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InferenceMAP: Mapping of Single-Molecule

1. i8 Jean Baptiste Masson Patrice Dionne Charlotte Salvatico Marianne Renner Christian G Specht Antoine Triller and Maxime Dahan Mapping the Energy and Diffusion Landscapes of Membrane Proteins at the Cell Surface Using High Density Single Molecule Imaging and Bayesian Inference Application to the Multiscale Dynamics of Glycine Receptors in the Neuronal Membrane Biophysical Journal 106 1 74 83 2014 In this paper we extend the inference scheme to larger scales up to the full mapping of cell membranes We show the efficiency of the inference at various scales and for very heterogeneous environments We demonstrate the sensitivity of the method on experimental data by proving that diffusion and potential maps in synapses can be quantified for various mutants of the glycine receptor Furthermore we demonstrate that Gillespie schemes can be used to simulate trajectories in the inferred maps Numerous simulations in the supplementary materials prove the efficiency of the scheme and discuss possible bias We also detail more strategies to design priors such as Jeffreys prior and regularization schemes for the fields Maximilian U Richly Silvan T rkcan Antoine Le Gall Nicolas Fiszman Jean Baptiste Masson Nathalie Westbrook Karen Perronet and Antigoni Alexandrou Calibrating optical tweezers with Bayesian Inference Optics Express 21 25 31578 31590 2013 In this paper we show that optical tweezers confinement
2. 1 Place the contents of the ViSP installation package directly in your HD path e g place them in a directory such as C InferenceMAP 2 Try running ViSP after renaming the dll files in the installation directory e g rename opengl32 dll to opengl32 temp dll and see if it runs 3 Assure that you have the latest drivers for your graphics card installed 2 2 Mac OS X InferenceMAP has been tested on versions 10 6 x Snow Leopard 10 7 x Lion 10 8 x Mountain Lion and 10 9 x Mavericks of the Mac OS X operating system The installation instructions are as follows 1 Mount InferenceMAP for Mac dmg by double clicking it 2 Double click the InferenceMAP pkg file and follow the on screen installation instructions 3 Click the InferenceMAP file in the chosen installation directory to start the program 2 2 1 Known Issues Reported issues with the Mac version of InferenceMAP may potentially be circumvented trying the following steps 1 If opening InferenceMAP app presents the message InferenceMAP can t be opened because it is from an unidentified developer Instead right click InferenceMAP app and select Open The following the message will appear InferenceMAP is from an unidentified developer Are you sure you want to open it Select Open to launch InferenceMAP 2 If opening InferenceM A P app presents the message InferenceMAP app is damaged and can t be opened You should move it to the Trash
3. D V Inference WRandomized Optimization Selection Radius nm Cost Tolerance Maximum Iterations Ei CNN YA Polynomial Potential Inference x Points MDiffusion Coefficient Force Magnitude MPotential Energy Polynomial Order Blog Arrows 208 Zones v Update Display InferenceMAP User Manual Stepped Through Examples 7 Perform Inference Select the Inference tab and potential_example trxyt press the Infer button to infer the diffusion forces and poten tial energy in each of the zones in the mesh using randomized optimization Subregions of the mesh appearing white will ap pear white indicating that they are being optimized The idea is to perform the randomized opti mization until the cost function has sufficiently decayed In this example this corresponds to ap ESI Trajectories 1263 Points 11877 11879 Duration s 37 8 Dimensions um 5 0 x 5 0 Acquisition Time ms 25 Average Step nm 124 Start Time s 2 ee NI End Time s i Iu M Draw Trajectories Intensity Offset Draw Localizations M Animate Trajectories enn Accumulation Elintervai20 D cMax epa 19 Zones 18608 7 4 proximately 200 iterations SER 4 4 7 h At roughly 200 iterations in the randomized optimization indicated in the Ran domized Optimization window press the Pause double verticle lines button then the Stop red square to stop the inference calcu lation
4. Go to System Preferences select Security amp Privacy Choose the General tab Click the lock in the bottom left corner after which you will be request to enter your user credentials and password Under the Allow apps downloaded from select Anywhere Now when launching InferenceMAP app a window will appear showing InferenceMAP app is an application downloaded from the Internet Are you sure you want to open it select Open InferenceMAP User Manual File Formats 3 File Formats InferenceM AP supports two ASCII text file formats for single particle trajectory information 1 Columns are tab delimited 2 All geometric units are in micrometers ym 3 Temporal information is given in seconds s Files are opened by selecting Open in the File menu Up to 10 files may be opened in a session tabs for which will appear in the File Tabs panel of the main interface see Section 4 3 1 xy t File xyt This format is for single trajectories The user has the option of selecting multiple files of this type in the File Open dialog box each one corresponding to a single trajectory Columns are defined as follows Column 1 Column 2 Column 3 x Coordinate um y Coordinate um Time Stamp s 3 2 tr x yt File trxyt This format is for multiple trajectories Columns are defined as follows Column 1 Column 2 Column 3 Column 4 Trajectory Number x Coordinate ym y Coordinate um Time Stamp s InferenceMAP Us
5. D z Fast Jeffreys Diffusion and Drift Smoothing Uniform ae D V D F V Medium Jaros Diffusion Conservative Force a Sao hine and Potential Uniform Diffusion Force and Pol l Potential D F V Sl A dd ui Jeffreys Confined Potential D Inference D F Inference D Drift Inference MO D V Inference ized Polynomial Potential Inference p E Figure 10 Inference mode selection in meshing interface 2 Adjustments to the mesh may be made as described in Section 6 4 e g activating or deactivating selected regions choosing neighbour connections etc 3 The localization precision is specified with the Localization Precision slider in the Inference tab of the meshing interface 4 Priors may be selected or deselected in the Prior tab of the meshing interface 5 Depending on the number of zones and the inference mode selected Randomized Optimization may be activated in the Advanced tab of the meshing interface 6 Physical parameters are inferred by pressing the Infer button in the Inference tab of the meshing interface 7 2 D Inference The D Inference mode estimates solely the diffusion coefficient in the active zones of a mesh Diffusion is estimated in each zone independently from the others resulting in a rapid calculation as this mode consists of a single variable optimization The posterior probability used to infer the diffusion in a given zone is given by apf aty 4 Di At gt
6. Press the Potential Energy button to overlay the potential energy values to the mesh with yellow arrows corresponding to the force di rection overlaid Clearly seen from the yellow force arrows is the directional bias of the trajectories In fact for the deep wells will have a strong bias whereas the weaker ones wil not In the bottom left quadrant the depth of the potential well corresponds to 1 0 kgT which is roughly the background potential energy due to thermal fluctuations potential example trxyt 2 PEG SMS gt as 8 Stop Calculation j f E R Vaz A 2 IREA P o MA c Pn C SNC EISE P gt MEKA COSE Y id ARS Ew b PIN UN SIA PE 40 101 135 Iterations t BF orce pc 208 Zones E E Update Display Trajectories 1263 Points 11877 11879 Duration s 37 8 Dimensions um 5 0 x 5 0 Acquisition Time ms 25 Average Step nm 124 Start Time s 2 ee i End Time s Draw Trajectories Intensity Offset Draw Localizations Animate Trajectories chin Accumulation Elintervai20 JD cMax resp Quad Tree Meshing Minimum Capacity Minimum Leaf Power e E Minimum Side Size nm e Minimum Points Zone A D V Inference Ie A E M Points Diffusion Coefficient ml Force Magnitude Potential Energy Mi Log J Arrows 208 Zones kT Iv Update Display InferenceMAP User Manual For more intuitive visu
7. VV VU MAP By VV 8 i j The penalization factor 6 can be specified in the Advanced tab of the chosen meshing interface Figure 11 7 3 2 Applicability The D F Inference mode is well suited to trajectories in the following situations 16 InferenceMAP User Manual Inference Potential Energy Penalization Beta D F Inference Figure 11 Potential energy penalization factor 6 selection slider e Mapping of local force components e The presence of non potential forces e g a rotational component e Rapid characterization of the diffusion coefficient and directional biases of the trajectories 7 4 D Drift Inference The D Drift Inference mode estimates the diffusion coefficient and drift E in the active zones of a mesh Prameters are estimated in each zone independently from the others Specifically the Bayesian inference effectuated in each zone 1 7 is an optimization of D and 2 in the zonal posterior probability 2 id At kgT rk ak u 1 H 4 D jt At bod T aAaAa 5 joo P D I D 9 y 2 TI I Ora C x Ps Di 9 k pk ES j exp P iw Where D is the diffusion coefficient F is the force vector 7 is the friction viscosity 4 designates the index for which the points a of the k trajectory are in Si j the current zone being analyzed and is the experimental localization accuracy 30 nm by default The P Di term in 6 designates the opti
8. ls ees s s ases 34 15 2 Example 2 Generating a Potential Interaction Energy Map e 31 15 5 Examples Membrane Micro domall sins raca a en Uh nad uode P RUE de uss dopo Ld CMS 42 15 4 Example 4 Neurotransmitter Receptors uuum 9 OU EO EORR E Reeve E Xon WU XX Rosendo xc Res 45 16 Acknowledgments 50 10 1 Development Eiras xus a a ob Bow 6 NIE Pn cn ee ee A e ee mo X S Be eA oc we Re 50 I6 2 co rt A es Ge AAA E A AA EA A A 50 Sr Open rs A E el ee edo de dde Y A E iia 50 OE OCRE 1d amp A A AAA A 24228284 1 14 ds A e e a 50 Osos LLO 24423 984322 24 20 AA EARL 2 Bd oeh 28 se 50 16 06 Cls tere Alcor IDS Ae usce gl deme Se wa cn ag de E da e Uc Dee e Ur DP a pa ea 50 17 Contact Information 51 InferenceMAP User Manual Preliminary Remarks 1 Preliminary Remarks The trajectory inference technique utilized by InferenceM AP first described in 8 is used to study the dynamics of single molecules Specifically it generates maps of the dynamic parameters that dictate the motion of single molecules These parameters may include the diffusion forces directional biases interaction potential energies and drift Mapping these spatially dependent parameters is of great interest for a variety of studies First dynamical maps can be used to decipher physical interactions a molecule may have with its surroundings Secondly generated maps reliably distinguish physical parameters from one another Finally it is a means of probi
9. 7 It is recommended to keep the maximum number of iterations between 5 10 Parameter values for the subregion zones are updated after the maximum number of iterations has been reached thereafter another selection circle is chosen e A stopping condition may be specified based on the percent error between consecutive posteriori cost function values defined in the Cost Tolerance slider It is recommended to keep this tolerance below 1 as the stopping condition may be met before all zones in the mesh have been visited Often it is suggested to define a 0 96 tolerance and to manually stop the calculation by pressing the Pause button in the Inference tab when the cost function has decayed sufficiently as in Figure 13 For especially large meshes stopping the calculation will be delayed in these cases the user is advised to press the Pause button keep the cursor hovering above and wait 5 014e 03 55 115 Iterations Figure 13 Randomized Optimization interface demonstrating the decay in the cost function Generally the Random ized Optimization calculation may be stopped when the cost function has sufficiently decayed as indicated 7 8 Freehand Selection Inference For determination of the diffusion coefficient and force components in a localized region of a trajectory overlay Infer enceMAP includes a Freehand Selection tool in the main interface shown in Figure 14 This is useful in cases where only subregio
