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Single Molecule Light Microscopy ImageJ Plugins

1. As before but ignore pixels on the image boundary 11 5 1 Image Residuals The residuals of an image are calculated for each pixel using the total difference to the 4n connected pixels These are normalised so that the sum of the residuals squared is the same as the sum of the image pixels squared Comparing each pixel to its neighbours provides a robust method of estimating noise if the underlying signal is adequately sampled Variations between neighbour pixels are expected to be small consequently large variations indicate high noise All the image residuals methods are based on the Least trimmed square robust estimator described in P Rousseeuw and A Leroy Robust Regression and Outlier Detection New York Wiley 1987 11 5 2 Noise estimation within the Peak Fit plugin The fitting code currently uses the QuickResipuatsLEASTMEANOFSquares This method is more stable than using the standard deviation of the image pixels since large variations around the high intensity localisations are smoothed by using the image residuals The noise estimation method can be changed in the Peak Fit plugin by holding the Suiet or Aut key down when running the plugin to see the extra options Page 212 225 GDSC SMLM ImageJ Plugins 11 6 Median Filter Compute the median of an image on a per pixel basis using a rolling window at set intervals Super resolution image data can contain a low amount of background which a
2. DepTH RECALL The recall of localisations that were within the depth specified by the Summary DEPTH parameter Note that the parameter is halved to set a range for z set above and below zero so that the depth of field equals the Summary DEPTH DISTANCE The average distance between fitted results and the true localisation SIGNAL FACTOR The average signal factor between fitted results and the true localisation AT LIMIT A flag to indicate if the optimal filter from the filter set was at the limit of the range for any of the expanded parameters 9 14 Image Background Produces a background intensity image and a mask from a sample image The Imace Backcrounb plugin is used to generate suitable input for the Create Data plugin The Create Data plugin creates an image by simulating fluorophores using a distribution One allowed distribution is the region defined by a mask The fluorophores are created and then drawn on the background The background can be an input image Both the mask and background image can be created from a suitable in vivo image using the Imace Backcrounp plugin The purpose would be to simulate fluorophores in a distribution that matches that observed in super resolution experiments The plugin requires that an image is open The plugin dialogue is show in Illustration 34 The plugin has two parameters the bias and the blur These are described in the following Page 176 225 GDSC SMLM ImageJ Plugins
3. CLUSTERING ALGORITHM Set the clustering algorithm See below for details PULSE INTERVAL Sets the pulse interval for clusters in frames Clusters will only Page 83 225 GDSC SMLM ImageJ Plugins contain localisations from within the same pulse Set to zero to disable pulse analysis See section 7 2 2 1 Pulse Analysis SPLIT PULSES Enable this to ensure clusters contain only localisations within a single pulse defined by the Pulse inTERVAL Use this setting if your imaging conditions use pulsed activation and you have imaged for long enough between pulses to be sure that all fluorophores have photo bleached SAVE CLUSTERS When the clustering is complete show a file selection dialogue to allow the clusters to be saved SHOW HISTOGRAMS Present a selection dialog that allows histograms to be output showing statistics on the clusters e g total signal on time and off time SAVE CLUSTER DATA Save all the histogram data to a results directory to allow further analysis A folder selection dialog will be presented after the clustering has finished REFIT OPTION Provide the option to extract all the frames corresponding to a single cluster from the source image into a combined image and perform PSF fitting The plugin will cluster the localisations and store the results in memory with a suffix Clustered Two additional datasets are created all single localisations which
4. Comparison Metrics The score metrics are shown in a results table Optionally a table of the matched pairs can be displayed showing the matched and unmatched localisations The pairs table supports interactive identification of the selected points on the source image See 6 10 1 Any previous results in the pairs table will be cleared Since matches are computed at a set distance threshold the plugin provides the ability to perform analysis at many distances In this case the pairs are matched at the largest distance threshold Then the scores for lower distance thresholds can be computed by eliminating pairs that are too far apart The following parameters can be set Parameters Description ResuLs1 The first results set REsuLTS2 The second results set DISTANCE The minimum distance for a match INCREMENTS The number of times to increment the distance threshold DELTA The value to increment the distance threshold BETA Controls the weighting between Precision and Recall for the custom F score SHOW TABLE Display a table of the match statistics SHow Pairs Display a table of the matched pairs with coordinates and distances Page 64 225 GDSC SMLM ImageJ Plugins Parameters Description SAVE CLASSIFICATIONS The data from results set 2 will be saved to a PeakResults file If the point matches a point in results set 1 then the original value will be set to 1 otherwise the orignal value is
5. Uses the same SNR and width parameters from the SNR Fitter iterating over them as before The SNR is used to set the lower SNR limit Contains additional parameters to set the gap to the upper limit The user can configure the min and max gap and the increment to move between them HysTERESIS PRECISION FILTER Mark all results with a precision below a lower level as valid Remove all results with a precision above an upper level Any result with a precision between the upper and lower levels is a candidate result Candidates are retained if they can be traced traced directly or via other candidates to a valid result Uses the same precision parameters from the Precision Fitter to set the lower limit Contains additional parameters to set the gap to the upper limit The user can configure the min and max gap along with the increment to move between them Note that the hysteresis filters perform tracing using a time threshold of 1 and a distance threshold of 2x the average precision of the results More flexibility over the filters to use in the analysis is provided by using the Create Fitters and Fitter Anacysis Fite plugins see the following sections 7 9 3 Additional parameters After the filters have been configured there are additional parameters controlling the analysis Parameter Description SAVE FILTERS Save the filters to file The filters can be read using the Fitter Anavysis Fite plugin
6. The Z position relative to the focal plane in nm MIN PHOTONS The minimum number of photons for a localisation Max PHOTONS The maximum number of photons for a localisation Raw IMAGE Select this option to output an image using 32 bit floating point numbers The default is to use 16 bit unsigned integers Page 145 225 GDSC SMLM ImageJ Plugins Parameter Description SAVE IMAGE Show a dialog allowing the image to be saved as a file SAVE IMAGE RESULTS Show a dialog allowing the image localisations to be saved as a PeakResults file Note that this does not contain the molecule Z position Save LOCALISATIONS Show a dialog allowing the localisations to be saved The file contains the time and X Y Z positions of each fluorophore when it was in an on state SHOW HISTOGRAMS Show histograms of the generated data CHOOSE HISTOGRAMS Set to true to allow the histograms to be selected otherwise all histograms are shown HISTOGRAM BINS The number of bins in the histogram REMOVE OUTLIERS Remove outliers before plotting histograms Outliers are 1 5 times the interquartile range above below the upper lower quartiles Outliers are always removed for the Precision data since low photon signals can produce extreme precision values DENSITY RADIUS Specify the radius relative to the Half Width at Half Maxima HWHM of the PSF to use when calculating the localisation density around each molecul
7. 10 4 Mean Variance Test EM CCD ceccsesssesssesesesesessseecseeeseeeseeseeeseneensaauaeeeneess 187 10 4 1 Multiple Input IMAGES a 187 LOAZ AI SS A A A E E ATT 188 TOA SOU ni O e aaa says NA ERANO aiaa a 188 10 4 4 Single Image MOCE ccccccccccccceccceccccceeeeceneceeeeeeceeseseeseseceseenssesesessssaonseetsecss 189 10 5 EMANAN io 189 10 5 1 EM CCD Probability Mode us 189 LD ZAPATA ne A Ee tastes e aeaa eL N ENEAS E ASE 190 10 5 3 P r metel Si enseri enteni arap a EEE Troilo 191 10 5 4 Simulation MO Casi A ea iacmbodblasciee 191 e SA A teehee ance a 192 106 MARS af PME mooipraat ee eaea ae Aeda Aaaa duengatns Gitakooel 193 10 7 Diffusion Rate TES icc dasca ae A A A AO 195 10 7 14 Grid Walk Sim lati N i ias ici 195 10 7 2 Random Move simulation A 195 10 7 3 Confined DITUSION sr iO is lol 195 TOTAANAIYSIS AA a a eaS Ea 196 TOFS OUP a AO 196 10 8 Trace DIFUSION AAA E E EE AN 199 T0 8 LANAlIYSIS adoreren ae EAEE e 199 10 8 2 Jump Distance analySiS oonconnnonnconnnorncorro crono roooro corro crono ro nor ono nono ro rro 200 10 8 3 Selected the best aca in a cla igen 201 TOBA ParamMeterS a as id 201 O NN 203 TATOOS a Us y S APPO PUO CO005 anaandaa aaa anaa aia aiaei dA aa eaaa 208 PTA Smooth Mageni aa aa A sla E a aN Ea E EE Ea 208 11 1 1 Smoothing within the Peak Fit plUgiN oooocccccccccnccnccnnnnnnnnnnnnnnnnnonacinannos 209 LEZ Binary DiS Dai ds A ad OA 210 IES Reset Ma dia 210 Pa
8. This uses the same Page 54 225 GDSC SMLM ImageJ Plugins fitting algorithm as the Peak Fit plugin The following parameters are available Parameter Description Fit FUNCTION e Fixed Fits X Y centre and amplitude e Circular Fits X Y centre combined X Y deviation and amplitude e Free Circular Fits X Y centre individual X Y deviation and amplitude e Free Fits X Y centre individual X Y deviation rotation angle and amplitude Fit BACKGROUND Enable background fitting If disabled then the background is assumed to be zero Note that cellular images contain background fluorescence and cameras may have a bias offset to allow characterisation of noise This setting is best left on Fit Criteria The fit uses a non linear least squares routine until convergence If convergence is not achieved by the maximum iterations then the fit fails Convergence can be using Least squares convergence of the mean squared error of the fit to a given number of significant digits Least squares plus convergence of the mean squared error of the fit to a given number of significant digits Convergence is also achieved if 3 consecutive improvements are the same relative improvement and half of the maximum iterations has passed This avoids slowly converging fits Coordinates convergence of the X Y centre coordinates to within a specified delta Parameters convergence of each of the Gaussian parameters e g c
9. valid XML filters that can be passed to the Free Fitter Resucts plugin An example set of all the valid filters can be output to the ImageJ log window using the Free Fitter Resutts plugin see section 6 9 Each XML filter template is processed into a filter set The attributes of the filter are scanned for the pattern min max increment If this is found a filter is created with the attribute set at each value from the minimum to the maximum using the specified increment If not then the filter value is left untouched If a filter has multiple attributes then all combinations will be enumerated Use the ENUMERATE EARLY ATTRIBUTES FIRST Checkbox to enumerate the attributes in the order they appear in the template Otherwise they will be enumerated in reverse order The output filter set will be named using the name of the filter For example lt SNRFilter snr 10 20 2 gt Becomes lt FilterSet name SNR gt lt filters class linked list gt lt SNRFilter snr 10 gt Page 101 225 GDSC SMLM ImageJ Plugins lt SNRFilter snr 12 gt lt SNRFilter snr 14 gt lt SNRFilter snr 16 gt lt SNRFilter snr 18 gt lt SNRFilter snr 20 gt lt filters gt lt FilterSet gt When the plugin has generated all the filters it will present a file selection dialogue allowing the user to specify the output filter file If the file already exists it will be overwritten 7 11 Filter Analysis File Performs
10. 2 1 Pulse Analysis The options Purse Interval and Purse Winbow allow the user to specify a repeating period within the image time sequence Only traces that originate within a frame defined by the pulse will be included in the output Page 77 225 GDSC SMLM ImageJ Plugins For example a pulse could be defined using Purse Intervat 30 and Purse Winbow 3 Only traces that have their first localisation in frames 1 3 31 33 61 63 etc will be output in the final traces This option was added to allow analysis of images acquired using a pulsed activation laser Consequently only localisations that could be traced back to a short period after the activation pulse are of interest All other localisations are likely to be random background fluorescence events The options should be disabled when using a continuous activation laser by setting to the parameters to zero When using a pulse activation it is possible to photo bleach all fluorophores that were activated by the pulse before the next pulse This requires a long pulse interval If you are confident that all molecules have bleached then it does not make sense for a trace to span pulse intervals Use the Spit PuLses option to break apart any traces that span a pulse interval boundary into separate traces 7 2 3 Optimisation It is possible to produce an estimate of the optimum distance and time thresholds if the blinking rate of the fluorophore is known Note that the blinking rate can be
11. 2 5 Multiple Peak Fitting ParameterS c ssssssssssssssssssssssseeeeeessseaaaeeeseeeenaes 36 5 2 6 Filtering Parade a A uae eek 37 5 2 7 Results PAM SA auedesrencn hess 38 5 2 8 Interactive Results Tables nui es eas aided Ai 41 5 2 9 Live image dsd aaa hee a 41 2 LOMAS A Sa 42 5 21 TRUNKING Peak Plica o ad 43 5 2 12 Additional Fitting OPUS din nner aes keel aeaes 44 32113 ISM ACE DT 1 re e aria 45 5 3 Template COMO O sececivnesvCuaseeecaauoieatcane codes gov cscs vaceukeniuwers te paceouepeieaumeciaiepenaunee 46 5 4 Fit COMMGQUIAUOM x s0isivkcevenerecspnmrcqrunennsnueioertmedatus teautaaguudeaveacuaieanactay rar 47 5 5 Peak Fit SEES sirleri aa aa aa ADE AE RA VRAA EEEE EDE EUNE 48 A Fiten naa atts a E a r a a eee ne 49 56 1 C nfig ration Pla ia 49 5 62 RUN Mea pedak das adari O a a STi 51 EA TT E ETET 52 5 8 Spot Finder S res ud a a a RS 52 O 52 E A oea e e a unt a el UE aaa aeaea a EE ad ed 53 510 Madman A A AA A 54 5102 SAUS ANA A AR 54 6 Results RISE ds 57 Page 2 225 GDSC SMLM ImageJ Plugins OL RESUIS MANTE a iaa 57 sks 5 IMPULOOMOMS A Ad 57 6 1 2 OUIDUTO HONS 2 ragina anem A is 57 6 2 SUMMANSe RESUNS A A E E ia A ee eas 58 6 3 Clear MENORES died 58 6 4 Re a am Rel A AA RaR A e EREE dae 58 6 5 Resequenc RESUMS aerea eian tes 59 6 6 Calibrate ResUlS miis ao aia 60 6 7 Show Results Head eden clas scada 61 6 8 Filter Results ra a E a E Ea say ts aati a ereie Rec 61 6 9 Free Filter RES
12. 99 1 10 A O 100 UN A O letter tinanoes 102 E AN A 102 RAZA MPU UM OS 2 cia ed ole ce naa cae aAA el cael ae EAE EAEE sr EEPE ESEIA ER NRAN 102 Page 3 225 GDSC SMLM ImageJ Plugins 7 12 2 Plugin IMA A A Ea 103 123 Analysis WOW A 108 7 124 Results FileS niia a A wastes ede Eaa EEE 108 T LXSpot Analysis AGC si tun a aea naaa AAE A aE aaa Eaa aa AAT 109 7 14 Fourier Image Resol dE 109 7 14 1 Threshold MENOS inspira 111 A E S 111 8 PC PALM PIUGQINS ta AA AAA AA AA 113 9 PC PALMIMBIECUIES a a 113 8 2 PE PANAS Sd as 113 8 3 PC PALM Spatial AmalySiSess a O aia 113 8 4 PC PALM Save ReSullS odisea ii parados 113 8 5 PE PALM Load Result ra 113 AS A E EELEE 114 8 7 PC PALM Cl Ste iN seriei s A A A ea N 114 A A aa aaa Aa Nee eae salah ih AAEE Aaaa 115 A A E 115 9 2 PSPC Otal 115 92 WA PUl IMAGES ios o ira 116 A cctushtaons taieiiue cipu ase tse sn a l upheld esp gasck tanucexadunibamndng du daemaunase Maewtamcal 116 D253 GRACO Set OS 119 O 120 OS PSF Di sricamsads iii eii e 122 33 Dit Calcula yinjeeganns 123 9 3 2 e NA CDE a eee aa A ner ery ae 124 9 S SOPU apea Sate eet eet see week a aa AA det ial aens ees 125 9 34 Saving the Driftas isis dal asad eee a ci cion 127 JA PSF COMDINE eine Seven atare Ena Ma EEEN ARa E Nae E o EETA T 128 9 5 Create Dala O in 129 SES A A ewe een ee 129 9 5 2 PONE Spread FUN CO aa 131 NOS ld a a aie eae 132 9 5 4 Particle dista 133 9 5 5 Paramelet u nn ias 135 9 5 6 Date SUMMA acorta O meine Ee
