax user manual type scons user_manual_pdf in the base directory SCons will then run a series of shell commands to create the manual from the IXTEX sources located in the docs latex directory This is dependent on the programs latex makeindex dvips and ps2pdf being located within the environment s path 9 5 4 Compilation of the user manual HTML version The HTML version of the relax user manual is made by typing scons user_manual_html in the base directory One command calling the program latex2html wil
237. ise is meaningless in this sample script as the NOE values are directly calculated rather than optimised 4 4 Loading the data The first thing which need to be completed prior to any residue specific command is to generate the sequence from a PDB file In this case the command structure read_pdb name Ap4Aase new 3 pdb will load the PDB file Ap4Aase_new_3 pdb into relax Then structure load spins spin id QN will generate the molecule residue and spin sequence for the current data pipe In this situation there will be a single spin system per residue generated corresponding to the backbone amide nitrogens Although the PDB coordinates have been loaded into the program the structural information serves no purpose when calculating NOE values 4 5 SETTING THE ERRORS 21 The next two commands noe read file ref list spectrum_type ref noe read file sat list spectrum_type sat load the peak heights of the reference and saturated NOE experiments although the volume could be used instead The keyword argument format has not been specified hence the default format of a Sparky peak list saved after typing 1t is assumed If the program XEasy was used to analyse the spectra the argument format xeasy is necessary The first column of the file should be the Sparky assignment string and it is assumed that the 4 column contains either the peak height or peak volume If you have any other fo
238. ised runs then the minimisation statistics chi squared value iteration count function count gradient count and Hessian count will be reset to None Examples To load CSA values for the run m1 from the file csa_values in the directory data type any of the following relax value read m1 CSA data csa value relax value read m1 CSA data csa value 0 1 2 3 None 1 relax value read run mi param CSA file data csa_value num_col 0 name_col 1 data_col 2 error col 3 sep None 360 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Regular expression The python function match which uses regular expression is used to determine which data type to set values to therefore various data_type strings can be used to select the same data type Patterns used for matching for specific data types are listed below This is a short description of python regular expression for more information see the regular expression syntax section of the Python Library Reference Some of the regular expression syntax used in this function is A sequence or set of characters to match to a single character For example Ss 2 will match both S2 and s2 Match the start of the string Match the end of the string For example Ss 2 will match s2 but not S2f or s2s lt Match any character xx
239. ithms and Monte Carlo simulations built into relax are utilised then the relax script will need to construct the chi squared distributions from the results as this is not yet coded into relax The specific step up hypothesis testing model selection of Mandel et al 1995 is available through the model_selection user function Coding the rest of the protocol into a script should be straightforward 6 6 The diffusion seeded paradigm Ever since the original Lipari and Szabo papers Lipari and Szabo 1982a b the question of how to obtain the model free description of the system has followed the route in which the diffusion tensor is initially estimated Using this rough estimate the model free models are optimised for each spin system 1 the best model selected and then the global model G of the diffusion model D with each model free model is optimised This procedure is then repeated using the diffusion tensor parameters of G as the initial input Finally the global model is selected The full protocol is illustrated in Figure 6 2 6 6 THE DIFFUSION SEEDED PARADIGM 51 Initial estimate oe CR Optimise Optimise Optimise Optimise Optimise mi m2 m3 m4 m5 Monte Monte Monte Monte Monte Carlo sims Carlo sims Carlo sims y Carlo sims Carlo sims No No Final model Optimise global a No Convergence Yes pud Figure 6 1 A schematic of the model free optimisation protocol of Mandel et al 1995 This speci
240. l type relax gt spin copy spin_from 01d mol 1 spin_to New molQ5 To copy the spin data of spin 1 from the data pipe m1 to m2 assuming the current data pipe is m1 type relax gt spin copy spin_from 1 pipe_to m2 relax gt spin copy pipe_from m1 spin from 01 pipe_to m2 spin_to 1 10 2 THE LIST OF FUNCTIONS 327 Identification string documentation The identification string is composed of three components the molecule id token begin ning with the character the residue id token beginning with the character and the atom or spin system id token beginning with the character Each token can be composed of multiple elements separated by the character and each individual element can either be a number which must be an integer in string format a name or a range of numbers separated by the character Negative numbers are supported The full id string specification is jmol_namej jres_idj jres_idj jres_idj Qjatom_idj jatom id jatom_idj where the token elements are jmol_name the name of the molecule res_id the residue identifier which can be a number name or range of numbers atom_id the atom or spin system identifier which can be a number name or range of numbers If one of the tokens is left out then all elements will be assumed to match For example if the string does not conta
241. l Sxyl Sxzl Syzl Szz2 Sxxyy2 Sxy2 Sxz2 Syz2 Szz3 Sxxyy3 Sxy3 Sxz3 Syz8 Leve ees 0 2 SzzN SxxyyN SxyN SxzN SyzN The relationships between the geometric and unitary basis sets are 148 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Szz Sxx Syy Sxxyy Sxx Syy The SVD values and condition number are dependendent upon the basis set chosen 10 2 THE LIST OF FUNCTIONS 149 10 2 10 angle diff frame Synopsis Calculate the angles defining the XH bond vector within the diffusion frame Defaults angle diff frame self Description If the diffusion tensor is isotropic then nothing will be done If the diffusion tensor is axially symmetric then the angle o will be calculated for each XH bond vector If the diffusion tensor is asymmetric then the three angles will be calculated 150 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 11 calc Synopsis Function for calculating the function value Defaults calc self verbosity 1 Keyword Arguments verbosity The amount of information to print to screen Zero corresponds to minimal output while higher values increase the amount of output The default value is 1 10 2 THE LIST OF FUNCTIONS 151 10 2 12 consistency_tests set_frq Synopsis Function for selecting which relaxation data to use in the consistency tests Defaults consistency_tests set_frq self frq None Keyword Arguments frq The spect
242. l be executed which will create HTML pages from the IATEX sources 9 5 THE SCONS BUILD SYSTEM 131 9 5 5 Compilation of the API documentation HTML version The HTML version of the relax API documentation is made by typing scons api manual html in the base directory The programs Epydoc and Graphviz are required for creat ing this documentation The resultant HTML pages will be located in the director docs api index html 9 5 6 Making distribution archives Two types of distribution archive can be created from the currently checked out sources the source and binary distributions To create the source distribution type scons source_dist whereas to create the binary distribution whereby the C modules are compiled and the resultant shared objects are included in the bzipped tar file type scons binary_dist If a binary distribution does not exist for your architecture feel free to create it yourself and contribute the archive to be included on the download pages To do this you will need to check out the appropriate tagged branch from the relax subversion repository If the current stable release is called 1 2 3 check out that branch by typing svn co svn ssh bugmanOsvn gna org svn relax tags 1 2 3 relax replacing bugman with your user name if you are a relax developer otherwise typing svn co svn svn gna org svn relax tags 1 2 3 relax Then build the binary distribution and send a message to the re
243. l to permit linking proprietary applications with the library If this is what you want to do use the GNU Library General Public License instead of this License 388 CHAPTER 11 LICENCE Bibliography Abragam A 1961 The Principles of Nuclear Magnetism Clarendon Press Oxford Bloembergen N Purcell E M and Pound R V 1948 Relaxation effects in nuclear magnetic resonance absorption Phys Rev 73 7 679 712 Broyden C G 1970 The Convergence of a Class of Double rank Minimization Algo rithms 1 General Considerations J Inst Maths Applics 6 1 76 90 Chen J Brooks 3rd C L and Wright P E 2004 Model free analysis of protein dynamics assessment of accuracy and model selection protocols based on molecular dynamics simulation J Biomol NMR 29 3 243 257 Clore G M Szabo A Bax A Kay L E Driscoll P C and Gronenborn A M 1990 Deviations from the simple 2 parameter model free approach to the interpretation of N 15 nuclear magnetic relaxation of proteins J Am Chem Soc 112 12 4989 4991 d Auvergne E J 2006 Protein dynamics a study of the model free analysis of NMR relaxation data PhD thesis Biochemistry and Molecular Biology University of Mel bourne http eprints infodiv unimelb edu au archive 00002799 d Auvergne E J and Gooley P R 2003 The use of model selection in the model free analysis of protein dynamics J Biomol NMR 25 1 25 39
244. lax development mail ing list If compilation does not work please submit a bug to the bug tracker system at https gna org bugs group relax detailing the relax version operation system ar chitecture and any other information you believe will help to solve the problem More information about donating binary distributions to the relax project is given in the open source infrastructure chapter 9 5 7 Cleaning up If the command scons clean is run in the base directory all Python byte compiled files pyc all C object files o and os all C shared object files so and any backup files with the ex tension bak are removed from all sub directories In addition any temporary ATEX compilation files are removed from the docs latex directory 132 CHAPTER 9 RELAX DEVELOPMENT 9 6 The core design of relax To enable flexibility the internal structure of relax is modular By construction the large collection of independent data analysis tools can be used individually and relatively easily by any new code implementing other forms of relaxation data analysis or even by other programs The core modular design of the program is shown in Figure 9 1 9 6 1 The divisions of relax s source code relax s source code can be divided into five major areas the initialisation code the user interface UI code the functional code the number crunching code and the code storing the program state Initialisat
245. llected at the same field strength have the same label 296 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Examples The following commands will read the protein NOE relaxation data collected at 600 MHz out of a file called noe 600 out where the residue numbers residue names data errors are in the first second third and forth columns respectively relax relax_data read NOE 600 599 7 1e6 noe 600 out relax relax data read ri label NOE frq label 600 frq 600 0 1e6 file noe 600 0ut The following commands will read the R4 data out of the file r2 out where the residue numbers residue names data errors are in the second third fifth and sixth columns respectively The columns are separated by commas relax relax data read R2 800 MHz 8 0 1e8 r2 out 1 2 4 5 relax relax data read ri label R2 frq_label 800 MHz frq 8 0 1e8 file r2 out res num col 1 res name col 2 data_col 4 error col 5 sep The following commands will read the R4 data out of the file r1 out where the columns are separated by the symbol relax relax data read R1 300 300 1 1e6 ri out sep 10 2 THE LIST OF FUNCTIONS 297 10 2 105 relax data write Synopsis Function for writing R1 R4 or NOE relaxation data to a file Defaults relax data write self ri_label None frq_label None file None dir None for
246. los uo Dae roba a a Romo ago 311 10 2 11865ulis display o c c sa o Roto RR x RR ERS R m mg 313 LI NEL Inc P ew he bo Ee ws Be Bode 314 102 a O a BR Gow ees Pee EU NOEL 315 A en ei ea eG eae 0T 316 10 2 1288lect read i cse RR era Pe e RR RB RO 317 DU TARR reverse PIC P x 319 MOD Na i Pr a a 320 AA poe o s 2d oie c9 xR Po R EOE ono ROR T 9 30 Xo Xo vox 9 321 10 2 124eqneuce display 2 2 kso ow RR ERR EUR ea 322 IS NEU HE s PC IT 323 10 2 128e0q00eA ce Write eaa coo m 9m kom m m o m n Rom Rs 325 x CONTENTS V2 LZPDULBDDN 236g o dera SO eee eee bee eee eed 326 IEA LARES lt a Ea wid Se Geek eee ee Ra wee ds 328 E21 pin delete 2 2 dcs i a ark a a ek s 330 102 LSpHLEDSDIAN us dee ok ee a ee PO ee OS 332 TOS LSPpHLDDODES 2 9 mss AN 333 MPA us 2 ee we ee Be ew we we oe eo 335 eZ ASEO EC he ee a ee e e ee 337 al Cr 338 10 2 13 tructure create diff tensor pdb o 340 10 2 136tructure create vector dist lle 342 J0 2 1238teucture load spins na domom RR RR RE RR E a a 343 10 2 DaSteucture read pab 2s uo uk uox o emo Oe RO Xs 344 IO a tanta a os s bea eo RE RO SHE RE Ree S ELE AR EU 345 10 2 148tcacture Ate DAD uus eee xk o Re cw e 347 IO IdbysbeH s e Ge euo oe a Se ee ee a Oe we dd a cem 348 10 2 142emMp ralure 2 we a a a ee 349 102 148 Ag CODY oscar a ea mov E Eee xoxo 350 102 144 m displa ace 9c nde RR Re ee Re eum TRO 355 a AAG ken lu uuu
247. ly set values together with the supplied value to calculate the new internal parameters For spheroidal diffusion when supplying multiple geometric parameters the set must belong to one of Um Da iso Da Um Dratio 1D Di Uus Diels where either 0 or both orientational parameters can be additionally supplied For ellipsoidal diffusion again when supplying multiple geometric parameters the set must belong to one of twi Das Dret Sao Da Dry Ts Dy Da where any number of the orientational parameters a 3 or y can be additionally supplied Diffusion tensor parameter string matching patterns 10 2 THE LIST OF FUNCTIONS Data type Global correlation time Tin Isotropic component of the diffusion tensor Diso Anisotropic component of the diffusion tensor Da Rhombic component of the diffusion tensor D Eigenvalue associated with the x axis of the diffusion diffusion tensor Dy Eigenvalue associated with the y axis of the diffusion diffusion tensor D Eigenvalue associated with the z axis of the diffusion diffusion tensor D Diffusion coefficient parallel to the major axis of the spheroid diffusion tensor D Diffusion coefficient perpendicular to the major axis of the spheroid diffusion tensor D Ratio of the parallel and perpendicular components of the spheroid diffusion tensor Dratio The first Euler angle of the ellipsoid diffusion tensor The second Euler angle of th
248. manual and the archives of the mailing lists The relax web site is hosted by the Gna project https gna org which is described as a central point for development distribution and maintenance of Libre Software Free Software projects relax is a registered Gna project and its primary Gna web site is https gna org projects relax This site contains many more technical details than the main web site 3 2 The mailing lists A number of mailing lists have been created covering different aspects of relax These include the announcement list the relax users list the relax development list and the relax committers list 3 2 1 relax announce The relax announcement list relax announce at gna org is reserved for important an nouncements about the program including the release of new program versions The amount of traffic on this list is relatively low If you would like to receive infor mation about relax you can subscribe to the list by vising the information page at https mail gna org listinfo relax announce Previous announcements can be viewed at https mail gna org public relax announce 15 16 CHAPTER 3 OPEN SOURCE INFRASTRUCTURE 3 2 2 relax users If you would like to ask questions about relax discuss certain features receive help or to communicate on any other subject related to relax the mailing list relax users at gna org is the place to post your message To subscribe to the list go to the
249. meter Tm Or Diso the variable k is equal to zero Therefore i 0 The single weight cy is equal to one and the single correlation time 79 is equivalent to the global tumbling time Tm given by 1 Tm 6Diso 6 21 This is diffusion equation presented in Bloembergen et al 1948 6 1 6 The model free models Extending the list of models given in Mandel et al 1995 Fushman et al 1997 Orekhov et al 1999 Korzhnev et al 2001 Zhuravleva et al 2004 the models built into relax include m0 6 22 0 m1 5 6 22 1 m2 S Te 6 22 2 m3 S Ree 6 22 3 mA 8 Te Rea 6 22 4 m5 S 52 rs 6 22 5 WB 4 TE Teh 6 22 6 AAS Fr Rd 6 22 7 m8 87 75 SF Ts Rex 6 22 8 m9 Rex 6 22 9 The parameter Re is scaled quadratically with field strength in these models as it is assumed to be fast In the set theory notation the model free model for the spin system i is represented by the symbol Through the addition of the local Tm to each of these 36 CHAPTER 6 MODEL FREE ANALYSIS models only the component of Brownian rotational diffusion experienced by the spin system is probed These models represented in set notation by the symbol T are tMO Tm tml Tm 8 im2 Tm S Te tm3 Tm 8 Res tm4 Tm 8 Te Rex tm5 Tm S S Ts tm6 Ins rush imd a8 S Ts Rez im8 Tm S 75 S Ts Rest m9 A tas Reg 6 1 7 Model free optimis
250. model free model elimination and model free model selection between models from m0 to m9 is modsel py The text of the script is Set the data pipe names pipes mO m1 m2 m3 m4 m5 m6 m7 m8 m9 Loop over the data pipe names for name in pipes print n n name 4 Create the data pipe 50 CHAPTER 6 MODEL FREE ANALYSIS pipe create name mf Reload precalculated results from the file mi results etc results read file results dir name Model elimination eliminate Model selection model_selection method AIC modsel_pipe aic Write the results state save save force True results write file results force True 6 4 2 The rest Please write me Until this section is completed please look at the sample script modsel py 6 5 The methodology of Mandel et al 1995 By presenting a systematic methodology for obtaining a consistent model free description of the dynamics of the system the manuscript of Mandel et al 1995 revolutionised the application of model free analysis The full protocol is presented in Figure 6 1 All of the data analysis techniques required for this protocol can be implemented within relax The chi squared distributions required for the chi squared tests are constructed by Modelfree4 from the Monte Carlo simulations If the optimisation algor