10. E ES Ly p TIE ue HEEL BEE ee HE ABE ler ABA LEE eee abe BEES fo ee t EEL 1 d j f ES erdt d cS i E os 39 EEA nee Stepped Through Examples Trajectories 1263 Points 11877 11879 Duration s 37 8 Dimensions um 5 0 x 5 0 Acquisition Time ms 25 Average Step nm 124 Start Time s end tine 37 75 RENI Intensity Offset Draw Trajectories Draw Localizations Animate Trajectories Accumulation Mi interval 20 cMax ees Ba A EE E Diffusion um s 0 2528 mter 0 F Iter 0 Drift Force pN cMin 7 77 8 22 Landscape Minimum Leaf Power Minimum Capacity feo e OT Minimum Side Size nm _ Minimum Points Zone MAIA Mode D Inference LA a die ag Points H Diffusion Coefficient Force Magnitude WlPotential Energy Bi Log Arrows 208 Zones v Update Display Trajectories 1263 Points 11877 11879 Duration s 37 8 Dimensions um 5 0 x 5 0 Acquisition Time ms 25 Average Step nm 124 Start Time s e e NI i End Time s Intensity Offset Draw Trajectories Draw Localizations Animate Trajectories chin Accumulation Mintervai 201 cMax espe LL Em z 0 2528 Diffusion um s o oo ooo AO ETS Localization Precision nm Maximum Neighbor Distance View Neighbor Connections 1000 0 Potential Energy Penalization Beta D F Inference
11. Section 13 5 InferenceMAP User Manual Meshing 6 Meshing InferenceM AP offers three types of meshing shown in Figure 3 The type of meshing method deemed appropriate for a given data set depends principally on the density of localizations not necessarily trajectories and not unrelated the desired resolution with which the dynamic landscape is mapped The user is reminded that the main assumption in meshing is that the inferred parameter diffusion coefficient force components drift components or potential energy remains constant in each zone o CEREBLLI N N da pty NON vi METTI EI M d Fd g A gt EPA 2 a b Square Meshing c Voronoi Figure 39 Meshing types available in InferenceM AP for a simulated spiral trajector Meshing and d Quad Tree Meshing A 6 1 Square Meshing Square Meshing involves spatial partitioning the trajectory overlay space into identically sized squares It is most appro priate in cases where the localization density throughout the data set is relatively homogeneous The Square Meshing dialog box is shown in Figure 4 Side Length nm Minimum Points Zone Mode Localization Precision nm D Inference ETE a Ta KiPoints AOiffusion Coefficient Force Magnitude JJ Potential Energy m a Arrows 55 Zones Figure 4 Square Meshing interface An appropriate option for the square side length is the average trajectory step length this
12. and probing dome with the same laser can be calibrated more precisely than previously used method using a Bayesian inference scheme Silvan T rkcan and Jean Baptiste Masson Bayesian Decision Tree for the Classification of the Mode of Motion in Single Molecule Trajectories PLoS ONE 8 12 e82799 2013 In this paper we use the inference and various statistical estimators to quantify the nature of biomolecule motion from freely diffusing to harmonically confined We also apply it to time changing states Silvan T rkcan Maximilian U Richly Antigoni Alexandrou and Jean Baptiste Masson Probing Membrane Protein Interactions with Their Lipid Raft Environment Using Single Molecule Tracking and Bayesian Inference Analysis PLoS One 8 1 e53073 2013 In this paper we analyse the hopping of biomolecules between confining environments We demonstrate that the amount of energy necessary to hop can be accurately inferred that the diffusivity map can be accurately inferred even in the hopping area and that the inference can be applied with time varying diffusivity and potential fields The method is applied to the hopping of e toxin Time evolving fields are induced by the removal of cholesterol and sphingolipids by respectively cholesterol oxidase and sphingomyelinase Supplementary materials give a large amount of simulations supporting our claims Silvan T rkcan Antigoni Alexandrou and Jean Baptiste Masson A Bayesian Inferenc
13. d SEES TOE APPAIA dd 4 4 4 2 a als s olk dec ein 5 da aec die Tou Oe 234 sad a Ter Randomized ODLOInlzdtiQB s ped GE opo 2 a eee aS ee EEE ee eo RS a 8 Freehand Selection Imicrence aane di Is ee ae 1908 8 Priors NM UON as Ae Be aaa BO Oe let AS Se ee TT UM Iur seca a es Beek Ue me AA n ee eh ee an A Se ee tn i ee cd enu ni 1 Ry de A A heey Sah a tans aa ain E A Ae ena ened eh ad e AL tee Gee a ec ee a ts 9 Posterior Sampling 10 Trajectory Simulation 11 Landscape Viewing CONTENTS Ot Ot OT OT Q m WwW Ww QJ o 23 25 26 InferenceMAP User Manual CONTENTS 12 Freehand Selection 27 13 Tools 28 131 AM OLALIONS e deeds eee os AA SH Be SOS Behe BS 28 laz Density Calculation anat Ok he Ew woe ee Eo Wee SER TE Suy WE A SEEDERS OED HS 28 Me AOI i OC CLONE a o E net al eek e Bet eal de IRE He cee ne iie Se eo ae ee Be 29 I9 ave CON e oY Se Eas mo wk he oe Se e E EMM DDS eee Oo ey eh A IA 29 o TEOG a hives ee IN ETE 29 19 06 White Backeround 4 244624 Sob ends ss OR ALL 4 Te decem 9 EES OP irse EEE AAS 30 14 Performance 31 IMMINET RM ton te ce ees ae crac e Whee BE eek y Be a or BU 5 a 31 142 Number or bocalizatiofiS s s 6 9 sad ESL a RES SE Oe ERS GS 31 149 Mode selel gt oe eb eur dedu Se das 8 OSES OES ee as AAA eee ee ES 31 HAA Pror roba DIES 20503 RS TO E T a ed ea ras ees ate ee E ie hace a ae ee es ye ae es 33 15 Stepped Through Examples 34 15 1 Example 1 Generating a Diffusion Map
14. difference of potentials in two zones 24 InferenceMAP User Manual Trajectory Simulation 10 Trajectory Simulation After an inference calculation has been performed to generate diffusion and potential energy maps there is the possibility to generate simulated trajectories based on the inferred parameter values This is based on the Gillespie method described in 1 The user may be motivated to create simulated trajectories in a few different situations Namely in cases where trajectories are short e g less than 10 points and certain long trajectory metrics would like to be estimated These may include measuring whether a trajectory experiences anomalous motion residence time and binding and dissociation rates Simulated trajectories are generated via the Simulation tab of the meshing interface seen in Figure 18 pem Humber of Trajectories Delta ms Maximum Time Steps 5ave Trajectories Figure 18 Simulation tab of the meshing interface In this tab the user may select the number of trajectories the time spacing delta between consecutive points and the maximum time steps in an individual trajectories Pressing the Save Trajectories button outputs all trajectories into a rxyt file described in Section 3 Output trajectories will have a spatial resolution corresponding to that of the mesh 20 InferenceMAP User Manual Landscape Viewing 11 Landscape Viewing InferenceM AP offers to option to v
15. of points steps Quali tatively the distributions narrow with the increased number of points 4 Points 30 Points gt 0 8 50 Points Es 70 Points a 90 Points E O 0 6 o 04 g an 2 0 2 0 0 5 1 1 5 2 Diffusion Coefficient um s Figure 26 Plots of posterior probabilities of the diffusion coefficient as a function of number of points translocations in the parameter estimation The Bayesian inference estimator that we use is unbiased and we illustrate this in Figure 27 Here the nominal diffusion coefficient 0 5 jum s for trajectories of different numbers of translocations is estimated Correspondingly the error in the estimation is embodied by its standard deviation stdev which is described with a 1 N profile This is an important result as the Bayesian inference method employed by InferenceM AP is unbiased regardless of the number of translocations per trajectory or analogously translocations per zone of a generated map 14 3 Mode Selection InferenceM AP offers numerous modes to perform inference calculations to generate maps of dynamic parameters This sections seeks to compare the D Inference and D V Inference modes for two simulated datasets one in which trajec tory motion is purely diffusive and another in which an interaction region is present Effectively two models of motion are being compared and depending on which is selec
16. specified diffusiv ity Deselect the Make Selection button in the Main Interface and open the Square Mesh ing interface by accessing File gt Inference gt Meshing gt Square As we know the diffu sivity to be relatively constant within each quadrant we can choose relatively large grid spac ings in the mesh In the Side Length nm slider manually type in 500 nm Afterwards press the Apply button to gen erate the mesh The default col orcode corresponds to the num ber of points in each zone seen in the Colorbar 3 Custom Selection Inference Stepped Through Examples diffusion example trxyt 4 Generate a Square Mesh Trajectories 1680 Points 32890 32891 Duration s 50 5 Dimensions um 10 0 x 10 0 Acquisition Time ms 25 Average Step nm 160 Start Time s ge NN RR Draw Trajectories i Offset Draw Localizations E aaa Animate Trajectories e Accumulation Bintervaio reso 0 Make Selection Points Diffusion um s 0 9750 Inter D 0r Force pN 0 05 0 32 calization Precision nm Force Magnitude pN 0 323 22 Area fume 4415 Calculate Neighbor Radius nm 8 Iteration 13 Update Display diffusion_example trxyt 39 Trajectories 1680 Points 32890 32891 Duration s 50 5 Dimensions um 10 0 x 10 0 Acquisition Time ms 25 Average Step nm 160 Start Time s 2 ee i End Time s CEN Draw Trajectories Intensity Offset Draw Localizati
17. the spatially dependent friction coefficient or viscosity D is the spatially dependent diffusion coefficient and t is a zero average Gaussian gt noise term In our case we may model forces from a potential as F r 2 VV The associated Fokker Planck equation which governs the time evolution of the particle transition probability P r t2 r t4 is given by d P r to r1 t1 c ad VV r dt i y r There is no general analytic solution to Equation 2 for an arbitrary diffusion coefficient D and potential energy V However if we spatially partition mesh the area explored by the single particle trajectory we may assume a constant D and V within each partition upon which the general solution to Equation 2 is a Gaussian described in sum VV 625 ta V 173 ri 2 exp gt a A Di jc s t5 t1 P r t2lri ta WD FP 3 talFi t 2 P r2 talri t1 Dij Vig 3 AT Dij con to t1 Where 2 j represent indices for the zones of the mesh and o represents the experimental localization precision An advantage to this approach is that each mesh zone is free to have a different D and V they are not necessarily constant over the entirety of the trajectory The overall probability of a trajectory T due to the spatially dependent variables D and V is computed by multiplying the probabilities of all the individual subdomains P T D j Vij to give an expression for the likelihood P
18. to an open trajectory file by selecting the TIFF Overlay button in the Tools menu in the Main Menu shown in Figure 25 Of note TIFF images must be 16 bit black and white to be properly overlaid eonetry inoge Sequence p Inoge Sequence Resolution nm px Alpha Image Number L L i ims x Align nm y Align nm Gamma i brightness IDEEN Clamp Figure 25 TIFF Overlay interface tabs The Geometry tab permits adjustment of the pixel size and allows adjustments to image orientation The Image tab contains functions for image rendering The Clamp box clamps the images to the maximal dimensions of the loaded trajectory file The Sequence tab applies to overlaid multi image stacks The Image Number slider allows traversal of the images in the stack The Sync button synchronizes images loaded in the stack to trajectory animations activated by clicking the Animate Trajectories button in the Visualization Panel of the Main Interface 29 InferenceMAP User Manual Tools 13 6 White Background The user may change the default black background of the Display Window to white by toggling the View gt White Background option 30 InferenceMAP User Manual Performance 14 Performance This section outlines the performance and robustness of the inference technique subject to changes in calculation parameters We emphasize that default calculation parameters are largely sufficient to yield accurate estimates of dynam
19. with the Minimum Points slider in the meshing interface for example In this case it is recommended to manually reactivate these zones by right clicking on them An additional cause for the appearance of holes is if meshing parameters are not appropriately selected e Square Meshing The side length is chosen too small e Voronoi Tessellation To many cells are chosen considering the number of localizations in the loaded file e Quad Tree Meshing The minimum capacity or minimum side length is chosen too small For large maps containing thousands of zones an easy way to see the inactive zones is by setting the cMax slider to zero deselecting the Draw Trajectories check button and changing the grid color or turning it off in the Overlay tab of the meshing interface Holes in the mesh are made much more evident as shown in Figure 9 40 before Holes to be avoided Figure 9 In adjusting visualization parameters holes in the mesh can be made obvious Holes such as these should be avoided to activate the inactivate zones it suffices to right click on them 13 InferenceMAP User Manual Inference 7 Inference InferenceMAP uses the Bayesian inference technique that was first described in 8 We model the motion of single particles with an overdamped Langevin equation df F P di ES 2D r t 1 Where F is the particle displacement vector F T is the spatially dependent force directional bias y r is