13. All the ROIs in the manager will be used to calculate the drift Ensure that you choose regions containing a constant bright spot that is present through the majority of frames If multiple spots are within the ROI only the brightest one per frame will be used Ideally these are fluorescent beads added to the image as fiducial markers The Marked ROIs method performs the following steps 1 Initialise the drift for each time point to zero 2 Calculate the centre of mass of all the spots selected within each ROI 3 For each frame and each ROI calculate the shift from the spot to the centre of mass of the ROI 4 For each frame produce a combined shift using a weighted average of the shift from each ROI The weight is the spot signal number of photons 5 Smooth the drift curve 6 Calculate the change to the drift and repeats from step 2 until convergence The Marked ROIs method requires no additional parameters only ROIs within the ROI Manager Note however that each ROI s bounds x y width height are used to find spots within the input localisations and so the ROI should be selected using an image with the same scale and image bounds as the input data Ideally this should be an average intensity projection of the original image but it can be a super resolution reconstruction of the data made using an image scale of 1 7 1 5 Image alignment using correlation analysis Image alignment in the Locatisation SUB IMAGE and REFERENCE Stack ALIGNME
14. Any missing names are ignored allowing the user to delete many entries that should be unchanged If the left and right side are identical then the name will be unchanged Any invalid names not corresponding to an existing dataset cause an error to be displayed The destination names are then checked any duplicates cause an error to be displayed If no errors occurred then the datasets are renamed Renaming may cause an existing dataset to be over written if that dataset is not also renamed This is allowed behaviour as it may be desirable to over write a set of named results with the latest analysis results 6 5 Resequence Results Allows the frame number of results to be rebuilt assuming a repeating pattern of data and non data frames The Peak Fit plugin will fit a stack of images using a continuous frame number starting at 1 However this image may have been extracted from a larger image with interlaced data or been taken with a custom image acquisition workflow In this case the frame number will be an incorrect representation of time This is relevant for any analysis using the time gaps between localisations For example if every 20 images is a white light image and this was removed before fitting the frame number can be restored to add blank frames at 1 21 41 etc Or the image may represent 1000 frames of imaging interspersed with 5 second gaps Resequencing the results can put an appropriate gap between localisations in frame 1000 and 1
15. CMAES optimiser This algorithm depends on randomness and so can benefit from restarts The plugin allows the number of restarts to be varied For the optimisation of the sum of squares against the cumulative histogram a least squares fitting algorithm Levenberg Marquardt or LVM optimiser is used to improve the initial score where possible The plugin will log messages on the success of the optimisers to the ImaceJ log window Extra information will be logged if using the Deus Fittinc option 10 8 3 Selected the best fit The Bias Corrected Akaike Information Criterion CAIC Hurvich amp Tsai 1989 is calculated for the fit using the log likelihood L the number of data points n and the number of parameters p AIC 2p 2L cAIC AIC 2 p p 1 n p 1 The corrected AIC penalises additional parameters The model with the lowest AIC is preferred If a higher AIC is obtained then increasing the number of fitted species in the mixed population has not improved the fit and so fitting is stopped Note that when performing Maximum Likelihood Estimation the Log Likelihood L is already known and is used directly to calculate the corrected AIC When fitting the sum of squared residuals SS the Log Likelihood can be computed as L 0 5 n In 2m 1 In n In SS 10 8 4 Parameters The plugin dialogue allowing the data to be selected is shown in below Page 201 225 GDSC SMLM ImageJ Plugins 2 Input For alex 25ms CW2 tra
16. DSy amp The average and standard deviation of the difference of the fit to the actual PSF standard deviation in the Y dimension This is only reported for the Free and Free circular fit functions Time amp The average and standard deviation of the time for fitting per localisation DACTUALSIGNAL amp The average and standard deviation of the difference of the fit to the actual signal for the localisation Note that the Create BencHmark Dara plugin stores the number of photons that were simulation per localisation after Poisson sampling to allow this comparison DSAx amp The average and standard deviation of the difference of the fit to the actual PSF standard deviation in the X dimension adjusted for square pixels DSAx amp The average and standard deviation of the difference of the fit to the actual PSF standard deviation in the Y dimension adjusted for square pixels This is only reported for the Free and Free CIRCULAR fit functions 9 9 Benchmark Analysis Compute statistics on the accuracy and precision of fitting using different methods Statistics are only computed for all the localisations that were fit successfully by each Page 149 225 GDSC SMLM ImageJ Plugins method The Benchmark Analysis plugin can be used to compare different fitting methods on the same benchmark data Note that if the Fit Benchmark Data plugin is run for multiple fitting methods the recall may be dif
17. ImageJ the table can draw ROI points on the image e Double clicking a line in the results table will draw a single point overlay on the frame and at the coordinates identified e Highlighting multiple lines with a mouse click while holding the shift key will draw multiple point overlay on the coordinates identified Each point will only be displayed on the relevant frame in the image The frame will be set to the first identified frame in the selection The coordinates for each point are taken from the X amp Y columns for the fitted centre not the original candidate maxima position 5 2 9 Live image display The super resolution image is computed in memory and displayed live during the fitting process To reduce the work load on ImageJ the displayed image is updated at set intervals as more results become available The image is initially created using a blank frame the size is defined by the input image The image is first drawn when 20 localisations have been recorded The image is then redrawn each time the number of localisations increases by 10 Finally the image is redrawn when the fitting process is complete Page 41 225 GDSC SMLM ImageJ Plugins 5 2 10 Image examples Illustration 6 shows examples of different image rendering methods The Locatisations and SIGNAL INTENSITY Methods are able to plot the location of the fibres to a higher resolution than the original average intensity projection The Point Spread Function PSF
18. The fitting configuration used to produce the results 6 8 Filter Results Filters a set of localisations using various criteria Requires the fitting results to be loaded into memory When the plugin is run the user is presented with a selection dialogue of the available results The user can select the results to filter The plugin analyses the selected results and computes limits for each of the filters based on the data A second dialogue is then shown that allows the filters to be adjusted The Page 61 225 GDSC SMLM ImageJ Plugins following filters are available Parameter Description Max DRIFT The maximum distance the fitted centre is allowed to be from the original maxima location Min SIGNAL The minimum signal strength Min SNR The minimum signal to noise ratio Min Precision The minimum precision Min WiDTH The minimum width for a localisation Width is defined as the peak width at half maxima PWHM Max WIDTH The maximum width for a localisation Width is defined as the peak width at half maxima PWHM Mask Select an image to use as a mask Only localisations that occur in non zero mask pixels will be included in the results The mask is scaled to match the width and height of the result source If any parameter is set to zero it will be ignored 6 9 Free Filter Results Filters a set of localisations using various criteria Requires the fitting results to be load
19. This is equal to 2d in the score distance weighting formula BETA Controls the weighting between Precision and Recall for the custom F score Show Pairs Display a table of the matched pairs with coordinates and distances Page 66 225 GDSC SMLM ImageJ Plugins Parameters Description Sort Pairs Specify the sort method for the pairs Time or Score 6 12 Spot Inspector Extracts the fitted spots from an image into a stack ordered by the user selected score The Spot Inspector plugin allows visualisation of the fitted spots from a result set held in memory The results are ordered using a user selected score Then the pixels surrounding each spot centre are extracted into an image stack named using the plugin title The plugin also produces a results table containing all the results in their rank order If a line on the table is double clicked using the mouse then the appropriate slice of the image stack is selected Any spot from the entire results set will be labelled on the image using a multi point ROI This can produce many labels on the image which can be dismissed by clicking on the image or using Epit gt SeLectrion gt Setect None CtTRL SHIFT A The plugin will check if the original source can be located This may be an image open in ImageJ or the original file or image series located on disk This allows inspection of fitting results from an image series too large to fit into memory If the o
20. a diffusion coefficient of zero and the other non zero The remaining section of the compound specification is the list of atoms These are fluorophore positions relative to the origin The distances are specified in nanometres The atom mass is used to weight the centre of mass for the compound If omitted it is assumed all the atoms are the same An example compound using a 2 1 ratio of fixed monomer to moving dimer is shown below lt linked list gt lt Compound fraction 2 0 D 0 0 gt lt atoms gt lt Atom mass 10 0 x 0 0 y 0 0 z 0 0 gt lt atoms gt lt Compound gt Page 140 225 GDSC SMLM ImageJ Plugins lt Compound fraction 1 0 D 1 0 gt lt atoms gt lt Atom mass 30 0 x 0 0 y 0 0 z 0 0 gt lt Atom mass 20 0 x 1000 0 y 0 0 z 0 0 gt lt atoms gt lt Compound gt lt linked list gt When the compound is created the centre of mass is placed at the randomly chosen location The compound can be rotated around the centre of mass This rotation can be done once when the compound is created Rotate INITIAL ORIENTATION and during the simulation Rotate DURING simulation If the Enaste 2D rotation option is chosen then the rotation only occurs around the Z axis otherwise the axis is a randomly chosen unit vector The rotation is a random angle from 0 360 degrees at each simulation step Currently is it not possible to configure the rotation speed of the compound Note that rotation will
21. a distance threshold of 1 or more Note the candidates generated by spot finder have coordinate accuracy to integer pixel values so a threshold of at least 1 pixel is recommend e Fitting the traces of neighbours using the refit option of Trace MoLecuLes e Fitting the remaining candidates using the Fit Maxima plugin to select the combined Trace Fit results Fit Maxima ignores any localisations which span multiple frames and only fits the remaining single frame candidates The resulting dataset will be the output of fitting the neighbouring localisations across time frames and all the other candidate maxima per time frame 7 3 Cluster Molecules Cluster localisations into clusters using distance and optionally time thresholds When using a time threshold each cluster can only have one localisation per time frame With the correct parameters a cluster should represent all the localisations of a single fluorophore molecule including blinking events This plugin is very similar to the Trace Motecutes plugin and many of the options are the same The following options are available Parameter Description INPUT Specify the localisations to use Distance THRESHOLD Nm Maximum distance in nm for two localisations to belong to the same cluster Time THRESHOLD Maximum distance in seconds for two localisations to belong to SECONDS the same cluster should cover a minimum of 1 frame This is only used for some algorithms
22. a limit on the initial cumulative probability to remove from the plot This allows removing the start of the curve where the convolution of the Poisson Gamma distribution with the Gaussian is incomplete REMOVE TAIL Set a limit on the final cumulative probability to remove from the plot This allows removing the tail of the curve where the convolution of the Poisson Gamma distribution with the Gaussian is incomplete It also allows removing the long tail which can take up a large amount of the plot width RELATIVE DELTA Check this to show the difference between the actual PMF and the approximate PMF as a relative score The default is absolute Page 193 225 GDSC SMLM ImageJ Plugins Examples of the PMF are shown below The magenta line on the plot shows the position of the average number of photons after the gain has been applied Gain 40 0 noise 3 0 photons 1 0 0 50 100 150 200 ADUs Gain 40 0 noise 3 0 photons 5 0 0 003 0 002 0 001 0 100 200 300 400 500 The PME is skewed for low photons with a spike at c 0 blurred by the Gaussian read noise Increasing photon counts return a shape more characteristic of a Poisson distribution For this reason it is possible to use a simple Poisson model for the camera noise when performing Maximum Likelihood Estimation i e ignoring the effect of EM gain and read noise if the number of photons within the localisation is large This is an option available with
23. a localisation in the first frame to the last frame All the algorithms only allow localisations to be joined to the closest localisation in a different frame i e not the same frame However only those closer than the distance threshold are joined Illustration 18 shows the plugin dialogue Page 92 225 GDSC SMLM ImageJ Plugins Compute the cumulative dark time histogram Search distance nm hoo Max dark time seconds 0 00 Percentile oo Histogram bins 100 Dark time Analysis v Y Qs Input Localisation Data Create Data 10342 OK Cancel Help illustration 18 Dark Time Analysis plugin dialogue The plugin supports the following parameters Parameter Description INPUT Specify the results to use for analysis METHOD Specify the tracing or clustering method Details of the tracing and clustering algorithms can be found in the sections describing the Trace Molecules and Cluster Molecules plugins SEARCH DISTANCE NM Specify the maximum distance between localisations to be part of the same molecule Max DARK TIME SECONDS Specify the maximum allowed dark time between localisations to analyse Any dark time distances above this are ignored Set to zero to allow any dark time PERCENTILE Specify the percentile limit used to report the maximum dark time HISTOGRAM BINS Specify the number of bins to use for the histograms When started the progress of the algorithm i
