DeerAnalysis2013 User Manual - EPR@ETH
Contents
1. once you load a data set via the Load button Different models for the background can be selected in the Background models panel center of bottom half of Fig 1 as described in more detail below Similarly Tikhonov regularization or fitting of the data by a model dis tance distribution can be selected in the Distance analysis panel As these approaches are time consuming fitting is not started automatically but only after clicking on the corresponding Fit button Adjustable parameters can be edited directly the most common errors such as non digit input or values out of range are corrected automatically or incremented or decremented by and buttons respectively Several parameters can be adjusted or reset by automatic procedures described below This is done with the buttons Display in each of the plot windows can be toggled In the plot below the Original data panel display of the imaginary part magenta trace can be switched on or off by clicking on the imaginary checkbox If two data sets have been loaded the real part of the previous set data set B can be displayed as a blue trace by clicking on the dual display checkbox This automatically suppresses display of the imaginary part of the active data set data set A and changes the imaginary checkbox into amod depth scaling checkbox Dual display and modulation depth scaling also effect the other two plots where results corresponding to data set B are also displayed as blue t2. the distribution is homogeneous in d 3 dimensions This case applies to most solutions Membrane proteins in a liposome may be confined to d 2 dimensions If possible such confinement should be established by control measurements on singly labelled proteins for which d 2 is expected give a better fit than d 3 For labels attached to a stretched polymer chain d 1 may be appropriate Note also that a choice of d 6 corresponds to a Gaussian background decay as it has been observed with the single frequency SIFTER experiment 9 The dimension is not necessarily an integer number if experimental data of a singly labelled sample can be nicely fitted with a fractal dimension it is advisable to use the same fractal dimension for background correction of the corresponding doubly labelled sample When the Fit dimensionality checkbox is selected both k and d are fitted This mode is suggested only for determining the fractal dimension of purely homogeneous singly labelled samples In this case the Bckg control in the Original data panel should be set to zero green and blue cursors coincide as the early decay of the data is most sensitive to the parameter d 9 5 2 Polynomial Short distances are underrepresented in the intermolecular distance distribu tion ff the spin labels are attached to nanoobjects that cannot penetrate each other As a result the intermolecular contribution decays more slowly at early times than would be expecte
3. 0 25 ds 4 0 s ds 03 Par 6 na O Eoerm tod _ Add ES Par 8 Retain modulation depth information n a www epr ethz ch gt Software Status c G Jeschke 2006 2013 Figure 1 Graphical user interface of DeerAnalysis 2013 The user interface has been programmed with the following ideas in mind 1Unfortunately once a user interface has been edited in Matlab 2008a there is no way to go back The MathWorks did not warn about this problem in their release information of Matlab 2008 no unnecessary complexity no hidden functionality no menus default behavior should give reasonable results for most data e experienced users can easily override default behavior Default behavior is to read Elexsys Xepr data files assume that the last three quarters of the data can be used for the background fit adjust the phase automatically and correct for exponential background decay homogeneous spa tial distribution of nanoobjects Initially no points are cut off at the end of the data set the distance distribution is obtained by approximate Pake transforma tion APT 6 and the mean distance r and standard deviation o by moment analysis within the range from 1 5 to 8 nm using distance domain smmothing with a filter width of 0 2 nm A suggestion for cutting off noisy or distorted data points at the end of the data set is made All this happens automatically
4. R Timmel D Hilger H Jung Appl Magn Reson 2006 30 473 498 The underlying mathematical problem is moderately ill posed i e qual ity of the analyzed data is very crucial Pre processing tools are implemented to correct for experimental imperfections phase errors displacements of the time origin of the modulation and to separate the intramolecular distances of interest from the intermolecular background contribution Furthermore the program provides several independent approaches for extracting the distance distribution which helps to get a feeling for the reliability of the distribution Characterization of the distance distribution in terms of its mean value r and width standard deviation o is usually reliable 5 and is therefore a standard output The performance of the different approaches for data analysis depends on the type of distance distribution narrow or broad peaks or both and was discussed in some detail in Ref 5 DeerAnalysis2013 features a module for validation of distance distributions obtained by Tikhonov regularization With this module a systematic error anal ysis can be performed that may consider experimental noise uncertainties in background correction for a given dimensionality of the background and uncer tainties in the dimensionality of the background This analysis can provide error bars for the points in the distance distribution DeerAnalysis2011 is based on experience with earlier progra