20. x Py Di x Ps Dia 6 P Dis 47 II Il k HTE CSi Where D is the diffusion coefficient designates the index for which the points p of the k trajectory are in S the current zone being analyzed and c is the experimental localization accuracy 30 nm by default The P Dj term in 6 designates the optional Jeffreys prior Section 8 2 Jeffreys prior may be activated and de activated in the Priors tab of the meshing interface 15 InferenceMAP User Manual Inference The Ps D term is the diffusion smoothing prior which is described in Section 8 3 The final result of this calculation is the maximum a posteriori MAP estimate and is updated to the mesh in the display window MAP DM 7 2 1 Applicability The D Inference mode is well suited to trajectories in the following situations e Freely diffusing molecules e Rapid characterization of the diffusivity 7 3 D F Inference The D F Inference mode estimates the diffusion coefficient and force components in the active zones of a mesh Parameters are estimated in each zone independently from the others Specifically the Bayesian inference effectuated in each zone 1 5 is an optimization of D and F in the zonal posterior probability gt gt 2 exp Py TTE Dus Fi At ksT EE EE C brad P Dis 0 0 x II 4r Dij e At ij T At k LTE ESi j x Py Dij x Ps Di 7 Where D is the diffusion coefficient F is the force vector u desi
21. 3 Density Panel top in the Main Interface with localizations density plot below 28 InferenceMAP User Manual Tools 13 3 Interval Selection Specific time intervals in a loaded trajectory dataset can be selected for analysis This is useful if a temporally windowed analysis is desired The Start Time Slider and End Time Slider in the Main Interface are used to select the desired interaval Only trajectories in the selected window will be updated to the display as shown in Figure 24 Afterwards a mesh may be applied as usual Section 6 but only trajectories within the selected interval will be considered Of note the interval selection is disabled once a mesh has been applied Start Time s CN End Time s Figure 24 Interval selection sliders in the Main Interface 13 4 Save Screen At any moment while using InferenceMAP a screen shot of the Display Window may be taken by selecting Save Screen in the Tools menu of the Main Menu This feature will also save a screen shot of the colorbar in a separate file with colorbar postfix 13 5 TIFF Overlay An important feature in InferenceM AP is the ability to overlay experimentally acquired TIFF images to corresponding trajectories Both single image files e g DIC or transmission images and multi image stacks such as the raw images from which the trajectories are constructed may be overlaid to open trajectory files described in Section 3 A TIFF image can be overlaid
22. 4 eode ded Side US Box M Gela uS e by iem DA 4 Main Interface 5 Trajectory Visualization 6 Meshing OMNES comi lnc a 4 a es A 885 eee ee 44 ae MMe A 0 2 Vorono Lesscllation 24 uns A MEG ilo a 8 pte A A A eds GA ME Oe td I 0 2 2 Tesselation sourire ie tomar d xx ei Ste Se ue ee ee E BERS ae a 0 9 Quads Tres Mes NE s uuu aue dno ded ole dr rara qol eed es ege Y OO OS spec hole ew ou OA Wes hie Ad VICE ded cle eS box ER AO E dr erai UP OS woe duet obo xd 6 4 1 Neighboring Zone Connections ud 6 de a ee a CR REC acere ti 6 4 2 Manual Zone Activation and Deactivation e 6 4 3 Preventing Holes in the Mesh a 2 6 cado Ree Re pen ERU ee BE rot ee ee 7 Inference Tol Jferenco VW On TION OR cur a di pop ano dedit A AN Se aa a Vai ey we add ute Oe ee n td e ee Se a ca NM PANIS NU a SS eee Sn og th a E ese ee ata ee ed ey Se ese Mee ee es ad a So ta Lo spPUCaDIty suka 29 asjad 0 0 OE 4 8 oboe diede dei See eS GS or DEINO E TTPLI T rrrr iow Fotona Calculation pst ds ey ce Ege vta SES E et e P Su UE Bex dre RT E s 0 4 SNDDROSDIIU La ur os dng om oue E Sew sd E I EN Ru REN oes iu ute E Ig d Ew BE o Ten O M es Ga ee ee Oe eS Se eee ee E E a a he p vl APPLAD amp 2 3 66 28 5B kh da k te BRE mu eee daa ecu XE AAA eo DN Ten ad ba Be oY ees Sy med ad ee e a ALA ee eS Tol o0 s iM a a e See we nis ec nae A pe tee eg is a oe ce cece t a ee A 7 6 Polynomial Potential Inference 4 1 0 kee ko EGER EUG KN e E ok dod dE RSS
23. Average Step nm 157 Start Time ts1 o oo i End Time ts 292 33 Draw Trajectories Intensity Offset Draw Localizations 1 000 cMin Animate Trajectories Accumulation EE interval 20 cMax E T EE Diffusion um s 0 o o 10 0 Localization Precision nm Force Magnitude pN 0 L Area um 0 View Landscape Scale MN LT Light y Fog Start 0 Es Ti e Light x Fog End M Points Diffusion Coefficient mForce Magnitude Potential Energy JK rd Arrows 50 Zones InferenceMAP User Manual 15 4 Example 4 Neurotransmitter Receptors Stepped Through Examples This example demonstrates how to create a diffusion map for glycine receptors on a mouse hippocampal neuron membrane Experimentally these trajectories were captured in a uPAINT configuration in a similar fashion to 1 Select the Glycine Recep tors on Mouse Hippocam pal Neuron file from the File gt Examples menu The tra jectories will start animating in an accumulation mode demon strating how rapidly the surface of the apical membrane is ex plored by the tracked glycine re ceptors A GFP image is over laid to show the shape of the neuron Deselect the Animate Trajec tories button and select the Draw Trajectories button in the Main Interface to overlay all the trajectories in the file 1 Load Neurotransmitter Receptor File lycine receptor trxyt 2 Visualize Trajectories glycine receptor tr
24. Duration s 199 9 Dimensions um 25 2 x 17 4 Acquisition Time ms 5 Average Step nm 178 Start Time s e es A End Time s 200 00 v DIT Trajectories Draw Localizations M Animate Trajectories Accumulation H Interval LUE EE Points 0 Diffusion um s Dos oo O NT 0 0 Localization Precision nm Force Magnitude pN 0 TI area tum o Vo Tessellation Number of Zones Minimum Points Zone Maximum Iterations ce Type 9L1 9L2 ient glForce Magnitude Potential Energy v Arrows 730 Zones Trajectories 9453 Points 178264 178333 Duration s 199 9 Dimensions um 25 2 x 17 4 Acquisition Time ms 5 Average Step nm 178 Start Time s e es End Time s 200 00 Draw Trajectories Draw Localizations Intensity Offset M interval 20 cMax ese OF je Points 58709 Diffusion um s Force pN 10 03 Localization Precision nm Force Magnitude pN cam RR area tum o V oronoi Tessellation inference vertoy Advanced prior Posterior Simulation Landscape Number of Zones Minimum Points Zone e AMSTEL K Means Distance Type OL1 L2 lll D F Inference Maximum Iterations m BiPoints gDiffusion Coefficient W Force Magnitude Potential Energy 47 E Log m Arrows 730 Zones InferenceMAP User Manual REFERENCES References 1 2 3 4 5 d 6 7
25. InferenceMAP Mapping of Single Molecule Dynamics with Bayesian Inference Mohamed El Beheiry Maxime Dahan and Jean Baptiste Masson Physico Chimie Curie Institut Curie CNRS UMR 168 Universit Pierre et Marie Curie Paris 6 26 rue d Ulm 75248 Paris France Institut Pasteur Physics of Biological Systems CNRS UMR 3525 25 28 rue du Docteur Roux 75015 Paris France Janelia Research Campus Howard Hughes Medical Institute Ashburn VA 20147 USA Single particle tracking SPT grants unprecedented insight into cellular function at the molecular scale 1 Throughout the cell the movement of single molecules is generally heterogeneous and complex Hence there is an imperative to understand the multi scale nature of single molecule dynamics in biological systems We have previously shown that with high density SPT spatial maps of the parameters that dictate molecule motion can be generated to intricately describe cellular environments 2 3 4 To date however there exist no publically available tools that reconcile trajectory data to generate the aforementioned maps We address this void in the SPT community with InferenceMAP an interactive software package that uses a powerful Bayesian method to map the dynamic cellular space experienced by individual biomolecules Supplementary Software High density SPT methods such as sptPALM 5 and uPAINT 6 capture thousands of molecule trajectories in a few minutes of acquisition at high spat
26. It was originally developed by Sam Leffler at Silicon Graphics 16 5 TexFont TexFont is the textured font library used in InferenceM AP to display text in the display window It was originally developed by Mark Kilgard 16 6 Clustering Algorithms Clustering algorithms K Means and H Means available for the voronoi tessellation modes are based on the C code by John Burkardt original Fortran Code by David Sparks available at http people sc fsu edu jburkardt c_src asa136 asa136 htm1 50 InferenceMAP User Manual Contact Information 17 Contact Information Mohamed El Beheiry Developer mohamed elbeheiryQgmail com Jean Baptiste Masson jbmasson pasteur fr ol
27. Maximum Iterations slider The clustering algorithms used are based on those from John Burkardt available at http people sc fsu edu jburkardt c src asai36 asa136 html An additional reference for Voronoi Tessellation is Spatial Tessellations Concepts and Applications of Voronoi Diagrams by Atsuyuki Okabe et al 10 InferenceMAP User Manual Meshing 6 2 2 Tessellation The number of clusters which will correspond to the number of cells in the generated mesh is specified with the Number of Zones slider in the Voronoi Tessellation interface seen in Figure 5 Based on the clusters defined from Section 6 2 1 a Voronoi diagram is generated Effectively it involves spatially partitioning clusters into convex polygons such that each of the clustered points inside the polygon is closest to its associated barycenter than to any other An important point to consider is that there is no restriction on the minimal dimensions of the Voronoi polygons meaning the characteristic dimension of zones in the voronoi mesh may end up smaller than the average trajectory step size If this is observed the simplest way to avoid the appearance of such zones is to regenerate the mesh with a smaller number of cells specified in the Number of Zones slider In practice however even with such zones present in the generated mesh the final calculated parameter values are not greatly perturbed 6 3 Quad Tree Meshing Quad tree Meshing is an a
28. Mode Jeffreys Prior P 1 D D Afro Dj j D F Di jAt 02 D Drift oma Dj oy Di Atty D Polynomial Potential DA An important remark is that in the cases of D F and D V inference Jeffreys prior prevents inferrring negative diffusion coefficients even when position noise is high 8 9 Smoothing The smoothing prior penalizes gradients of the physically inferred parameters either the diffusion or the potential energy depending on the inference mode This prior is appropriate for use in biological systems where notions of the strength of 21 InferenceMAP User Manual Priors diffusion coefficient and potential energy gradients exist It is meant to reinforce the physical behavior that is to be expected in certain biological systems For example in certain situations we do not expect large jumps zone to zone in the diffusion coefficient The diffusion smoothing prior is defined by the surface integral in Equation 12 The coefficient p is the diffusion gradi ent penalization factor which modulates the strength of smoothing in the area S Ps Dig exp n ff Iv Das 12 The potential smoothing prior is defined by the surface integral in Equation 13 The coefficient A is the potential gradient penalization factor which modulates the strength of smoothing in the area S Ps Vig exp A ff IIvVlf as 13 Values for u and A are specified in the Prior tab of the meshing interface as in Figure 15
29. T D V P TID Vis 4 1 3 With Equation 4 we apply Bayes Rule which states P TID V P D V T P T Where P D V T is the posterior probability P D V is the prior probability and P T is the evidence which is treated as a normalization constant P D V T For each mesh zone we perform an optimization of the posterior probability P D V T for the model parameters D V or gt F This is the maximum a posteriori MAP Bayesian inference approach which is used in InferenceMAP 7 1 Inference Workflow InferenceM AP offers different modes of performing the inference calculation Selection between the different modes depends largely on the biological context and what dynamic information the user desires to have extracted Table 1 summarizes the features of each of the inference modes The inference mode is selected from the Mode drop down menu in the chosen meshing interface Figure 10 To perform the inference calculation for a mesh the following steps are generally taken 1 The mesh is applied by pressing the Apply button of the meshing interface 14 InferenceMAP User Manual Inference Table 1 Summary of different inference modes available in InferenceM AP Inference Mode Parameters Speed Priors Generated Maps Uniform D D Fast Jeffreys Diffusion Maps Smoothing Uniform T o D F D F V Fast Jeffreys Diffusion Force and indirect did i Potential Smoothing B Uniform D Drift