251. mple of the output after modifying the axes is shown in figure 4 1 24 CHAPTER 4 CALCULATING THE NOE Chapter 5 The R4 and R relaxation rates relaxation curve fitting 5 1 Introduction Relaxation curve fitting involves a number of steps including the loading of data the calculation of both the average peak intensity across replicated spectra and the standard deviations of those peak intensities selection of the experiment type optimisation of the parameters of the fit Monte Carlo simulations to find the parameter errors and saving and viewing the results To simplify the process a sample script will be followed step by step as was done with the NOE calculation 5 2 The sample script Script for relaxation curve fitting Create the rx data pipe pipe create rx relax_fit Load the backbone amide 15N spins from a PDB file structure read pdb Ap4Aase new 3 pdb Structure load spins spin id QN Load the peak intensities relax fit read file T2 ncyci list relax time 0 0176 relax fit read file T2 ncycib list relax time 0 0176 relax fit read file T2 ncyc2 list relax time 0 0352 relax fit read file T2 ncyc4 list relax time 0 0704 relax fit read file T2 ncyc4b list relax time 0 0704 relax fit read file T2 ncyc6 list relax time 0 1056 relax fit read file T2 ncyc9 list relax time 0 1584 relax fit read file T2 ncyc9b list relax time 0 1584 25 26 CHAPTER
252. mples The following sequence of commands will renumber the sequence 1 ALA 2 GLY 3 LYS to 101 ALA 102 GLY 103 LYS relax gt residue number 1 101 relax gt residue number 2 102 relax gt residue number 3 103 Identification string documentation The identification string is composed of three components the molecule id token begin ning with the character the residue id token beginning with the character and the atom or spin system id token beginning with the character Each token can be composed of multiple elements separated by the character and each individual element can either be a number which must be an integer in string format a name or a range of numbers separated by the character Negative numbers are supported The full id string specification is jmol_namej jres_idj jres_idj jres_idj Qjatom_idj atom id jatom_idj where the token elements are 312 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS jmol_name j the name of the molecule res_id the residue identifier which can be a number name or range of numbers atom_id the atom or spin system identifier which can be a number name or range of numbers If one of the tokens is left out then all elements will be assumed to match For example if the string does not contain the character then all molecules will match the string Regular expression
253. n Regular expression is allowed for example HE spin id The spin identification string struct index The index of the structure to extract bond vectors from which if set to None will cause all vectors to be extracted verbosity The amount of information to print to screen Zero corresponds to minimal output while higher values increase the amount of output The default value is 1 ave A flag which if True will cause all extracted bond vectors to be averaged If only one vector is extracted this argument will have no effect unit A flag which if True will cause the unit vector to calculated rather than the full length bond vector Description For a number of types of analysis bond vectors or unit bond vectors are required for the calculations This user function allows these vectors to be extracted from a loaded structure The bond vector will be that from the spin system loaded in relax to the bonded atom specified by the attached argument For example if attached is set to H all attached protons will be searched for If set to CA all atoms named CA in the structure will be searched for The extraction of vectors can occur in a number of ways For example if an NMR structure with N models is loaded or if multiple structures from any source of the same compound are loaded there are three options for extracting the bond vector Firstly the bond vector of a single model or structure can be extra
254. n the CC list If this occurs please ask the person if the message was meant to be private and refrain from discussing any of the comments within the post Save these comments until after the person responds by saying that the message was private or re sends the message to the mailing list Try to encourage public messages if you think that the post need not be private and if you think that it would be useful for the mailing list archives For thread consistency if you send a message which accidentally misses the mailing list please do not then forward the previously sent message to the list For better readability of the mailing list archives it is best that you create an entirely new message responding to the original post Just cut and paste your miss directed message into your new message That way the thread will be continuous there will not be any messages missing from the middle of the thread in between the original post and your forwarded message To simplify the process of checking if the message was supposed to be private you could cut and paste the following message modifying it as you see fit The following is the standard pre composed response to a post not sent to the relax mailing lists and not labelled as private If you would like to start a private conversation about relax please label your message as such If you really must start a private exchange please respond to this message saying so If your message was meant to
255. na org gt for r2593 However this was not the only place that the Scientific Python PDB data structure peptide_chains was being accessed The chains were being accessed in the file gt generic_fns sequence py when the sequence was being read out of the PDB file This has now been modified with changes similar to r2591 and r2593 An example of a commit message for changes relating to a task is This change implements half of task 3630 https gna org task 3630 The docstring in the generic optimisation function has been modified to clear up the ambiguity cased by supplying the option None together with Newton optimisation One last commit message example is Added the API documentation creation using Epydoc to the Scons scripts 128 CHAPTER 9 RELAX DEVELOPMENT The Scons target to create the HTML API documentation is called api_manual_html The documentation can be created by typing scons api_manual_html The function compile_api_manual_html was added to the scons manuals py file This function runs the epydoc command All the Epydoc options are specified in that function 9 4 5 Discussing major changes If you are contemplating major changes either for a bug fix to add a completely new fea ture or user function for your own work to improve the behaviour of part the program or any other potentially disruptive modifications please discuss these ideas on the relax devel mailing list
256. nacos Bcosy 8 202c Oa Oy 0 PO cos a cos D cos y E cosacos siny 8 202d cos a sin 3 RD cos a sin f sin y x cosasin PB cos y 8 202e we 5 202 LT sin a sin y cosa cos f cos y 5 i sina cosy cosacos Psin y 8 202f A 0 The Dy Hessian The second partial derivatives of the unit vector D with respect to the Euler angles are RO cosa sin y sina cos D cos y ar cosa cos y sin a cos B sin y 8 203a 3 sin a sin 8 RT cos asin 9 cos y 5 3 cosasin siny 8 203b qe cos amp cos 3 PO sin Q cos y cosa cos f sin y 5 3 sinasiny cosacosZcosy 8 203c a Oy 0 8 13 ELLIPSOIDAL DOT PRODUCT DERIVATIVES 115 RT sin Q cos Bj cos y JA sinacos siny 8 203d sinasin 3 Za sin asin f sin y y sinasin cosy 8 203e ob dy 0 2T cos q sin y sina cos D cos y 2 cosa cos y sin a cos B sin y 8 203f Oy 0 The D Hessian The second partial derivatives of the unit vector D with respect to the Euler angles are EM 0 E equ 8 204a 0 E 0 2 8 8 204b 0 23 0 2 gt k 8 204c 0 2A sin B cos y gt sinfsiny 8 204d B cos 8 2d cos f sin y cos cosy 8 204e qa sin B cos y sin siny 8 204f 1 0 116 CHAPTER 8 VALUES GRADIENTS AND HESSIANS 8 14 Spheroidal dot product derivatives 8 14 1 The dot product of t
257. name of the data pipe to copy the diffusion tensor data to Description This function will copy the diffusion tensor data between data pipes The destination data pipe must not contain any diffusion tensor data If the pipe_from or pipe_to arguments are not supplied then both will default to the current data pipe hence giving one argument is essential Examples To copy the diffusion tensor from the data pipe m1 to the current data pipe type relax gt diffusion_tensor copy m1 relax gt diffusion tensor copy pipe from mi To copy the diffusion tensor from the current data pipe to the data pipe m9 type relax diffusion tensor copy pipe to m9 To copy the diffusion tensor from the data pipe m1 to m2 type relax diffusion tensor copy mi m2 relax diffusion tensor copy pipe from mi pipe to m2 10 2 THE LIST OF FUNCTIONS 10 2 21 diffusion tensor delete Synopsis Function for deleting diffusion tensor data Defaults diffusion tensor delete self Description This function will delete all diffusion tensor data from the current data pipe 161 162 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 22 diffusion_tensor display Synopsis Function for displaying the diffusion tensor information Defaults diffusion_tensor display self 10 2 THE LIST OF FUNCTIONS 163 10 2 23 diffusion tensor init Synopsis Function for initialising the diffusion
258. nary The name of the executable Dasha program file Execution Dasha will be executed as dasha lt dasha script tee dasha_results If you would like to use a different Dasha executable file change the keyword argument binary to the appropriate file name If the file is not located within the environment s path include the full path in front of the binary file name 154 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 15 dasha extract Synopsis Function for extracting data from the Dasha results file Defaults dasha extract self dir None Keyword Arguments dir The directory where the file dasha_results is found 10 2 THE LIST OF FUNCTIONS 10 2 16 deselect all Synopsis Function for deselecting all spins Defaults deselect all self Examples To deselect all spins simply type relax deselect all 155 156 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 17 deselect read Synopsis Function for deselecting the spins contained in a file Defaults deselect read self file None dir None mol name col None res num col 0 res name col None spin num col None spin name col None sep None change_all False Keyword Arguments file The name of the file containing the list of spins to deselect dir The directory where the file is located mol_name_col The molecule name column this defaults to no column res num col The residue number
259. ne of these four movements yield an improvement then the simplex is shrunk halfway towards the vertex with the lowest function value The other algorithm is the commonly used Levenberg Marquardt algorithm Levenberg 1944 Marquardt 1963 which is implemented in Modelfree4 Dasha and Tensor2 This technique is designed for least squares problems to which the chi squared equation 6 25 belongs The key to the algorithm is the replacement of the Hessian with the Levenberg Marquardt matrix JTJ AI where J is the Jacobian of the system calculated as the matrix of partial derivatives of the residuals A gt 0 is a factor related to the trust region radius and Z is the identity matrix The algorithm is conceptually allied to the trust region methods and its performance varies finely between that of the steepest descent and the pure Newton step When far from the minimum A is large and the algorithm takes steps close to the gradient when in vicinity of the minimum A heads towards zero and the steps taken approximate the Newton direction Hence the algorithm avoids the problems of the Newton algorithm when non convex curvature is encountered and approximates the Newton step in convex regions of the space Constraint algorithms To guarantee that the minimum will still be reached the implementation of constraints limiting the parameter values together with optimisation algorithms is not a triviality For this to occur the space and its boundaries must
260. nian rotational diffusion tensor D the rhombic component of the Brownian rotational diffusion tensor Dratio the ratio of D to Di the eigenvalue of the Brownian rotational diffusion tensor in which the corresponding eigenvector defines the x axis of the tensor 2 the eigenvalue of the Brownian rotational diffusion tensor in which the corresponding eigenvector defines the y axis of the tensor D the eigenvalue of the Brownian rotational diffusion tensor in which the corresponding eigenvector defines the z axis of the tensor e elimination value J w spectral density function NOE nuclear Overhauser effect pdf probability distribution function r bond length xiii xiv R4 spin lattice relaxation rate R spin spin relaxation rate Rex chemical exchange relaxation rate S 2 and S model free generalised order parameters Te Tf and 7 model free effective internal correlation times Tm global rotational correlation time LIST OF FIGURES Chapter 1 Introduction The program relax is designed for the study of the dynamics of proteins or other macro molecules though the analysis of NMR relaxation data It is a community driven project created by NMR spectroscopists for NMR spectroscopists It supports exponential curve fitting for the calculation of the R4 and Ra relaxation rates calculation of the NOE reduced spectral density mapping and the Lipari and Szabo model free analysis The aim of relax is to provide a se
261. nk you decrease the overhead of following the mailing list 9 9 2 Search engine indexing Having a large web of links across relax s infrastructure aids in the search engine indexing of the mailing list archives and the http nmr relax com web site The web of links is useful for catching those Google bots That way the Google searching of the mailing list archives located on the communication web page will be more up to date However to increase the search engine ranking of the web site links to http nmr relax com from external sites is required This is one reason why relax is a registered freshmeat project 138 CHAPTER 9 RELAX DEVELOPMENT Chapter 10 Alphabetical listing of user functions The following is a listing with descriptions of all the user functions available within the relax prompt and scripting environments These are simply an alphabetical list of the docstrings which can normally be viewed in prompt mode by typing help function 10 1 A warning about the formatting The following documentation of the user functions has been automatically generated by a script which extracts and formats the docstring associated with each function There may therefore be instances where the formatting has failed or where there are inconsistencies 10 2 The list of functions Each user function is presented within it s own subsection with the documentation bro ken into multiple parts the synopsis the default arguments and
262. ntifier which can be a number name or range of numbers 10 2 THE LIST OF FUNCTIONS 307 If one of the tokens is left out then all elements will be assumed to match For example if the string does not contain the character then all molecules will match the string Regular expression can be used to select spins For example the string H will select the protons H H2 H98 308 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 113 residue display Synopsis Function for displaying information about the residue s Defaults residue display self res_id None Keyword Arguments res_id The residue identification string Identification string documentation The identification string is composed of three components the molecule id token begin ning with the character the residue id token beginning with the character and the atom or spin system id token beginning with the character Each token can be composed of multiple elements separated by the character and each individual element can either be a number which must be an integer in string format a name or a range of numbers separated by the character Negative numbers are supported The full id string specification is jmol_namej res_id ires id jres_idj Qjatom_idj jatom id jatom_idj where the token elements are jmol_name the name of the molecule res_id
263. num flag A flag whic if True will cause the residue number column to be shown res_name_flag A flag whic if True will cause the residue name column to be shown spin num flag A flag whic if True will cause the spin number column to be shown spin name flag A flag whic if True will cause the spin name column to be shown force A flag which if True will cause the file to be overwritten Description If no directory name is given the file will be placed in the current working directory 326 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 127 spin copy Synopsis Function for copying all data associated with a spin Defaults spin copy self pipe_from None spin_from None pipe to None spin_to None Keyword Arguments pipe_from The data pipe containing the spin from which the data will be copied This defaults to the current data pipe spin_from The spin identifier string of the spin to copy the data from pipe_to The data pipe to copy the data to This defaults to the current data pipe spin_to The spin identifier string of the spin to copy the data to Description This function will copy all the data associated with the identified spin to the new non existent spin The new spin must not already exist Examples To copy the spin data from spin 1 to the new spin 2 type relax gt spin copy spin_from 1 spin_to 2 To copy spin 1 of the molecule Old mol to spin 5 of the molecule New mo
264. o 0 o where Tm 1 6Diso iso 1 3 9 22 De Di i Dratio D D The spherical angles 0 orienting the unique axis of the diffusion tensor within the PDB frame are defined between while the angle a which is the angle between this axis and the given XH bond vector is defined between 0 a 27 The spheroid_type argument should be oblate prolate or None The argument will be ignored if the diffusion tensor is not axially symmetric If oblate is given then the constraint Da lt 0 is used while if prolate is given then the constraint Da gt 0 is used If nothing is supplied then Da will be allowed to have any values To prevent minimisation of diffusion tensor parameters in a space with two minima it is recommended to specify which tensor is to be minimised thereby partitioning the two minima into the two subspaces along the boundry Da 0 166 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS The ellipsoid rhombic diffusion When all three eigenvalues of the diffusion tensor are different the molecule diffuses as an ellipsoid This diffusion is also known as fully anisotropic asymmetric or rhombic The full tensor is specified by six pieces of information the three geometric parameters Diso Da and D representing the isotropic anisotropic and rhombic components of the tensor and the three Euler angles a 3 and y orienting the tensor within the PDB frame The