5. amino acid residues be tween the two labels including both labeled residues v is the scaling exponent 0 602 for good solvents expected for soluble proteins in water 0 5 for 6 solvent less than 0 5 for poor solvents e Rice3d m Single Rice peak 13 with mean distance v and standard deviation o in three dimensions Note that for the Gaussian limit of the Rice distribution the standard deviation is by a factor Y2 smaller than the value of in the Gaussian distribution as implemented in DeerAnalysis e Sphere_Surface n Homogeneous distribution of spin labels on the surface of a sphere The sphere diameter d has a Gaussian distribution with standard deviation o d e Triangle _DGauss m Assumes a three spin system equilateral triangle with double Gaussian distribution of the center vertex distance two Gaussian peaks Use ful for homotrimers with two distinct conformations or significantly non Gaussian distance distributions Pair and three spin contributions to the 23 form factor are considered based on 1 with a correction in the fraction of two spin contributions The total modulation depth A Delta and the number of Monte Carlo trials nmc are fixed parameters whereas A should be set to the modulation depth obtained with background fitting Triangle_Gauss m Assumes a three spin system equilateral triangle with Gaussian distri bution of the distance between the center and the vertices Useful for homotrimer
6. as DeerAnalysis2006 does it during Tikhonov regularization r nm Figure 8 Excitation bandwidth correction Blue distance distributions were obtained without black ones with correction a Tikhonov regularization with optimum regularization parameter a 1 b Fit by a single Gaussian peak However simulations of the dipolar evolution function from a distance distri bution as they are required in model fits or at the end of Tikhonov regulariza tion can be performed with a pre computed kernel for the expression given by eqn 5 while the kernel must be computed on the fly for the expression given by eqn 12 This is because the latter expression depends on an additional vari able parameter Aw and furthermore does not allow for scaling In the former 28 expression a scaling of the t axis by a factor x can be compensated by scaling of the distance axis by a factor x 3 Without bandwidth correction DeerAnal ysis2006 uses fast computations with a pre computed ideal kernel Therefore bandwidth correction considerably slows down simulations and model fits and is thus not selected as default behavior of the program It can be activated by selecting the Exci bandwidth checkbox in the Dipolar evolution panel The effect of excitation bandwidth correction is illustrated in Fig 8 for data set deer_bi_oligo_n8_50K from the calibdepth subdirectory Data were cut off at 1504 ns to improve the background fit Without correction bl
7. off automatic modulation depth scal ing between simulated and experimental form factors in the display 4 Changes with respect to Deer Analysis2008 DeerAnalysis2009 is a minor upgrade of DeerAnalysis2008 which fixes a few bugs and can be run on Mac Mac executable for Tikhonov regularization cour tesy Glenn Millhauser The following list gives an overview of the changes automatic phase correction including offset of the imaginary part irregular cutoff behavior and occasional failures in data loading fixed user defined models for three spin systems with equilateral geometry improved automatic determination of the corner of the L curve Mac executables of the Tikhonov regularization modules There is one Microsoft Windows Vista bug that cannot be fixed Some times the Tikhonov regularization executable crashes for unknown reasons In this case the same computation has to be performed once again There is usually no crash on second call The bug seems to be fixed in Windows 7 5 Changes with respect to DeerAnalysis2006 DeerAnalysis2008 is a major upgrade of DeerAnalysis2006 which fixes a few bugs and introduces a number of improvements in data analysis and interpre tation The following list gives an overview of the most important changes e no limitations on minimum time increment and maximum number of data points in experimental data resolution of 1 ns by interpolation for zero time setting display option for error estimates with