30. Table 3 lists the types of smoothing priors available for the different inference modes Table 3 Forms of smoothing priors for the different inference modes Inference Mode Smoothing Prior Ps D Diffusion D F Diffusion D Drift Diffusion D V Diffusion Potential Polynomial Potential N A Although the D D F are D Drift modes are generally rapid calculations the computation time increases substantially when the diffusion smoothing prior is activated The reason for this is that the problem becomes a calculation in which parameters in all zones e g diffusion force drift are being optimized simultaneously without the smoothing prior parameters are optimized in each zone independently which greatly reduces the dimensionality of the problem For this reason it may be of interest to use a Randomized Optimization Section 7 7 in large mapping problems which utilize smoothing priors 22 InferenceMAP User Manual Posterior Sampling 9 Posterior Sampling As explained in Section 7 the maximum value of the posterior probability distribution the MAP is used to estimate the dy namic parameters diffusion coefficient force components drift components and potential energy Sampling of the posterior probability see Section 7 gives insight into the precision of the estimations Typically the posterior probability distribution takes the approximate form of a Gaussian where the full width at half maximum may be c
31. a slow and expensive calculation and necessitates the randomized optimization feature to com plete in a reasonable amount of time However as there are only 50 zones in this mesh the cal culation time will not be too lengthy roughly 2 minutes lipid raft xyt 1 ipid_raft xyt 3 Adjust Mesh 43 Stepped Through Examples Trajectories 1 Points 4028 4028 Duration s 292 3 Dimensions um 3 3 x 4 7 Acquisition Time ms 25 Average Step nm 157 stare tise iie 1 1 1 ad RI Intensity Offset Draw Trajectories Draw Localizations WAnimate Trajectories o oo Accumulation Minterva 20 TI cMax espe 1 1 000 Diffusion um s 0 KE KEK co 0 0 Localization Precision nm Force Magnitude pN 0 Area um 0 cMin Voronoi Tess r Localization Precision nm Maximum Neighbor Distance View Neighbor Connections Potential Energy Penalization Beta D F Inference po J DTO D V Inference Randomized Optimization Selection Radius nm Cost Tolerance E JEE Polynomial Order Points Diffusion Coefficient Force Magnitude W Potential Energy ES Arrows 50 Zones Maximum Iterations Trajectories 1 Points 4028 4028 Duration s 292 3 Dimensions um 3 3 x 4 7 Acquisition Time ms 25 Average Step nm 157 start tine ts PO End Tine s z9z 33 CidYdY Intensity Offset Draw Trajectories M Draw Localizations M Animate Trajectories lll Ac
32. alculated to measure variance of the estimation InferenceM AP offers the possibility to sample posterior values for the different parameters For each of the different meshing types after the inference calculation the user has the option to sample to posterior probability for the different parameters Posteriors are sampled for different zones enabling the user to compare the parameter estimation precision in different parts of the mesh The different inference modes impose constraints on which parameters may be sampled as Table 4 shows Table 4 Availability of posterior probability sampling for different parameters for different inference modes Inference Mode Diffusion Coefficient Force Magnitude Drift Magnitude Potential Energy D Yes No No No D F Yes Yes No No D Drift Yes No Yes No D V Yes No No Yes Polynomial Potential N A N A N A N A After the inference calculation posterior probabilities are sampled in the Posterior tab of the meshing interface shown in Figure 16 The steps to sampling the posterior are the following Inference Overlay avances Prior Posterior simulation Landscape Diffusion MAP 0 211 um 5 Force i i i Potential Reference Minimum e T Maximum Samples peo Save m Points Diffusion Coefficient A Force Magnitude Potential Energy mi Log Arrows 55 zones Figure 16 Posterior tab in the meshing interface 1 A zone in the mesh in which to sample t
33. alization the potential energy map can be viewed in a 3D landscape mode Select the Landscape tab in the meshing interface and press View Landscape The Dis play Window becomes manip ulatable in 3D clearly show ing the different potential en ergy wells between the different quadrants Sliders in the Land scape tab can be used to ad just some of the landscape dis play properties Here we see that the approximate depths of the potential energy wells corre spond to the specified values 9 Landscape Viewing A Stepped Through Examples 1263 Points 37 8 25 Average Step nm Start Time s 2 ee 00 End Time s EX 75 Dm ty Offset 11877 11879 5 6 x 5 gt Trajectories Duration s Dimensions um Acquisition Time ms Draw Trajectories Draw Localizations Animate Trajectories Accumulation Interval ses Ba Diffusion um s 0 2528 KEE Nm Localization Precision nm Force Magnitude pN 11 312 Area um 0 343 cMax Neighbor Radius nm i 8 Iteration 274 3 5 1 2 Calculation Time 210 63 s Update Display InferenceMAP User Manual Stepped Through Examples 15 3 Example 3 Membrane Microdomain This example demonstrates how to generate a potential interaction energy map based on the trajectory of an e toxin receptor tagged with an amine coated lanthanide oxide nanoparticle on an MDCK cell 6 The receptor is seen to hop between three different lipid
34. and Tessellation which are discussed in Sections 6 2 1 and 6 2 2 respectively Number of Zones Minimum Points Zone Maximum Iterations mA K Means Distance Type L1 L2 Mode Localization Precision nm E TTT lt 1 Ci Points MDiffusion Coefficient Force Magnitude JJ Potential Energy Log Arrows 6 Zones Figure 5 Voronoi Tessellation interface The Voronoi tessellated mesh is generated by pressing the Apply button This will create the internal data structure necessary to perform the inference calculation 6 2 1 Clustering The first step to generate a Voronoi tessellated mesh is to cluster or group localizations together in a supervised fashion The different modes of clustering are available in the Clustering drop down menu in the Voronoi Tessellation interface Figure 5 The available modes include e K Means Localizations are clustered to globally minimize the within cluster sum of squares of all the clusters e H Means A simpler algorithm than K Means which assigns localizations to the closest randomly chosen cluster centers After assignment clusters centers are replaced by the centroid and the process is iteratively repeated Additionally there is the option to choose between square distance minimization L2 or absolute distance minimization L1 available in the Voronoi Tessellation interface seen in Figure 5 Maximum clustering iterations can also be specified by the user in the
35. ariant by reparameterization Moreover it protects the inference of diffusion in cases of high local confinement The smoothing prior is used to penalize gradients in the inferred parameters between neighboring zones To demonstrate the effect of the smoothing prior we apply it to the case of a simulated trajectory set with different diffusion step gradients Accordingly the effect of the diffusion smoothing prior i e the u parameter described in Section 8 3 on the diffusive map is illustrated in Figure 29 0 25 to 0 10 um s 0 50 to 0 10 um s 1 00 to 0 10 um s rt ty z n M e gt Figure 29 Table illustrating the effect of the diffusion map smoothing prior based on the coefficient 4 on simulated trajectories The trajectory space has two diffusive populations separated by a step gradient of different sizes in the different columns Increasing the value of u smooths the interface between the two diffusive regions to different degrees This prior is useful in cases in which large gradients in the diffusion are not to be expected This is analogous to the use of the potential energy prior i e the A parameter described in Section 8 3 33 InferenceMAP User Manual Stepped Through Examples 15 Stepped Through Examples In this section a few examples for the different inference modes in InferenceM AP are stepped through in detail All the examples are used with the included example files accessible from the Fil
36. ctories and to represent inferred dynamical parameters diffusivity force components and interaction potentials a Typical analysis workflow in InferenceMAP from left to right First panel trajectory of an toxin receptor tagged to an amine coated lanthanide oxide nanoparticle on an MDCK cell hopping between different lipid rafts 3 The color code is associated to time from blue beginning to red ending for a duration of 290 s Second panel same trajectory in red overlaid with a quad tree mesh Note the multi scale nature of the mesh which depends on both the number of points and the local diffusivity Third panel force map directional bias acting on the receptor in its various confinement areas indicated by white arrows Fourth panel Three dimensional landscape view of diffusivity Fifth panel Landscape view of interaction energy map revealing three membrane confinement domains b Diffusivity map of glycine receptor construct pHluorin TMD 6 Loop 400AA 4 in a mouse hippocampal neuron from a uPAINT measurement with an anti GFP antibody coupled to atto647N Top panel 9 453 trajectories of the GIyR construct overlaid to an ensemble GFP fluorescence image of receptors Color code distinguishes different trajectories Bottom panel three dimensional diffusivity map plotted overtop the employed Voronoi tessellated mesh The Voronoi mesh allows for efficient mapping of cells with complex geometries and clearly shows local variabil
37. cumulation Minterva 20 TI TT espo D Diffusion um s 0 A E 0 0 Localization Precision nm Force Magnitude pN 0 Area um 0 cMin Number of Zones Minimum Points Zone Maximum Iterations EAL k Means Distance Type OL1 OL2 se ll D V Inference EZHEETEETE NUN a ETE Points iDiffusion Coefficient M Force Magnitude Potential Energy Rv Arrows 50 Zones InferenceMAP User Manual Based on the force arrows it is seen that the toxin receptor is separately confined in three distinct parts of the trajectory To see the potential energy field which gives rise to this con fining force select Potential Energy in the bottom of the meshing interface Adjust the cMin and cMax sliders in the Main Interface to 0 2 and 0 8 respectively Now select the Overlay tab and choose Blue Red Map drop down menu Next select the Landscape tab and press View Land scape The Display Win dow becomes manipulatable in 3D Represented are three po tential energy wells the bottom most one being much deeper roughly 5 kgT than the top two roughly 2 kpT Essen tially the bottom strongly sta bilizes the toxin receptor while the top two wells are too shallow to keep the receptor confined for long 5 Landscape Viewing lipid raft xyt 44 Stepped Through Examples Trajectories 1 Points 4028 4028 Duration s 292 3 Dimensions um 3 3 x 4 7 Acquisition Time ms 25
38. daptive meshing method that recursively generates subzones leaves based on a localization capacity metric Being a meshing technique that conforms to the density of localizations it is especially relevant in cases where trajectory densities are strongly heterogeneous Hinimum Capacity Minimum Leaf Power L e Minimum Side Size nm Minimum Points Zone 3 a TTT E EPoints MDiffusion Coefficient Force Magnitude M Potential Energy Los Arrows 6 Zones Figure 6 Quad Tree Meshing interface Algorithmically the quad tree mesh is generated through the addition of localizations into a single square region Points are added sequentially until the capacity is exceeded At this point the mesh is subdivided into four identical squares This process recursively takes place as more points are added until no zones exceed the user specified capacity although some constraints may prevent this from being the case in practice see below The result is a hierarchical mesh A few constraints related to trajectory overlay data distinguish the quad tree implementation in InferenceMAP to those that may be used for data structures and other applications e The side length of zones are limited by default to the average trajectory step size of the trajectories This setting may be adjusted by selecting the minimum side length in the Minimum Side Size slider e There is an additional iteration at the end of the generation of the