265. o create the molecules Ap4Aase ATP and MgF4 type relax molecule create Ap4Aase relax molecule create ATP relax molecule create MgF4 210 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 43 molecule delete Synopsis Function for deleting molecules Defaults molecule delete self mol_id None Keyword Arguments mol_id The molecule identifier string Description This function can be used to delete a single or sets of molecules Identification string documentation The identification string is composed of three components the molecule id token begin ning with the character the residue id token beginning with the character and the atom or spin system id token beginning with the character Each token can be composed of multiple elements separated by the character and each individual element can either be a number which must be an integer in string format a name or a range of numbers separated by the character Negative numbers are supported The full id string specification is jmol_namej jres id jres_idj jres_idj Qjatom_idj jatom_idj jatom_idj where the token elements are jmol_name j the name of the molecule res_id the residue identifier which can be a number name or range of numbers atom_id the atom or spin system identifier which can be a number name or range of numbers 10 2 THE LIST
266. of states Synopsis Set the number of states in the N state model Defaults n state model number of states self N None Keyword Arguments N The number of states Description Prior to optimisation the number of states in the N state model can be specified If the number of states is not set then this parameter will be equal to the number of loaded structures Examples To set up an 8 state model type relax n state model number of states N 8 246 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 62 n state model ref domain Synopsis Set the reference domain for the 2 domain N state model Defaults n state model ref domain self ref None Keyword Arguments ref The domain which will act as the frame of reference This is only valid for the 2 domain N state model Description Prior to optimisation of the 2 domain N state model which of the two domains will act as the frame of reference must be specified The N states will be rotations of the other domain so to switch the frame of reference to the other domain simply transpose the rotation matrices Examples To set up a 5 state model with C domain being the frame of reference type relax n state model ref domain ref C 10 2 THE LIST OF FUNCTIONS 247 10 2 63 n state model select model Synopsis Select the N state model type and set up the model Defaults n state model select model self model None
267. of the Hes sian V fx and is steadily increased until the factorisation is successful The resultant Cholesky lower triangular matrix L can then be used to find the approximate Newton direction If 7 is too large the convergence of this technique can approach that of the steepest descent algorithm The second method is the Gill Murray and Wright GMW algorithm Gill et al 1981 which modifies the Hessian during the execution of the Cholesky factorisation V f LIL where L is a lower triangular matrix and D is a diagonal matrix Only a single factorisation is required As rows and columns are interchanged during the algorithm the technique may be slow for large problems such as the optimisation of the model free parameters of all residues together with the diffusion tensor parameters The rate of convergence of the technique is quadratic Other methods Two other optimisation algorithms which cannot be classified within line search trust region or conjugate gradient categories will also be investigated The first is the well known simplex optimisation algorithm The technique is often used as the only the function value is employed and hence the derivation of the gradient and Hessian can be avoided The simplex is created as an n dimensional geometric object with n 1 vertices The first vertex is the starting position Each of the other n vertices are created by shifting the starting position by a small amount parallel to one of unit ve
268. ol None spin_num_col None spin name col None sep None boolean OR change_all False Keyword Arguments file The name of the file containing the list of spins to select dir The directory where the file is located mol_name_col The molecule name column this defaults to no column res num col The residue number column the default is 0 i e the first column res_name_col The residue name column this defaults to no column spin num col The spin number column this defaults to no column spin_ name_col The spin name column this defaults to no column sep The column separator the default is white space boolean The boolean operator specifying how spins should be selected change_all A flag specifying if all other spins should be changed Description Empty lines and lines beginning with a hash are ignored The change_all flag argument default is False meaning that all spins currently either selected or deselected will remain that way Setting the argument to True will cause all spins not specified in the file to be deselected Examples To select all residues listed with residue numbers in the first column of the file isolated_peaks type one of relax gt select read isolated_peaks 318 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS relax gt select read file isolated_peaks To select the spins in the second column of the relaxation data file r1 600 while dese lec
269. ometric parameter 6 is Iw 2X ari ga 1 wr _ gay 12 re T wrens 06 2 06 s arma ete ene OG _ S 1 S 7 Ti Te T 36 a 5 LG 8 66 O partial derivative The partial derivative of 8 64 with respect to the orientational parameter 0 is k OJ w _2 Oc 5 1 S Te Ti Te 8 67 00 5 30 1 WT Te Ti wreri S partial derivative The partial derivative of 8 64 with respect to the order parameter S is k OJ w 2 1 Te Ti Te e An o A 8 68 88 5 2 vs wt Te T ren na Te partial derivative The partial derivative of 8 64 with respect to the correlation time Te is OJ w 2 2 E 9 Te 75 wre 1 5 Gini o E 8 69 OTe 5 E ren wreny 76 CHAPTER 8 VALUES GRADIENTS AND HESSIANS 8 9 3 The original model free Hessian The model free Hessian of the original spectral density function 8 64 is the matrix of second partial derivatives The matrix coordinates correspond to the model parameters which are being optimised 6 6 partial derivative The second partial derivative of 8 64 with respect to the geometric parameters 6 and Gy is k 8 J uw _2 s On On didis 3 Co 06 06 5 E 06 06 1 w7 9 Te Ti Su 737 Te Ti wre r z 2 ql TERRACE URS OTi Oc P Or Oe T O rj 92 1 w7 06 08 08 06 796 08 1 wr _ 2 petn wren 05 Te m a a 1 s Ll 2 e
270. on Edit Subject as this currently mangles the email headers creates a new thread on the mailing list and makes it difficult to follow the thread 3 3 Reporting bugs One of the philosophies in the construction of relax is that if there is something which is not immediately obvious then that is considered a design bug If any flaws in re lax are uncovered including general design flaws bugs in the code or documentation issues these can be reported within relax s bug tracker system The link to submit a bug is https gna org bugs group relax amp func additem while the main page for browsing submitting viewing the statistics or searching through the database is at https gna org bugs group relax Please do not report bugs to personal email ad dresses or to the mailing lists 3 4 LATEST SOURCES THE RELAX REPOSITORIES 17 When reporting a bug please include as much information as possible so that the problem can be reproduced Include information such as the release version or the revision number if the repository sources are being used Also include all the steps performed in order to trigger the bug Attachment of files is allowed so scripts and subsets of the input data can be included However please do not attach large files to the report Prior to reporting the bug try to make sure that the problem is indeed a bug and if you have any doubts please feel free to ask on the relax users mailing list To avoid duplicates be sure th
271. ond partial derivatives are the components of the R 0 Hessian matrices 0 0 partial derivative The second partial derivatives of the relaxation equations with respect to the spectral density function parameters 0 and 0j are O R4 0 Ri R4 dj eg 8 50a 00 00 p O R3 0 d Ba JR ENT ien Je 50b o ju uos 8 50b 2 O Oxon 9 d JINOB 8 50c 80 90 8 8 Rj 0 VALUES GRADIENTS AND HESSIANS 71 0 pe partial derivative The second partial derivatives of the relaxation equations with respect to the spectral density function parameter 0 and the chemical exchange parameter pe are 3R 0 pe 8 51a PRA O A Ok 5 doa o 8 51b O oxoz 0 AL 0 col 50 Bes 7 8 51c 0 Ao partial derivative The second partial derivatives of the relaxation equations with respect to the spectral density function parameter 0 and the CSA parameter Ac are 0 R4 0 EN R4 00 OAc J 3 8 52a O R3 0 c Ro AN 52b 00 Odo 67 esum O oxog 0 AL 92 00 OAc Ed 0 r partial derivative The second partial derivatives of the relaxation equations with respect to the spectral density function parameter 0 and the bond length parameter r are 2 om g dJ 8 53a J O R3 0 d 2 axon 0 4 JONOE Pex Pex partial derivative The second partial derivatives of the relaxation equations with respect to the chemical exchange parameter pex twice are
272. one Examples To copy the CSA values from the run m1 to m2 type relax gt value copy m1 m2 CSA Regular expression The python function match which uses regular expression is used to determine which data type to set values to therefore various data_type strings can be used to select the same data type Patterns used for matching for specific data types are listed below This is a short description of python regular expression for more information see the regular expression syntax section of the Python Library Reference Some of the regular expression syntax used in this function is A sequence or set of characters to match to a single character For example Ss 2 will match both S2 and s2 7 Match the start of the string 10 2 THE LIST OF FUNCTIONS 351 Match the end of the string For example 8s 2 will match s2 but not S2f or s2s 6 Match any character xx Match the character x any number of times for example x will match as will XXXXX Match any sequence of characters of any length Importantly do not supply a string for the data type containing regular expression The regular expression is implemented so that various strings can be supplied which all match the same data type Model free set details Setting a parameter value may have no effect depending on whi
273. ons arbitrarily defined as motions slower than 200 ps For residues described by model free models m5 to m8 the order parameter S is plotted if 7 gt 200 ps For models ml to m4 S is plotted if re gt 200 ps The default colour gradient is the same as that for S The correlation time Te The default colour gradient starts at turquoise and ends at blue The correlation time rr The default colour gradient is the same as that of Te The correlation time Ts The default colour gradient starts at blue and ends at black Model independent display of the timescale of fast motions For models m5 to m8 only the parameter Ty is plotted For models m2 and m4 the parameter 7 is plotted only if it is less than 200 ps All other residues are assumed to have a correlation time of zero The default colour gradient is the same as that of Te Model independent display of the timescale of slow motions For models m5 to m8 only the parameter Ts is plotted For models m2 and m4 the parameter Te is plotted only if it is greater than 200 ps All other residues are coloured white T he default colour gradient 226 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Molmol RGB colour arrays The following table is a list of colours used in Molmol and their corresponding RGB colour values ranging from 0 to 1 Name Red Green Blue black 0 000 0 000 0 000 navy 0 000 0 000 0 502 blue 0 000 0 000 1 00
274. ootstrap model selection CV Single item out cross validation Expect The expected overall discrepancy the true values of the parameters are re quired Farrow Old model free method by Farrow et al 1994 Palmer Old model free method by Mandel et al 1995 Overall The realised overall discrepancy the true values of the parameters are re quired For the methods Bootstrap Expect and Overall the function monte_carlo should have previously been executed with the type argument set to the appropriate value to modify its behaviour If the pipes argument is not supplied then all data pipes will be used for model selection 206 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Example For model free analysis if the preset models 1 to 5 are minimised and loaded into the program the following commands will carry out AIC model selection and to place the selected results into the mixed data pipe type one of relax gt model_selection AIC mixed relax gt model_selection method AIC modsel_pipe mixed relax model_selection AIC mixed mi m2 m3 m4 m5 relax gt model_selection method AIC modsel_pipe mixed pipes m1 m2 m3 m4 m5 10 2 THE LIST OF FUNCTIONS 207 10 2 41 molecule copy Synopsis Function for copying all data associated with a molecule Default
275. or allegation of patent infringement or for any other reason not limited to patent issues conditions are imposed on you whether by court order agreement or otherwise that contradict the conditions of this License they do not excuse you from the conditions of this License If you cannot distribute so as to satisfy simultaneously your obligations under this License and any other pertinent obligations then as a consequence you may not distribute the Program at all For example if a patent license would not permit royalty free redistribution of the Program by all those who receive copies directly or indirectly through you then the only way you could satisfy both it and this License would be to refrain entirely from distribution of the Program If any portion of this section is held invalid or unenforceable under any particular cir cumstance the balance of the section is intended to apply and the section as a whole is intended to apply in other circumstances It is not the purpose of this section to induce you to infringe any patents or other property right claims or to contest validity of any such claims this section has the sole purpose of protecting the integrity of the free software distribution system which is implemented by public license practices Many people have made generous contributions to the wide range of software distributed through that system in reliance on consistent application of that system it is up to the author donor to d
276. or itself For example colour_start white and colour_start 1 0 1 0 1 0 both select the same colour Leaving both arguments at None will select the default colour gradient which for each type of analysis is described below When supplying the colours as strings two lists of colours can be selected from which to match the strings These are the default Molmol colour list and the X11 colour list both 224 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS of which are described in the tables below The default behaviour is to first search the Molmol list and then the X11 colour list raising an error if neither contain the string To explicitly select these lists set the colour_list argument to either molmol or x11 Examples To create a Molmol macro mapping the order parameter values S onto the structure using the classic style type relax gt molmol write S2 relax gt molmol write data_type S2 relax gt molmol write data_type S2 style classic file s2 mac dir molmol Classic style Creator Edward d Auvergne Argument string classic Description The classic style draws the backbone of a protein in the Molmol neon style Rather than colouring the amino acids to which the NH bond belongs the three covalent bonds of the peptide bond from Ca to Ca in which the NH bond is located are coloured Deselected residues are shown as black lines Supported data types
277. orithm Eleven increments per dimension of the model in this case the two dimensions R5 Jo is sufficient The user function for executing the grid search is grid search inc 11 The next step is to select one of the minimisation algorithms to optimise the model pa rameters Currently for relaxation curve fitting only simplex minimisation is supported This is because the relaxation curve fitting C module is incomplete only implementing the chi squared function The chi squared gradient the vector of first partial derivatives and chi squared Hessian the matrix of second partial derivatives are not yet implemented in the C modules and hence optimisation algorithms which only employ function calls are supported Simplex minimisation is the only technique in relax which fits this criteron In addition constraints cannot be used as the constraint algorithm is dependent on gradient calls Therefore the minimisation command for relaxation curve fitting is forced to be minimise simplex constraints False 5 6 Error analysis Only one technique adequately estimates parameter errors when the parameter values where found by optimisation Monte Carlo simulations In relax this can be implemented by using a series of functions from the monte_carlo user function class Firstly the number of simulations needs to be set monte_carlo setup number 500 For each simulation randomised relaxation curves will be fit using exactly the same metho
278. osel p o co du kae RE Eom a De 240 10 2 59 n state model CoM conri ba ETa es 242 10 2 60n state model conepdb llle 243 10 2 61 n state model number ofstates a 245 10 2 62 siate model rel doma lt lt lt ovio REG m RR cR n 246 10 2 63n state modelselect model 247 10 2 64n state modelset domain ss 248 10 2 65 n statemodel settype o o o suse ko Rom a x 249 TR OG CIO PEDE uou s Ense bw eX Roy RGR a Rom A S 250 1 qa cl Cc 251 JU LBS paler erede uuo seu e euh BOR wee gee aed Ge a 253 10269 palmera o o soe doe dE EROR cw be Evo UE RON RE Y a 255 I2 TU pabuerexituel conca cada REY da 256 10 2 Tlposbagkceale 2223 o9 go x eR UR Oe ba eg um Rex i 257 IX D CSM ce ae ee A oe mh RR Se Sd aca 258 IX TI pCO e mamon ee a men BOX 9 we Roe hes 259 102 1 pes delete iu sese oko RAP RD om e Ee 260 JUL TODOS UBEDA uu ius eee A xd alee a di 261 ITI T CC T 262 IO TZ DOS WIDE oca Oe A e em Roche RR RD ee i 263 CONTENTS ix IUZ BIO fe bee ROG SOR Oe He Deedee ow xb Rd m sede 5 264 10 2 79 PIBES oos os ia a woo Rp EUR E x P EPOR 265 10 2 50 pipe c rreHb gt o so asr masta A A A m Rem a 266 10 2 81 pipe delet amp soo Ro En RR eed R9 vee cx GA 267 10282 pipe io ok hee a ee Be S xU ADU 268 IS So pipe Neh a es ouo ee dea m RUE aoe we ws er RS ees 269 10 2 84 pipe Swit uu sd ono o9 hae Sew eee ee S io 270 102 55 pymol artoon socs apo ae wae bad Bae es bee ee S GE e a 271 I