24. along with the recall against the z depth The z axis is limited to the input z depth or the available depth of the PSF whichever is lower Page 125 225 GDSC SMLM ImageJ Plugins 9 3 3 1 Drift Curve The drift curves show the original data points in blue with magenta vertical bars for the standard error of the mean A high standard error would indicate that the curve is not a good estimate at the given point The smoothed curve is shown as a blue line Green vertical lines mark the points where the recall falls below the configured limit The following example shows a curve computed for an equivalent pixel pitch of 107nm scaling a 10 7nm PSF 10 fold The drift is minimal when the PSF is in focus however the fit Y centre drifts nearly a full pixel as the PSF moves out of focus This is due to an alignment error with the microscope optics d PSF Drift Drift Y 2 See 9 3 3 2 Recall Curve The recall curve shows the recall above the recall limit using a blue line and below the limit using a red line The limit is shown using a magenta line The following example shows that fitting is successful until 720 nm out of focus The z depth used for analysis could be extended as the recall is still 1 at the maximum negative depth 1000nm Page 126 225 GDSC SMLM ImageJ Plugins PSF Drift Recall 9 3 4 Saving the Drift When the calculation is complete the user is presented with the opti
25. are aligned to their centre of mass over the entire image e Reference stack alignment Images from a reference stack e g a white light image are aligned to a global projection e Drift file The drift is loaded from file Further details of the methods are shown in the sections below Each method will produce an X and Y offset drift for specified frames Not all frames must have a drift value The calculated values are smoothed using LOESS smoothing a local regression of the points around each value The drift error is calculated as the total sum of the drift per frame The current drift is applied to the results and the drift calculation repeated This process is iterated until the drift has converged Shown by a small relative change in the drift error In the case of loading the curve from file no iteration is performed but the drift points may be smoothed The calculated drift curve is interpolated to assign values for any frames without a drift value Any frames outside the range of frames with drift values cannot be interpolated These are assigned the same drift as the closest frame with a known drift value i e no extrapolation of the drift curve is performed to avoid errors from poor data at the ends of the analysis range The plugin requires the following parameters Parameter Description INPUT Select the results set to analyse Fitting results can be stored in memory by the Peak Fit plugin or loaded from
26. are the same as those available within the Peak Fit plugin The plugin provides some parameters to control how the combined image is constructed and then fitted Parameter Description Fit CLOSEST TO CENTROID When enabled the candidate maxima is seeded using the centroid position of the trace only one maxima should be fitted If disabled the fitting algorithm is allowed to detect maxima in the combined image and fit them all The closest maxima to the centroid is then chosen DISTANCE THRESHOLD Specify the maximum distance that a fitted maxima can deviate from the centroid before it is rejected EXPANSION FACTOR Fitting in Peak Fit uses a region surrounding the candidate This is defined using the expected peak standard deviation multiplied by the search width This default region is enlarged by the expansion factor to allow a larger region to be input into the fitting routine This allows inclusion of all the trace localisations and some surrounding pixels DEBUG FAILURES The success of each fit is recorded This option will show an image of the first few fits that fail for each different reason The reason will be written to the ImageJ log and the stack of localisations will be displayed The final image in the localisation stack is the average intensity projection of the stack It should be a clear PSF spot if fitting succeeds and a poor spot if fitting failed The fitting routine will fit all the traces that con
27. be changed using the extra options available by holding the Shirr key when running the plugin Page 37 225 GDSC SMLM ImageJ Plugins Min PHOTONS The minimum number of photons in a fitted peak This requires a correctly calibrated gain to convert ADUs to photons WiptH Factor Any peak whose final fitted width is a factor different from the start width is discarded e g 2x different PRECISION Any peak with a precision above this level is discarded i e not very good precision If a precision threshold is specified then the plugin will calculate the precision of the localisation using the Mortensen et al 2010 formula see Appendix A Localisation Precision The appropriate formula for either the Maximum Likelihood and Least Squares Estimator is used The precision calculation requires the expected background noise at each pixel The noise can be estimated two ways The first method is to use the noise estimate for the entire frame This is computed automatically during fitting for each frame or can be provided using the additional options See section below The second is to use the local background level that is computed when fitting the localisation This background level is the background number of photons at the localisation position that will contribute photon shot noise to the pixels The global noise estimate will be a composite of the average photon shot noise over the entire frame and the read noise of t
28. compared using time and distance thresholds with priority on the closest distance gap within the time threshold Only the Distance PRIORITY AND Time PRIORITY methods use the time information All the other algorithms will ignore the Time THRESHOLD and optional Pulse intervat parameters All the clustering algorithms except Pairwise are multi threaded for at least part of the algorithm The number of threads to use is the ImageJ default set in Epit gt Options gt Memory amp THREADS The Pairwise algorithm is not suitable for multi threaded operation but is the fastest algorithm by an order of magnitude over the others All other algorithms have a similar run time performance except the Pairwise witHouT NEIGHBOURS algorithm which doesn t just search for the closest clusters but also tracks the number of neighbours The algorithm should return the same results as the Closest algorithm but the analysis of neighbours has Page 85 225 GDSC SMLM ImageJ Plugins run time implications At very low densities this algorithm is faster since all pairs without neighbours can be joined in one step However at most normal and high densities tracking neighbours is costly and the algorithm is approximately 3x slower than the next algorithm 7 4 Draw Clusters Draws collections of localisations with the same ID on an image for example the output from Trace Mo tecutes CLusteR MoLecutes Or TRACE DIFFUSION The Draw Cuusters plugin colle
29. cyan squares r Ly e Spot Analysis Raw mea A Nh WA vi A A RLT Frame List Save Copy Ed Spot Analysis Raw SL 2 0 1 5 Signal Ala i f 200 300 400 500 List Save Copy Illustration 26 Spot Analysis mean and standard deviation profiles of the spot region The current frame is shown as a vertical pink line Candidate on frames from Peak Fit results are shown as cyan box Selected on frames are shown as magenta circles The red line is the LOESS smoothing of the plot data Page 106 225 GDSC SMLM ImageJ Plugins 7 12 2 2 Adding on frames Any fluorophore on frame should have a higher mean that the frames around it These can be easily viewed as spikes on the plot profile and the relevant frames in the spot image inspected When the spot image is moved to a new frame the plugin will update the signal and SNR figures for the frame The signal is calculated as the sum of the raw spot minus the LOESS smoothing fit of the mean profile i e the background The noise is calculated using the LOESS smoothing fit of the standard deviation profile The plugin also runs the Peak Fit algorithm on the raw and blurred spot image Identified localisations will be marked on the image with an overlay The signal and SNR for the raw fit and blur fit are shown in the plugin window Combining inspection of the spot images with consideration of the signal and SNR of the raw data and fi
30. derivative based function solvers Poisson Gaussian noise model This model is suitable for modelling a standard CCD camera This model accounts for the photon shot noise and the read noise of the camera e when the number of electrons is read from the camera chip there can be mistakes The read noise is normally distributed with a mean of zero The two noise distributions can be combined by convolution of a Poisson and a Gaussian function to the produce the following model lt 1 n kli o 2 he Xx e pl 2 n V2 ro with k equal to the pixel count A equal to the expected pixel count and o equal to the standard deviation of the Gaussian read noise This model is evaluated using a saddle point approximation as described in Snyder et al 1995 the implementation is adapted from the authors example source code 1 2 1 on No gradient is available for the function and so non derivative based methods must be used during fitting Poisson Gamma Gaussian noise model This model is suitable for modelling a Electron Multiplying EM CCD camera This model accounts for the photon shot noise the electron multiplication gain of the EM register and the read noise of the camera The EM gain is modelled using a Gamma distribution The read noise is normally distributed with a mean of zero The convolution of the Poisson and Gamma distribution can be expressed as E A T cp G m c e P5 c o Bessell 2 P where p The
31. draw The list only contains results where all the localisations have an ID IMAGE Specify the output image to draw on If None is selected then the output will be to an image named Draw Clusters IMAGE SIZE The size of the default output image on the long edge Small images will be zoomed EXPAND TO SINGLES Expand any localisation with a different start and end frame into a series of singles with the same coordinates This option is useful for drawing multi frame localisations for example centroid representations of clusters The expansion is performed before the size filtering Page 87 225 GDSC SMLM ImageJ Plugins Parameter Description MIN SIZE The minimum size of clusters All clusters below this will be ignored Max SIZE The maximum size of clusters All clusters above this will be ignored Set below the Min size to disable TRACES Select this option to assume the localisations are connected as a time series trace The output will draw lines connecting the points If not selected the output will draw each point individually Sort Specify how the clusters will be sorted before drawing The sort order determines the colour taken from the look up table SPLINE FIT If selected the line will be drawn as a spline fit This is only valid when Traces Is selected USE STACK POSITION If selected the plugin will draw each cluster on the specific frame containing the localisation If an ou
32. drawn on the image HWHM The Half Width at Half Maxima HWHM of the PSF S The standard deviation of the Gaussian equivalent of the PSF This is the exact SD of the Gaussian PSF or if using an Airy or Image PSF it is the Gaussian that best matches the width profile of PSF Sa The standard deviation of the Gaussian equivalent of the PSF adjusted for square pixels The pixel adjustment in computed as S Vs a 12 where s is the standard deviation and a is the pixel size both in nanometers This should be used as the input width to Peak Fit SIGNAL FRAME The average signal emitted by a fluorophore per frame SiGnat FRAME CONTINUOUS The average signal emitted by the fluorophores that were continuous for the entire frame TOTAL SIGNAL The average total signal for fluorophores BLINKS The average number of blinks of a fluorophore TON The average on time of a fluorophore TOFF The average off time of a fluorophore SAMPLED BLINKS The average number of blinks of a fluorophore if perfectly sampling at integer frame intervals See 9 5 8 Page 139 225 GDSC SMLM ImageJ Plugins Field Description SAmPLED TON The average on time of a fluorophore if perfectly sampling at integer frame intervals see 9 5 8 SAMPLED TOFF The average off time of a fluorophore if perfectly sampling at integer frame intervals see 9 5 8 Noise The average noise of the region surroundin
33. e the spot is not circular and may be a doublet two spots close together If the residuals analysis is above the threshold then it is refitted as a doublet The doublet fit is compared to the single fit and only selected if the fit is significantly improved Note the residuals threshold only controls when doublet fitting is performed and not the selection of a doublet over a single Lowering the threshold will increase computation time Dupticate DISTANCE Each new fit is compared to the current results for the frame If any existing fits are within this distance then the fit is discarded This avoids duplicate results when multiple peak fitting has refit an existing result peak Note that doublets are allowed to be closer than this distance since the results of the latest fitting are only compared to all existing results 5 2 6 Filtering Parameters These parameters control the fitted peaks that will be discarded Parameter Description ShirT Factor Any peak that shifts more than a factor of the initial peak standard deviation is discarded SIGNAL STRENGTH Any peak with a signal noise below this level is discarded The signal is the calculated volume under the Gaussian The image noise is calculated per frame using the least mean of squares of the image residuals This is a method that returns a value close to the image standard deviation but is robust to outliers Note The noise method can
34. factor Increasing this value will slow down the algorithm HALF CIRCLE The Fourier image is symmetric Speed up computation by using only half of the ring to compute the FRC Results may differ slightly due to sample points on the full circle not being rotationally symmetric to the half circle sample points THRESHOLD METHOD The method for determining the correlation cut off see 7 14 1 Page 110 225 GDSC SMLM ImageJ Plugins Parameters Description SHow FRC curve Display the FRC curve The curve shows the raw data the smoothed data and the correlation cut off SHow FRC Time Sort the results by time and compute the FIRE number using 10 EVOLUTION step increments up to the max time This shows how the resolution has changed at the time increases This option is computationally intensive 7 14 1 Threshold methods The FRC plugin can compute the correlation threshold using the following methods 7 14 1 1 Fixed Use the value 1 7 0 142857 This is threshold value preferred by Niewenhuizen et al 2013 7 14 1 2 Half bit Compute the threshold at each frequency 7 from the number of data points N used to compute the FRC with the following formula _0 2071 V N 1 9102 i 1 2701 VN 0 9102 7 14 1 3 Three sigma Compute the threshold at each frequency 7 from the number of data points N used to compute the FRC with the following formula A N 2 7 14 2 FRC Curve The FRC curve d
35. file using the Resutts ManaGER METHOD The method for calculating the drift curve Max ITERATIONS The maximum number of iterations when calculating the drift curve Page 68 225 GDSC SMLM ImageJ Plugins RELATIVE ERROR Stop iterating when the relative change in the total drift is below this level SMOOTHING The window width to use for LOESS smoothing values below 0 1 are unstable for small datasets Set to zero to ignore smoothing LIMIT SMOOTHING Select this option to adjust the smoothing parameter so that smoothing uses a number of points within the configured minimum or maximum MIN SMOOTHING POINTS The minimum number of points to use for LOESS smoothing Max SMOOTHING POINTS The maximum number of points to use for LOESS smoothing A lower value will allow the drift curve to track the raw drift data more closely but may start to model noise SMOOTHING ITERATIONS The number of iterations for LOESS smoothing 1 is usually fine PLOT DRIFT Produce an output of the drift for the X and Y shifts Shows the raw drift correction for each frame and the smoothed correction see Illustration 12 Use this option to see the effects of different smoothing parameters before applying the drift correction to the data An example of a calculated drift curve is shown in Illustration 12 The drift curves show that drift in the X and Y axis are independent and drift may be approximate