39. e Scheme to Extract Diffusivity and Potential Fields from Confined Single Molecule Trajectories Biophysical Journal 102 10 2288 2298 2012 We give more details on the implementation of the inference method the effect of positioning noise the effect of confine ment the correction function for highly confined motion and the projection of the confining potential on polynomials to increase precision of the confining potential Furthermore it 1s demonstrated that the inference does not generate potentials or force fields if there are no fields interacting with the random walker Silvan T rkcan Jean Baptiste Masson Didier Casanova Genevi ve Mialon Thierry Gacoin Jean Pierre Boilot Michel R Popoff Antigoni Alexandrou Observing the Confinement Potential of Bacterial Pore Forming Toxin Receptors Inside Rafts with Nonblinking Eu Doped Oxide Nanoparticles Biophysical Journal 102 10 2299 2308 2012 In this paper we apply the method on the e toxin receptor motion inside a lipid raft showing the diffusivity map in the raft and the non local confining potential in the raft Guillaume Voisinne Antigoni Alexandrou and Jean Baptiste Masson Quantifying Biomolecule Diffusivity Using an Optimal Bayesian Method Biophysical Journal 98 4 596 605 2010 In this paper we demonstrate the optimality of the Bayesian inference method to infer diffusivity Furthermore we quan tify the acquisition of information gathered via infe
40. e menu of the Main Menu 15 1 Example 1 Generating a Diffusion Map This example demonstrates how to generate a diffusion map of simulated molecule trajectories with realistic diffusivities The trajectory file is partitioned into four quadrants each corresponding to a different specified diffusion coefficient The localization precision positioning noise is specified to be 30 nm 1 Load Diffusion Example File Select the Diffusion Exam diffusion example trxyt ple Simulation file from the Trajectories 1680 Points 32890 32891 A Duration s 50 5 Dimensions um 10 0 x 10 0 File gt Examples menu The Acquisition Time ms 25 Average Step nm 160 trajectories will start animat start time io OO ing The specified diffusion co end Time s 50 53 O efficient for the respective guad mi Draw Trajectories i Draw Localizations on rants is overlaid as a back Animate Trajectorid I Accumulation ground image Gl Intervar 0 Resolution nm px eeso pe inter or am x Align nm Align nm SE A A HE Localization Precisi Transpose Update Display 2 Visualize Trajectories Deselect the Animate Trajec A tories button and select the Trajectories mand riina e SENE A E i Duration s 50 5 Dimensions um 10 0 x 10 0 Draw Trajectories button 1n Acquisition Time ms 25 Average Step nm 160 the Main Interface to overlay SZ D NIE VE E ay start time s3000 all the trajectories in the f
41. e trxyt 36 Stepped Through Examples 1680 Points 32890 32891 50 5 Dimensions um 10 0 x 10 0 25 Average Step nm 160 Start T me s 2 ee i End Time 5 Intensity Offset Trajectories Duration s Acquisition Time ms Draw Trajectories Draw Localizations Animate Trajectories chin Accumulation Ml interval 20 cMax ersa 0 9750 Diffusion um s i o oo AA E SEEDS Precision CE USE ee Force Magnitude pN 0 323 CENE ERR 1 a Area um 4 415 Calculate rT Radius nm Square Meshing D Inference Zone 382 382 Calculation Time 1 18 s 8 559 um s 8 312 um s 9 064 um s J Update Display 168 Points 32890 32891 50 5 Dimensions um 10 0 x 10 0 25 Average Step nm 160 Start Time s 2 ee NI i CEN End Time s Trajectories Duration s Acquisition Time ms Draw Trajectories Intensity Offset Draw Localizations 0 136 Animate Trajectories uli Accumulation XN Hintervai ze cMax esso J 1 2 803 eoo Square Meshing View Landscape Scale Light x L Iv Fog Light y Fog Start Pss Light z Fog End 1 gs Iv EES Points Diffusion Coefficient Force Magnitude J Potential Energy E Log MArrows 382 Zones 0 312 um s 9 064 um s e Update Display InferenceMAP User Manual Stepped Through Examples 15 2 Example 2 Generating a Potential Interaction Energy Map This example demonstrates how to generate a potential i
42. er Manual Main Interface 4 Main Interface InferenceM AP is controled with an interactive graphical user interface as shown in Figure 1 e InferenceMAP File Plot Inference View Help NEUE 200 InferenceMAP Users mohamed Documents C Projects InferenceMAP Release glycine receptor trxyt glycine_receptor trxyt EEE TII Trajectories 9453 Points 178264 178333 Duration s 199 9 Dimensions um 25 2 x 17 4 Acquisition Time ms 5 Average Step nm 178 Start Time s e es End Time s Iv Die Trajectories Intensity Offset Die Localizations Animate Trajectories man Accumulation Mintervai e J cMax n Make Selection Points Diffusion um s po coo O m 0 0 Localization Precision nm Force Magnitude pN 0 Area um 0 Calculate Neighbor Radius nm Figure 1 InferenceMAP main interface Main Menu Access to input output options and all the main functions in InferenceMAP Display Window Window displaying current trajectory data set File Tabs Indication of files opened in current session File Panel Spatiotemporal data concerning the current file Interval Selection Select to activate trajectories within a specified time window Freehand Panel Macro for selecting a custom region in the current file and performing a direct trajectory inference Color Bar Color code corresponding to the selected meshing parameter overlay Visualization Panel Current file viewing o
43. gnates the index for which the points 3 of the k trajectory are in S j the current zone being analyzed and is the experimental localization accuracy 30 nm by default The P Dj term in 6 designates the optional Jeffreys prior Section 8 2 Jeffreys prior may be activated and de activated in the Priors tab of the meshing interface The Ps D term is the diffusion smoothing prior which is described in Section 8 3 The final result of this calculation are the maximum a posteriori MAP estimates Do and Lar and are updated to the mesh in the display window For further information regarding this calculation see reference 1 7 3 1 Potential Calculation PM AP calculation described in Section The user has the option of estimating the potentials V following the and DM AP iJ 7 3 Potential values are estimated with a least squares minimization between E AP or AAA AP and the gradient of the theoretical values for the potential under thermal equilibrium conditions VV A user defined penalization factor 5 is introduced to penalize the effect of strong potential gradients A typically used value for 8 is 2 0 default It is emphasized that low values of 6 favor large local variations in the potential field while high values will act to damp large variations Specifically the minimization is performed on zones that have at least one neighbor The calculation minimizes xi as descibed in E Vij Y
44. hall use the default s SVB 3 value Press the Apply button TO OCT me abi 5 BA E to generate the Voronoi mesh in SN SOME A Minimum Points Zone only the custom selected region Po CN do ou m R i e 7 x x e A Maximum Iterations which may take a couple min 3 SA Piha AS twats ary JALTA k Heans Distance Type OLI OL2 utes BERE ete iS PSA VEE BELLI D Inference a Points Bi bDiffusion Coefficient Force Magnitude Potential Energy iin Blog Arrows 730 Zones 46 InferenceMAP User Manual The yellow lines connecting each of the zones corresponds to which neighboring zones see each other Described in Sec tion 6 4 1 However we shall be using D F Inference in this example which does not re quire zones to see each other Select the D F Inference in the mode drop down menu Press Infer to perform the inference Select No when prompted to compute the po tentials Select the Diffusion Coeffi cient button in the bottom of the meshing interface Create a box to zoom in on parts of the dendrites of the neuron Di rectional arrows indicate regions where motion is systematically biased in a certain directions animating the trajectories will confirm this glycine receptor trxyt glycine receptor trxyt 5 Perform Inference Y PTT x SES va ces Compute potentials 5 Viewing Biases in Motion Stepped Through Examples Trajectories 9453 Points 178264 178333
45. he posterior is selected with the mouse in the Display Window 2 The estimation parameter diffusion coefficient force magnitude or potential energy is selected in the top left of the tab 3 Sampling ranges are selected via the Minimum and Maximum sliders 4 The number of equally spaced samples are selected with the Samples slider 5 The posterior for the chosen parameter in the selected zone is sampled by pressing the Sample button a trace of which is displayed in the interface 6 Posterior sampling data may be exported to a simple ASCII file by pressing the Save button 23 InferenceMAP User Manual Posterior Sampling For the D V Inference mode the posterior of the potential may be sampled in two ways 1 A single zone of the mesh can have its potential sampled across a user defined range 2 The posterior of the difference of potentials between two zones may be sampled For sampling the posterior of the difference of potentials the first zone is selected with the mouse in the Display Window Following by pressing the Reference button the second may be selected see Figure 17 At this point the user may select the range of potential differences to sample between the two zones specified with the Maximum slider This type of calculation is useful for measuring the precision of potential energy barriers for example Diffusion Force Minimum e o Maximum i Samples CE Figure 17 Posterior sampling of
46. ic parameters from trajectories For more extensive simulations and discussion of the performance of the technique it is recommended that the user consult previous papers discussed in the References section To give an overview of the performance we use the diffusion as our test parameter Other inferred parameters such as the forces potential energy and drift follow similar trends 14 1 Trajectory Length As discussed in Section 7 our trajectory inference technique does not depend on the length of trajectories Equations 6 7 9 and 10 clearly show that the posterior probability distribution is dependent on trajectory translocations i e m 417 ae and not trajectory lengths Effectively the long trajectory likelihood is simply the product of the individual likelihoods of each translocation 14 2 Number of Localizations We show the effect of the number of localizations translocations effectively on the inferred diffusion coefficient by sam pling the posterior probability of the diffusion for increasingly long trajectories This is entirely analogous to analyzing the posterior probability in a single zone of a mesh This treatment is valid as per the logic of the previous section as our tech nique uses individual translocations for parameter inference i e it sees a long trajectory as a sum of two point trajectories Figure 26 shows the form of the posterior for five different trajectories with different numbers
47. iew dynamical maps as three dimensional landscapes for more intuitive interpretation This feature is accessed with the Landscape tab of the meshing interface shown in Figure 19 p L ht z Fog End Tal Axes Figure 19 Landscape tab of the meshing interface Here the user has various visualization options for viewing the three dimensional landscape To change between landscapes simply press the parameter boxes on the button of the meshing interface The landscape viewing mode is available for all meshing types see Section 6 Color scales can be adjusted with the cMin and cMax sliders in the Main Interface Figure 20 shows the three dimensional landscapes for the same trajectory file a simulated potential well Figure 20 Potential energy landscapes of the same trajectory file a simulated potential well for the different meshing types a square mesh b Voronoi tessellated mesh and c a quad tree mesh 26 InferenceMAP User Manual Freehand Selection 12 Freehand Selection Often it is desired to only generate a dynamical map for a subregion of the entire trajectory space InferenceM AP enables users to select custom subregions with the freehand selection tool by selecting the Make Selection button in the Freehand Panel of the main interface window top panel of Figure 14 whereafter the user selects the desired subregion in the Display Window by clicking and holding the right mouse button Once a closed
48. ile SAS ie e e c ye ama Ree AI end Time s 5053 00 Y S Draw Trajectories Intensity Offset raw Localizat ions Ew 4 cMin M Animate Trajectories TE QC MM Mintervai 28 cMax resa I Make Selection Points 7 Diffusion um s 7 onne on 10 0 Localization Precision nm Force Magnitude pN 0 Area um 7 Calculate Neighbor Radius nm Density eT a 8 Users mohamed Documents C P 1 1 Image Stack Update Display 34 InferenceMAP User Manual The diffusion coefficient for a custom selected zone can be es timated using the Freehand Panel As the localization pre cision is already specified to 30 nm in the file there is no need to adjust the Localiza tion Precision nm slider Select the Make Selection button and draw a region in side the top left quadrant of the trajectory file by pressing and holding the left mouse button Release the left mouse button to close the region Now press the Infer D F button to in fer the diffusion and force inside the selected region A diffusion value very close to the specified 1 0 um s should be estimated displayed in the right side of the Freehand Panel Notice that the directional bias indi cated by the yellow arrow is ex tremely weak in magnitude in dicated in the Freehand Se lection panel not by the size of the arrow This calculation can be redone for the different quadrants giving accurate esti mates of the