279. ot has been shifted to this position and the CoM is at the position 0 0 1 type one of relax gt n_state_model CoM centre 0 0 1 relax gt n_state_model CoM centre 0 0 0 0 1 0 relax gt n state model CoM pivot point 0 0 0 0 0 0 centre 0 0 0 0 1 0 10 2 THE LIST OF FUNCTIONS 243 10 2 60 n state model cone pdb Synopsis Create a PDB file representing the cone models from the centre of mass CoM analysis Defaults n state model cone pdb self cone type None scale 1 0 file cone pdb dir None force False Keyword Arguments cone type The type of cone model to represent scale Value for scaling the pivot CoM distance which the size of the cone defaults to file The name of the PDB file dir The directory where the file is located force A flag which if set to True will overwrite the any pre existing file Description This function creates a PDB file containing an artificial geometric structure to represent the various cone models These models include diff in cone diff on cone The model can be selected by setting the cone_type argument to one of these strings The cone is represented as an isotropic cone with its axis parallel to the average pivot CoM vector the vertex placed at the pivot point of the domain motions and the length of the edge of the cone equal to the pivot CoM distance multipled by the scaling argument The resultant PDB file can subsequently read
280. otation 163 167 220 242 246 277 340 341 ScientificPython 11 SCons 18 130 API documentation 131 binary distribution 18 131 C module compilation 130 clean up 131 help 130 source distribution 131 user manual HTML version 130 user manual PDF version 130 scons 11 12 Sconstruct 11 script 134 scripting 7 216 273 sample scripts 8 script file 152 216 273 sequence 172 180 182 192 228 231 234 236 238 240 251 268 299 305 309 311 321 321 322 322 323 323 324 325 325 328 333 335 343 350 351 355 356 360 366 376 software Dasha 3 14 39 42 152 152 153 153 154 154 Grace 1 3 13 22 23 179 179 180 180 181 Modelfree 3 14 42 253 256 MOLMOL 1 3 14 215 215 216 216 217 217 219 219 220 220 222 223 223 224 226 226 275 282 282 OpenDX 1 3 13 169 170 PyMOL 1 3 14 relax 43 Sparky 21 27 252 299 Tensor 42 XEasy 21 27 252 300 spherical angles 106 SRLS 1 2 standard deviation 25 string 4 134 Subversion 17 119 126 book 17 check out 17 18 129 131 commit 129 conflict 129 INDEX merge 129 patch 125 remove 130 svnmerge py init 129 svnmerge py merge 129 svnmerge py uninit 129 update 129 support request 135 SVN 17 119 svnmerge py 128 symbolic link 12 tab completion 6 tar 12 264 task 135 terminal 4 test suite 8 126 tracker bug 135 support request 135 task 135 UI
281. ou Rod uu eR Ue mmm Be 359 IAS 2 hee eee a Sa oe da a A 364 UNA AE C Cc 375 IQ 2 14 yn OW sous sus ata ee ee eh a mt 3 dee Aas 379 11 Licence 381 11 1 Copying modification sublicencing and distribution of relax 381 E eos 6 etree e woe Go oot en ey Bend ERS A 381 List of Figures 4 1 6 1 6 2 6 3 8 1 8 2 8 3 9 1 NOE plat lt c ccs edhe SSeS a be X ER RO OR S S Ld 23 A schematic of the model free optimisation protocol of Mandel et al 1995 51 Model free analysis using the diffusion seeded paradigm 52 A schematic of the new model free optimisation protocol 54 The construction of the model free gradient sss 61 The model free Hessian kite aa 63 x dependencies of the values gradients and Hessians 64 The core design of relax o sa s oso o m Rx ma 133 xi xii LIST OF FIGURES Abbreviations AIC Akaike s Information Criteria AICc small sample size corrected AIC BIC Bayesian Information Criteria C 7 correlation function x chi squared function CSA chemical shift anisotropy the set of diffusion tensor parameters D the eigenvalue of the spheroid diffusion tensor corresponding to the unique axis of the tensor D the eigenvalue of the spheroid diffusion tensor corresponding to the two axes perpen dicular to the unique axis Da the anisotropic component of the Brownian rotational diffusion tensor Diso the isotropic component of the Brow
282. p number 500 Step 3 relax gt monte_carlo create_data method back_calc Step 4 relax gt calc Step 6 relax gt monte_carlo error_analysis Step 8 236 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 56 monte_carlo off Synopsis Function for turning simulations off Defaults monte carlo off self Monte Carlo Simulation Overview For proper error analysis using Monte Carlo simulations a sequence of function calls is required for running the various simulation components The steps necessary for imple menting Monte Carlo simulations are 1 The measured data set together with the corresponding error set should be loaded into relax 2 Either minimisation is used to optimise the parameters of the chosen model or a calculation is run 3 To initialise and turn on Monte Carlo simulations the number of simulations n needs to be set 4 The simulation data needs to be created either by back calculation from the fully minimised model parameters from step 2 or by direct calculation when values are calcu lated rather than minimised The error set is used to randomise each simulation data set by assuming Gaussian errors This creates a synthetic data set for each Monte Carlo simulation 5 Prior to minimisation of the parameters of each simulation initial parameter estimates are required These are taken as the optimised model parameters An alternative is to use a grid search for each simulation
283. pin system id token beginning with the character Each token can be composed of multiple elements separated by the character and each individual element can either be a number which must be an integer in string format a name or a range of numbers separated by the character Negative numbers are supported The full id string specification is jmol_namej res_id ires id jres_idj Qjatom_idj jatom id jatom_idj where the token elements are jmol_name the name of the molecule res_id the residue identifier which can be a number name or range of numbers atom_id the atom or spin system identifier which can be a number name or range of numbers If one of the tokens is left out then all elements will be assumed to match For example if the string does not contain the character then all molecules will match the string Regular expression can be used to select spins For example the string H will select the protons F H2 H98 10 2 THE LIST OF FUNCTIONS 333 10 2 131 spin name Synopsis Function for naming spins Defaults spin name self spin id None name None Keyword Arguments spin_id The spin identification string corresponding to one or more spins name The new name Description This function simply allows spins to be named or renamed Examples The following sequence of commands will rename the sequence 1 C1
284. pin_id 6 inc 20 file map dir dx relax gt dx map params S2 S2f ts spin_id 6 type Iso3D inc 20 file map dir dx To map the model free space m4 for residue 2 spin N6 defined by the parameters 5 Te Rex name the results test and to place the files in the current directory use one of the following commands relax dx map S2 te Rex spin id 20N6 file test dir None relax gt dx map params S2 te Rex spin_id 2 QN6 inc 100 file test dir None Regular expression The python function match which uses regular expression is used to determine which data type to set values to therefore various data_type strings can be used to select the same data type Patterns used for matching for specific data types are listed below This is a short description of python regular expression for more information see the regular expression syntax section of the Python Library Reference Some of the regular expression syntax used in this function is 172 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS A sequence or set of characters to match to a single character For example Ss 2 will match both 2 and s2 Match the start of the string Match the end of the string For example Ss 2 will match s2 but not S2f or s2s
285. pported The full id string specification is jmol_namej jres id jres id jres_idj Gjatom id jatom id jatom_idj where the token elements are 10 2 THE LIST OF FUNCTIONS 329 jmol_name the name of the molecule res_id the residue identifier which can be a number name or range of numbers atom_id the atom or spin system identifier which can be a number name or range of numbers If one of the tokens is left out then all elements will be assumed to match For example if the string does not contain the character then all molecules will match the string Regular expression can be used to select spins For example the string H will select the protons H H2 H98 330 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 129 spin delete Synopsis Function for deleting spins Defaults spin delete self spin_id None Keyword Arguments spin_id The spin identifier string Description This function can be used to delete a single or sets of spins See the identification string documentation below for more information Identification string documentation The identification string is composed of three components the molecule id token begin ning with the character the residue id token beginning with the character and the atom or spin system id token beginning with the character Each token can be composed of multiple elements
286. r changes 2 es 128 940 Branches coso osea be e ee SR e we a 128 9 5 The SCons build system ccc aa coruo ee RR eee 130 A Rein es as a ds a ce ks a e ee a RR 9 Go ay qo eR gee UE E 130 9 5 2 C module compilation s e s coe m oo m A eA 130 CONTENTS vil 9 5 3 Compilation of the user manual PDF version 130 9 5 4 Compilation of the user manual HTML version 130 9 5 5 Compilation of the API documentation HTML version 131 9 5 6 Making distribution archives 00000 eee 131 DI IESO UN dao Sad 9 Bae eed eee nw Pe d 131 9 6 The core design of relax se sco w aaas ee ee 132 9 6 1 The divisions of relax s source code less 132 9 6 2 The major components of relax 0 o 132 07 The mailing lisis 220 2 00400 ese Ed moy AA ed 135 9 7 1 Private vs public messages 135 9 8 The bug task and support request trackers 135 481 Submitting a Due report esee aeae e M o RR 135 9 8 2 Assigning an issue to yourself 136 0 52 closing an SUG cu boo a 3o Eon Y p 9e 136 9 9 Links links and more links eee ee eee ne 136 A Navigation cu er ed ee Gt Bal Cose A hc og RED S RE e 136 932 earch engine indexing care wa wae eo ea SOR A aes 137 10 Alphabetical listing of user functions 139 10 1 A warning about the formatting os ss e cece a acraea aoa dee ie aaa 139 102 The lisi of DuncboHS cria a PO
287. re sponding to pipe_to must not yet exist Examples To copy the contents of the m1 data pipe to the m2 data pipe type relax pipe copy mi1 m2 relax pipe copy pipe_from m1 pipe to m2 If the current data pipe is m1 then the following command can be used relax pipe copy pipe to m2 10 2 THE LIST OF FUNCTIONS 265 10 2 79 pipe create Synopsis Function for initialising a data pipe Defaults pipe create self pipe name None pipe_type None Keyword Arguments pipe_name The name of the data pipe pipe_type The type of data pipe Description The data pipe name can be any string however the data pipe type can only be one of the following jw Reduced spectral density mapping mf Model free analysis N state N state model of domain motions noe Steady state NOE calculation relax_fit Relaxation curve fitting srls SRLS analysis Examples To set up a model free analysis data pipe with the name m5 type relax gt pipe create m5 mf 266 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 80 pipe current Synopsis Print the name of the current pipe Defaults pipe current self Examples To run the user function type relax pipe current 10 2 THE LIST OF FUNCTIONS 10 2 81 pipe delete Synopsis Function for deleting a data pipe Defaults pipe delete s
288. relax Version 1 3 1 A program for NMR relaxation data analysis September 29 2008 11 Contents 1 Introduction 1 11 uou ca lt a a a OR we Re iw ow ee A 1 LIT o ek ce Ge hk ee he er BO Se we es ee ee ee 1 1 1 2 Supported NMR theories sec ero esca e ra e 2 1139 Data analysis Goole o ek Se eR ues 2 LLA Data vietalisali n lt lt e eee m e x9 Swe E XR ee 3 1 1 5 Interfacing with other programs 2 0 3 116 The user interfaces UL snc de eee a eee RR R9 aAa 3 US Howie tise elas o2 ee ee g Ro A A RA a RO Red 4 L2Zl Dhe prompt res eee kom Ro cm Dee ae Rok ea E X ERR 4 122 Python sacose dd o gem Rem ek gg Re bo ee 4 12 94 User fictions 2s m o m RB RAE RE s 5 1241 The helo est dou ees PUR Um Xs ew as 5 125 Tabcomplt onm essa em a ge eb Fad ROS ER gn 6 1 46 Thedaba pg sierra a Ha eG X ROBORE mE eres 6 LI BORE 2 245355 kie B xo muB R99 6 4 8 RO RUE Bop RAGA 7 LAS Bamplegenpie css Pee ae hes 8 12 9 Whe best suite c sace zo Rm eee SRS UE RUBRO RR Y E Bg 8 LAIO TRG lt lt ae ee ba he ke aa pew ewe Lee ge a 8 1 2 11 Access to the internals of relax lll 9 13 Usageof the name relax 22 225929 Roo a Re ds 9 2 Installation instructions 11 2l Dependenties s sue su do der eee ee eaa we hee eee GR RE kes 11 22 Installation 425222222335 o 9 e e 0X os eee e ea GS 11 2 2 1 The precompiled verses source distribution 11 222 Tostallation on GNU Linux
289. relax users information page at https mail gna org listinfo relax users You can also browse the mailing list archives at https mail gna org public relax users 3 2 3 relax devel A second mailing list exists for posts relating to the development of relax The list is relax devel at gna org and to subscribe go to the relax devel information page at https mail gna org listinfo relax devel Feature requests program design or any other posts relating to relax s structure or code should be sent to this list instead The mailing list archives can be browsed at https mail gna org public relax devel 3 2 4 relax commits One last mailing list is the relax commits list This list is reserved for automatically generated posts created by the version control software which looks after the relax source code and these web pages If you would like to become a developer you can subscribe to the list at relax commits information page https mail gna org listinfo relax commits The list can also be browsed at https mail gna org public relax commits 3 2 5 Replying to a message When replying to a message on these lists remember to hit respond to all so that the mailing list is included in the CC field Otherwise your message will only be sent to the original poster and not return back to the list Only messages to relax users and relax devel will be accepted If you are using Gmail s web based interface please do not click
290. remain smooth thereby allowing the algorithm to move along the boundary to either find the minimum along the limit or to slide along the limit and then move back into the centre of the constrained space once the curvature allows it One of the most powerful approaches is the Method of Multipliers Nocedal and Wright 1999 also known as the Augmented Lagrangian Instead of a single optimisation the algorithm is iterative with each iteration consisting of an independent unconstrained minimisation on a sequentially modified space When inside the limits the function value is unchanged but when outside a penalty which is proportional to the distance outside the limit is added to the function value This penalty which is based on the Lagrange multipliers is smooth and hence the gradient and Hessian are continuous at and beyond the constraints For each iteration of the Method of Multipliers the penalty is increased until it becomes impossible for the parameter vector to be in violation of the 6 1 THEORY 43 limits This approach allows the parameter vector 0 outside the limits yet the successive iterations ensure that the final results will not be in violation of the constraint For inequality constraints each iteration of the Method of Multipliers attempts to solve the quadratic sub problem min 4 0 A y 0 Y V ei 0 AE ux 6 32 icJ where the function V is defined as A ci 0 2 0 if c 0 uA lt 0 6 33 E AF ot
291. res_num_col 0 res_name_col 1 spin num col None spin_name_col None sep None Keyword Arguments file The name of the file containing the sequence data dir The directory where the file is located mol_name_col The molecule name column this defaults to no column res num col The residue number column the default is 0 i e the first column res_name_col The residue name column the default is 1 i e the second column spin num col The spin number column this defaults to no column spin_ name_col The spin name column this defaults to no column sep The column separator the default is white space Description If no directory is given the file will be assumed to be in the current working directory Examples The following commands will read the sequence data out of a file called seq where the residue numbers and names are in the first and second columns respectively relax gt sequence read seq relax gt sequence read seq num_col 0 name_col 1 relax gt sequence read file seq num_col 0 name_col 1 sep None The following commands will read the residue sequence out of the file noe out which also contains the NOE values relax gt sequence read noe out relax gt sequence read noe out num_col 0 name_col 1 324 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS relax gt sequence read file noe out num_col 0 name_col 1 The following commands will read
292. rguments at None will select the default colour gradient which for each type of analysis is described below When supplying the colours as strings two lists of colours can be selected from which to match the strings These are the default PyMOL colour list and the X11 colour list both 282 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS of which are described in the tables below The default behaviour is to first search the PyMOL list and then the X11 colour list raising an error if neither contain the string To explicitly select these lists set the colour_list argument to either molmol or x11 Examples To create a PyMOL macro mapping the order parameter values S onto the structure using the classic style type relax pymol write S2 relax pymol write data_type S2 relax gt pymol write data_type S2 style classic file s2 mac dir pymol Molmol RGB colour arrays The following table is a list of colours used in Molmol and their corresponding RGB colour values ranging from 0 to 1 10 2 THE LIST OF FUNCTIONS 283 Name Red Green Blue black 0 000 0 000 0 000 navy 0 000 0 000 0 502 blue 0 000 0 000 1 000 dark green 0 000 0 392 0 000 green 0 000 1 000 0 000 cyan 0 000 1 000 1 000 turquoise 0 251 0 878 0 816 royal blue 0 255 0 412 0 882 aquamarine 0 498 1 000 0 831 sky green 0 529 0 808 0 922 dark violet 0