36. for the simulation Noise The read noise for the simulation PHOTONS The average number of photons per pixel for the simulation SAMPLES The number of samples for the simulation Sampe PDF Check this to generate the Probability Mass Function PMF using the provided parameters Then sample randomly from within this PMF The default is to generate a random Poisson sample using the average photon number then use this to generate a Gamma sample from the photon count and then generate a Gaussian sample from the amplified photon count Simulation mode can be used to see if the fitting process is working given the expected parameters for bias gain noise and photons 10 5 5 Results The plugin will create a histogram of the pixel values and attempt to fit it using the Poisson Gamma Gaussian PMF The estimated and fitted parameters are written to the ImageJ log The histogram of pixel values fitted PMF and the fit parameters are shown on a plot as show below Fitted bias 500 gain 39 85 noise 3 034 photons 1 243 0 04 Frequency o o o o N LJ o o p 0 00 E e 500 600 700 800 900 1000 ADU The values for the gain bias and noise should be constant for different background photon levels This can be evaluated using different input calibration images The parameters can be used within the Peak Fit plugin to perform Maximum Likelihood Estimation modelling the camera noise of the EM CCD camera Page 192 225 GDSC SM
37. from 0 to 1 is taken for the total Airy power If outside the 4 zero ring it is ignored Otherwise the radius for the power is interpolated and the radius used with a randomly orientated vector to generate the X and Y coordinates The location is added to the image 9 5 2 3 Image PSF The PSF image can be created using the PSF Creator and PSF Comeiner plugins see sections 9 2 and 9 4 Page 131 225 GDSC SMLM ImageJ Plugins When the plugin is run it will check all open images for the PSFSettings XML tag in the image info property This contains details of the image pixel width and depth scales and the location of the z centre in the image stack If no valid images are found then the Image PSF option is not available The PSF image pixel scale may not match the simulation ideally the PSF image should have a smaller pixel scale than the output image so that many pixels from the PSF cover one pixel in the output image The resolution of the output i e the accuracy of the centre of the spot will be determined by the ratio between the two image scales For example a PSF image of 15nm pixel and an output width of 100nm pixel will have a resolution of 15 100 0 15 pixels During initialisation the PSF image is normalised so the z centre has a sum of 1 and all the other slices are scaled appropriately A cumulative image is then calculated for each slice No cumulative image is allowed a total above 1 PSF sampling is performed by selecti
38. illumination for the image i e specify the intensity of light across the image as uniform or radial falloff PULSE INTERVAL The interval at which the activation laser is used Set to zero to disable PULSE RATIO The strength of the activation laser relative to the background activation level e g 100 means 100 times more activation photons in a pulse than all the frames between pulses Set to zero to disable Page 135 225 GDSC SMLM ImageJ Plugins Parameter Description BACKGROUND IMAGE Ony presented if there are suitable background images Images must be grayscale and square Select the image that will form the background photon level The image will be scaled so that the maximum value is the level defined by the Backcrounp parameter Each frame will use this image as the background with each pixel subject to Poisson noise BACKGROUND The background level in photons This is subject to Poisson noise Convert to actual ADU value by multiplying by the product of the camera gain EM gain and quantum efficiency EM cain The EM gain of the simulated camera CAMERA GAIN The camera gain in ADU electron QUANTUM EFFICIENCY The efficiency converting photons to electrons in the camera READ NOISE The average Gaussian read noise to add to each pixel in electrons Bias The bias offset to add to the image Allows negative noise values to be displayed PSF MopeL
39. in the frame Alternatively use the keyboard shortcut that has been mapped to the Spot Analysis App command The frame will be added to the list with the signal estimate for the spot Remove bad frames from the list by highlighting them and using the Remove button Double clicking a frame in the list will select that frame on the detail images Save the frames listed in the window to the results summary by clicking the Save button The summary shows the fluorophore signal on and off times and number of blinks The list can only be saved once It must be updated Abo Remove before it can be saved again 10 Repeat steps 3 9 for different candidate spots 11 Save all the results to file using the Save Traces button Only results that are present in the table are saved Duplicate or unwanted results can be removed using the table Epit gt Clear command to remove selected rows 7 12 4 Results Files Fluorophore sequences in the summary table can be saved to file The plugin saves only the sequences within the table Any sequence that is removed from the table using the Ebir gt Clear command will be discarded Click the Save Traces button to open a folder selection dialogue Following selection the plugin will write several files to the directory Any old files will be over written The following files are saved Page 108 225 GDSC SMLM ImageJ Plugins File Description TRACES TXT Contains a summary of each fluorophore Eac
40. indicates total disagreement between prediction and observation The statistic is also known as the phi coefficient MCC tp tn fp fn Vtp fp tp fnx tn fp tnx fn Informedness Informedness TPR TNR 1 Markedness Markedness PPV NPV 1 Page 223 225 GDSC SMLM ImageJ Plugins 13 References Abraham A V Ram S Chao J Ward E S Ober R J 2009 Quantitative study of single molecule location techniques Optical Express 17 23352 Annibale P Vanni S Scarselli M Rothlisberger U Radenovic A 2011 Quantitative Photo Activated Localization Microscopy Unravelling the Effect of Photoblinking PLoS ONE 6 7 e22678 Coltharp C Kessler RP Xiao J 2012 Accurate Construction of Photoactivated Localization Microscopy PALM Images for Quantitative Measurements PLoS One 7 12 Edelstein A Amodaj N Hoover K Vale R and Stuurman N 2010 Computer Control of Microscopes Using Manager Current Protocols in Molecular Biology 14 20 1 14 20 17 Henriques R Lelek M Fornasiero E F Valtorta F Zimmer C amp Mhlanga M M 2010 QuickPALM 3D real time photoactivation nanoscopy image processing in ImageJ Nature Methods 7 339 340 Hurvich C M Tsai C L 1989 Regression and time series model selection in small samples Biometrika 76 297 307 Mortensen KI Churchman LS Spudich JA Flyvbjerg H 2010 Optimized localization analysis for single molecule tracking and su
41. localisations 5 2 11 Running Peak Fit When the plugin is run it will process the image using multi threaded code Each frame will be added to a queue and then processed when the next worker is free The number of workers is configured using the ImageJ preferences Epit gt Options gt Memory amp THREADS The Parallel THREADS FOR STACKS parameter controls the number of threads Note that the image is not processed using ImageJ s standard multi threaded plugin architecture for processing stacks The SMLM fitting engine code is written so it can run outside of ImageJ as a Java library The plugin just uses the configured ImageJ parameter for the thread count Page 43 225 GDSC SMLM ImageJ Plugins Progress is shown on the ImageJ progress bar The plugin can be stopped using the Escape key If stopped early the plugin will still correctly close any open output files and the partial results will be saved 5 2 12 Additional Fitting Options The standard Peak Fit plugin allows the user to set all the parameters that control the fitting algorithm However there are some additional options disabled by default that provide extra functionality These can be set by running the Peak Fit plugin with the Shirr or Att key down This will add some extra fields to the plugin dialogue Parameter Description INTERLACED DATA Select this option if the localisations only occur in some of the image frames for example in the case where 2 chann
42. nm for two localisations to belong to the same trace Distance EXCLUSION Nm Exclusion distance in nm where no other localisations are allowed Use this setting to be sure that a trace links together localisations that are not close to any other localisations Ignored if less than the distance threshold Time THRESHOLD Maximum distance in seconds for two localisations to belong to SECONDS the same trace should cover a minimum of 1 frame TRACE MODE LaresTFORERUNNER Search from the closest time distance in the past for earlier localisations of the same fluorophore This is the best mode for moving molecules EarLiesTFORERUNNER Search from the maximum time distance in Page 76 225 GDSC SMLM ImageJ Plugins the past for earlier localisations of the same fluorophore SingleLinkage Search all time points in the past up to the maximum time distance to find the closest localisation This is equivalent to single linkage clustering This mode is slower since the other modes will stop searching time points when a localisation has been found within the distance threshold PULSE INTERVAL Sets the pulse interval for traces in frames Set to zero to disable pulse analysis See section 7 2 2 1 Pulse Analysis PULSE WINDOW Sets the pulse window for traces in frames Set to zero to disable pulse analysis See section 7 2 2 1 Pulse Analysis SPLIT PULSES Enable this to split traces that spa
43. plot of the displacement of the particle over time The red line shows the X displacement and the blue shows the Y displacement 10 7 5 3 Analysis results The fitting analysis results are output to the ImageJ log window e g Diffusion Rate Test D 0 9 um 2 sec Mean displacement per dimension 1342 0 nm sec Simulation step size 189 7 nm 2D Diffusion rate 0 9849 um 2 sec 5 705 ms 3D Diffusion rate 1 11 um 2 sec 5 705 ms The input diffusion coefficient is shown for reference the units are um 2 sec This is converted to the expected mean displacement in nm per second and the simulation step size in nm This will allow the user to experiment with the radius of the confinement sphere and the number of simulation steps Remember that the step size should be less than the sphere radius The fitted diffusion coefficients from the 2D and 3D fitting are then shown These should be close to the input diffusion rate If the simulation was performed using confinement then the final distance to the origin for each particle will be saved The average distance will be shown along with the expected asymptote distance i e the mean distance to the centre of a sphere which is calculated as 3 4 of the confinement radius e g 3D asymptote distance 702 7 nm expected 750 00 10 7 5 4 Memory Results The coordinates of each diffusing particle starting at the origin 0 0 are saved to a results dataset in memory Each consecutive st
44. plugin will ask the user to select a mask image The image must be square but width height dimensions are scaled to match the simulation Any stack image must have the z depth of each slice defined so the plugin asks for the slice depth in nm The particles will be placed randomly within a non zero pixel selected from the mask If a single slice is used then the z depth uses the DeptH parameter If a stack is used then the mask slice is chosen with a frequency proportional to the number of non zero pixels in the slice compared to the total non zero pixels The particle is then placed randomly in a non zero pixel in the mask and the z coordinate randomly selected from the slice z depth GRID Particles are placed on a grid The plugin will ask the user to specify the grid parameters The image area is divided into square cells of Cel size dimensions in pixels A particle is placed randomly in the middle 50 of the cell A second particle can be placed in the cell with the specified probability P simarY The second particle is randomly located from the first using a minimum and maximum distance in nm The grid distribution simulates an exact proportion of monomer dimer localisations The distribution can be used for benchmarking techniques for identification of single double localisations Once the particles are distributed within the volume they can move using a diffusion coefficient To prevent the particles moving to
45. plugin will compute the pairwise comparison of consecutive frames in the image and for each pair compute the approximate camera gain gain variance mean bias The bias must be provided since there is no input bias image the plugin will ask the user to input the camera bias The results will be displayed in a table as described above The plugin provides a plot of gain verses slice and a histogram of the values These can be used to determine if the gain is constant throughout the image and so is a good estimate 10 4 Mean Variance Test EM CCD This plugin is similar to the Mean Variance Test plugin but is used on images taken using an Electron Multiplying EM CCD camera An EM CCD camera uses a multiplication device to increase the number of electrons that are extracted from the imaging sensor before the electrons are counted The average number of electrons output from the multiplying device for each input electron is a constant known as the EM gain The plugin will compute the EM gain of the camera using a set of calibration images A single image mode is available but will provide less information on the camera The analysis can only be performed if the gain for the camera in non EM mode is already known If the Mean Variance Test plugin has been used to calculate the gain in the same ImageJ session then the value will be stored in memory If the camera gain is not known then using a value of 1 will allow the plugin to run and the out
46. point spread function Background photons are also captured The photons are amplified and then read into an image Each frame starts with an empty image A background level of photons is sampled from a Poisson distribution and added to each pixel to simulate a background fluorescence image Alternatively the background can be specified using an input image subject to Poisson noise Note that at this stage the quantum efficiency is not factored in to save computational time It is assumed all photons are captured The camera read noise for each pixel is simulated using a Gaussian distribution This is computed as a separate read noise image Then all the localisations are processed For each active fluorophore the total on time is computed If a correlation between on time and photon emission rate is modelled a second set of on times tCorr are created with a specified correlation to the actual on times Page 132 225 GDSC SMLM ImageJ Plugins These are used to specify the average emission rate for each fluorophore using a proportion of the input emission rate tCorr rate rate gt tCorr N If no correlation is used then the emission rate is the sampled from the configured distribution either a Gamma or custom distribution with the mean set to the input emission rate The emission rate for each fluorophore is constant The mean number of photons emitted for each simulation step is calculated using the photon emission rate m