49. iotemporal resolution By using one of the many available particle tracking algorithms 7 trajectories are reconstituted and accepted as input to InferenceMAP This massive trajectory data is thereafter treated with a Bayesian inference algorithm that notably imposes no constraints on trajectory lengths 2 3 4 Our algorithm is compatible with different models of single molecule motion including hopping diffusion Fig la active processes confinement and interaction energy driven systems Fig 1b Model specific physical processes are distinguished and mapped revealing rich landscapes of molecule dynamics Generating dynamical maps from single particle trajectories is critically dependent on the meshing utilized As local diffusivities may vary by orders of magnitude in a few hundred nanometers meshes should locally adapt to match the characteristic size of molecule displacements To this end InferenceMAP offers adaptive meshing techniques that users may tune to fit the spatial organization of their single molecule trajectories Fig 1a c In each zone of a mesh dynamic parameters are inferred to give rise to a parameter landscape Supplementary Information Calculations can be performed in an automated fashion irrespective of the biological system or parameters may be carefully adjusted to conform to desired mapping resolution and optimization constraints Additionally beforehand knowledge of the biological system can be incorporated in ca
50. ious inference modes and features InferenceM AP handles trajectory motion that can be modeled by an overdamped Langevin equation This model is a good approximation to memoryless Markovian motion which single molecules typically exhibit Below potential constraints to the use of InferenceM AP are listed e Limited Localization Density If datasets have a low number of trajectory points i e localizations the precision of inferred parameters may be impeded A possible way to get around this issue is to reduce the spatial resolution of the mesh in which parameters are inferred General rules for localization numbers are given in Section 6 e Timescale of Dynamics Users should be aware of the general timescale of dynamics within their system e g the duration of an interaction or a transport event InferenceM AP allows trajectories to be temporally windowed to accommodate different event durations e Viscoelastic Motion Viscoelastic motion is not accurately described by the overdamped Langevin equation in which case InferenceM A P is not advised for estimating dynamics Such motion is observed in the motion of large cytosolic vesicles for example e Immobile Trajectories The overdamped Langevin equation does not describe entirely immobilized trajectories In cases where trajectories have mixed mobile and immobile populations it is advised to segregate populations prior to analysis with InferenceMAP InferenceMAP User Manual Prelimi
51. is the minimal and initial default value in the Side Length slider of the Square Meshing interface However if trajectory points localizations are not sufficiently dense the side length should be increased at least 20 points per zone is recommended for accurate parameter estimation To apply a square mesh to the current file press the Apply button This will create the internal data structure neces sary to perform the inference calculation The Minimum Points Zone slider permits filtering of mesh zones based on the number of localizations contained in them It is generally recommended to have roughly 20 points per cell This notably adds constraints to the selected zone side length In the case that the side length needs to be readjusted the user may select the Reset button which reinitializes InferenceMAP User Manual Meshing the mesh selection options The fields in the Mode drop down menu are described in detail in Section 7 6 2 Voronoi Tessellation Voronoi Tessellation is one of the adaptive meshing methods available in InferenceM AP It is most appropriate in cases where there is significant heterogeneity in the density of localizations not necessarily trajectories In contrast to Square Meshing it will generate more zones in regions where localizations are more dense and additionally adapt the size of zones based on the density of localizations within it that eventually mesh generation includes two steps Clustering
52. ity of the diffusivity c Whole cell interaction energy map of glycine receptor construct Dendra2 TMD 8 Loop WT with gephyrin clusters using TIRF microscopy Top left panel ensemble fluorescence image of Cerulean Gephyrin clusters yellow boxes in a COS 7 cell Top right panel Three dimensional map of force amplitudes at the basal membrane of the cell Note that the map is mostly flat except in highly localized regions colocalized with gephyrin clusters white boxes Interaction energy wells corresponding to the boxed regions are indicated in the bottom three panels Acknowledgments We thank A Alexandrou D Casanova S T rkcan and M Richly for providing lipid raft data For glycine receptor constructs gephyrin plasmids and neuronal datasets we thank C Salvatico P Dionne C Specht M Renner and A Triller We also thank C Zimmer J C Olivo Marin and D Krapf for useful discussions in the preparation of this work This work was supported by funding from the state program Investissements d avenir managed by Agence Nationale de la Recherche Grant ANR 10 BINF 05 Pherotaxis and Grant ANR 10 INSB 04 France Biolmaging the Institut Curie International PhD Program Paris Science Lettres program ANR 10 IDEX 0001 02 PSL and from ANR grants TRIDIMIC and SYNAPTUNE References l Kusumi A et al Nat Chem Biol 10 524 532 2014 2 Masson J B et al Phys Rev Lett 102 048103 2009 3 T rkcan S et a
53. l Biophys J 102 2299 2308 2012 4 Masson J B et al Biophys J 106 78 83 2014 5 Manley S et al Nat Methods 5 155 157 2008 6 G Giannone G et al Biophys J 99 1303 1310 2010 7 N Chenouard et al Nat Methods 11 281 289 2014 InferenceMAP User Manual Version 1 0 Mohamed El Beheiry Institut Curie Centre de Recherche Laboratoire Physico Chimie Curie UMR168 26 rue d Ulm 79248 Paris France mohamed elbeheiry gmail com Jean Baptiste Masson Institut Pasteur Physics of Biological Systems 25 28 rue du Docteur Roux 75015 Paris France jbmasson pasteur fr InferenceMAP is registered with the Agency for the Protection of Programs APP under reference FR 001 350042 000 S P 2014 000 20700 InferenceMAP User Manual Contents 1 Preliminary Remarks Tel Modelo Mooie s erum ELI X3 Gut 9 dE eee dr e e A b ssim vido da 1 2 CONAS te nce SG 41 GY DE d men Euh ER SRO Soe EEE EGE a ees xu de ete UNE on Sen E TRUE NE T ET S E TR ee Be eis Bd ee ek Eh Be prava 2 Installation amp Execution 2 Windows Pu a m d dede ede Rh Peas s Salud dd es ee OSS dedi dre hebdo eee dde de dado 2114 Knor oS as uie edu ge ue Sos OWE EERE ue ROCA ELE ERE dox X X YR EES RR E DS WES S FR ee tgs rca Ge Sp Ha A ae Gen Ss Sg ns ea Haga a Oe Sean eee ARS AA Ge Ae et Gee 1909 Ge ee E 221 KOMA IS CREE E S TIE TOT nea sa cA ao e E os A a ada aa 3 File Formats DENS ile set AA E AE B ks qp ule SEIS s n 2
54. lculations via user defined prior probabilities Supplementary Information Furthermore a randomized optimization algorithm is available for exceptionally large problems permitting mapping of entire cells such as in Fig 1b Highly localized analysis in sub regions is easily performed through a custom selection macro Resulting inferred data is exportable in image and ASCII formats InferenceMAP offers a host of features to address a major concern of the single particle tracking community it reveals the parameters that dictate the motion of molecules Moreover in the burgeoning age of big data experimental biophysics it is an important contribution that extracts sensible results from otherwise dense and complicated observations using a robust Bayesian method InferenceMAP is controlled with a user friendly interface and is compatible with Mac OS X and Windows The software is freely available for academic use source code is available upon signature of a Material Transfer Agreement and latest versions may be downloaded from http umr168 curie fr en research groups locco software and from http www pasteur fr en research genomes genetics units groups jean baptiste masson The authors request acknowledgment of the use of InferenceMAP in published works suu 2 2609 HTH HE HH Figure 1 Caption Fig 1 Various uses of InferenceMAP on experimental single particle trajectories Shown are various ways to meshing the area explored by traje
55. mag nitude and strongly directional towards the well displayed in the right side of the Freehand Panel The more shallow wells will show weaker tendencies 3 Calculate Density potential example trxyt 3 Custom Selection Inference potential example trxyt 38 Stepped Through Examples Trajectories 1263 Points 11877 11879 Duration s 37 8 Dimensions um 5 0 x 5 0 Acquisition Time ms 25 Average Step nm 124 Start Time SIT End Time s Draw Trajectories Intensity Offset Draw Localizations Animate Trajectories Accumulation X Elintervaiz0 cMax i cMin Diffusion um s 0 2082 oo doo PTT Localization Precision nm Force Magnitude pN 1 029 e Area um 1 452 Neighbor Radius nm i 6 Density Calculation 100 1 Density Calculation Complete J Update Display Trajectories 1263 Points 11877 11879 Duration s 37 8 Dimensions um 5 0 x 5 0 Acquisition Time ms 25 Average Step nm 124 Start Time SIT End Time s EX Draw Trajectories Intensity Offset Draw Localizations Animate Trajectories Accumulation Elintervai20 7 cMax Make Selection Points 202 Diffusion um s 0 2528 ooo m 777822 Localization Precision nm Force Magnitude pN 11 312 EC Area um 0 343 Neighbor Radius nm 8 Iteration 18 Update Display InferenceMAP User Manual Deselect the Make Selection button in the Main Inter face and open
56. nary Remarks 1 3 Tracking Software As InferenceMAP is used downstream from the single molecule tracking step it takes trajectories as input data a tracking software is needed to reconstruct trajectory translocations from acquired microscopy images A few of the freely available tracking software tools are listed in the references below e u track Jaqaman et al Nature Methods 5 pp 695 702 2008 e MTT Serg et al Nature Methods 5 pp 687 694 2008 e Various Chenouard et al Nature Methods 11 pp 281 289 2014 InferenceMAP User Manual Installation amp Execution 2 Installation amp Execution 2 1 Windows XP amp 7 InferenceMAP has been tested on the Windows XP Windows 7 and Windows 8 operating systems The installation instructions are as follows 1 Assure that the Microsoft Visual C 2010 Redistributable Package is installed It can be found here http www microsoft com en us download details aspx id 5555 2 Double click the install package InferenceMAP Windows zip and follow the on screen installation instructions 3 Double click the InferenceMAP exe in the install directory to start the program The execution of InferenceM AP is coupled with that of a Windows Command Prompt The purpose of this is to display the progress in potentially lengthy calculations 2 1 1 Known Issues Reported issues with the Windows version of InferenceMAP may potentially be circumvented trying the following steps
57. nates the optional Jeffreys prior Section 8 2 Jeffreys prior may be activated and de activated in the Priors tab of the meshing interface 17 InferenceMAP User Manual Inference The Ps D j Vi j term is the diffusion and potential smoothing prior which is described in Section 8 3 7 5 1 Applicability The D V Inference mode is well suited to trajectories in the following situations e Systems with stable interaction sites 7 6 Polynomial Potential Inference In contexts where there is clear confinement of a tracked particle it is useful to describe the confining energy as a polynomial of order C in X At 11 C j 0 1 0 2 J Where the constants a are fitted to the experimental force fields using standard simplex methods This description of the potential is integrated into the inference calculation as in Eguation 7 This type of inference is prohibitively expensive for large maps it is recommended for localized trajectories in small regions Further information regarding this type of modelling is described in reference 8 7 6 1 Applicability The Polynomial Potential Inference mode is well suited to trajectories in the following situations e Confined trajectories 7 7 Randomized Optimization To tackle large problems consisting of several hundred or thousand of individual zones a Randomized Optimization function is available which greatly reduces computation time It can be used in the following infere