293. rmat you would like read by relax please send an email to the relax development mailing list detailing the software used the format of the file specifically where the residue number and peak intensity are located and possibly attaching an example of the file itself 4 5 Setting the errors In this example the errors where measured from the base plain noise The Sparky RMSD function was used to estimate the maximal noise levels across the spectrum in regions containing no peaks For the reference spectrum the RMSD was approximately 3600 whereas in the saturated spectrum the RMSD was 3000 These errors are set by the commands noe error error 3600 spectrum type ref noe error error 3000 spectrum type sat For the residue G114 the noise levels are significantly increased compared to the rest of the protein as the peak is located close to the water signal The higher errors for this residue are specified by the commands noe error error 122000 spectrum type ref res_num 114 noe error error 8500 spectrum type sat res num 114 4 6 Unresolved residues As the peaks of certain residues overlap to such an extent that the heights cannot be resolved a simple text file was created called unresolved in which each line consists of a single residue number By using the command deselect read name file unresolved all residues in the file unresolved are excluded from the analysis 4 7 The NOE At this point the NOE can be
294. rning where the data names correspond to xk The array of minimised parameter values fk The minimised function value k The number of iterations f_count The number of function calls g_count The number of gradient calls h_count The number of Hessian calls warning The warning string Minimisation algorithms A minimisation function is selected if the minimisation algorithm argument which should be a string matches a certain pattern Because the python regular expression match statement is used various strings can be supplied to select the same minimisation algo rithm Below is a list of the minimisation algorithms available together with the corre sponding patterns This is a short description of python regular expression for more information see the regular expression syntax section of the Python Library Reference Some of the regular expression syntax used in this function is A sequence or set of characters to match to a single character For example Nn ewton will match both Newton and newton Match the start of the string Match the end of the string For example L1 Mm will match Im and LM but will not match if characters are placed either before or after these strings To select a minimisation algorithm set the argument to a string which matches the given pattern
295. rometer frequency in Hz Description This function will select the relaxation data to use in the consistency tests corresponding to the given frequencies Examples relax gt consistency_tests set_frq 600 0 1e6 relax gt consistency_tests set_frq frq 600 0 1e6 152 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 13 dasha create Synopsis Function for creating the Dasha script Defaults dasha create self algor LM dir None force False Keyword Arguments algor The minimisation algorithm dir The directory to place the files force A flag which if set to True will cause the results file to be overwritten if it already exists Description The script file created is called dir dasha_script Optimisation algorithms The two minimisation algorithms within Dasha are accessible through the algor argument which can be set to LM The Levenberg Marquardt algorithm NR Newton Raphson algorithm For Levenberg Marquardt minimisation the function Imin will be called while for New ton Raphson the function min will be executed 10 2 THE LIST OF FUNCTIONS 153 10 2 14 dasha execute Synopsis Function for executing Dasha Defaults dasha execute self dir None force False binary dasha Keyword Arguments dir The directory to place the files force A flag which if set to True will cause the results file to be overwritten if it already exists bi
296. rs H8 spin_id G relax gt structure vectors H5 spin id C relax structure vectors H6 spin_id C relax gt structure vectors H3 spin id U relax gt structure vectors H5 spin_id U relax gt structure vectors H6 spin_id U Alternatively assuming the desired spins have been loaded regular expression can be used relax structure vectors H 10 2 THE LIST OF FUNCTIONS 347 10 2 140 structure write pdb Synopsis The PDB writing function Defaults structure write_pdb self file None dir None struct index None force False Keyword Arguments file The name of the PDB file dir The directory where the file is located struct_index The index of the structure to write force A flag which if set to True will overwrite the any pre existing file Description If the struct_index argument is None then each loaded structure will be written to a single file as different models This index covers all the structures loaded from individual files and all the structures present as different models within each file Example To write all structures to the PDB file ensemble pdb within the directory pdb type one of relax gt structure write_pdb ensemble pdb pdb relax gt structure write_pdb file ensemble pdb dir pdb To write the 4 model loaded from a PDB file into the new file test
297. ruction of the gradient 8 43 Construction of the Hessian o e 8 5 The value gradient and Hessian dependency chain 8 6 The X value gradient and Hessian BRI They valie ociosas Penden eee odes Sine They sadoni acon en dawn AR ea kee 86 3 The y Hessian 6 6 ec o Ro Ra Rs 8 7 The R 0 values gradients and Hessians llle Bik Te Ree Wee we Ro oso oe SOR eK eR ee RS 8 72 TheR ies r om Rogue Hoe A eee eee ews ELS The Fae Hessians poc Sa ee A Ge eee a ERR 8 8 R 0 values gradients and Hessians o o 8 8 1 Components of the R 0 equations o o Ree Ty SI 21 38 5707 0 ETT Pm Set IL BAS ues Xe anao gue od poe ORES OS 8 9 Model free analysis aaa 8 9 1 The model free equations 000000 eee eee 8 9 2 The original model free gradient 8 9 8 The original model free Hessian lle 8 9 4 The extended model free gradient 8 9 5 The extended model free Hessian o 8 9 6 The alternative extended model free gradient 8 9 7 The alternative extended model free Hessian 8 10 Ellipsoidal diffusion tensor sc e does moe e 8 10 1 The diffusion equation of the ellipsoid 8 10 2 The weights of the ellipsoid c n 8 10 3 The weight gradients of the ellipsoid
298. s R 0 6 1 4 The spectral density functions J w 6 1 5 Brownian rotational diffusion 6 1 6 The model free models 6 1 7 Model free optimisation theory Optimisation of a single model free model 6 2 1 The sample script 6 2 2 The rest Optimisation of all model free models 6 3 1 The sample script 6 3 2 The rest Model free model selection 6 4 1 The sample script 6 4 2 The rest 6 1 6 2 6 3 6 4 Optimisation Error analysis Figishing OF e s a cue ek pis we ee CONTENTS CONTENTS 7 8 6 5 The methodology of Mandel et al 1995 lr 6 6 The diffusion seeded paradigm e 6 7 The new model free optimisation protocol sen Reduced spectral density mapping Values gradients and Hessians Ed a sooo a s xowubchok Swe REOR mo Ye reed a dw SS can tene Te 5 2 Minimisation Concepts lt c s s redea w eaa mas aa 21 The function value o eca 05 464 054446 ca bbe 6 BUR S B22 Chegradinh osos as e ao o ya a aa Rew The Hessian ici adas a eet Rabu A ra 8 3 The four parameter combinations 2 22 8 3 1 Optimisation of the model free models 8 3 2 Optimisation of the local Tmn models 8 3 3 Optimisation of the diffusion tensor parameters 8 3 4 Optimisation of the global model G 8 4 Construction of the values gradients and Hessians 8 4 1 The sum of chi squared values aooaa sss 8 4 2 Const
299. s The R 0 Hessians in vector notation are V R 0 V R1 0 V Ra 0 V RI 0 ViNOE 0 2 amp 1 7 soe 0 2v T6 vr 0 7 R1 0 V R1 0 Yx Ri 0 Ri 0 Vosox 6 VR1 0 7 R 0 V 0sos 0 65 8 18a 8 18b 8 18c 8 19a 8 19b 8 19c 8 20a 8 20b 8 20c 66 CHAPTER 8 VALUES GRADIENTS AND HESSIANS 8 8 R values gradients and Hessians The partial and second partial derivatives of the relaxation equations of the set R 0 are different for each parameter of the vector 0 The vector representation of the gradient VR 0 and the matrix representation of the Hessian V R 0 can be reconstructed from the individual elements presented in the next section 8 8 1 Components of the R 0 equations To simplify the calculations of the gradients and Hessians the R 0 equations have been broken down into a number of components These include the dipolar and CSA constants as well as the dipolar and CSA spectral density terms for each of the three transformed relaxation data types R4 Re Onon The segregation of these components simplifies the maths as many partial derivatives of the components are zero Dipolar constant The dipolar constant is defined as 1 2y ya yxh d 21 lt r gt eal 4 NAm This component of the relaxation equations is independent of the parameter of the spectral density function 0 the chemical exchange parameter pez and the CSA param
300. s molecule copy self pipe_from None mol_from None pipe to None mol_to None Keyword Arguments pipe_from The data pipe containing the molecule from which the data will be copied This defaults to the current data pipe mol_from The molecule identifier string of the molecule to copy the data from pipe_to The data pipe to copy the data to This defaults to the current data pipe mol_to The molecule identifier string of the molecule to copy the data to Description This function will copy all the data associated with a molecule to a second molecule This includes residue and spin system information The new molecule must not yet exist Examples To copy the molecule data from the molecule GST to the new molecule wt GST type relax gt molecule copy GST wt GST relax molecule copy mol_from GST mol_to wt GST To copy the molecule data of the molecule Ap4Aase from the data pipe m1 to m2 assuming the current data pipe is m1 type relax gt molecule copy mol_from ApAase pipe_to m2 relax gt molecule copy pipe_from m1 mol_from ApAase pipe_to m2 mol_to ApAase Identification string documentation The identification string is composed of three components the molecule id token begin ning with the character the residue id token beginning with the character and the atom or spin system id token beginn
301. s of Hertz 5 Azz Axx yy Axy Axz Ayz units of Hertz 6 Pxx Pyy Pxy Pxz Pyz unitless 7 Pzz Pxx yy Pxy Pxz Pyz unitless Other formats may be added later The relationship between the Saupe order matrix S and the alignment tensor A is 10 2 THE LIST OF FUNCTIONS 145 S 3 2 A The probability matrix P is related to the alignment tensor A by A P 1 3 I where I is the identity matrix For the alignment tensor to be supplied in Hertz the bond vectors must all be of equal length Examples To set a rhombic tensor to the run CaM type one of relax align tensor init 8 6322e 05 5 5786e 04 3 1732e 05 2 2927e 05 2 8599e 04 param types 1 relax align tensor init 8 6322e 05 5 5786e 04 3 1732e 05 2 2927e 05 2 8599e 04 param types 1 relax align tensor init params 8 6322e 05 5 5786e 04 3 1732e 05 2 2927e 05 2 8599e 04 param types 1 relax align tensor init params 8 6322e 05 5 5786e 04 3 1732e 05 2 2927e 05 2 8599e 04 param types 1 146 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 8 align tensor matrix angles Synopsis Function for calculating the 5D angles between all alignment tensors Defaults align tensor matrix angles self basis set 0 tensors None Keyword Arguments basis set The basis set to operate with tensors A list of the tensors to apply the calculation to If None all tensors are used Descrip
302. s of the selected residues is represented as a single carbon atom of the residue COM The ellipsoidal geomet ric shape consists of numerous H atoms of the residue TNS The axes of the tensor when defined are presented as the residue AXS and consist of carbon atoms one at the centre of mass and one at the end of each eigenvector Finally if Monte Carlo simulations were run and the diffusion tensor parameters were allowed to vary then there will be multiple SIM residues one for each simulation These are essentially the same as the AXS residue representing the axes of the simulated tensors and they will appear as a distribution As the Brownian rotational diffusion tensor is a measure of the rate of rotation about different axes the larger the geometric object the faster the diffusion of a molecule For example the diffusion tensor of a water molecule is much larger than that of a macro molecule The effective global correlation time experienced by an XH bond vector not to be con fused with the Lipari and Szabo parameter 7 e will be approximately proportional to the component of the diffusion tensor parallel to it The approximation is not exact due to the multiexponential form of the correlation function of Brownian rotational diffusion If an XH bond vector is parallel to the longest axis of the tensor it will be unaffected by 10 2 THE LIST OF FUNCTIONS 341 rotations about that axis which are the fastes
303. s strings two lists of colours can be selected from which to match the strings These are the default Molmol colour list and the X11 colour list both of which are described in the tables below The default behaviour is to first search the Molmol list and then the X11 colour list raising an error if neither contain the string To explicitly select these lists set the colour_list argument to either molmol or x11 218 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Examples To map the order parameter values S onto the structure using the classic style type relax gt molmol macro_exec S2 relax molmol macro_exec data_type S2 relax molmol macro_exec data_type S2 style classic 10 2 THE LIST OF FUNCTIONS 219 10 2 49 molmol ribbon Synopsis Apply the Molmol ribbon style Defaults molmol ribbon self Description This function applies the Molmol ribbon style which is equivalent to clicking on ribbon in the Molmol side menu To do this the following commands are executed CalcAtom H CalcAtom HN CalcSecondary XMacStand ribbon mac Example To apply the ribbon style to the PDB file loaded type relax gt molmol ribbon 220 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 50 molmol tensor_pdb Synopsis Function displaying the diffusion tensor PDB geometric object over the loaded PDB Defaults molmol tensor_pdb self file None Keywor
304. s the final rotation around the z axis again The angles are defined between Within the PDB frame the XH bond vector is described using the spherical angles 0 and where 0 is the polar angle and is the azimuthal angle defined between 168 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Units The time_scale argument should be a floating point number The only parameter af fected by this value is Tm The d_scale argument should also be a floating point number Parameters affected by this value are Diso Dj D1 Da Dz Dy and D Significantly D is not affected The angle_units argument should either be the string deg or rad Parameters affected are 0 a DB and y Examples To set an isotropic diffusion tensor with a correlation time of 10 ns type relax gt diffusion tensor init 10e 9 relax diffusion tensor init params 10e 9 relax diffusion tensor init 10 0 1e 9 relax diffusion tensor init params 10 0 time scale 1e 9 fixed True To select axially symmetric diffusion with a Tm value of 8 5 ns Dratio of 1 1 0 value of 20 degrees and value of 20 degrees type relax diffusion tensor init 8 5e 9 1 1 20 0 20 0 param types 2 To select a spheroid diffusion tensor with a 2 value of 1 698e7 D value of 1 417e7 0 value of 67 174 degrees and value of 83 718 degrees type one of relax diffusion tensor init 1 698e7 1 417e7 67 174 83 718 param types 3 relax
305. s the parameter vector For example for model free model m4 to place lower and upper bounds on the order 44 CHAPTER 6 MODEL FREE ANALYSIS parameter and lower bounds on the correlation time and chemical exchange parameters the vectors are 0 S 1 0l lt tT lt ol 6 38 0 Res 00 The default setting in the program relax is to use linear constraints which are defined as A 0 2 b 6 39 where A is an m x n matrix where the rows are the transposed vectors a of length n the elements of a are the coefficients of the model parameters 0 is the vector of model parameters of dimension n b is the vector of scalars of dimension m m is the number of constraints and n is the number of model parameters For model free analysis linear constraints are the most useful type of constraint as the correlation time 7 can be restricted to being less than 7 by using the inequality Ts Tf gt 0 In rearranging 6 39 the linear constraint function c 0 returns the vector A 0 b Because of the linearity of the constraints the gradient and Hessian are greatly simplified The gradient Vc 0 is simply the matrix A and the Hessian V c 0 is zero For the parameters specific to individual residues the linear constraints in the notation of 6 39 are 10 0 0 000 0 0 0 1 0 0 0 000 0 0 1 0 1 0 0 0 00 0 0 0 6 1 0 0 0 00 0 0 1 0 0 1 00000 0 Se 0 0 0 10 000 0 0 S 1 1 1 0 0 000 0 0 s 0 1 0 1 0 0 00 0 0 Te 0 0 0 0 1 0 00 0 0 te 2
306. sary for imple menting Monte Carlo simulations are 1 The measured data set together with the corresponding error set should be loaded into relax 2 Either minimisation is used to optimise the parameters of the chosen model or a calculation is run 3 To initialise and turn on Monte Carlo simulations the number of simulations n needs to be set 4 The simulation data needs to be created either by back calculation from the fully minimised model parameters from step 2 or by direct calculation when values are calcu lated rather than minimised The error set is used to randomise each simulation data set by assuming Gaussian errors This creates a synthetic data set for each Monte Carlo simulation 5 Prior to minimisation of the parameters of each simulation initial parameter estimates are required These are taken as the optimised model parameters An alternative is to use a grid search for each simulation to generate initial estimates however this is extremely computationally expensive For the case where values are calculated rather than minimised this step should be skipped although the results will be unaffected if this is accidentally run 10 2 THE LIST OF FUNCTIONS 241 6 Each simulation requires minimisation or calculation The same techniques as used in step 2 excluding the grid search when minimising should be used for the simulations 7 Failed simulations are removed using the techniques of model elimination 8
307. scaling is the transformation of parameter values such that each value has a similar order of magnitude Certain minimisation techniques for example the trust region methods perform extremely poorly with badly scaled problems In addition methods which are insensitive to scaling such as Newton minimisation may still benefit due to the minimisation of round off errors In Model free analysis for example if S 0 5 Te 200 ps and Rez 15 1 s at 600 MHz the unscaled parameter vector would be 0 5 2 0e 10 1 055e 18 Rex is divided by 2 7 600 000 000 2 to make it field strength independent The scaling vector for this model may be something like 1 0 le 9 1 2 m 6e8 2 By dividing the unscaled parameter vector by the scaling vector the scaled parameter vector is 0 5 0 2 15 0 To revert to the original unscaled parameter vector the scaled parameter vector and scaling vector are multiplied Examples To apply Newton minimisation together with the GMW81 Hessian modification algorithm the More and Thuente line search algorithm a function tolerance of 1e 25 no gradient tolerance a maximum of 10 000 000 iterations constraints turned on to limit parameter values and have normal printout type any combination of relax gt minimise newton relax gt minimise Newton relax gt minimise newton gmw relax gt minimise newton mt relax gt minimise newton gmw mt