47. precision calculation It is expected that the value would be in the range around 100nm Input of an incorrect value will lead to incorrect precision estimates and require the user to adapt the analysis plugins and their results Gain Specify how many pixel values are equal to a photon of light The units are Analogue to Digital Units ADUs photon This allows conversion of the pixel values to photons It is used to convert the volume of the fitted 2D Gaussian to a photon count the localisation signal The gain is the total gain of the system ADU photon and is equal to Camera gain ADU e x EM gain x Quantum Efficiency e photon Note Check the units for this calculation as the camera gain can often be represented as electrons ADU In this case a reciprocal must be used EM gain has no units Quantum Efficiency should be in the range 0 1 the units are electrons photon For an EM CCD camera with an EM gain of 250 the total gain may be in the range around 40 Camera gain and EM gain can be calculated for your camera using the Mean variance Test plugins see section 10 3 The gain values and Q E may also Page 20 225 GDSC SMLM ImageJ Plugins have been provided on a specification sheet with the camera Input of an incorrect value will lead to incorrect precision estimates These estimates are used in various analysis plugins to set parameters relative to the average fitting precision
48. run the plugin Note The latest version of the SMLM Tools txt file is packaged within the SMLM Jar file This can be manually extracted using an archiving utility The Instan SMLM Tootset plugin simply extracts this file and writes it to the ImageJ macros toolsets directory if the user has the correct access permissions 12 2 Show SMLM Tools Displays a window with buttons to run all the SMLM plugins The window is constructed using a configuration file The plugins listed in the configuration file are used to build a window with buttons to allow them to run The file is searched for in the following locations ImageJ Pathl plugins smim config SMLM Jar File gdsc smlm plugins config Noted that the plugins config file within the jar file is used by ImageJ to build the entries for the plugins menu To customise the ImageJ menus the plugins config file can be extracted from the Jar file modified and replaced This will also change the SMLM Tools window unless a separate smlm config file is placed in the ImageJ plugins directory The plugins config file has entries consisting of 3 fields separated by commas Lines starting with are ignored e g ImageJ menu Plugin name full java plugin ClassName arguments Plugins gt GDSC SMLM Peak Fit gdsc smlm ij plugins PeakFit Plugins gt GDSC SMLM Peak Fit gdsc smlm ij plugins PeakFit spot Plugins gt GDSC SMLM This example shows that the Spot Finper
49. shown in Illustration 25 The average spot image shows a blurred spot biased to the upper right corner but the signal is distinct so the spot if suitable for analysis The Fino Peaks fitting algorithm is applied to the current frame of the raw and blurred spot using the configured PSF width If a spot is detected within 50 of the distance to the centre of the frame it is marked on the image using an cross overlay F J by Spot Analysis Average spot 15x15 pixels 32 bit 1K 81 500 15x15 pixels 3 bit 439K 81 500 15x15 pixels 32 bit 439K PE j IE See Illustration 25 Spot Analysis raw spot blurred spot and average spot images The centre of the fitted peak for the raw and blurred image for the current frame is shown using a cross overlay The plugin then analyses the spot region and creates profile plots of the mean and the signal standard deviation per frame as shown in Illustration 26 The currently selected Page 105 225 GDSC SMLM ImageJ Plugins frame in the spot images is shown using a vertical magenta line The profile can be very noisy and so a LOESS smoothing is applied to the raw plot data to produce a background level shown in red Any selected on frames are labelled using magenta circles In addition the plugin searches the Fino Peaks results that are held in memory for any results that were created from the input image If so then these are potential candidates for on frames and are shown as
50. the Mean Variance TEST plugin The final calculated EM gain and total gain is reported to the ImageJ log e g Mean Variance Test Directory images CameraCalibration CameraGain 2 EmGain 250 Bias 512 3 13 15 ADU Variance 36550 0 79 66 mean Read Noise 0 3301 e Gain 1 6 422 ADU e EM Gain 255 8 Total Gain 39 83 ADU e The total gain is the EM gain multiplied by the camera gain As can be seen from comparison of the analysis results with and without the EM mode the use of EM amplification dramatically reduces the camera read noise and greatly enhances the pixel values ADUs produced per electron This allows images of weak photon signals to be made for example in single molecule light microscopy The total gain can be used to convert the ADUs into photons if the camera Quantum Efficiency QE is known The QE states how many photons are converted into an electron charge when they hit the camera sensor the QE units are electrons per photon Page 188 225 GDSC SMLM ImageJ Plugins e photon This can be provided by the camera manufacturer and is dependent on the wavelength of light The photon signal is therefore ADUs Photons total gain xQE The total gain multiplied by the QE is known as the system gain The system gain is used as an input parameter in the Peak Fit plugin to convert the pixel values into photons 10 4 4 Single Image Mode The plugin can be ru
51. the camera is computed as bias variance gain read noise If the bias has multiple difference images then the average variance is used to calculate the read noise 10 3 3 Output The plugin produces a summary table of the analysis for each pair of frames The table shows the following data Column Description IMAGE The source image EXPOSURE The image exposure This is the first integer number delimited by a space or period in the image title or if no number can be found in the image title zero for the first image and 9999 for the others SLice1 The first frame slice used from the image SLicE2 The second frame slice used from the image Page 185 225 GDSC SMLM ImageJ Plugins Meanl The mean of slice 1 MeEan2 The mean of slice 2 MEAN The mean of both slices VARIANCE The variance of the difference image GAIN R variance The gain estimate gain ___ mean bias The plugin will produce a plot of the mean variance data as show in Illustration 38 The plot will show the best fit line in red If the data points with the highest mean lie well under the line it is possible that these images had saturated pixel values and should be removed from the input data set Du Mean Variance Test results y UR 1500 o o o Variance un o o 2000 4000 6000 8000 10000 Mean List Save Copy X 7362 Y 643 Illustration 38 Mean varia
52. the depth of localisations used for the depth recall analysis in the summary table e the recall of localisations within the specified depth of field PLoT TOP N Show a plot of the performance score against the parameter value for each filter in the top N scoring filter sets This is useful for filters that have one main parameter e g signal to noise or localisation precision However combination filters that test many fit parameters together are only partially supported In this case the main parameter value for the filter will determine the x axis value This option is not available when an optimisation search has been performed on the filter set SAVE BEST FILTER Select this to save the best filter from all filter sets to file The user will be prompted for a filename when the analysis is complete CALCULATE SENSITIVITY Select this to perform sensitivity analysis on the top filter from each filter set DELTA The relative change in the parameter value to use to calculate the sensitivity CRITERIA The metric used for the minimum criteria CRITERIA LIMIT The value for the minimum criteria Score The metric used to rank all filters that reach the minimum criteria UPPER MATCH DISTANCE The distance limit defining the minimum score 0 for a match between a fitted localisation and the true localisation The distance is expressed relative to the match distance used with the Fit Spot Data plugin S
53. the particles PARTICLES The number of molecules to simulate DENSITY The density of the molecules in squared micrometres MIN PHOTONS The minimum number of photons for a localisation Max PHOTONS The maximum number of photons for a localisation Raw IMAGE Select this option to output an image using 32 bit floating point numbers The default is to use 16 bit unsigned integers SAVE IMAGE Show a dialog allowing the image to be saved as a file Page 143 225 GDSC SMLM ImageJ Plugins Parameter Description SAVE IMAGE RESULTS Show a dialog allowing the image localisations to be saved as a PeakResults file Note that this does not contain the molecule Z position Save LOCALISATIONS Show a dialog allowing the localisations to be saved The file contains the time and X Y Z positions of each fluorophore when it was in an on state SHOW HISTOGRAMS Show histograms of the generated data CHOOSE HISTOGRAMS Set to true to allow the histograms to be selected otherwise all histograms are shown HISTOGRAM BINS The number of bins in the histogram REMOVE OUTLIERS Remove outliers before plotting histograms Outliers are 1 5 times the interquartile range above below the upper lower quartiles Outliers are always removed for the Precision data since low photon signals can produce extreme precision values DENSITY RADIUS Specify the radius relative to the Half Width at Half Maxima HWHM
54. the previous frame starting from the start frame plus the frame spacing The Rererence Stack Aticnment method performs the following steps 1 Initialise the drift for each time point to zero 2 Calculate an average projection of the slices shifted by the current drift 3 Aligns each slice to the average projection using correlation analysis to compute the drift 4 Smooth the drift curve 5 Calculate the change to the drift and repeats from step 2 until convergence Page 73 225 GDSC SMLM ImageJ Plugins The following parameters can be specified Parameter Description START FRAME The actual slice number from the original image for the first frame from the reference stack FRAME SPACING The number of frames from the original image between each slice in the reference stack For example if a white light image was taken at the start and then every 20 frames then the method should be called with parameters start_frame 1 frame_spacing 20 The drift will then be calculated as if the slices were at time points 1 21 41 etc 7 1 4 Marked ROIs This method uses constant fiducial markers that are placed within the image to allow the drift to be tracked e g fluorescent beads The method is only available in the drop down options when there are ROIs listed in the ImageJ ROI manager Rectangular ROIs can be placed around the fiducial markers on the original image and then added to the ROI manager press CrrL T
55. they can be traced through time potentially via other candidates to a valid result The distance used for tracing is the search distance multiplied by the average precision of the candidates Precision HYsTERESISFILTER Filter results using a precision threshold Any results below the lower precision limit are included Any results above the upper precision limit are excluded Any results between the limits candidates are included only if they can be traced through time potentially via other candidates to a valid result The distance used for tracing is the search distance multiplied by the average precision of the candidates TRACEFILTER Filter results that can be traced over time frames The trace distance is specified in pixels and the time threshold in frames COORDINATEFILTER Filter results using a coordinate range This can be used to crop the results to a rectangular region for example when batch processing results subsets in a macro ANDFILTER Filter results using the combination of two filters Results must pass both filters ORFILTER Filter results using the combination of two filters Results can pass either filter The Free Fitter plugin provides a powerful tool for customising the subset of results that are extracted For example it is possible to extract only the results that have either 1 a Signal to noise ratio above 10 and a Precision of less than 30nm or 2 that can be traced to ano
56. to actual ADU value by multiplying by the product of the camera gain EM gain and quantum efficiency EM Gain The EM gain of the simulated camera CAMERA GAIN The camera gain in ADU electron QUANTUM EFFICIENCY The efficiency converting photons to electrons in the camera READ NOISE The average Gaussian read noise to add to each pixel in electrons Bias The bias offset to add to the image Allows negative noise values to be displayed PSF MobeL Specify the PSF model to use The Imace PSF option is only available if a valid PSF image is open ENTER WIDTH Select this option to enter the PSF width in nm for the Gaussian Airy PSF A second dialog will prompt the user for the PSF SD Standard Deviation For an Airy PSF the SD is converted to the Airy pattern width by dividing by 1 323 If not selected a second dialog will prompt the user for the emission wavelength of the fluorophore and the numerical aperture of the microscope These will be used to define the PSF width PARTICLES The number of molecules to simulate DENSITY The density of the molecules in squared micrometres MIN PHOTONS The minimum number of photons for a localisation Max PHOTONS The maximum number of photons for a localisation Raw IMAGE Select this option to output an image using 32 bit floating point numbers The default is to use 16 bit unsigned integers SAVE IMAGE Show a dialog allowing the imag
57. to select a results directory where the raw data will be saved This is the data that is used to produce all the histograms and output plots SHOW HISTOGRAMS Show histograms of the trace data If selected a second dialogue is presented allowing the histograms to be chosen and the number of histogram bins to be configured 10 8 5 10 8 5 1 Output MSD verses time The plugin will plot the mean squared distances against the time as show in Illustration 41 The plot shows the best fit line If the data is not linear then the diffusion of particles may be confined for example by cellular structures when using in vivo image data In this case the diffusion coefficient will be underestimated Page 203 225 GDSC SMLM ImageJ Plugins Trace Diffusion MSD Save Copy X 4 66 Y 2 62 Illustration 41 Plot of mean squared distance verses time produced by the Trace Diffusion plugin The mean of the raw data Is plotted with bars representing standard error of the mean The best fit line is shown in magenta 10 8 5 2 Jump distance histogram The plugin produces a cumulative probability histogram of the jump distance see Illustration 42 The best fit for a single species model will be shown in magenta Any significant deviations of the histogram line from the single species fit are indicative of a multi species population If a multiple species model has a better fit than the single species model then it wi
58. under the precision recall curve AUC2 The area under the adjusted precision recall curve The adjustment is made by using the highest precision at that recall or above FaiL95 The failure count that must be allowed to achieve 95 of the maximum true positive count Fait99 The failure count that must be allowed to achieve 99 of the maximum true positive count FA 100 The failure count that must be allowed to achieve 100 of the maximum true positive count 9 12 Fit Spot Data Fits all the candidate spots identified by the Fitter Spot Data plugin This plugin requires Page 156 225 GDSC SMLM ImageJ Plugins the results generated by the Fitter Spot Data plugin If these results are not available an error will be displayed 9 12 1 Analysis The Fit Spot Data plugin fits each candidate spot identified in the benchmark image by the Fitter Spot Data plugin The spot candidates are identified in each frame in the image and ranked by the filter for example by estimated intensity However there will be many candidates that are not valid spots since the Create Simete Data or Create Spot Data plugin generates an image with noise which may be identified as a spot candidate Thus it is usually possible to stop processing candidates when a successive number of candidates fail This is the method employed by the main Peak Fit plugin when processing single molecule localisation images For the purpose of benchmarking it is possible to speed up proce