8. pump pulse and hence larger modulation depth The power of the pump pulse should be adjusted for optimum flip angle optimum echo inversion using an inversion recovery sequence Tpump T T 2obs T Tobs T echo This has to be done with coinciding pump and observer frequency at the position in the microwave mode where the pump pulse is applied After this step the pump frequency should not be changed anymore If this procedure is not followed modulation depths are ill defined and should not be compared between samples The step is also an absolute requirement if concentrations are to be determined We suggest that the pump pulse is applied at the maximum of the nitroxide spectrum which maximizes modulation depth This minimizes artifacts due to nuclear modulations phase noise and spectrometer imperfections The observer pulses are then applied at the low field local maximum which corresponds to increasing the observer frequency spectrometer frequency by approximately 65 MHz You may measure the field difference AB between the two maxima and multiply it by 2 8 to obtain the exact frequency difference for your particular nitroxide A phase cycle a x should be applied to the first observer pulse to eliminate offsets in the detector channels If this phase cycling is omitted any phase correction of the primary data will not be exact and hence background correction by program DeerAnalysis2006 will not be exact Furth
9. red range to recognition of a long distance contribution that cannot be quantified The computed distribution is displayed only up to the distance recognition limit This new feature is intended to caution users against overinterpretation of data For preparing figures of distance distributions for papers it may be re quired to suppress these background colors This can be achieved by deactivat ing the checkbox Guidance 18 0 03 0 02 0 01 0 2 4 6 8 10 r nm Figure 6 Color coding for reliability ranges Pale green Shape of distance distribution is reliable Pale yellow Mean distance and width are reliable Pale orange Mean distance is reliable Pale red Long range distance contributions may be detectable but cannot be quantified The example data were cut off at a maximum dipolar evolution time of 10 us In this particular case the shape of the distribution can safely be interpreted 10 3 Approximate Pake Transformation APT A very fast algorithm relies on an approximate integral transformation to dipo lar frequency domain subsequent correction of cross talk artifacts and mapping to distance domain APT 6 Ill posedness is moderated by proper discretiza tion in dipolar frequency domain If SNR is too small the distance distribution may still be influence by strong noise artifacts A better compromise between reliability of the distribution and resolution can then be achieved by distance domain smoothing i e by givi
10. resonator and experimental settings and use the same background model you can directly read off concentrations from the edit field Density Note that the program looses calibration on restart 9 7 Long pass filtering The major artifact contribution to DEER time domain signals is usually nuclear modulation due to matrix protons At X band frequencies such proton mod ulation corresponds to a distance of approximately 1 5 nm By restricting the distance range for analysis to 1 75 8 nm contributions by nuclear modula tion can be suppressed However as computation of distance distribution is an ill posed problem an out of range artifact may still influence the result within the range of interest Very strong proton modulations as they are sometimes encountered for membrane proteins in liposomes or detergent micelles should thus be eliminated by filtering This can be achieved by completely eliminating contributions above a cer tain maximum frequency which roughly corresponds to suppressing distances below a certain minimum distance Such complete suppression was described in Ref 4 For broad distance distributions with contributions both below and above 1 75 nm complete suppression may introduce an artificial hole at t 0 into the time domain data and may thus replace the nuclear modulation arti fact with a suppression artifact To avoid this filtering in DeerAnalysis2006 is performed by fitting a third order polynomials to the real a