308. scripts have been provided in the directory sample_scripts These can be copied and modified for different types of data analysis 1 2 9 The test suite To test that the program functions correctly relax possesses an inbuilt test suite The suite is a collection of simple tests which execute or probe different parts of the program checking that the software runs without problem The test suite is executed by running relax using the command relax test suite 1 2 10 The GUI relax has been designed primarily for scripting and as such no graphical user interface GUI currently exists The internal structure of the program has been specifically designed so any type of control mechanism can be easily added including a GUI therefore in the future one may be written A GUI will however detract from the power and flexibility inherent in the control by scripting 1 3 USAGE OF THE NAME RELAX 9 1 2 11 Access to the internals of relax To enable advanced Python scripting and control many parts of relax have been designed in an object oriented fashion If you would like to play with internals of the program the entirety of relax is accessible by importation For example all data is contained within the object called the relax data store which to be able to access it needs be imported by typing relax gt from data import Data as relax_data_store This is a dictionary type object which contains the multiple data pipes All of rela
309. sed this option will have no effect hence back_calc and direct are identical For error analysis the method argument should be set to back_calc which will result in proper Monte Carlo simulations The data used for each simulation is back calculated from the minimised model parameters and is randomised using Gaussian noise where the standard deviation is from the original error set When the method is set to back_calc this function should only be called after the model is fully minimised The simulation type can be changed by setting the method argument to direct This will result in simulations which cannot be used in error analysis and which are no longer Monte Carlo simulations However these simulations are required for certain model selection techniques see the documentation for the model selection function for details and can be used for other purposes Rather than the data being back calculated from the fitted model parameters the data is generated by taking the original data and randomising using Gaussian noise with the standard deviations set to the original error set Monte Carlo Simulation Overview For proper error analysis using Monte Carlo simulations a sequence of function calls is required for running the various simulation components The steps necessary for imple menting Monte Carlo simulations are 1 The measured data set together with the corresponding error set should be loaded into rel
310. selected is the GMW algorithm 10 2 THE LIST OF FUNCTIONS 195 Hessian type Patterns Quasi Newton BFGS Bb Ff Gg Ss Newton Nn ewton For Newton minimisation the default line search algorithm is the More and Thuente line search while the default Hessian modification is the GMW algorithm 196 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 36 model_free create_model Synopsis Function to create a model free model Defaults model_free create_model self model None equation None params None spin_id None Keyword Arguments model The name of the model free model equation The model free equation params The array of parameter names of the model spin_id The spin identification string Model free equation mf_orig selects the original model free equations with parameters S Te mf_ext selects the extended model free equations with parameters S Tf S2 Ts miro selects the extended model free equations with parameters S5 T S Ts Model free parameters The following parameters are accepted for the original model free equation S2 The square of the generalised order parameter te The effective correlation time The following parameters are accepted for the extended model free equation S2 The square of the generalised order parameter of the faster motion tf The effective correlation time of the faster motion
311. sidue dependent vector Vx the partial derivatives with respect to the model free parameters of where i 4 j are zero These blocks are left uncoloured The complete gradient of G is the sum of the vectors V x2 62 CHAPTER 8 VALUES GRADIENTS AND HESSIANS denoted by the symbol 0D the orange blocks and summing these for all residues This sum is given by 8 11 and Vx dim 9 8 13 For the parameter set which consists of the local Tm parameter and the model free parameters of a single residue the gradient Vx for the residue i is simply the combination of the single orange block and single yellow block of the index i Figure 8 1 The model free parameter set 3 is even simpler In Figure 8 1 the gradient Vx is simply the vector denoted by the single yellow block for the residue 7 8 4 3 Construction of the Hessian The construction of the Hessian for the models Ti D and G is very similar to the procedure used for the gradient The chi squared Hessian for the global models D and G 1S l Y es US 8 14 i 1 Figure 8 2 demonstrates the construction of the full Hessian for the model G The Hessian for the model is the sum of all the red blocks The Hessian for the model is the combination of the single red block for residue i the two orange blocks representing the sub matrices of chi squared second partial derivatives with respect to the diffusion parameter 2 and the model free parameter 3E and the sin
312. sines defining the XH bond vector within the diffusion frame are s XH Dy 8 135a y XH D 8 135b 6 XH D 8 135c Let the set of geometric parameters be D Dead 8 136 and the set of orientational parameters be the Euler angles D e du my 8 137 The weights The five weights c in the correlation function of the Brownian rotational diffusion of an ellipsoid 8 134 are c l d e 8 138a dus 30282 8 138b co 36282 8 138c ei 35207 8 138d co i d e 8 138e 94 CHAPTER 8 VALUES GRADIENTS AND HESSIANS where d 3 02 0 62 1 e 5 1 3D 01 20302 1 39 91 26202 2 68 26262 The factor SK is defined as R 14322 8 10 3 The weight gradients of the ellipsoid D partial derivative The partial derivatives with respect to the orientational parameter 0 are MES d 8 Dos y 530 ys xs Nd D 00 3D 73D dO 66 6 us mu l a 65 0 o i 2 3 68 8 set je 7 3 aD gt ss ap 55 Fo T dD where Oe 1 00 06 08 hom 3 abi y oO mp ree a ao 9 a0 72 06 00 00 06 06 05 9 58 99s 2 z 2 s 4 058 02 FA 8 139 8 140 8 141 8 1422 8 142b 8 142c 8 142d 8 142e 8 143 8 10 ELLIPSOIDAL DIFFUSION TENSOR Tm partial derivative The partial derivatives with respect to the Tm geometric
313. sis Delete the PCS data corresponding to the alignment id Defaults pcs delete self id None Keyword Arguments id The alignment identification string Examples To delete the PCS data corresponding to id PH_gel type relax pcs delete PH gel 10 2 THE LIST OF FUNCTIONS 10 2 75 pcs display Synopsis Display the PCS data corresponding to the alignment id Defaults pcs display self id None Keyword Arguments id The alignment identification string Examples To display the phage PCS data type relax pcs display phage 261 262 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 76 pcs read Synopsis Read the PCS data from file Defaults pcs read self id None file None dir None mol_name_col None res num col 0 res name_col 1 spin_ num_col None spin_name_col None data_col 2 error col 3 sep None Keyword Arguments id The alignment identification string file The name of the file containing the PCS data dir The directory where the file is located mol_name_col The molecule name column this defaults to no column res num col The residue number column the default is 0 i e the first column res_name_col The residue name column the default is 1 i e the second column spin num col The spin number column this defaults to no column spin_ name_col The spin name column this defaults to no column data_col The PCS data column
314. spectral density values the bond length CSA and heteronucleus type Reduced spectral density mapping data type string matching patterns Data type J 0 J wx J wn Bond length CSA Heteronucleus type Proton type Object name Patterns jo Jj lo or Jj31 COD jwz Jj w Xx or TIN Gi Xx D juh D131w EHh1 or CJ V Gr Eh p r or Bb ond _ Ll ength csa Cc Ss Aa heteronuc_type Hh eteronucleus proton_type Pp roton 10 2 THE LIST OF FUNCTIONS 353 Relaxation curve fitting set details Only three parameters can be set the relaxation rate Rx the initial intensity I0 and the intensity at infinity Iinf Setting the parameter Tinf has no effect if the chosen model is that of the exponential curve which decays to zero Relaxation curve fitting data type string matching patterns Data type Object name Patterns Relaxation rate HEX Rr x Average peak intensities series ave_intensities Aa ve Iilnt Initial intensity i0 Ti 0 Intensity at infinity iinf Iilinf Relaxation period times series relax_times Rr elax _ Tt imes N state model set details Setting parameters for the N state model is a little different from the other type of analyses as each state has a set of parameters with the same names as the other states To set the parameters for a specific st
315. ssian The model free Hessian of the extended spectral density function 8 65 is the matrix of second partial derivatives The matrix coordinates correspond to the model parameters which are being optimised 6 6 partial derivative The second partial derivative of 8 65 with respect to the geometric parameters 6 and 5 is 8 J w 2 E On OF 22 39 gt wri Seu ir a 2c ge MN 0B 06 5 pa 06 06 io 1 wr 2 rg Ti 3w 27 Ty 75 wrp r rg 74 worry Te 74 3602187 7 7i em 1 527 2 9272 5j Sr rs 7 ors Or Oc OT Oc 077 s 1 w7 06 08 08 06 TU 06 06 1 wr 2 72 T 7 wr pti f Cr T Ti wrpri 2 2 gny2 Ts 71 rai 57 sy ete enm E e a 1 Si rf tr S 8 t 223 1 7 06 06 NI wr TEHTI UTT Ta 4 WTsTi 8 86 6 Ox partial derivative The second partial derivative of 8 65 with respect to the geometric parameter 6 and the orientational parameter Dz is k 0 J w 2 OT Oc f a 1 wr x ix sdcenr 06 i OO D 06 OO 1 w7 i k Tg Ta wr pti rg 74 orgri y sepes itat tar 1 529 E ts Ti wrs7 2 Pe ga Sirene SF S rs Tits 8 87 id 0G 0D ld ew rea WTE Ts Ti lun 82 CHAPTER 8 VALUES GRADIENTS AND HESSIANS Di S partial derivati
316. t relax_data read R2 600 600 0 1e6 r2 600 out relax_data read NOE 600 600 0 1e6 noe 600 out relax_data read Ri 500 500 0 1e6 r1 500 out relax_data read R2 500 500 0 1e6 r2 500 out relax_data read NOE 500 500 0 1e6 noe 500 out Setup other values diffusion_tensor init 10e 9 fixed True value set 1 02 1e 10 bond length value set 160 1e 6 csa value set 15N heteronucleus value set 1H proton Select the model free model 48 CHAPTER 6 MODEL FREE ANALYSIS model_free select_model model name Grid search grid_search inc 11 Minimise minimise newton Monte Carlo simulations monte_carlo setup number 100 monte_carlo create_data monte_carlo initial_values minimise newton eliminate monte_carlo error_analysis Finish results write file results force True state save save force True 6 2 2 The rest Please write me Until this section is completed please look at the sample script model free py 6 3 Optimisation of all model free models 6 3 1 The sample script The sample script which demonstrates the optimisation of all model free models from m0 to m9 of individual residues is mf_multimodel py The important parts of the script are Set the data pipe names also the names of preset mo
317. t rotations of the molecule and therefore its effective global correlation time will be maximal To set the size of the diffusion tensor within the PDB frame the unit vectors used to generate the geometric object are first multiplied by the diffusion tensor which has the units of inverse seconds then by the scaling factor which has the units of second Aand has the default value of 1 8e 6 s Angstrom Therefore the rotational diffusion rate per Ais equal the inverse of the scale value which defaults to 5 56e5 s 1 Angstrom 1 Using the default scaling value for spherical diffusion the correspondence between global correlation time Diso diffusion rate and the radius of the sphere for a number of discrete cases will be Tm ns Diso s 1 Radius A 1 1 67e8 300 3 5 56e7 100 10 1 67e7 30 30 5 56e6 10 The scaling value has been fixed to facilitate comparisons within or between publications but can be changed to vary the size of the tensor geometric object if necessary Reporting the rotational diffusion rate per Awithin figure legends would be useful To create the tensor PDB representation a number of algorithms are utilised Firstly the centre of mass is calculated for the selected residues and is represented in the PDB by a C atom Then the axes of the diffusion are calculated as unit vectors scaled to the appropriate length multiplied by the eigenvalue Dz Dy Dz Dp D1 or Diso as well as the scale value and a C atom place
318. t with as much information possible including the details described next to https gna org bugs group relax amp func additem the python and SCons version num bers may also be useful Once the file has been created post a message to the relax development mailing list describing the compilation and the creation of the archive the relax version number the machine architecture operating system and the name of the new file Do not attach the file though You will then receive a response explaining where to send the file to For security the archive will be thoroughly checked and if the source code is identical to that in the repository and the C modules are okay the file will be GPG signed and uploaded to http download gna org relax Chapter 4 Calculating the NOE 4 1 Introduction The calculation of NOE values is a straight forward and quick procedure which involves two components the calculation of the value itself and the calculation of the errors To understand the steps involved the execution of a sample NOE calculation script will be followed in detail 4 2 The sample script Script for calculating NOEs Create the data pipe pipe create NOE noe Load the sequence from a PDB file structure read_pdb name Ap4Aase new 3 pdb structure load_spins spin_id N Load the reference spectrum and saturated spectrum peak intensities noe read file ref list spectrum_type ref noe re
319. ta_col 2 error col 3 sep None Keyword Arguments id The alignment identification string file The name of the file containing the RDC data dir The directory where the file is located mol_name_col The molecule name column this defaults to no column res num col The residue number column the default is 0 i e the first column res_name_col The residue name column the default is 1 i e the second column spin num col The spin number column this defaults to no column spin_ name_col The spin name column this defaults to no column data_col The RDC data column the default is 2 error_col The experimental error column the default is 3 sep The column separator the default is white space Examples The following commands will read the RDC data out of the file Tb txt where the columns are separated by the symbol and store the RDCs under the identifier Tb relax gt rdc read Tb Tb txt sep If the individual spin RDC errors are located in the file rdc_err txt in column number 5 then to read these values into relax type one of relax gt rdc read phage rdc_err txt error_col 4 relax gt rdc read id phage file rdc_err txt error_col 4 290 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 99 rdc write Synopsis Write the RDC data to file Defaults rdc write self id None file None dir None force False Key
320. te method dir The directory name force A flag which if True will cause the results file to be overwritten format The format of the output compress_type The type of compression to use when creating the file Description To place the results file in the current working directory set dir to None If dir is set to the special name pipe_name then the results file will be placed into a directory with the same name as the current data pipe The default behaviour of this function is to compress the file using bzip2 compression If the extension bz2 is not included in the file name it will be added The compression can however be changed to either no compression or gzip compression This is controlled by the compress_type argument which can be set to O No compression no file extension 1 bzip2 compression bz2 file extension 2 gzip compression gz file extension The complementary read function will automatically handle the compressed files 316 CHAPTER 10 10 2 119 select all Synopsis Function for selecting all spins Defaults select all self Examples To select all spins simply type relax gt select allO ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 THE LIST OF FUNCTIONS 317 10 2 120 select read Synopsis Function for selecting the spins contained in a file Defaults select read self file None dir None mol_name_col None res_num_col 0 res_name_c
321. ted with this data pipe The spin_id string is used to select which molecules which residues and which atoms will be recognised as spin systems within relax If spin_id is left as None then all molecules residues and atoms will be placed within the data store If the ave_pos flag is True the average position of all structures will be loaded into the spin container If False then the positions from all structures will be loaded Example For a model free backbone amide nitrogen analysis to load just the backbone N sequence from the file 1F3Y pdb which is a single protein type the follow two user functions relax structure read_pdb 1F3Y pdb relax gt structure load spins spin id QN For an RNA analysis of adenine C8 and C2 guanine C8 and N1 cytidine C5 and C6 and uracil N3 C5 and C6 type the following series of commands assuming that the PDB file with this atom naming has already been read relax structure load spins spin_id A C8 amp C2 relax structure load_spins spin_id G C8 amp N1 relax structure load_spins spin_id C C5 amp C6 relax gt structure load_spins spin_id VON3 amp C5 amp C6 344 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 138 structure read pdb Synopsis The PDB loading function Defaults structure read pdb self file None dir None model None parser scientific Keyword Arguments file The name of the PDB