58. nce modes e D Inference when a smoothing prior is used e D F Inference when a smoothing prior is used e D Drift Inference when a smoothing prior is used e D V Inference This feature is available for all meshing modes parameters of which can be adjusted in the Advanced tab of the meshing interface seen in Figure 7 7 fa Randomized Optimization Selection Radius nm Cost Tolerance Maximum Iterations Se ono T Figure 12 Randomized Optimization options in the meshing interface To activate the Randomized Optimization mode a compatible mode must be selected in the Inference tab of the mesh ing interface the smoothing prior also needs to be activated for the cases of D D F and D Drift inference modes Activation consists in clicking the Randomized Optimization check box seen in Figure 7 7 This function works as follows e Subregions of zones are selected in a circle of radius defined by the Selection Radius nm slider Figure 7 7 The zone in which the circle is centered is selected randomly among the activated zones of the mesh It is advisable to select a radius such that roughly 10 zones or more will be encompassed 18 InferenceMAP User Manual Inference e The inference calculation is performed only for the subregion zones parameters e g diffusion in all other zones remaining constant Calculations are limited to the number of iterations specified in the Maximum Iterations slider Figure 7
59. ng the strength of single molecule interactions To date this technique has been used to study the dynamics of single molecules in many biological contexts these include e Neurotransmitter receptors 1 e Membrane microdomains 6 e Transcription factors e Viral capsid fusing proteins e Proteins on unilamellar vesicles 1 1 Models of Motion The widespread applicability of InferenceMAP is largely due to the different models of single molecule motion it supports Below the models are briefly described a full description is available in Section 7 e Diffusion Only Solely the diffusivity is estimated from the trajectories e Diffusion and Force Local force components in addition to the diffusion are inferred with an option to estimate interaction energies e Diffusion and Drift Local drift speed in addition to the diffusion are inferred This model is applicable to systems possessing active processes where forces may not be conservative e Diffusion and Potential Potential interaction energy force and diffusion components are estimated from trajec tories e Polynomial Potential Potential interaction energy force and diffusion components are estimated from trajectories This model is applicable to small regions where there is trajectory confinement 1 2 Constraints Users should be aware of constraints regarding the single molecule trajectory inference technique implemented in Infer enceMA P With its var
60. not phys ically related These connections are indicated with yellow lines connected between the barycentres of the localizations in each mesh zone These erroneous connections can be particularly apparent in the adaptive meshing types the Quad Tree and Voronoi Tessellation Figure 8 shows how erroneous connections may be removed between zones to ensure a more accurate poten tial calculation Figure 8 In adjusting the Maximum Neighbor Distance slider connections between neighboring zones can be added or removed indicated with yellow lines This figure demonstrates the removal of erroneous neighboring zone connections 6 4 2 Manual Zone Activation and Deactivation After a mesh has been applied prior to the inference calculation the user may manually activate and deactivate zones The motivation here is to add flexibility to the otherwise non flexible zone filtering options e g Minimum Points Minimum Leaf Power Maximum Neighbor Distance etc Mesh zones are made active or inactive by selection or deselection via right clicking with the mouse 12 InferenceMAP User Manual Meshing 6 4 3 Preventing Holes in the Mesh In general holes inactive zones surrounded by active ones should be avoided This may perturb the potential calculation as it can greatly affect local values of the potential gradient that may propagate to other zones Holes may appear if zones do not contain the minimal number of points specified
61. ns of the trajectory space need to be analyzed To select a freehand region the Make Selection button is pressed whereafter the user can select in lasso style a closed region of the trajectory overlay by pressing and holding the left mouse button Once a region has been circled the user releases the left mouse button which will close the selected region In the Freehand Panel Figure 14 the user may specify the Localization Precision Afterwards the diffusion coefficient and force or drift components determined and displayed by pressing the Infer D F or Infer D Drift buttons respectively The inferred region is highlighted in white with an overlaid arrow to represent the angle of the force or drift the size of the arrow does not correspond to the magnitude of the force or drift 19 InferenceMAP User Manual Inference Points 225 Diffusion um s 4 9276 Localization Precision nm Force Magnitude pN 0 001 A Area um 0 629 Figure 14 Freehand Panel top with selected and inferred region bottom 20 InferenceMAP User Manual Priors 8 Priors In general prior probabilities are used to impose our beliefs to the dynamic parameter estimates that InferenceM AP per forms when generating maps This section describes three types of prior probabilities that users may incorporate in the inference calculation They are enabled via the Priors tab of the meshing interfaces shown in Figure 15 Enable Jeffreys Prio
62. nteraction energy map of simulated molecule trajectories with realistic diffusivities The trajectory file is partitioned into four quadrants each containing a potential energy well with a different depth the specified depth value is indicated in the background image The form of each well is Gaussian with a variance of 300 nm The localization precision for the trajectories is specified to be 30 nm The trajectories are set to diffuse at 0 2um s 1 Load Potential Example File Select the Potential Exam potential example trxyt ple Simulation file from the Trajectories 1263 Points 11877 11879 Duration s 37 8 Dimensions um 5 0 x 5 0 File gt Examples menu The Acquisition Time ms 25 Average Step nm 124 Macias a sarm tale TT ing The specified potential en end tine s1 37 75 TY ergy depths for the respective Draw Trajectories Intensity Offset a A M Draw Localizations guadrants is overlaid as a back Animate Trajectorie 6 3 si I Accumulation round image 8 8 d intervar 28 Resolution nm px E CNN GN x Align nm Align nm L 6 11 e Im Localization Precisi L1 Transpose Update Display 2 Visualize Trajectories Deselect the Animate Trajec tories button and select the Trajectories mad hated es ae i Duration s 37 8 Dimensions um 5 0 x 5 0 Draw Trajectories button in Acquisition Time ms 25 Average Step nm 124 the Main Interface to overlay 8 peer a ey NES sat me i
63. onal Jeffreys prior Section 8 2 Jeffreys prior may be activated and de activated in the Priors tab of the meshing interface The Ps D term is the diffusion smoothing prior which is described in Section 8 3 gt MAP F Vag gt The final result of this calculation are the maximum a posteriori MAP estimates 2 and and are updated to the mesh in the display window 7 4 1 Applicability The D Drift Inference mode is well suited to trajectories in the following situations e Active processes e g active transport phenomena 7 5 D V Inference The D V Inference mode directly computes the diffusion coefficient and the gradients of the potential in each active zone in the mesh Naturally the calculation is expensive as it estimates all the variables the diffusion coefficients and potential energies in all the zones of the mesh at the same time A randomized optimization method Section 7 7 is included to alleviate its generally high computational requirements The zonal posterior probability is described as fiat Dam edet 4 Dij At P Di gS AV Vaj HAT x Il LI 4n Dij e At ij T AT k pir E Si j x P Di x Ps Dij Vij 10 Where D is the diffusion coefficient V is the potential energy designates the index for which the points 5 of the kt trajectory are in S the current zone being analyzed and is the experimental localization accuracy 30 nm by default The P Dj term in 6 desig
64. ons 000 EEs Animate Trajectories M Accumulation oo Square Meshing tnterence overtoy avanes Prior Posterior imation Landscape Side Length nm Minimum Points Zone Mode D Inference E Points MDiffusion Coefficient Force Magnitude MPotential Energy MLog Arrows 382 Zones 63 J Update Display LI InferenceMAP User Manual Make sure that the D Infer ence is selected in the Mode drop down menu in the mesh ing interface The localization precision may be adjusted in the Advanced Tab of the mesh ing interface however its de fault value is set to 30 nm which corresponds to the value in the trajectory file Press the Infer button to infer the diffusion co efficient in each of the zones in the mesh The Colorbar will automatically update to the dif fusion values Notice that val ues in each of the zones accu rately corresponds to the diffu sion specified in the file For more intuitive visualization the diffusion map can be viewed in a 3D landscape mode Se lect the Landscape tab in the meshing interface and press View Landscape The Dis play Window becomes manip ulatable in 3D clearly showing the differences in diffusion be tween the different quadrants Sliders in the Landscape tab can be used to adjust some of the landscape display proper ties 5 Perform Inference diffusion example trxyt AA T a mu SEEN dut ue ERE 6 Landscape Viewing diffusion exampl
65. oo J all the trajectories in the file d Deans o e end tine t igs 1 1 Diffusion um s A io 10 0 Localization Precision nm Force Magnitude pN 7 Area um Calculate Neighbor Radius nm ZEN D 9 Users mohamed Documents C P 1 1 Image Stack Update Display 37 InferenceMAP User Manual To help reveal regions of at traction we can perform a naive density calculation to show where trajectory points are most concentrated Press the Calculate Density but ton in the Density Panel of the Main Interface here we leave the Neighborhood Ra dius to its default value Upon calculation the colorcode will correspond to the relative den sity of each localization in the loaded trajectory file red being the highest and dark blue being the lowest Before generate the potential energy map we can infer di rectional bias of trajectories at the proximity of high density localization regions The force for a custom selected zone can be estimated using the Free hand Panel As the localiza tion precision is already spec ified to 30 nm in the file there is no need to adjust the Localization Precision nm slider Select the Make Selec tion button and draw a region adjacent to a high density re gion revealed by the density cal culation Now press the Infer D F button to infer the dif fusion and force inside the se lected region For the deepest wells the force is strong in
66. ptions Density Panel Calculate the localization density for the displayed trajectories Progress Panel Displays calculation progress Fullscreen Button Toggle between full and default screen size InferenceMAP User Manual Trajectory Visualization 5 Trajectory Visualization Upon starting InferenceMAP trajectories may be inspected with various visualization functions After loading a trajectory file via the File menu data may be visualized with options in the Visualization Panel shown in Figure 2 Draw Trajectories Intensity Offset Draw Localizations L Animate Trajectories O Accumulation Mintervai 20 FPS Figure 2 Visualization Panel in the main interface of InferenceMAP For a loaded trajectory the user has access to the following visualization options Draw Trajectories Displays all trajectories in loaded file For trxyt files trajectories are distinguished by different colors Animate Trajectories Animates the trajectories either in Accumulation mode which animates and accumulates all the trajectories in the loaded file or in an Interval mode which animates the trajectories in a sliding window mode in which the interval size may be adjusted with its corresponding slider 20 steps by default The FPS slider adjusts the frames per second of animations in the Display Window Trajectory viewing may additionally be synchronized to raw acquisition films using the TIFF Overlay tool described in