11. sample or of similar samples first load one of the data sets and process it as usual To keep the same processing parameters for the second data set you may then want to uncheck the Reset checkbox below the Load button in the Data sets panel After loading the second data set its file name is shown in line A of the Data sets panel This is the active data set The file name of the previous data set is shown in line B The original data and processing results can now be compared by selecting the Dual display checkbox in the Original data panel Traces corresponding to the previous data set are now shown in blue in all plots In the Dipolar evolution plot only experimental data but no fits are shown for the previous data set If the two data sets differ considerably in their modulation depth but have similar distance distribution the samples may just differ in the extent of spin labelling or the measurement conditions flip angles resonator pulse lengths may have been slightly different To check for this use modulation depth scal ing 5 by selecting the mod depth scaling checkbox in the Original data panel Differences in the distance distribution are noise related if the original data are not significantly different after such modulation depth scaling 13 Output 13 1 Saving data Unlike its predecessor program Deer Ananlysis2004 the new version DeerAnal ysis2006 does not automatically save results except as an option during pro c
12. to T T2 see Fig 2 Because pulse lengths are finite the relation between this equation and actual delays in the pulse sequence may not be trivial We therefore suggest determination of the time origin zero time from experimental data with a good signal to noise ratio SNR for the pulse lengths and 7 delay that you actually use To obtain a precise value a standard sample with a short distance should be used If you later measure on the same spectrometer with the same pulse lengths and 7 you can use the same value Knowing this value is important for data with poor SNR where automatic determination is likely to fail Automatic determination of zero time to is based on the expectation that the real part of the signal should be symmetric about the time origin For the proper choice of to the first moment of the signal in a range symmetric about to should thus be zero In a first step the program approximates zero time by the time tax at which the real part is maximum Then the first moment is determined in a window tztmax 2 where tx is shifted through the whole data set The optimum value of to is the time ty where the first moment is minimum This procedure is performed with a time resolution of 1 ns obtained by interpolation of the experimental data Such enhanced time resolution improves results for very short distances where it may be important that the true zero time may fall in between two experimental data points Zero time is influe
13. 12 13 14 15 16 17 18 19 20 21 22 G Jeschke M Pannier A Godt H W Spiess Chem Phys Lett 331 2000 243 252 D Hinderberger H W Spiess G Jeschke J Phys Chem 108 2004 3698 3704 A Godt M Schulte H Zimmermann G Jeschke Angew Chem Int Ed 45 2006 7560 7564 T von Hagens Y POlyhach M Sajid A Godt G Jeschke Phys Chem Chem Phys under revision S Domingo Kohler M Spitzbarth K Diederichs T E Exner M Drescher J Magn Reson 208 2011 167 170 G Jeschke ChemPhysChem 3 2002 927 932 Y W Chiang P P Borbat J H Freed J Magn Reson 172 2005 279 295 A G Maryasov Y D Tsvetkov Appl Magn Reson 18 2000 583 605 A D Milov B D Naumov Y D Tsvetkov Appl Magn Reson 26 2004 587 599 A N Tikhonov V Y Arsenin Solutions of Ill Posed Problems Wiley New York 1977 J Honerkamp J Weese Cont Mech Therm 2 1990 17 J Weese Comput Phys Commun 69 1992 99 111 1992 A D Milov A B Ponomarev Y D Tsvetkov Chem Phys Lett 110 1984 67 72 G Jeschke M Sajid M Schulte A Godt Phys Chem Chem Phys 11 2009 6580 6591 41
14. Analysis2006 immediately sets the cutoff cursor to the right border Generally cutting off a significant amount of data will suppress noise but will also cause a suppression of long distances by background correction Proper background correction may become more difficult 9 5 Background correction In most cases EPR distance measurements are performed to elucidate the struc ture of a nanoscopic object Only distances within this object are of interest 11 examples VT_deer_8nm 0 8 0 6 0 4 0 2 10 20 30 0 5 10 15 t us t us Figure 4 Cutting off the noisy part at the end of variable time DEER data a Dipolar evolution plot for the whole data set The orange cursor shows the suggested cutoff time b Dipolar evolution function black and fit red by a distance distribution obtained with APT after cutting the data at the suggested time The contribution of distances to neighboring objects should be suppressed If you think about a biradical or bilabelled protein molecule you want to mea sure the intramolecular distance and suppress contributions from intermolecular distances Such a separation of the signal V t 1 1 AD t B t into a dipo lar evolution function D t for the nanoobject itself and a background decay B t due to neighboring objects requires a criterion for distinguishing the two contributions Furthermore the functional form of the background decay has to be known This functiona