59. 001 This plugin can resequences the results using the regular repeat of the original image The following parameters are required Parameter Description INPUT The results to process Results will be directly updated and there is no Undo operation START The first frame containing data in the original image BLock The number of continuous frames that contain data in the original image SKIP The number of continuous frames to skip before the next block of data in the original image LOG MAPPING Log to the Image log the mapping between the current and the new frame number Page 59 225 GDSC SMLM ImageJ Plugins It is not possible to undo the Resequence Resutts plugin Before running the plugin you can save the results to file using the Results Manacer These can be reloaded if the resequence operation produced an incorrect frame by frame mapping Note If the data is interlaced it can be directly handled by the Peak Fit plugin using the extra options hold the SHirr or Att key down when running the plugin There is no need to extra all the relevant data frames from the source image before running Peak Fit 6 6 Calibrate Results Allows results held in memory to be calibrated e g the pixel pitch and camera gain can be adjusted Note that the raw data held in memory is stored using pixel units and image frames Many of the plugins require calibrated units such as nanometers micrometres milliseconds a
60. CATION The x location to insert the overlay measured from the top left corner Y LOCATION The y location to insert the overlay measured from the top left corner Opacity The opacity of the overlay 100 will totally obscure the underlying image TRANSPARENT BACKGROUND Select this to use a transparent background for any pixels with a value of zero This allows the underlying image to be seen even when the opacity is set to 100 REPLACE OVERLAY Select this to replace the current overlay Uncheck this to add to the current overlay i e combine overlays Page 214 225 GDSC SMLM ImageJ Plugins 12 Toolset Plugins The following plugins add functionality to ImageJ to allow the SMLM plugins to be run using the ImageJ toolbar or a dedicated window panel of buttons The plugins are described in the following sections using the order presented on the PLucins gt GDSC SMLM gt TooLser menu 12 1 Install SMLM Toolset You can install a toolset for the SMLM plugins using the GDSC SMLM gt Instan SMLM TooLser plugin This will create a text file in the ImageJ macros toolsets directory The toolset can be activated using the More Tools menu button the last button on the ImageJ toolbar as shown in Illustration 45 The toolset defines 8 buttons for the ImageJ menu bar that allow various plugins to be run When the mouse is over the button the name of the plugin will be shown in the ImageJ window Click the button to
61. CCD camera or the Poisson Gamma Gaussian function very slow for an EM CCD camera Methods for determining the bias read noise and gain of a camera can be found in the sections describing the Mean Variance Test and The plugin provides a plot of gain verses slice and a histogram of the values These can be used to determine if the gain is constant throughout the image and so is a good estimate plugins 5 2 5 Multiple Peak Fitting Parameters These parameters control how the algorithm handles fitting high density localisations where the region surrounding a maxima used for fitting may contain other maxima If only the single target peak is fitted it is possible the fitting engine will move the Gaussian centre to the higher peak causing a duplicate fit This can be avoided by fitting multiple peaks but with the penalty of increased computation time and likelihood of failure In the event that multiple fitting fails the algorithm reverts to fitting a single peak In this case duplicates fits can be eliminated using the DurLicaTE DISTANCE parameter Note that peaks are processed in height order Thus any candidate maxima with neighbours that are higher will be able to use the exact fit parameters of the neighbour If they are not available then fitting of the neighbour failed In this case as with lower neighbour peaks the initial parameters for the neighbour are estimated Parameter Description INCLUDE NEIGHBOURS Include any neighbour
62. Exposure Time This is the length of time captured by each frame in milliseconds The exposure time is used in various analysis plugins Input of an incorrect value will only effect the time scales reported in the results Peak Width Specify the expected width of the Gaussian function that approximates the Point Spread Function Airy disk This is how spread out the spot of light is when in focus The width is specified in pixels This value is used as an input to the fitting process to avoid having to guess the initial width for each spot processed Since the width is approximately constant for the microscope it is valuable to input the expected width The width is updated during the fitting process allowing fitting of out of focus spots The width can be calculated using knowledge of the microscope objective and the wavelength of light It can also be estimated from an image see section 10 1 PSF Calculator It is expected that this should be in the range around 1 pixel Input of an incorrect value will lead to poor fitting performance since by default peaks that are too wide narrow are discarded When the Smr Fit plugin is run it attempts to load the SMLM configuration file This is located in the user s home directory and is named gdsc smlm settings xml If no configuration file can be found then a configuration wizard is run to guide the user through calibration If any dialog is cancelled then the Simece Fit plugin termina
63. FUNCTION The fit function See section 5 2 4 Fitting Parameters INCLUDE NEIGHBOURS See section 5 2 5 Multiple Peak Fitting Parameters NEIGHBOUR HEIGHT See section 5 2 5 Multiple Peak Fitting Parameters RESIDUALS THRESHOLD See section 5 2 5 Multiple Peak Fitting Parameters DUPLICATE DISTANCE See section 5 2 5 Multiple Peak Fitting Parameters 9 12 3 Results After spot candidates have been fitted and scored using their distance to the true localisations the results are summarised For all the fitted results that were within the March bistance of a true localisation a histogram is computed of the distances the z depth of the original localisations and the computed precision of the fit using the Mortensen formula This allows a visualisation of how close the fitted results are to the actual localisations and also of the depth of field of the localisation algorithm Note that the Match Depth histogram will not be useful if the data were originally simulated with a fixed depth or the PSF does not vary with z depth If results were simulated using a fixed photon level then the standard deviation of the match distance should be approximately the same as the average of the calculated precision Since the precision calculation represents the standard deviation of the distance from the true location assuming fitting a 2D Gaussian PSF with Poisson noise The results of scoring are used computed the match statistics Recall Pr
64. GDSC SMLM ImageJ Plugins Single Molecule Light Microscopy ImageJ Plugins Alex Herbert MRC Genome Damage and Stability Centre School of Life Sciences University of Sussex Science Road Falmer BN1 9RQ a herbert sussex ac uk Page 1 225 GDSC SMLM ImageJ Plugins Table of Contents A A O O ea aes cok EE EEE 7 AT VPP DIA iia sa ela A 8 2 FRE SUES DIAS Ad ia 9 T 3AnalysiS PIUgJIN Sieci credito E A AE E D REEE E A E A AES 10 TA Model PINOS aaa a a 11 A lo O O EN ON 12 ESTO PIAR ns A US 12 2 Backgrounder NOOO TA 14 2 1 Diffraction limit of light MICKOSCOPY viciado 14 2 2 Approximation using a Sas Md 15 2 3 Localisation Fitting MSI rd AA diia 15 A O 17 3 1 Install using IMA Pl dee cones cenen eet iedaei at te tnentenapecamaseaeeeecazecabies 17 3 2 Install USING ImageJ version l ccccnnnnninoninonccnononncnonononnnnonononnononnnnonononononccnnannnnconnss 17 4 mage PILAS aa 18 5 Fitting PUSO a Eia 19 AA AA ae tins Sa aaa la ea aala peaa aaa ea aaae aa Ea aa e Ea as Seea aaa 19 5 1 1 Pafamet l Sota naa e a a told a A A ATAN 19 A o MEES EREE IEE AEE AE EA E A T AE 20 SLS Advanced SettiNgS AAA 24 5 2 Peak Plis sra aia 25 5 2 1 Imaging Calibration ParaMeterS ooooonccconconnconocoonocn nono nonnncnnnnnnnnnnnnn nono nnnn non nnnnnnnos 26 5 2 2 Ga ssian ok Parameters cnra A ene 26 5 2 3 Maxima Identification ParamMeters oooccccccccnnnnnononennnnninnnonininininininininininininonnns 27 5 24 Fitting Parametros bea 29 5
65. Gaussian parameters e g centre width and signal to a set number of SIGNIFICANT DIGITS SIGNIFICANT DIGITS When comparing two numbers defines the significant digit for equality e g specify 3 to recognise 1 and 1 001 as equal Note that Java floating points have a limited precision preventing comparisons to high numbers of significant digits Using a value over 15 will generally not allow convergence Page 30 225 GDSC SMLM ImageJ Plugins Parameter Description Coorp DELTA Define the smallest shift in pixels that specifies a movement of the X Y coordinates Used in the CoorbinaTes fit criteria LAMBDA The initial lambda for the Levenberg Marquarat algorithm Higher favours the gradients of the parameters Lower favours the Hessian matrix gradients second partial derivatives Lower is used when very close to the solution Note that the algorithm updates the lambda during fitting to refine the improvement to the fit A value of 10 is a good initial value Max ITERATIONS Stop the fit when this is reached and return a failure 5 2 4 2 Maximum Likelihood Estimation Maximum Likelihood estimation is the processes of fitting a function expected values toa set of observed values by maximising the probability of the observed values MLE requires that there is a probability model for each data point The function is used to predict the expected value E of the data point and the probability model is
66. LM ImageJ Plugins 10 6 EM Gain PMF Displays a plot of the probability mass function PMF of the expected value of a pixel on an EM CCD camera given an average number of photons The form of the PMF is a convolution of a Poisson Gamma and Gaussian distribution See 10 5 1 EM CCD Probability Model for more details The PME is then approximated by analytically calculating the PMF of a Poisson Gamma distribution and then approximating a convolution with a Gaussian distribution The method for this approximation is taken from the supplementary Python software provided by Mortensen et al 2010 They used this approximation when fitting the images of single fluorophores in TIRF Total Internal Reflection Fluorescence images taken with an EM CCD camera A second plot showing the difference between the real PMF and the approximation is displayed This allows investigation of any situation where the approximation is not appropriate for modelling the PMF It is rare for the approximation to differ by more than 1 The plugin has the following parameters Parameter Description Gain The total gain for EM CCD camera Noise The camera read noise PHOTONS The average number of photons per pixel for the simulation SHOW APPROXIMATION Show on the PMF plot the approximation function Note This approximate PMF is used to model the EM Gain when performing Maximum Likelihood Estimation fitting within the Peak Fit plugin REMOVE HEAD Set
67. Manacer plugin Note that the output options for a batch are limited to results files The intended purpose for the Batcu Fit plugin is to allow multiple settings to be run on input test images The results can then be further processed to determine which combinations of settings are the best parameters for fitting Page 51 225 GDSC SMLM ImageJ Plugins 5 7 Spot Finder Finds all the candidate maxima in an image This plugin uses the same algorithm as the Peak Fit plugin to identify maxima However all the candidates are saved to the output No 2D Gaussian fitting or peak filtering is performed The fit configuration is the same as in the Peak Fit plugin As with the Peak Fit plugin the settings contained in the configuration file are loaded when the plugin is initialised If no file exists then a default set of settings will be created A different file can be selected by double clicking in the text box This will open a file selection dialogue If the file name is changed and the new file exists the plugin will provide the option to reload the settings from the new configuration file When the plugin runs all the settings will be saved to the configuration file overwriting any existing file 5 8 Spot Finder Series Allows the Spot Finoer plugin to be run on a folder containing many images This allows the code to run on images that are too large to fit into memory or have been imaged ina sequence The plugins allows the user
68. N points of the MSD plot SHOW EXAMPLE Show an example image of a diffusion path MAGNIFICATION The magnification of the example image The pixels will represent pixel pitch magnification nanometres 10 7 5 10 7 5 1 Output MSD plot For each particle the plugin will compute the squared displacement from the origin over the time course of the simulation Distance are computed in 2D and 3D The plugin will plot the mean squared distance against time for the population as shown in Illustration 40A The 2D and 3D MSD data are then fit using a linear regression The gradient of the fit can be used to calculate the diffusion coefficient by dividing by 4 or 6 respectively Page 196 225 GDSC SMLM ImageJ Plugins Diffusion Rate Test E pa N W E o o o o o o o o Mean squared Distance um 2 o Time seconds List Save Copy X 15 27 Y 377 9 Ls Diffusion Rate Test Op ul 10 15 20 25 30 Time seconds List Save Copy X 9 73 Y 3 216 Illustration 40 Mean squared displacement chart produced by the Diffusion Rate Test plugin for A random diffusion and B confined diffusion Black 2D MSD Red 2D MSD fitted Blue 2D MSD Standard Deviation Magenta 3D MSD Green 3D MSD fitted If confined diffusion is performed the MSD will reach a natural upper limit This will result in a plateau of the MSD plot as shown in Illustration 40B In this
69. NT methods is done using the maximum correlation between images including sub pixel registration using cubic interpolation This is computed in the frequency domain after a Fast Fourier Transform FFT of the image The method of producing and then aligning images is computationally intensive so the plugin uses multi threading to increase speed The Page 74 225 GDSC SMLM ImageJ Plugins number of threads to use is the ImageJ default set in Epit gt Options gt Memory amp THREADS 7 2 Trace Molecules Traces localisations through time and collates them into traces using time and distance thresholds Each trace can only have one localisation per time frame With the correct parameters a trace should represent all the localisations of a single fluorophore molecule including blinking events 7 2 1 Background The fluorophores used in single molecule imaging can exist is several states When in an active state it can absorb light and emit it at a different frequency fluorescence The active state can move into a dark state where it does not fluoresce The dark state can move back to the active state Eventually the molecule moves into a bleached state where it will no longer fluoresce photo bleached The rates of the transitions between states are random as are the number of times this can occur This means that it is possible for the same molecule to turn on and off several times causing blinking To prevent over counting of molecules d
70. Note that some algorithms support a bounded search This is a way to constrain the values for the parameters to a range for example keep the XY coordinates of the localisation within the pixel region used for fitting When using a bounded search the bounds are set at the following limits The lower bounds on the background and signal are set at zero The upper bounds are set at the maximum pixel value for the background and twice the sum of the data for the signal The coordinates are limited to the range of the fitted data The width is allowed to change by a value of 2 fold from the initial standard deviation Powell Search using Powell s conjugate direction method This method does not require derivatives It is the recommended method for the camera noise models http en wikipedia org wiki Powell 27s_method Powell bounded Search using Powell s conjugate direction method using a mapping adapter to ensure a bounded search This method maps the parameters from a bounded space to infinite space and then uses the Powell method BOBYQA Search using Powell s Bound Optimisation BY Quadratic Approximation BOBYQA algorithm BOBYQA could also be considered as a replacement of any derivative based optimiser when the derivatives are approximated by finite differences This is a bounded search This method does not require derivatives http en wikipedia org wiki BOBYQA Page 34 225 GDSC SMLM ImageJ Plugins CMAES Sear