67. quad tree mesh which will act to ensure subdivided zones have above the minimal number of points required by stepping up the quad tree structure This is why certain zones may have more than the capacity defined in the Minimum Capacity slider e Subzones may be filtered based on their power side length with the Minimum Leaf Power slider The quad tree mesh is generated by pressing the Apply button This will create the internal data structure necessary to perform the inference calculation 11 InferenceMAP User Manual Meshing 6 4 Meshing Advice In general there are some key considerations the user should keep in mind when generating a mesh for the inference calculation described in Section 7 This section describes these considerations in some detail 6 4 1 Neighboring Zone Connections Calculation of the potential interaction energy in a given zone necessarily depends on the potential values in neighboring zones InferenceM AP enables the user to define the neighbors of given zones via the Advanced tab of the meshing interface window shown in Figure 7 Invalid neighbor connections can bias the inference calculation and may reduce the accuracy of the potential energy map Maximum Neighbor Distance nm View Neighbor Connections Figure 7 Neighbor connection options in Advanced tab of meshing interface In adjusting the Maximum Neighbor Distance slider the user can remove connections between zones that are
68. r Enable Smoothing Prior Penalisation lambda D Penalization mu ese 1 1 Figure 15 Prior tab of the meshing interface 8 1 Uniform If no information is known regarding the parameters being inferred e g the diffusivity the Uniform Prior should be used It is applied by default if no other priors are activated Specifically use of this prior means that the results yielded from the Bayesian inference calculation are identical to those that would be obtained from a maximum likelihood estimation 8 2 Jeffreys Jeffreys prior is used to ensure that the posterior probability distribution of an inference calculation is invariant by re parameterization Moreover it allows protecting inference of the diffusion in cases of high local confinement In such situations the effective diffusion introduced by a non zero positioning noise can lead to inference of a negative diffusion value 1 We emphasize that without positioning noise the inference never leads to negative diffusion Table 2 lists forms of Jeffreys prior for the different inference modes Jeffreys prior is applicable to a large number of situations Situations where it is not recommended are in cases where 2 the diffusion is similar to the effective noise diffusion which we estimate as 53 It may be activated and deactivated in the Prior tab of the meshing interface Table 2 Forms of Jeffreys prior for the different inference modes Inference
69. rafts each of which having a different strength of confinement Experimentally these trajectories were captured in a wide field fluorescent microscope configuration 1 Load Toxin Receptor Example File Select the Toxin Receptor in InferenceMAP File Plot Inference View Help NEED Lipid Raft file from the File rY InferenceMAP Users mohamed Documents C Projects InferenceMAP Debug lipid_raft xyt gt Examples menu ipid_raft xyt 1 Points Trajectories Duration s 4026 4028 292 3 Dimensions um 3 3 x 4 7 Acquisition Time ms 25 Average Step nm 157 Start Time s 0 00 End Time s 292 33 Intensity Offset Draw Trajectories M Draw Localizations cMin Accumulatio Interval cMax Make Selection Points 0 Diffusion um s 0 MO E 0 0 Localization Precision nm Force Magnitude pN 0 bo Area um 0 Calculate Neighbor Radius nm Update Display 2 Generate a Voronoi Mesh Open the Voronoi Mesh ing interface from the File gt Inference gt Meshing gt Voronoi menu For this mesh ing mode the number of zones lipid raft xyt Trajectories 1 Points 4028 4028 Duration s 292 3 Dimensions um 3 3 x 4 7 Acquisition Time ms 25 Average Step nm 157 Start Time s End Time s 292 33 Draw Trajectories Intensity Offset must be predefined beforehand InferenceMAP automatically M Draw Localizations Animate Trajectories fj Accumula
70. region has been selected releasing the right mouse button will create the subregion At this point the user opens a meshing interface as usual by choosing from the options in the Inference gt Meshing menu of the Main Menu The mesh generated in the subregion upon pressing the Apply button in the respective meshing interface Figure 21 shows an example of a map for a custom selected region using this feature Figure 21 Example of a map calculated for a custom selected subregion It is important to assure that the Make Selection button is toggled on before pressing Apply in the chosen meshing interface 27 InferenceMAP User Manual Tools 13 Tools 13 1 Annotations Various annotations may be adjusted or removed in the Display Window by accessing the Annotations interface in the Tools menu of the Main Menu seen in Figure 22 foe Bounding Box Grid fal Dimensions fal Ticks alum Units nm Units Grid Spacing nm 1 Figure 22 Annotations interface 13 2 Density Calculation The relative density of localizations can be calculated by pressing the Calculate Density button in the Density Panel of the Main Interface The density is determined by counting the number of localizations neighbors within the circle defined at each given localization The size of this circle is determined by the radius indicated in the Neighborhood Radius Slider Density Panel Figure 23 Neighbor Radius nm i Figure 2
71. rence Fisher Information and give analytical solutions for various confinement geometries Jean Baptiste Masson Didier Casanova Silvan T rkcan Guillaume Voisinne Michel R Popoff Massimo Vergassola and Antigoni Alexandrou Inferring Maps of Forces Inside Cell Membrane Microdomains Physical Review Letters 102 4 048103 2009 48 InferenceMAP User Manual REFERENCES The original paper in which the Bayesian Inference method for single molecule trajectory as well as the Langevin modelling and the solution of the Fokker Planck equation are introduced We prove that both diffusivity and force fields can be inferred accurately and the scheme is applied to test trajectories of the receptor of the e toxin 49 InferenceMAP User Manual Acknowledgments 16 Acknowledgments 16 1 Development Libraries Various freely available development libraries were used in InferenceM AP They are referenced below In all cases InferenceM AP conforms to all license agreements and no modifications to the original authors libraries are made 16 2 FLTK The Fast Light Toolkit FLTK is the cross platform graphical user interface library used in InferenceMAP It was originally developed by Bill Spitzak 16 3 OpenGL OpenGL is the graphics library used for displaying graphics in InferenceM AP It is maintained by the Khronos Group 16 4 Libtiff Libtiff is the library used for writing Tagged Image File Format files using InferenceM AP
72. ss the Make Selec E sn interval 2 TT Te tion button in the Freehand ur c esa l Panel and select a region sur WI Make selection Bal neis i 7 AA ed Diffusion um s 0 rounding the part of the neuron CPC E Infer D F Force pN 10 0 A i P a id i r A Localization Precision nm Force Magnitude pN 0 indicated in the figure EAD dE M TS i hoe e Users mohamed Documents C P 1 1 Image Stack Update Display 4 Generate a Voronoi Mesh In this example Voronoi mesh glycine_receptor trxyt ing will be used on the user Trajectories 9453 Points 178264 178333 A Duration s 199 9 Dimensions um 25 2 x 17 4 selected region of the trajecto p Us E gS NT e E Acquisition Time ms 5 Average Step nm 178 ries Open the Voronoi Mesh 7 E in start tine 51 0 05 ing interface from the File FT Ber ho ena tine 651 200 00 gt Inference gt Meshing gt o gee a Draw Trajectories Intensity Offset Voronoi menu For this mesh WE Biase cMin oS a aS 0 000 ing mode the number of zones ENTUM e T must be predefined beforehand sp T T InferenceMAP automatically ere q ON NE 58709 REA Diffusion um s 0 selects an appropriate number MEE o SA Is P Doo Pee ooo 10 0 0 b d th b tj A m 32 4 Localization Precision nm Force Magnitude pN 0 ased on the number ol local iw MEN TTE p X area tun 0 izations in the loaded data set co serie ess Here we s
73. ted key physical properties may be concealed Results of the aforementioned 31 InferenceMAP User Manual Performance 1 l 0 07 0 06 e eo e a a an MAP Diffusion um s FN stdev of MAP Diffusion um s Q e ho o n e 7 0 20 40 60 80 100 20 40 60 80 100 Trajectory Translocations Trajectory Translocations e Figure 27 left Maximum a posteriori MAP estimator of diffusion coefficient on trajectories of increasing number of translocations nominal diffusion of 0 5 um s right Standard deviation of the MAP estimator comparison are displayed in Figure 28 Purely Diffusive Motion Figure 28 Comparison of different parameter maps inferred for the D Inference and D V Inference modes The above examples clearly show that in the absence of an interaction energy top row of Figure 28 the corresponding potential energy map inferred using the D V Inference mode is essentially flat as is expected to be the case Conversely the D Inference mode does not model interaction energy and is hence not capable of revealing a large interaction region bottom row of Figure 28 32 InferenceMAP User Manual Performance 14 4 Prior Probabilities InferenceM AP offers two types of prior probabilities Jeffreys prior is recommended in many cases It is used to ensure that the posterior probability distribution of an inference is inv
74. the Quad Tree Meshing interface by accessing File gt Inference gt Mesh ing gt Quad Tree Here we opt for the default meshing val ues although the user is en couraged to test different values Press the Apply button to gen erate the mesh The yellow lines connecting each of the zones corresponds to which neighbor ing zones see each other De scribed in Section 6 4 1 The default colorcode corresponds to the number of points in each zone seen in the Colorbar Select the D V Inference option from the Mode drop down menu in the meshing in terface The localization pre cision may be adjusted in the Advanced Tab of the mesh ing interface however its de fault value is set to 30 nm which corresponds to the value in the trajectory file As the D V Inference calculation is quite computationally expensive we choose to perform a randomized optimization which greatly re duces the time needed to in fer parameters from the tra jectories In the Advanced tab select the Randomized Optimization button and in crease the Selection Radius nm slider to roughly 1000 nm and reduce the Cost Toler ance 9o slider to zero imply ing we will have to manually stop the calculation 5 Generate a Quad Tree Mesh potential example trxyt o 0 0 N Co I D m TOPIA co NO ao ar de E Aone med PA ae a CN au hg b st A o Sa uf UNT pop a EA SBUSBEBREE
75. tion Mintervarizo UNI cMin cMax selects an appropriate number based on the number of local izations in the loaded data set Here we shall use the default value of 50 zones Press the Apply button to generate the Voronoi mesh Points Diffusion um s 0 Force pN 0 0 Localization Precision nm Force Magnitude pN 0 Area um 0 Number of Zones Minimum Points Zone Maximum Iterations am k Means Distance Type OLI OL2 se HOPES D Inference II Ds Points ADiffusion Coefficient Force Magnitude Potential Energy ES Arrows 49 Zones 42 InferenceMAP User Manual The generated mesh is seen to possess a deactivated zone in the bottom right corner Ac tivate this zone by right click ing on it The yellow lines connecting each of the zones corresponds to which neighbor ing zones see each other De scribed in Section 6 4 1 In this case some of the con nections between zones do not make sense based on the lay out of the trajectory e g the top two rafts do not seem to be associated Select the Ad vanced tab and adjust Max imum Neighbor Distance nm to roughly 715 nm Ad ditionally adjust the Localiza tion Precision nm slider to 20 nm corresponding to the ap proximate experimental value In the Inference tab select the D V Inference mode To perform the inference calcula tion press Infer The D V Inference mode is generally
76. xyt 45 Trajectories 9453 Points 178264 178333 Duration s 199 9 Dimensions um 25 2 x 17 4 50 Average Step nm 178 Start Time s End Tine s Intensity Offset Acquisition Time ms M Draw Trajectories Draw Localizations Animate Trajectorie id Accumulation Sequence Interval Resolution nm px ise 20 Make Selectior y Flip x Align nm Align nm L eco 1 e 1 7 Localization Precisi ET Transpose Update Display Trajectories 9453 Points 178264 178333 Duration s 199 9 Dimensions um 25 2 x 17 4 5 Average Step nm 178 Start Time s End Tine s Intensity Offset Acquisition Time ms Draw Trajectories M Draw Localizations Resolution nm px see x Align nm y Align nm Localization Precisi r7 NINEN M NN Update Display InferenceMAP User Manual Stepped Through Examples 3 Make Custom Selection Zoom into the region to the left glycine receptor trxyt 9453 Points 178264 178333 by right clicking and dragging Trajectories Duration s 199 9 Dimensions um 25 2 x 17 4 the mouse to generate a box in DP LL Acquisition Time ms 50 Average Step nm 178 the Display Window Letting 3 E Nese remm go will zoom into the selected Ed Sb ena tine sif000 region double clicking will re z WEN NT Draw Trajectories EA Offset t th i Ti A i h wr i na Je 4 Draw Localizations 1 000 se e VIEW you WIS e Un Animate Traj cMin select Pre

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