15. DeerAnalysis2013 User Manual G Jeschke ETH Z rich Wolfgang Pauli Str 10 8093 Zurich Switzerland Gunnar Jeschke phys chem ethz ch http www epr ethz ch software index February 13 2013 1 Purpose of the program The program DeerAnalysis2013 can extract distance distributions from dead time free pulse ELDOR data constant time and variable time four pulse DEER 3 4 Furthermore it can be used for direct comparison of primary data of sim ilar samples 5 For a series of related samples an average distance distribution can be computed taking into account the signal to noise ratio of the individual data sets With some caution 6 the program may also be applied to the analy sis of dead time free double quantum coherence EPR experiments 7 It should not be used for data from experiments that have a significant dead time ta gt 2r ns nm 1 where r is the shortest distance in the distribution Except for fits of two user defined models for three spin systems 10 5 1 the program assumes isolated spin pairs If more than two spins are coupled e g spin labeled protein oligomers distance distributions are only approximate with artifact contributions at both short and long distances 1 A future version of DeerAnalysis will allow for an approximate correction of these contributions If you use DeerAnalysis2011 in your research please cite 2 e G Jeschke V Chechik P Ionita A Godt H Zimmermann J Banham C
16. ER experiment Based on these expressions the effect of finite pulse lengths on determining distance distributions was assessed in a later contribution by Milov et al 17 27 extended denotes a model that provides both distribution and deer trace To relax the remaining assumptions and extend the approach to four pulse DEER we examined the dependence of the modulation depth A on the dipolar frequency waa for typical lengths of the observer and pump pulses Numerical density matrix computations of the full pulse sequence were performed for this purpose Details will be published elsewhere The dependence of A on waa can be aproximated quite nicely by a Gaussian function A waa exp 285 11 where Aw is an effective excitation bandwidth with respect to dipolar frequen cies For a four pulse DEER experiments with a pulse length of 24 ns for all pump and observer pulses and for an experiment with a 12 ns pump pulse and 32 ns observer pulses we find the same excitation bandwidth of 16 MHz For a four pulse DEER experiments with a pulse length of 24 ns for all pump and observer pulses the excitation bandwidth is 12 MHz The expression in eqn 11 can be used as a correction of the kernel function eqn 5 1 2 Kir Aw exp cos 3x 1 waat dx 12 0 Aw so that effects of finite pulses length can be accounted for without much addi tional computational effort if the kernel is anyway computed during fitting
17. Ly WLC_rigid_Gauss m Worm like chain model convoluted with a Gaussian distribution with stan dard deviation o r that accounts for conformational distribution of the label These models and any models implemented by the user are included in the model fit popupmenu of the Distance analysis panel On selecting an en try of this menu the parameter definitions default values and limits of the corresponding model are read and the parameter controls in the model fit subpanel are updated A model can have up to eight parameters If it has less superfluous parameter controls are disabled 24 Models with Gaussian peaks that also included homogeneous background which were available in DeerAnalysis2006 have been discontinued There fitting behaviour was found to be too unstable Before fitting select the model fit radiobutton in the Data analysis panel The Distance distribution plot now shows the APT result as a black dotted narrow line and the distance distribution corresponding to the current model and parameter values as a red dotted bold line The Dipolar evolution plot displays the experimental data black line and the data simulated with the current model red dotted line You may now edit the starting values of the fit parameters in the model fit subpanel until you obtain a reasonable agreement between experimental and simulated data Of course this step can be skipped and fitting can be started immediately but by first improving
18. Tikhonov regularization including error estimates obtain by systematic analysis with respect to uncertainties in input data estimates for distance constraints are provided data reduction with use of the information from all data points for enhancing computation speed e enhanced display update during L curve computation and progress bar window with estimate of computation time remaining long computations can be interrupted e possibility for semi manual background correction input of modulation depth and decay time constant new model based fit for random coil conformations unfolded proteins user defined models can have up to eight fit parameters test data sets for training are provided and theoretical distance distributions are displayed for such data sets e Linux executables of the Tikhonov regularization modules Note that error estimates for Tikhonov regularization that can be displayed without using the new validation tool are not the true errors of the distance distribution They are nevertheless included as they provide some hint to problems in data analysis To obtain better estimates of the error please use the new validation tool To compute dipolar spectra with higher resolution you may edit the file zero filling dat This file is an ASCII file that contains a single integer number n Data are zero filled to n times the length of the original time domain data before Fourier transformation The default value is 4 Note that zero fil