322. tensity can either be from peak heights or peak volumes The format argument can currently be set to sparky xeasy If the format argument is set to sparky the file should be a Sparky peak list saved after typing the command 1t The default is to assume that columns 0 1 2 and 3 1 2nd 31 and 4 contain the Sparky assignment wl w2 and peak intensity data respectively The frequency data wl and w2 are ignored while the peak intensity data can either be the peak height or volume displayed by changing the window options If the peak intensity data is not within column 3 set the argument int_col to the appropriate value column numbering starts from 0 rather than 1 300 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS If the format argument is set to xeasy the file should be the saved XEasy text window output of the list peak entries command tw followed by le As the columns are fixed the peak intensity column is hardwired to number 10 the 11 column which contains either the peak height or peak volume data Because the columns are fixed the int_col argument will be ignored The heteronuc and proton arguments should be set respectively to the name of the het eronucleus and proton in the file Only those lines which match these labels will be used 10 2 THE LIST OF FUNCTIONS 301 10 2 108 relax_fit select_model Synopsis Function for the selection of the relaxation curve type
323. tensor Defaults diffusion tensor init self params None time scale 1 0 d_scale 1 0 angle units deg param_types 0 spheroid_type None fixed True Keyword Arguments params The diffusion tensor data time scale The correlation time scaling value d scale The diffusion tensor eigenvalue scaling value angle units The units for the angle parameters param types A flag to select different parameter combinations spheroid type A string which if supplied together with spheroid parameters will restrict the tensor to either being oblate or prolate fixed A flag specifying whether the diffusion tensor is fixed or can be optimised The sphere isotropic diffusion When the molecule diffuses as a sphere all three eigenvalues of the diffusion tensor are equal 9 Dy Dz In this case the orientation of the XH bond vector within the diffusion frame is inconsequential to relaxation hence the spherical or Euler angles are undefined Therefore solely a single geometric parameter either Tm or Diso can fully and sufficiently parameterise the diffusion tensor The correlation function for the global rotational diffusion is 1 tau tm C tau e 5 To select isotropic diffusion the parameters argument should be a single floating point number The number is the value of the isotropic global correlation time Tm in seconds To specify the time in nanoseconds set the time_scale argument to le 9
324. th respect to the order parameter and corre lation time Ty is 9 J w 12 082 Ors ae S 7 partial derivative The second partial derivative of 8 65 with respect to the order parameter and corre lation time T is k PI Ber Qa Ust my wet 8 130 0Sj 0r 8 5 rn wrn Tf Tf partial derivative The second partial derivative of 8 64 with respect to the correlation time Tf twice is Tp Ti 3o TTET 75 wri r TE Ti 0772 2 duri 1 5 S es 8 131 Ory E Tf Ts partial derivative The second partial derivative of 8 64 with respect to the correlation times ry and 7 is 0 J w A e i 132 OTs OTs Si Ts T partial derivative The second partial derivative of 8 64 with respect to the correlation time Ts twice is 2 4 3 o J uw is 3 en o Ts 7 Su 72 75 ms Ti Wri ri 8 133 ar rs 74 ursi i k 8 10 ELLIPSOIDAL DIFFUSION TENSOR 93 8 10 Ellipsoidal diffusion tensor 8 10 1 The diffusion equation of the ellipsoid The correlation function of the Brownian rotational diffusion of an ellipsoid is 2 Colt Z y Ge i 8 134 i 2 where c are the weights of the five exponential terms which are dependent on the ori entation of the XH bond vector and 7 are the correlation times of the five exponential terms 8 10 2 The weights of the ellipsoid Definitions The three direction co
325. the sections from the function s docstring 10 2 1 The synopsis The synopsis presents a brief description of the function It is taken as the first line of the docstring when browsing the help system 10 2 2 Defaults This section lists all the arguments taken by the function and their default values To invoke the function type the function name then in brackets type a comma separated list of arguments 139 140 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS The first argument printed is always self but you can safely ignore it self is part of the object oriented programming within Python and is automatically prefixed to the list of arguments you supply Therefore you can t provide self as the first argument even if you do try 10 2 3 Docstring sectioning All other sections are created from the sectioning of the user function docstring 10 2 THE LIST OF FUNCTIONS 141 10 2 4 align tensor copy Synopsis Function for copying alignment tensor data Defaults align tensor copy self tensor from None pipe_from None tensor_to None pipe_to None Keyword Arguments tensor_from The identification string of the alignment tensor to copy the data from pipe_from The name of the data pipe to copy the alignment tensor data from tensor_to The identification string of the alignment tensor to copy the data to pipe_to The name of the data pipe to copy the alignment tensor data to Description
326. the sequence out of the file noe 600 out where the residue numbers are in the second column the names are in the sixth column and the columns are separated by commas relax gt sequence read noe 600 out num_col 1 name_col 5 sep relax gt sequence read file noe 600 out num_col 1 name_col 5 sep The following commands will read the RNA residues and atoms including C2 C5 C6 C8 N1 and N3 from the file 500 NOE where the residue number residue name spin number and spin name are in the first to fourth columns respectively relax sequence read 500 NOE spin_num_col 2 spin_name_col 3 relax gt sequence read 500 NOE num col 0 name col 1 spin_num_col 2 spin_name_col 3 relax sequence read file 500 NOE spin_num_col 2 spin name col 3 relax gt sequence read file 500 NOE num col 0 name col 1 spin_num_col 2 spin_name_col 3 10 2 THE LIST OF FUNCTIONS 325 10 2 126 sequence write Synopsis Write the molecule residue and spin sequence to a file Defaults sequence write self file dir None sep None mol_name_flag False res_num_flag False res_name_flag False spin num_flag False spin_name_flag False force False Keyword Arguments file The name of the file dir The directory name sep The column separator the default of None corresponds to white space mol_name_flag A flag whic if True will cause the molecule name column to be shown res
327. tical models G identical x values and identical parameters 0 between two iterations The universal solution the best description of the dynamics of the molecule is determined using AIC model selection to select between the local Tm models for all spins the sphere oblate spheroid prolate spheroid ellipsoid and possibly hybrid models whereby multiple diffusion tensors have been applied to different parts of the molecule Chapter 7 Reduced spectral density mapping Please write me Until this chapter is written please look at the sample script jwmapping py 55 56 CHAPTER 7 REDUCED SPECTRAL DENSITY MAPPING Chapter 8 Values gradients and Hessians 8 1 Introduction A word of warning before reading this chapter the topics covered here are quite advanced and are not necessary for understanding how to either use relax or to implement any of the data analysis techniques present within relax The material of this chapter is intended as an in depth explanation of the mathematics involved in the optimisation of the parameters of the model free models As such it contains the chi squared equation relaxation equations spectral density functions and diffusion tensor equations as well as their gradients the vector of first partial derivatives and Hessians the matrix of second partial derivatives All these equations are used in the optimisation of models m0 to m9 models tm0 to tm9 the ellipsoidal spheroidal and spheri
328. tin and prints the program s introduction message Command line arguments This code processes the arguments supplied to the program and decides whether to print the help message initialise the prompt execute a script initialise a different UI run the program in test mode or run the program as a slave thread 9 6 THE CORE DESIGN OF RELAX 133 Command line arguments user functions not coded not coded Program state Generic code Specific Setup Specific code Mathematical Functions Python or C Figure 9 1 The core design of relax 134 CHAPTER 9 RELAX DEVELOPMENT Prompt The main user interface consisting of a Python prompt The namespace of the interpreter contains the various user functions which are front ends to the generic code The user functions are simply Python functions which test the supplied argu ments to make sure they are of the correct type string integer list or any other type before sending the values to the generic code The code for the prompt is located in the directory prompt Script If a script is supplied on the command line or executed within another user interface it will be run in the same namespace as that of the prompt Hence the script has access to all the user functions available at the relax prompt This allows commands which are typed at the prompt to be pasted directly and unmodified into a text file to be run as a script GUI The graphical user interface Although
329. ting all other spins for example type relax select read r1 600 res_num_col None spin num col 1 change_all True relax gt select read file r1 600 res_num_col None spin_num_col 1 change_all True Boolean operators The boolean keyword argument can be used to change how spin systems are selected The allowed values are OR NOR AND NAND XOR XNOR The following table details how the selections will occur for the different boolean operators Spin system 12 3 4 5 6 7 8 9 Original selection 0 1 1 1 1 O0 1 0 1 New selection 0 1 1 11 1 0 0 0 OR 0 1 1 1 1 1 1 0 1 NOR 1 0 0 0 0 0 0 1 0 XNOR 1 1 1 1 1 0 0 1 0 10 2 THE LIST OF FUNCTIONS 319 10 2 121 select reverse Synopsis Function for the reversal of the spin selection for the given spins Defaults select reverse self spin_id None Keyword Arguments spin_id The spin identification string Description By supplying the spin_id argument a subset of spin can have their selection status reversed Examples To select all currently deselected spins and deselect those which are selected type relax gt select reverse 320 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 122 select spin Synopsis Function for selecting specific spins Defaults select spin self spin id None boolean OR change_all False Keyword Arguments spin id The spin
330. tion This function will calculate the angles between all loaded alignment tensors for the current data pipe The matrices are first converted to a 5D vector form and then then angles are calculated The angles are dependent on the basis set If the basis set argument is set to the default of 0 the vectors Sxx Syy Sxy Sxz Syz are used If the basis_set argument is set to 1 the vectors Szz Sxxyy Sxy Sxz Syz are used instead 10 2 THE LIST OF FUNCTIONS 147 10 2 9 align_tensor svd Synopsis Function for calculating the singular values for all tensors and the condition number Defaults align_tensor svd self basis set 0 tensors None Keyword Arguments basis_set The basis set to operate with tensors A list of the tensors to apply the calculation to If None all tensors are used Description This function will using SVD calculate the singular values of all tensors loaded for the current data pipe If the basis_set argument is set to the default of 0 the matrix on which SVD will be performed is composed of the unitary basis set Sxx Syy Sxy Sxz Syz layed out as Sxxl Syyl Sxyl Sxzl Syzl Sxx2 Syy2 Sxy2 Sxz2 Syz2 Sxx3 Syy3 Sxy3 Sxz3 Syz3 SxxN SyyN SxyN SxzN SyzN If basis_set is set to 1 the geometric basis set consisting of the stretching and skewing parameters Szz and Sxx yy respectively Szz Sxxyy Sxy Sxz Syz will be used instead The matrix is zz1 Sxxyy
331. to generate initial estimates however this is extremely computationally expensive For the case where values are calculated rather than minimised this step should be skipped although the results will be unaffected if this is accidentally run 6 Each simulation requires minimisation or calculation The same techniques as used in step 2 excluding the grid search when minimising should be used for the simulations 7 Failed simulations are removed using the techniques of model elimination 8 The model parameter errors are calculated from the distribution of simulation param eters Monte Carlo simulations can be turned on or off using functions within this class Once the function for setting up simulations has been called simulations will be turned on The effect of having simulations turned on is that the functions used for minimisation grid search minimise etc or calculation will only affect the simulation parameters and 10 2 THE LIST OF FUNCTIONS 237 not the model parameters By subsequently turning simulations off using the appropriate function the functions used in minimisation will affect the model parameters and not the simulation parameters An example for model free analysis which includes only the functions required for imple menting the above steps is relax gt grid_search inc 11 Step 2 relax gt minimise newton Step 2 relax gt monte_carlo setup number 500 Step 3 relax gt monte_carlo creat
332. tory For more information see the open source infrastructure chapter Although the downloadable distribution archives can be modified it is best that the most current and up to date revision the head revision is modified instead More information about the basics of version control and how this is implemented in Subversion can be found in the Subversion book located at http svnbook red bean com If you are not currently a relax developer you can check out the head revision assuming that 1 2 is the current major version number by typing svn co svn svn gna org svn relax 1 2 relax Otherwise if you are a developer type svn co svntssh xxxxx svn gna org svn relax 1 2 relax 119 120 CHAPTER 9 RELAX DEVELOPMENT replacing xxxxx with your Gna login name If your version is out of date it can be updated to the latest revision by typing svn up Modifications can be made to these sources 9 2 Coding conventions The following conventions should be followed at all times for any code to be accepted into the relax repository A Python script which tests if code meets relax s coding conventions can be downloaded from http nmr relax com scripts code_validator The main reason for these conventions is for readability By using a consistent coding style and a high comment ratio the code becomes much easier to read for non coders and those new to Python It significantly decreases the barrier of entry into the relax source code
333. tral density function parameter 6 the chemical exchange parameter per CSA parameter Ac and bond length parameter r In model free analysis the spectral density parameters include both the parameters of the diffusion tensor and the parameters of the various model free models 0 partial derivative The partial derivatives of the relaxation equations with respect to the spectral density function parameter 0 are OR 9 _ q pra y o 8 46a 00 OR2 0 d Ro C Ro 46b n c PEE 846b O8 Nox 8 c LdJjNOB A 06 Jj 8 46c Pex partial derivative The partial derivatives of the relaxation equations with respect to the chemical exchange parameter pe are ORi 8 3 8 47a TET 2xwg 8 47b Ocwos 8 _ y 8 47c OPex 70 CHAPTER 8 VALUES GRADIENTS AND HESSIANS Ao partial derivative The partial derivatives of the relaxation equations with respect to the CSA parameter Ao are OR 0 7Ri A Ac EJA 8 48a OR 0 c Ro A Oonon 9 SOE N y A AS 0 8 48c r partial derivative The partial derivatives of the relaxation equations with respect to the bond length param eter r are 1 L E JR 8 49b Posos d JIN 8 49c 8 8 4 R 0 Hessians Again different second partial derivatives with respect to the spectral density function parameters 0 and 0 the chemical exchange parameter pez CSA parameter Ac and bond length parameter r These sec
334. tring matching patterns Data type Object name Patterns Relaxation rate rx Rr x Average peak intensities series ave_intensities Aa ve _ Ii nt Initial intensity P Ti 0 Intensity at infinity iinf Iilinf Relaxation period times series relax times Rr elax Tt imes Relaxation curve fitting default values These values are completely arbitrary as peak heights or volumes are extremely variable and the Rx value is a compensation for both the R and R4 values Data type Object name Value Relaxation rate rx 8 0 Initial intensity 10 10000 0 Intensity at infinity iinf 0 0 N state model set details Setting parameters for the N state model is a little different from the other type of analyses as each state has a set of parameters with the same names as the other states To set the parameters for a specific state c ranging from 0 for the first to N 1 for the last the number c should be added to the end of the parameter name So the Euler angle y of the third state is specified using the string gamma2 374 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS N state model data type string matching patterns Data type Object name Patterns Probabilities probs pO p1 p2 PN Euler angle a alpha alphaO alphat Euler angle 8 beta beta0 betal Euler angle y gamma
335. trings two lists of colours can be selected from which to match the strings These are the default PyMOL colour list and the X11 colour list both of which are described in the tables below The default behaviour is to first search the Molmol list and then the X11 colour list raising an error if neither contain the string To explicitly select these lists set the colour_list argument to either molmol or x11 276 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Examples To map the order parameter values S onto the structure using the classic style type relax gt pymol macro_exec S2 relax pymol macro_exec data_type S2 relax gt pymol macro_exec data_type S2 style classic 10 2 THE LIST OF FUNCTIONS 277 10 2 90 pymol tensor_pdb Synopsis Function displaying the diffusion tensor PDB geometric object over the loaded PDB Defaults pymol tensor_pdb self file None Keyword Arguments file The name of the PDB file containing the tensor geometric object Description In executing this user function a PDB file must have previously been loaded into this data pipe a geometric object or polygon representing the Brownian rotational diffu sion tensor will be overlain with the loaded PDB file and displayed within PyMOL The PDB file containing the geometric object must be created using the complementary pdb create_diff_tensor_pdb user function The tensor PDB file is read in us
336. trum type ref relax noe read file sat list spectrum type sat To read the reference and saturated spectra peak heights from the X Easy formatted files ref text and sat text type relax noe read file ref text spectrum type ref format xeasy relax noe read file sat text spectrum type sat format xeasy 10 2 THE LIST OF FUNCTIONS 253 10 2 68 palmer create Synopsis Function for creating the Modelfree4 input files Defaults palmer create self dir None force False binary modelfree4 diff_search none sims 0 sim type pred trim 0 steps 20 constraints 1 heteronuc_type 15N atom1 N atom2 H spin_id None Keyword Arguments dir The directory to place the files force A flag which if set to True will cause the results file to be overwritten if it already exists binary The name of the executable Modelfree program file diff_search See the Modelfree4 manual for diffusion_search sims The number of Monte Carlo simulations sim_type See the Modelfree4 manual trim See the Modelfree4 manual steps See the Modelfree4 manual constraints A flag specifying whether the parameters should be constrained The default is to turn constraints on constraints 1 heteronuc_type A three letter string describing the heteronucleus type ie 15N 13C etc atoml The symbol of the X heteronucleus in the pdb file atom2 The symbol of the H nucleus