71. Plugins Fits are accepted if the fitting algorithm successfully converged and the fitted signal is close to the actual signal defined by a limit of 2x higher or a user configured lower fraction 9 3 2 Parameters Parameters Description PSF The PSF used to compute the drift Use OFFSET Use an existing drift curve stored in the PSF to offset the insert location Note that this can be used to check that the existing drift curve is correct for the given image reconstruction and fitting settings SCALE The reduction scale for the PSF Z DEPTH The range of the PSF stack to compute the drift z positions outside this range will not be processed Use this option to speed up processing when the depth of field of the PSF is known GRID SIZE The number of intervals to use to construct the NxN grid for inserting the PSF into the centre pixel RECALL LIMIT The fraction of fits that must be successful for a valid drift calculation REGION SIZE Defines the size of the image to insert the PSF into The actual size is 2N 1 BACKGROUND FITTING Select this to allow the algorithm to fit the background Note that the background should be zero as no data is inserted into the image apart from the PSF This can be used to more closely match the fitting performed on real data Fit SOLVER The solver used to fit the data Note that a second dialog will be presented for the selected solver to be configured The values are ini
72. Plugins Note that the estimator may not find any peaks if the fitting parameters are badly configured The estimator can be reset to defaults by holding down the ControL key when running the plugin The default values are shown below 10 3 Parameter Value InrriaL StoDEvO 1 1 INITIAL ANGLE 0 SPOT FILTER TYPE Single SPOT FILTER Mean SMOOTHING 1 3 SEARCH WIDTH 1 BorDER 1 FITTING WIDTH 3 Fit SOLVER Least Squares Estimator FIT CRITERIA Least squared error SIGNIFICANT DIGITS 5 COORD DELTA 0 0001 LAMBDA 10 MAXx ITERATIONS 20 FIT FUNCTION Circular FAIL LIMIT 3 INCLUDE NEIGHBOURS True NEIGHBOUR HEIGHT 0 3 RESIDUALS THRESHOLD 1 SHIFT FACTOR 1 SIGNAL STRENGTH 0 Min PHOTONS 30 WIDTH FACTOR 2 Mean Variance Test The Mean Variance Test plugin can be used to calculate the gain and read noise of the microscope Charged Coupled Device CCD camera The plugin requires a set of calibration images A single image mode is available but will provide less information on the camera 10 3 1 Multiple Input Images When run the plugin will present a folder selection dialogue The folder should contain a Page 184 225 GDSC SMLM ImageJ Plugins set of calibration images All the images should be taken of the same view with the camera in the same gain mode At least one image should be taken with no exposure time This is the image the c
73. Results dir Fail limit 3 Binary results Y Include neighbours Neighbour height 0 30 Y Results in memory Residuals threshold Lo 1 00 Duplicate distance 0 50 OK Cancel Help Illustration 5 The Peak Fir dialogue The plugin will initialise using the previously selected configuration file If no file exists then a default set of settings will be created A different file can be selected by double clicking in the text box This will open a file selection dialogue If the file name is changed and the new file exists the plugin will provide the option to reload the settings from the new configuration file When the plugin runs all the settings will be saved to the configuration file overwriting any Page 25 225 GDSC SMLM ImageJ Plugins existing file The dialogue contains setting for the imaging conditions and then various parts of the fitting algorithm Imaging Calibration Gaussian PSF Maxima Identification Fitting Multiple Peak Fitting and Peak Filtering Additional parameters are used to control the output Each of the sections is described below Note The fitting algorithm is described in section 2 3 Localisation Fitting Method Understanding the method will ensure that the parameters can be adjusted to achieve the desired fitting result Using the Simpce Fit plugin will reset the parameters to their defaults 5 2 1 Imaging Calibration Parameters The imaging parameters describe the con
74. SC SMLM ImageJ Plugins The identification of the spot centre can be run automatically using configured parameters Alternatively the plugin can run in interactive mode In this instance the plugin will produce plots of the raw and smoothed data as shown in Illustration 30 The calculated centre is shown as a green line and the user is asked if the analysis result should be accepted or rejected see Illustration 31 The user is able to adjust the centre of the spot using a slider if the plugin appears to have miscalculated Ly om Spot Amplitude Y UY Amplitude 22050 0 1 0x z 0 0 nm 20000 0000 Amplitude 20 40 60 80 100 List Save Copy Ly e Spot PSf Y Y ey Width 127 9 nm 1 0x z 0 0 nm 2 20 40 60 80 100 List Save Copy Illustration 30 Amplitude and PSF plots generated by the PSF Creator plugin Amplitude plot shows raw data circles and smoothed data black line PSF plot shows raw data as spots and smoothed data from the in focus region as a line Width black X centre blue and Y centre red The centre z slice is marked with a green line Page 117 225 GDSC SMLM ImageJ Plugins Ly mn E Add spot 1 to the PSF Estimated centre using min PSF width Xx 268 85 y 233 82 z 74 sd 1 20 Slice 74 Yes No Illustration 31 PSF Creator Yes No dialogue show in interactive mode When all the spot centres have been identified the plugin will generate a combin
75. SHOW TABLE Show a table of the analysis results Page 98 225 GDSC SMLM ImageJ Plugins Parameter Description PLOT TOP N Produce a plot of the top N filter sets showing their Jaccard score verses a named parameter value If a filter set contains filters with different named parameters then the filters are plotted in sequential order CALCULATE SENSITIVITY Calculate how sensitive the scoring metric is to a change in each filter parameter Each filter parameter is adjusted by the delta and the gradient computed at the point of the optimum filter score DELTA The delta value used to adjust parameters to calculate the sensitivity 7 9 4 Output At least one output method must be chosen otherwise the plugin will show an error message 7 9 4 1 Table output If Show Taste is selected the plugin produces a table of the match statistics for the filtered results compared to the categorised inputs The results for all the filters in a filter set are shown together An empty row is used to separate filter sets The available scores are Precision Recall F score and Jaccard Details of the match statistics are given in Appendix B Comparison Metrics 7 9 4 2 Plot output If a value for PLot ToP n is provided the plugin produces a chart of the Jaccard score against one independent filter variable for each of the top N performing filter sets An example of the Hysteresis Precision filter chart is shown in Illu
76. Specify the PSF model to use The Imace PSF option is only available if a valid PSF image is open ENTER WIDTH Select this option to enter the PSF width in nm for the Gaussian Airy PSF A second dialog will prompt the user for the PSF SD Standard Deviation For an Airy PSF the SD is converted to the Airy pattern width by dividing by 1 323 If not selected a second dialog will prompt the user for the emission wavelength of the fluorophore and the numerical aperture of the microscope These will be used to define the PSF width DISTRIBUTION The random distribution of the particles PARTICLES The number of molecules to simulate COMPOUND MOLECULES Select this to allow compound molecules to be configured See section 9 5 7 Compound molecules DIFFUSION RATE The diffusion rate of the molecules Use GRID WALK Simulate diffusion using a grid walk Otherwise use movement along random vector which is a slower computation Page 136 225 GDSC SMLM ImageJ Plugins Parameter Description FixeD FRACTION The fraction of molecules that will not diffuse CONFINEMENT Specify the confinement of the diffusing molecules PHOTONS The average photon emission rate of a fluorophore The actual emission rate per fluorophore is sampled from a distribution with a mean of the PHotons parameter CUSTOM PHOTON DISTRIBUTION Select this option to choose a custom photon distributio
77. THouT Any integer SIGNIFICANT DIGITS 5 DECIMAL PLACES SLIDER Any floating point number SMOOTHING 0 5 CHECKBOX True False FIT BACKGROUND TRUE Drop pown List Use the upper case text Fit FUNCTION CIRCULAR In some case the allowed value does not match the user friendly name used in the dialogues Run the Fit CONFIGURATION plugin select the desired option and check the gdsc smlm settings xml file for the allowed value lt resultsDirectory gt Provide the full path of the results directory This is the directory used to save the Peak Fit settings and the fit results for each single run By default this initialises using the Java temporary directory lt runPeakFit gt Set this to true to run the Peak Fit plugin Set to false to only create the configuration files in the results directory This can be used to ensure that the batch file has correctly enumerated all the settings by checking the output configuration files 5 6 2 Running the batch Click OK to parse and run the batch file For each valid combination of parameters the Peak Fit plugin will be executed on each input image The results will be saved to a file named using the image filename and a sequential number from 1 e g InputImage 00001 The Peak Fit settings will be written to an XML file with the suffix xml The Peak Fit results will be saved to a text file of the same name with the suffix xls The fit results can be read using the Results
78. Z positions of each fluorophore when it was in an on state SHOW HISTOGRAMS Show histograms of the generated data CHOOSE HISTOGRAMS Set to true to allow the histograms to be selected otherwise all histograms are shown HisTOGRAM BINS The number of bins in the histogram REMOVE OUTLIERS Remove outliers before plotting histograms Outliers are 1 5 times the interquartile range above below the upper lower quartiles Outliers are always removed for the Precision data since low photon signals can produce extreme precision values DENSITY RADIUS Specify the radius relative to the Half Width at Half Maxima HWHM of the PSF to use when calculating the localisation density around each molecule The average density is shown in the summary table The density is the number of molecules within the specified radius Page 138 225 GDSC SMLM ImageJ Plugins 9 5 6 Data Summary The Create Data plugin summarises the dataset when the image has been constructed The mean of various statistics is shown These statistics can be plotted using the SHow HISTOGRAMS Option The summary shows the following fields Field Description DATASET The number of the dataset MoLEcuLES The number of fluorophore molecules that activated during the simulation PuLses The number of fluorophore pulses continuous emission from the on state LOCALISATIONS Total number of localisations Equals the number of spots
79. a AA 62 6 10 Results Match CalCulaton cc iicsct scseccisssaveadesinawsteseimesvssoneectesninanneanesbenoncsuerideivencressgebes 64 6 10 1 Interactive Results Ta DIG ui a 65 6 11 Trace Watch Calc sa ad ee ae Ree ee 65 0205 PO IAS ECON O eal beac nea ede ante haan das 67 TAS UA as 68 FL Dit ANGI WON Fasc oh A A RAI a 68 7 1 1 Localisation SUD AM AOS ida 72 TA DMA A O A nad EE EAT inks 73 7 1 3 Reference Stack AMM iii a cid 73 VEA Marked RO Sas 74 7 1 5 Image alignment using correlation analySiS ccccccccccnnncnnncnnnnnnnnnnnanacinnninonns 74 2 Trace MONS CUES eeno eit Toon vebaedsuasevaneoxerasuceateecbevendvacceies 75 a A daimadececeerteamsoleandeatoocia lee 75 7 2 2 Trace Molecules PUT Dad A A A eee ae 75 23 OPUS ON ii ae Rr ee EE 78 LA AO ita 80 Tie PIS O aa rs 81 1 20 REMO NA did 82 Te3 Cluster Mole Cules A ot AA A AA ARA 83 1 31 CIUStSFING Aldo aa 84 PA Draw CU a A E a a Ne 86 7 4 1 Drawing cluster CENtrOidS ccssscssecssscssscsssnssscsseccsecssecsseccsecsssecessseeeeeeesaeens 88 dor DENSAS A 88 7 5 1 Available Density Score TUNC IONS ccccccccnnnnnnnnnnnnnnnnnnnnnnnnnnnonnnonononnnnnanncnnnnnnns 90 132 RIP Sl Obie isa 91 10 DARK AAEE AN aTe T AEEA e E A E ana 92 at SUITES UV ANOW A ai 93 728 Neighbour AMAIYSIS eidar eane aa aia A a aah 95 WO Filter AMAlYSIS ui is 96 ft OA PPULDATA AP octane CUOTA 2S E ciara lotr thle EE 96 132 AValable Flia 96 7 9 3 Additional PUMAS A a a do dia ia 98 A O A E
80. a KAEA TOERANA 139 9 5 7 Compound mole Sui a ii aaah 140 ES ts A aust eS 141 9 59 Memo QUID ii leat recvard AERAN 141 9 6 Create Simple Dala israel eas aAA NAVIS EAEE OEA bs 142 9 7 Create Benchmark Data ccccccconccoconconononinnncncnnnnncnnnanonononanonanonannnnnncnnnononacrnncnnccos 144 A A A a e e EEN 146 9 8 FliBencaimaDada a a a E A AE A a a A 146 9 8 1 Data SUMMA mi a SS O as 147 9 9 Benchmark ANALYSIS 23 ccics ccesdscentacdvcbelencasalus gevedeneagty datas dede red 149 9 10 Create Spot Data ivan po 150 OAL Filter Spot DA a tb is E Aaa 152 AA Gee anea ieee ol nth hale hada eis ue ea aot rset ce 153 OEP IP IC SPD rod a 156 Page 4 225 GDSC SMLM ImageJ Plugins A ze farses ec cnsderensueivs tenaasoner A sae tauinee eat 157 9 12 2 Parametros 158 912 3 RESUNS us a A AA AR 159 9 13 Benchmark Filter A VAY Sii A eet eased 162 E IGE Sites cared neat A euctonnsiee 162 LS AMI SIS AAA araceanracie EA 163 A svtasndsbasageceduadenventireeuensernedens 167 O ASA RES US A A A AAA A 172 9 14 MAGS Background A ta Gane yates bade ine Ae eee aa 176 SE A ars eee a a e sarees eed eee ree 177 OAS koad Localisations a A a AAE EA 177 LO CAalbraton PIUJINS rai act ri 179 TOA PSF Calcula aio 179 A PS o O 181 TO MEah ValialCe Tdi A A sc 184 10 3 1 Multiple InpuUtIMADES ida 184 LOS ANI Sd a O ADD ak 185 10 3 S QUID aa 185 10 3 4 Single Image MOCE ccccccccccccccceceeeeeceeeeeeneceeeeeeeeeeeseseessaeseensseseeessssegsseeesecss 187
81. a digit is ignored Only the time points that are within the time range of the input results are used The file is assumed to contain the final drift curve and no iterations are performed to update the curve The curve may be smoothed using LOESS smoothing before being interpolated and applied to the data The DrirT Fite method allows the same drift to be applied to multiple data sets For example if an image is produced with a white light channel for drift tracking and two different colour channels with localisation data the same drift from the white light image can be used to correct both sets of localisations 7 1 3 Reference Stack Alignment The drift can be calculated using a reference stack image for example this may be a white light image taken during the experiment The reference stack must be a single stack image Some microscopes may make a separate image during acquisition for the white light However if all the frames are joined into a master image then you can extract reference stack slices from a master image using ImageJ s Substack Maker plugin Imace gt Stacks gt Toots gt Make SussTack The slice numbers in the reference stack will not correspond to the slices in the localisation results Therefore the plugin allows the user to specify the actual slice number of the first slice in the reference stack start frame and then the frame spacing between slices in the stack The actual frame for the stack is then calculated as