19. a sets series8 active set A black traces and series1 set B with modulation depth scaling e basname_res txt a summary of the program settings and the results e basname_bckg dat the phase corrected original data and background fit 1 column time axis in us 27d column real part of original data 3rd column background fit 4 column imaginary part of original data if present e basname fit dat the dipolar evolution function and its fit 1 column time axis in us 2rd column dipolar evolution function after background correction 3rd column fit of the dipolar evolution function e basname_spc dat the dipolar spectrum and its 1 column frequency axis in MHz 24 column experimental dipolar spectrum 3rd column fit of the dipolar spectrum e basname_distr dat the distance distribution 1 column distance axis in nm 2 d column distance distribution P r e basname_Lcurve dat the L curve of Tikhonov regularization only if computed 1 column log p 2 4 column log n ard a ees nd Re eee a The results file basname_res txt protocols all relevant program settings the mean distance width of the distance distribution and third moment and for Tikhonov regularization the regularization parameter For model fits the values of all fit parameters are also saved here 13 2 Copying or printing individual plots The three current plots of DeerAnalysis2006 can be copied into individual Mat lab figures by clicking
20. al_2 m saw tooth and create_test_data_special_3 m 11 Error analysis validation of distance distri butions For an ill posed problem the relation between noise in the input data and un certainty of the output data is difficult to predict Furthermore background deconvolution is not exact for experimental data which also introduces an error in the form factor Often this error due to imperfect background correction even dominates the error in distance distribution While error propagation in Tikhonov regularization cannot be predicted an alytically there is an obvious numerical approach for such a prediction Assume that the uncertainties of background correction can be modelled by variation of the starting time for the background fitting within certain bounds and of the dimensionality of the spatial distribution within certain bounds Background correction can now be performed for a sufficiently large number niziais of param eter sets within these bounds and the form factors obtained can be subjected to Tikhonov regularization This provides ntyjais distance distributions that can be statistically analyzed Thus a lower and upper limit a mean value and a standard deviation are obtained for each point in the distance distribution Alternatively uncertainty of background parameters can be given in terms of lower and upper bounds for the density proportional to concentration the modulation depth and the background dimensionality Th
21. am automatically recognizes if there is no imaginary part After successfully loading data the Status panel shows a short characterization of the data set const time variable time DEER complex real number of data points The filename is included in the title of the DeerAnalysis main window and is also shown in line A of the Data sets panel From version 2013 on data saved by DeerAnalysis can be reloaded when the DeerAnalysis radiobutton in the Data sets panel is activated By default this activates the Locked checkbox in the same panel Any of the DeerAnalysis out put files e g _bckg dat can be selected data from all files are loaded The same feature allows for loading output data from the DEER window of MMM provided that a comparison of experimental data with a simulated distance dis tribution was performed in MMM In Locked mode any automatic processing is switched off data and results are displayed in the form found in the saved files The Locked checkbox can be deactivated to allow for data processing Note however that not the full information from the primary data set is avail able after such reloading Only the real part of the primary data starting at the zero time determined by DeerAnalysis or by the user is saved and can be reloaded In other words phase correction and zero time determination should not be changed in such data sets 9 2 Determining zero time The time origin of the dipolar evolution function corresponds