337. ts are jmol_name the name of the molecule res_id the residue identifier which can be a number name or range of numbers atom_id the atom or spin system identifier which can be a number name or range of numbers If one of the tokens is left out then all elements will be assumed to match For example if the string does not contain the character then all molecules will match the string Regular expression can be used to select spins For example the string H will select the protons F H2 H98 10 2 THE LIST OF FUNCTIONS 305 10 2 111 residue create Synopsis Function for creating a new residue Defaults residue create self res num None res_name None mol_id None Keyword Arguments res num The residue number res name The name of the residue mol id The ID string for selecting the molecule to add the residue to Description Using this function a new sequence can be generated without using the sequence user functions However if the sequence already exists the new residue will be added to the end of the residue list the residue numbers of this list need not be sequential The same residue number cannot be used more than once A corresponding single spin system will be created for this residue The spin system number and name or additional spin systems can be added later if desired Examples The following sequence of commands will generate the sequence 1 ALA 2
338. turns the gradient d2func The function which returns the Hessian args The tuple of arguments to supply to the functions func dfunc and d2func x0 The vector of initial parameter value estimates as an array min_algor A string specifying which minimisation technique to use min_options A tuple to pass to the minimisation function as the min_options keyword func_tol The function tolerance value Once the function value between iterations de creases below this value minimisation is terminated grad_tol The gradient tolerance value maxiter The maximum number of iterations A Linear constraint matrix m n A x gt b b Linear constraint scalar vector A x gt b l Lower bound constraint vector x lt u u Upper bound constraint vector x lt u c User supplied constraint function dc User supplied constraint gradient function d2c User supplied constraint Hessian function full output A flag specifying which data structures should be returned print flag A flag specifying how much information should be printed to standard output during minimisation 0 means no output 1 means minimal output and values above 1 increase the amount of output printed 192 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS Minimisation output The following values of the full_output flag will return in tuple form the following data 0 xk 1 xk fk k f_count g_count h count wa
339. uclear magnetic resonance relaxation in macromolecules II Analysis of experimental results J Am Chem Soc 104 17 4559 4570 Mandel A M Akke M and Palmer 3rd A G 1995 Backbone dynamics of es cherichia coli ribonuclease HI correlations with structure and function in an active enzyme J Mol Biol 246 1 144 163 Marquardt D W 1963 An algorithm for least squares estimation of non linear param eters SIAM J 11 431 441 Mor J J and Thuente D J 1994 Line search algorithms with guaranteed sufficient decrease ACM Trans Maths Softw 20 3 286 307 Nocedal J and Wright S J 1999 Numerical Optimization Springer Series in Opera tions Research Springer Verlag New York BIBLIOGRAPHY 391 Orekhov V Y Korzhnev D M Diercks T Kessler H and Arseniev A S 1999 H 1 N 15 NMR dynamic study of an isolated alpha helical peptide 1 36 bacteriorhodopsin reveals the equilibrium helix coil transitions J Biomol NMR 14 4 345 356 Polak E and Ribi re G 1969 Note sur la convergence de m thodes de directions conjugu es Revue Francaise d Informatique et de Recherche Op rationnelle 16 35 43 Shanno D F 1970 Conditioning of quasi Newton methods for function minimization Math Comp 24 111 647 656 Steihaug T 1983 The conjugate gradient method and trust regions in large scale optimization SIAM J Numer Anal 20 3 626 637 Tugarinov V Liang
340. urrently be set to sparky xeasy 252 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS If the format argument is set to sparky the file should be a Sparky peak list saved after typing the command 1t The default is to assume that columns 0 1 2 and 3 1 2nd 31 and 4 contain the Sparky assignment wl w2 and peak intensity data respectively The frequency data wl and w2 are ignored while the peak intensity data can either be the peak height or volume displayed by changing the window options If the peak intensity data is not within column 3 set the argument int_col to the appropriate value column numbering starts from 0 rather than 1 If the format argument is set to xeasy the file should be the saved XEasy text window output of the list peak entries command tw followed by le As the columns are fixed the peak intensity column is hardwired to number 10 the 11 column which contains either the peak height or peak volume data Because the columns are fixed the int_col argument will be ignored The heteronuc and proton arguments should be set respectively to the name of the heteronucleus and proton in the file Only those lines which match these labels will be used Examples To read the reference and saturated spectra peak heights from the Sparky formatted files ref list and sat list type relax noe read file ref list spec
341. ve The second partial derivative of 8 65 with respect to the geometric parameter 6 and the order parameter S is k PI _ 2 y Al 1 wn a ek n wrn 06 082 5 06 1 wr E UTs 1 wrr i k ci 1 Ts Ti Ts de c tn a on 6 S partial derivative The second partial derivative of 8 65 with respect to the geometric parameter 6 and the order parameter S is 0 J w 2 3 OTi E rg i wrer me Ts 74 w7s7 uu A 96 V P rpm A OR Gm Oc TE Ti T Ts Ti Ts 06 c m WTE i Uns 7 WTsTi 8 89 6 Tf partial derivative The second partial derivative of 8 65 with respect to the geometric parameter 6 and the correlation time ry is Iw 2 i r ry T 3 wrgri ae aS sles 20 7 T Ti TE 75 3 58 95 5 22 pa EO c E Dog 496 3 rp t n erg 8 90 06 rp T wrer 6 7 partial derivative The second partial derivative of 8 65 with respect to the geometric parameter 6 and the correlation time Ts is Busy Oe os i Or Ts Ti 3 wrsi 52 35 20 3 TsTi Ts Tj 35 M M 4 25 2 UR UU gt 8 91 96 r 7 wrsTi 8 9 MODEL FREE ANALYSIS 83 Dj 9 partial derivative The second partial derivative of 8 65 with respect to the orientational parameters O and Oy is 82J p Re S 1 S ry m T a9 dD A 90 00 NIH or
342. will load the state saved in the bzip2 compressed file save bz2 relax gt state load save relax state load state save relax state load save bz2 relax state load state save bz2 338 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 134 state save Synopsis Function for saving the program state Defaults state save self state None dir name None force False compress_type 1 Keyword Arguments state The file name which can be a string or a file descriptor object to save the current program state in dirname The name of the directory in which to place the file force A boolean flag which if set to True will cause the file to be overwritten Description The default behaviour of this function is to compress the file using bzip2 compression If the extension bz2 is not included in the file name it will be added The compression can however be changed to either no compression or gzip compression This is controlled by the compress_type argument which can be set to O No compression no file extension 1 bzip2 compression bz2 file extension 2 gzip compression gz file extension Examples The following commands will save the current program state into the file save relax gt state save save compress_type 0 relax gt state save state save compress_type 0 The following commands will save the current program state into the bzip
343. word Arguments id The alignment identification string file The name of the file dir The directory name force A flag which if True will cause the file to be overwritten Description If no directory name is given the file will be placed in the current working directory The id argument are required for selecting which RDC data set will be written to file 10 2 THE LIST OF FUNCTIONS 10 2 100 relax data back calc Synopsis Function for back calculating relaxation data Defaults relax data back calc self ri label None frq_label None frq None Keyword Arguments ri label The relaxation data type ie R1 R2 or NOE frq_label The field strength label frq The spectrometer frequency in Hz 291 292 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 101 relax_data copy Synopsis Function for copying relaxation data from pipe_from to pipe to Defaults relax_data copy self pipe_from None pipe to None ri_label None frq_label None Keyword Arguments pipe_from The name of the pipe to copy the relaxation data from pipe_to The name of the pipe to copy the relaxation data to ri label The relaxation data type ie R1 R2 or NOE frq_label The field strength label Description This function will copy relaxation data from pipe_from to pipe_to If rilabel and frq_label are not given then all relaxation data will be copied otherwise onl
344. x s packages modules functions and classes are also accessible by import statements For example to create a rotation matrix from three Euler angles in the z y z notation type relax gt alpha 0 1342 relax gt beta 1 0134 relax gt gamma 2 4747 relax gt from maths_fns rotation_matrix import R_euler_zyz relax gt from numpy import float64 zeros relax gt R zeros 3 3 float64 relax gt R_euler_zyz R alpha beta gamma relax gt R 1 3 Usage of the name relax The program relax is so relaxed that the first letter should always be in lower case 10 CHAPTER 1 INTRODUCTION Chapter 2 Installation instructions 2 1 Dependencies The following packages need to be installed before using relax Python Version 2 4 or higher although any 2 x version may work Numeric Version 21 or higher ScientificPython Version 2 2 or higher Optik Version 1 4 or higher This is only needed if running python lt 2 2 Older versions of these packages may work use them at your own risk If for older dependency versions errors do occur please submit a bug report to the bug tracker at https gna org bugs group relax That way a solution may be created for the next relax release 2 2 Installation 2 2 1 The precompiled verses source distribution Two types of software packages are available for download the precompiled and source distribution Currently only relaxation curve fitting requires compilation to fun
345. x axis The two axes of the Grace plot can be absolutely any of the data types listed in the tables below The only limitation currently anyway is that the data must belong to the same data pipe The spin identification string can be used to limit which spins are used in the plot The default is that all spins will be used however these arguments can be used to select a subset of all spins or a single spin for plots of Monte Carlo simulations etc The property which is actually plotted can be controlled by the plot_data argument It can be one of the following 10 2 THE LIST OF FUNCTIONS 181 value Plot values with errors if they exist error Plot errors sims Plot the simulation values Normalisation is only allowed for series type data for example the R4 exponential curves and will be ignored for all other data types If the norm flag is set to True then the y value of the first point of the series will be set to 1 This normalisation is useful for highlighting errors in the data sets Examples To write the NOE values for all spins to the Grace file noe agr type one of relax gt grace write spin noe file noe agr relax grace write y_data_type noe file noe agr relax grace write x data type spin y_data_type noe file noe agr relax grace write y data type noe file noe agr force True g y yP g To create a Grace file of
346. xtension Example To apply this user function type relax gt pymol cartoon 272 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 86 pymol clear history Synopsis Function for clearing the PyMOL command history Defaults pymol clear history self 10 2 THE LIST OF FUNCTIONS 273 10 2 87 pymol command Synopsis Function for executing a user supplied PyMOL command Defaults pymol command self command None Keyword Arguments command The PyMOL command to execute Description This user function allows you to pass PyMOL commands to the program This can be useful for automation or scripting Example To reinitialise the PyMOL instance type relax gt pymol command reinitialise 274 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 88 pymol cone_pdb Synopsis Display as designed the cone PDB geometric object from the N state model Defaults pymol cone_pdb self file None Keyword Arguments file The name of the PDB file containing the cone geometric object Description The PDB file containing the geometric object must be created using the complementary n_state_model cone_pdb user function The cone PDB file is read in using the command load file The average CoM pivot point vector the residue AVE is displayed using the commands select resn AVE show sticks sele color blue sele The cone object the residue CON is display
347. y is required At the highest level the equation which is actually minimised is the chi squared function QR 2 x7 0 gt Ri SU 6 1 where the index 7 is the summation index ranging over all the experimentally collected relaxation data of all residues used in the analysis R belongs to the relaxation data set R for an individual residue a collection of residues or the entire macromolecule and includes the R4 Ra and NOE data at all field strengths R 0 is the back calculated relaxation value belonging to the set R 0 0 is the model parameter vector which when minimised is denoted by 6 and o is the experimental error The significance of the chi squared equation 6 1 is that the function returns a single value which is then minimised by the optimisation algorithm to find the model free parameter values of the given model 6 1 2 The transformed relaxation equations R 0 The chi squared equation is itself dependent on the relaxation equations through the back calculated relaxation data R 0 Letting the relaxation values of the set R 0 be the R4 0 R2 0 and NOE 0 an additional layer of abstraction can be used to simplify the calculation of the gradients and Hessians This involves decomposing the NOE equation into the cross relaxation rate constant oxog 0 and the auto relaxation rate R1 0 Taking 31 32 CHAPTER 6 MODEL FREE ANALYSIS equation 6 6 below the transformed relaxation equations are R1 9 Ry
348. y a specific data set will be copied Examples To copy all relaxation data from pipe m1 to pipe m9 type one of relax gt relax_data copy m1 m9 relax relax_data copy pipe from m1 pipe_to m9 relax gt relax_data copy m1 m9 None None relax relax_data copy pipe from m1 pipe_to m9 ri_label None frq label None To copy only the NOE relaxation data with the frq_label of 800 from m3 to m6 type one of relax gt relax_data copy m3 m6 NOE 800 relax relax_data copy pipe_from m3 pipe_to m6 ri_label NOE frq label 800 10 2 THE LIST OF FUNCTIONS 293 10 2 102 relax_data delete Synopsis Function for deleting the relaxation data corresponding to ri_label and frq_label Defaults relax_data delete self ri_label None frq_label None Keyword Arguments ri_label The relaxation data type ie R1 R2 or NOE frq_label The field strength label Examples To delete the relaxation data corresponding to ri_label NOE frq_label 600 type relax gt relax_data delete NOE 600 294 CHAPTER 10 ALPHABETICAL LISTING OF USER FUNCTIONS 10 2 103 relax_data display Synopsis Function for displaying the relaxation data corresponding to ri_label and frq label Defaults relax data display self rilabel None frq_label None Keyword Arguments ri_label The relax
349. y known as ACE gr or Xmgr The highly flexible relax user function grace write is capable of producing 2D plots of any x y data sets The three commands grace write y_data_type ref file ref agr force True grace write y_data_type sat file sat agr force True grace write y_data_type noe file noe agr force True create three separate plots of the peak intensity of the reference and saturated spectra as well as the NOE The x axis in all three defaults to the residue number As the x and y axes can be any parameter the command 4 8 VIEWING THE RESULTS 23 0 8 F n ud Me P i aL 0 25 m gat 7 0 wudde L li L i L li l Mi 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 Residue number Figure 4 1 A Grace plot of the NOE value and error against the residue number This is an example of the output of the user function grace write grace write x_data_type ref y data type sat file ref vs sat agr force True would create a plot of the reference verses the saturated intensity with one point per residue Returning to the sample script three Grace data files are created ref agr sat agr and noe agr and placed in the default directory grace These can be vi sualised by opening the file within Grace However relax will do that for you with the commands grace view file ref agr grace view file sat agr grace view file noe agr An exa
350. ython is not required to be able to fully use the program A few basics though will aid in understanding relax A number of simple programming axioms includes that of strings integers floating point numbers and lists A string is text and within Python as well as relax this is delimited by either single or double quotes An integer is a number with no decimal point whereas a float is a number with a decimal point A list in Python called an array in other languages is a list of anything separated by commas and delimited by square brackets an example is 0 1 2 a 1 2143235 Probably the most important detail is that functions in Python require brackets around their arguments For example relax gt minimise will commence minimisation however relax gt minimise will do nothing The arguments to a function are simply a comma separated list within the brackets of the function For example to save the program s current state type relax gt state save save force True 1 2 HOW TO USE RELAX 5 Two types of arguments exist in Python standard arguments and keyword arguments The majority of arguments you will encounter within relax are keyword arguments however you may in rare cases encounter a non keyword argument For these standard arguments just type the values in although they must be in the correct order Keyword arguments consist of two parts the key and the value For example the key may be file and t

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