22. ance range due to nuclear modulations or errors in background correction you may change the range for analysis using the and buttons for the blue and magenta cursor in the Distance distribution panel or direct input into the corresponding edit fields This option can also be used for extend ing the distance range if very long distances have been measured or for selecting only a single peak in a multimodal distance distribution and determining its mean distance and width When the Expand checkbox is selected the distance distribution is displayed only between the cursors 12 2 Checking for the relevance of small peaks With Tikhonov regularization one sometimes observes small peaks in the dis tance distribution that may be related to noise to errors in background cor rection or to genuine small contributions to the distance distribution It is instructive to check the contribution of such peaks to the simulated dipolar evo lution function or dipolar spectrum To suppress such peaks move the blue and magenta cursors so that they include them see Fig 10 and click on the green Suppress button The distance distribution without these peaks is shown as a green curve and the corresponding fit of the experimental data is displayed in the Dipolar evolution plot also as a green curve In the case illustrated in Fig 10 the small peaks are obviously artifacts The original red fit has a slightly better r m s value but is not perfect see fir
23. ariable parameter is combined with each allowed value of each other parameter One should be aware that this may lead to large numbers of trials and that for each trial a Tikhonov regularization has to be performed Computation times may be substantial The Rough grid and Fine grid but 31 tons make suggestions for the bounds and number of trials that are based on the result of the background correction performed in the main window These suggestions should only be used if there is no independent information on the bounds After starting the computation by clicking on the Compute button a progress bar will appear as soon as the first Tikhonov regularization has been performed At that point an estimate of the remaining computation time is displayed If necessary the computation can be interrupted by closing the progress bar For that the x button in the upper right corner of the progress bar has to be clicked After the next Tikhonov regularization is completed a window appears that allows for interrupt or continuation of the computation After all trials are computed the Distance distribution plot displays the distance distribution with the best r m s d as bold green line grey error bars that indicate the full variation of the probability of a given distance over all trials a lower error estimate corresponding to the mean value of the probability minus two times its standrad deviation and an upper error estimate correspond ing to the mean va
24. arization parameter may not be optimum If you have any information on the expected width of the distribution or of the most narrow features in the distribution it is usually best to select the regularization param eter manually The optimum choice is the one that just does not cause undue broadening of expected narrow features After a Tikhonov regularization has been performed the Validation button becomes accessible An error analysis with respect to noise and uncertainties in background correction can now be performed see Section 11 10 5 User models Generally the solution of an ill posed problem can be stabilized by introducing additional constraints A distance distribution P r that conforms to a sim ple model with only a few parameters for example a distribution consisting of one or two Gaussian peaks is strongly constrained Fitting of the data by a model distribution can thus improve reliability of the analysis Furthermore by comparing the parameters for a series of related samples trends can be easily recognized This approach is offered in DeerAnalysis2006 by an interface for fitting pre processed data by user defined models for the distance distribution P r Model functions with one and two Gaussian peaks are already imple mented The model library can be extended by the user as described below In applying this approach one should be aware that a model can impose constraints that do not apply to the true distance distribu
25. d for a homogeneous distribution If singly labelled objects are available the intermolecular part can be measured separately and an experimental background function can be derived Directly using the noisy experimental data set of the singly labelled sample would introduce significant statistical errors It is therefore prudent to use a smooth fit function for that purpose Almost any intermolecular decay can be reproduced by fitting a polynomial to the logarithm of the original data DeerAnalysis2006 allows for polynomials with an order of up to 15 but note that the lowest order should be selected that still gives a good fit flat trace in the Dipolar evolution plot Polynomial fits are mainly implemented for deriving and afterwards saving experimental background functions from singly labelled samples not for direct background correction 15 9 5 3 Experimental Once experimental background functions have been derived from singly labelled samples they can be used for correcting the background in corresponding dou bly labelled samples In this mode the relative magnitudes of the polynomial coefficients are kept fixed The background model is given by B t exp e 5 ot 3 n 0 where k is the density concentration parameter o the order of the polynomial and the cn are the polynomial coefficients determined previously on the singly labelled samples The only fit parameter is k In principle background data should be individually
26. e pump pulse is changed Protonated and deuterated nitroxide spin labels also require separate calibrations Determination of the number of coupled spins is more reliable when based on Tikhonov regularization or a fit of the data by a model distribution and is therefore discussed later on Section 12 3 For a 3D homogeneous distribution of objects the density is proportional to the local concentration The term local refers to the length scale of the DEER experiment which extends to approximately 1020 nm for the background Mea surements of local concentrations can be calibrated with a solution of an ap propriate spin label e g protonated or deuterated TEMPOL in toluene An example data set from our own calibration CT _DEER_tempol_2500uM is pro vided This data set was acquired with a 2mM TEMPOL solution in toluene 16 which corresponds to a concentration of 2 5 mM at 80 K as toluene shrinks to approximately 80 of its room temperature volume when freeze quenched in liquid nitrogen To calibrate 3D background fitting for determination of concentrations se lect Homogeneous as the background model set dimensions to 3 and load a data set for a sample with known concentration Adjust zero time and phase if necessary Now input the concentration in the units you prefer into the edit field Density The color of the density value then changes to green When you now load other experimental data sets that have been measured with the same
27. eer distr Triangle_Gauss r0 t0 par Model library of DeerAnalysis2008 triangle with Gaussian distribution of vertex positions single Gaussian peak with mean distance lt r gt and width standard deviation s r c G Jeschke 2009 enable 2 only the first two parameters are fitted by default PARAMETERS name symbol default lower bound upper bound par 1 lt rv gt 2 5 0 5 10 mean distance from C3 axis par 2 s v 0 5 0 02 5 std dev of vertex position par 3 Delta 1 0 1 1 total modulation depth par 4 nmc 5000 1000 100000 number of Monte Carlo trials SSK KS KKK KKK SKS XK 10 6 Accounting for limited excitation bandwidth Analysis of DEER distance measurements is usually based on analytical expres sions such as eqn 5 that assume ideal pulses Past versions of our analysis programs accounted for this by suggestion a lower limit of 1 75 nm for the re liability of the distribution Maryasov and Tsvetkov 16 first suggested to use corrected expressions to get more reliable results for short distances Their approach considered the full Hamiltonian during the pulse except for the pseu dosecular contribution of the dipole dipole coupling They still assumed that the observed spins are not excited by the pump pulse and the pumped spins are not excited by the observer pulse With these remaining assumptions which are however not very well fulfilled they could still obtain analytical expressions for the three pulse DE
28. eference trace and the second trace being the recoupled trace For any other size of experimental data program response is undefined If you unintentionally load a data set of some other experiment it is advisable to close the program and restart it Mainly as a support for ESP 380 machines the program has the capability to read data in WIN EPR binary format select by radio button in the Formats column of the As the binary number format of the ESP 380 is somewhat obscure this mode requires that the data are first read into WIN EPR on a PC and saved again from WIN EPR This mode is less well tested than the Elexsys mode and completely untested for two dimensional data Alternatively you can convert ESP 380 data to ASCII data also possible in WIN EPR with command sequence 1D processing Parameters List data file Save From an ASCII file only one dimensional data can be read If there are any header lines before the numerical data they must start with a percentage char acter By default the program expects the time axis in nanoseconds in the first column the real part of the data in the second column and the imag inary part if present in the third column These assignments can be adapted in the edit fields below the ASCII radio button For ASCH data exported from WIN EPR the proper settings are 2 3 and 4 instead of 1 2 and 3 The first six lines header lines have to be deleted or commented out by a charac ter The progr
29. ental to data analysis Automatic phase correction can be reactivated by the button left from the value It will always relate to the part of the data between the blue and orange cursors If you move any of these cursors the result may di