82. aced localisations to be compared The plugin scans the results held in memory and only allows results to be selected where they contain an entry that spans multiple time frames Such results can be generated using the Trace Motecutes plugin The plugin compares traces using the following distance weighted score Score overlap 1 1 d d where overlap is the number of frames where both traces are present d is the distance between the two points and d is a threshold distance The score is composed of two parts the overlap and the distance weighting The distance weighting has a maximum value of 1 and reduces to zero The weighting is 0 5 when d equals d Thus the score will favour a match between close traces and those with the largest overlap in time Since any overlapping traces will be scored a maximum allowed distance between the traces is set Page 65 225 GDSC SMLM ImageJ Plugins This is currently configured at 2d The plugin computes matches iteratively allocating the highest scoring pairs first until no more matches can be made The matches are used to compute comparison score metrics to show the similarity between the two results sets The available metrics are Precision Recall F score and Jaccard Details of the comparison metrics can be found in Appendix B Comparison Metrics The overall score is the sum of the scores for all of the matched pairs This score is then normalised by the maximum number of time points conta
83. age The fit configuration is the same as in the Fit Conricuration plugin with extra parameters provided to control the estimation The PSF Estimator dialogue is show in Illustration 37 Note that a second dialogue will collect parameters specific for the selected Fit soLver Page 181 225 GDSC SMLM ImageJ Plugins Mu PSF Estimator ESOS Estimate 2D Gaussian to fit maxima Gaussian fitting Initial StdDevo 07 58 Fit solver Maximum Likelihood Estimator MLE Initial StdDevl 0 735 Fit function Circular Initial Angle 0 000 Fail limit 3 Number of peaks 1000 Y Include neighbours p Value 0 0100 Neighbour height 0 30 Y Update preferences Residuals threshold 1 00 Peak filtering Discard fits that shift are too low or expand contract Y lterate Shift factor 1 36 Log progress Show histograms Signal strength 0 00 Histogram bins 100 Min photons 30 Spot filter type Single Width factor 2 00 Spot filter Mean Smoothing 1 30 Search width 1 00 Border 0 00 Fitting width 3 00 OK Cancel Help Illustration 37 PSF Estimator dialogue The estimator uses the starting configuration to fit N peaks taken from randomly selected frames in the image stack The averages of the fitted parameters are then used as the start parameters to perform fitting again This iterates until the Gaussian parameters do not significantly change The parameters controlling the est
84. ain the bias EM gain read noise and average photons per pixel EM Gain PMF Displays a plot of the probability mass function PMF of the expected value of a pixel on an EM CCD camera given an average number of photons Diffusion Rate Test Simulate molecule diffusion and fit a graph of mean squared displacement to determine the diffusion coefficient Trace Diffusion Trace molecules through consecutive frames Mean squared displacement analysis is performed on the traces to calculate a diffusion coefficient 1 6 Tool plugins In addition to the principle plugins for localisation fitting and analysis there are several utility plugins provided Install SMLM Toolset Adds an ImageJ Toolset containing common commands that can be used from the ImageJ toolbar Show SMLM Tools Display a SMLM Toots window with buttons to run plugins Page 12 225 GDSC SMLM ImageJ Plugins Create SMLM Tools Create a configuration file allowing the SMLM Toots panel to be config customised Smooth Image Performs smoothing on an image identical to that performed when identifying maxima Binary Display Switches an image to binary white black to allow quick visualisation of localisations Reset Display Resets a binary image back to the standard display Pixel Filter Perform filtering to remove hot pixels from an image Noise Estimator Estimate the noise in an image using various met
85. ame of the results dataset and then the following statistics e The number of results e The size of the results in memory e The bounds of the results minimum and maximum x and y coordinates of the source e The average median minimum and maximum of the precision and Signal to noise ratio SNR 6 3 Clear Memory Results Removes all the results currently stored in memory Presents a confirmation dialog showing the number of results that will be removed if the user selects OK 6 4 Rename Results Allows the name of a results set held in memory to be changed By default the results are named using the name of the input image or results set appended with details of how the new results were generated e g the name of the fitting engine or in the case of tracing analysis Traced The name is associated with the results Page 58 225 GDSC SMLM ImageJ Plugins set and used is analysis plugins or when reconstructing super resolution images It is also saved in the SMLM file format The names can be updated using the Rename Resutts plugin The plugin presents a dialog with a single large text field All the existing names are entered on the left side of the equals symbol The new name will be entered on the right side of the equals symbol followed by a semi colon The semi colon is needed to support this plugin within the ImageJ macro language When the plugin is run all the target results set are identified using the names on the left
86. amera records when no light has been registered on the sensor and is called the bias image The remaining images should be a representative series of different exposures The purpose is to analyse how the image noise varies with exposure time In order for the analysis to be valid no images should saturate the camera bit depth E g for a 12 bit camera all images should have pixel values below 210 1 4095 All the images in the folder are opened and processed by the plugin Each image must contain at least 2 frames If the filename contains a valid integer delimited by a space or a period character then this will be taken as the exposure time Otherwise an arbitrary exposure time is used either zero for the first image alphabetically sorted or 9999 for the rest 10 3 2 Analysis If all the images are valid contain at least 2 frames then the plugin will perform the mean variance test The average value of the bias images is used as the bias Each image is then analysed in turn The mean of each frame is computed Then a pairwise difference image i e one frame subtracted from the other is computed for all vs all frames The variance of the difference image is recorded and used to approximate the camera gain gain variance mean bias This is recorded in a Summary table A graph is then produced of the mean verses the variance This data is fitted with a straight line The gradient of the line is the camera gain The read noise of
87. ames should be processed followed by a block of frames to ignore The plugin must know the size of each block and the first frame that must be precessed If the INTERLACED Data option is selected then an addition dialogue will be shown Page 45 225 GDSC SMLM ImageJ Plugins 7 PeakHt wy wy amp Interlaced data requires a repeating pattern of frames to process Describe the regular repeat of the data Start The first frame that contains data Block The number of continuous frames containing data Skip The number of continuous frames to ignore before the next data E G 2 9 1 Data was imaged from frame 2 for 9 frames 1 frame to ignore then repeat Start Block 1 Skip 0 OK Cancel Illustration 7 Peak Fit Interlaced Data dialog Parameter Description START The first frame containing data BLock The number of continuous frames that contain data SKIP The number of continuous frames to skip before the next block of data The InterLaceo Data option is fully compatible with the IntecRate Frames option However note that the data is read from the interlaced frames and then aggregated None of the skipped frames will be aggregated The user must simply select how many consecutive data frames to integrate The use of the interlaced and integrate options together can produce results that have a larger gap between the start and end frame that the number of frames that were integrated For exam
88. ameters in the genome MEAN CHILDREN When performing crossover between two selected individuals the number of children will be equal to a Poisson variable sampled using this mean At least 1 child is always produced SELECTION FRACTION At each iteration the population is reduced to a fraction of the target population size The new size will be at least 2 RAMPED SELECTION Select individuals using a weighting so that each individual is weighted according to the rank of the fitness score This allows unfit individuals to be selected when reducing the population size albeit with lower probability When selecting for crossovers the selection is biased towards the highest ranking individuals If not selected the individuals will be selected in order of fitness when reducing the population and randomly from the population when selecting for crossovers Page 171 225 GDSC SMLM ImageJ Plugins Parameter Description STRICT FITNESS Only allow individuals that pass the Criteria LimiT to be selected This may results in an empty population after selection If not selected then the fitness score for the individual is score metric 1 criteria metric This will work for any criteria metric that is in the range of 0 1 allowing all those individuals that pass the criteria to be ranked above the others SAVE OPTION Allow the final population of filters after convergence to be saved to file This allows restar
89. an image coloured using the density score Dark Time Analysis Determines the maximum dark time for a fluorophore from localisation data Blink Estimator Estimate the blinking rate of fluorophores in a results set Neighbour Analysis Saves all localisations paired with their neighbour if present to file Filter Analysis Performs filtering on a set of categorised localisation results and computes match statistics for each filter Create Filters Used to prepare a large set of filters for use in the Fitter Analysis Fite plugin Filter Analysis File Performs filtering on a set of categorised localisation results and computes match statistics for each filter defined in the input file Spot Analysis Allows analysis of the signal and on off times for fixed fluorophore spots in an image stack Spot Analysis Add This plugin provides a named plugin command for the App button of the Spot Anavysis plugin Fourier Image Resolution Analyses the resolution of an image using Fourier Ring Correlation PC PALM Molecules Prepare a set of localisations for Pair Correlation analysis PC PALM Analysis Produce Pair Correlation curve for a set of localisations selected from a super resolution image Page 10 225 GDSC SMLM ImageJ Plugins PC PALM Spatial Analysis Performs spatial analysis to plot the molecule density around each localisation as a function of distance fro
90. an be selected by double clicking in the Conric Fite text box This will open a file selection dialogue Page 47 225 GDSC SMLM ImageJ Plugins If the file name is changed and the new file exists the plugin will provide the option to reload the settings from the new configuration file When the plugin runs all the settings will be saved to the configuration file overwriting any existing file The Fit Conricuration plugin allows the configuration to be viewed and updated without the need to have an image open Since all plugins can be called from ImageJ scripts this also allows creation of a batch macro to change the configuration file 5 5 Peak Fit Series Allows the Peak Fit plugin to be run on a folder containing many images This allows the code to run on images that are too large to fit into memory or that may have been imaged in a sequence When the Peak Fit Series plugin is executed it shows a folder selection dialogue where the user can select a folder containing a set of images The plugin then scans the folder for images and sorts them numerically into a list i e the first sequence of numeric digits in the filename are used to sort images E g image2 tif is before image10 tif The plugin then provides a dialogue to control how the series is loaded see Illustration 9 The dialogue shows the name and dimensions of the first image in the series It is assumed that all images in the folder have the same dimensions with the ex
91. an profile The equivalent Gaussian profile is created using a standard deviation of 1 323 times the Airy width The PSF Calculator will show a plot of the Airy profile blue and the corresponding Gaussian profile red This is interactively updated when the parameters for the calculator are changed 1 0 0 8 0 6 0 4 0 2 Note that the Gaussian is a good approximation until the tails of the Airy pattern The Airy pattern contains waves of decreasing power out to infinity which are not modelled by the Gaussian The calculator allows for additional adjustments to be made to the calculated Gaussian standard deviation To account for optical aberrations in the microscope the width is allowed to be wider by a set proportionality factor The Gaussian standard deviation s can then be adjusted sa for an accurate representation on square pixels using the following formula S Vs t a 12 The Gaussian Half Width and Half Maxima HWHM is calculated from the standard deviation by multiplying by 2 In 2 1 177 The following table describes the parameters of the plugin The calculated properties show in grey in the table below are updated dynamically Parameter Description PIXEL PITCH um The camera pixel size MAGNIFICATION The objective magnification Page 180 225 GDSC SMLM ImageJ Plugins Beam ExPANDER Any addition magnification PIXEL PITCH NM The calculated image pixel size WAVELENGTH NM T
92. ance from the origin Page 202 225 GDSC SMLM ImageJ Plugins Fit LENGTH Fit the first N points with a linear regression MAXIMUM LIKELIHOOD Perform jump distance fitting using Maximum Likelihood Estimation MLE The default is sum of squared residuals SS fitting of the cumulative histogram of jump distances Fit RESTARTS The number of restarts to attempt when fitting A higher number produces and more robust fit solution since the best fit of all the restarts is selected JUMP DISTANCE The distance between frames to use for jump analysis MINIMUM DIFFERENCE The minimum relative difference ratio between fitted diffusion coefficients to accept the model The difference is calculated by ranking the coefficient in descending order and then expressing successive pairs as a ratio Models with coefficients too similar are rejected MINIMUM FRACTION The minimum fraction of the population that each species must satisfy Models with species fractions below this are rejected Maximum N The maximum number of species to fit In practice this number may not be achieved if adding more species does not improve the fit DEBUG FITTING Output extra information to the ImaceJ log window about the fitting process SAVE TRACE DISTANCES Save the traces to file The file contains the per molecule MSD and D and the squared distance to the origin for each trace SAVE RAW DATA Select this
93. assed to the Peak Fit plugin The names of each image loaded in the image series will be saved with the results This allows other plugins to access the original data associated with the results Note that if the directory contains a mixed collection of images then the results will not make sense 5 6 Batch Fit The Barch Fit plugin runs the Peak Fit plugin for each configuration setting within a batch file The batch file allows the user to specify the input image files the values for each of the Peak Fit parameters and a results directory Running the Barch Fit plugin presents a simple dialogue window as shown in Illustration 10 The configuration file can be entered into the text box Double clicking in the text box will open a file selection dialogue to allow the file to be chosen Clicking on the Create conric Fite checkbox will open a file selection dialogue to allow a location to be chosen for a new default configuration file If an existing file is selected it will be overwritten dy Batch Peak At Y ae Config filename tmp batch xm Create config file OK Cancel illustration 10 Batch Peak Fit dialogue 5 6 1 Configuration File The default configuration file is an XML file with the following format note that the full list of Page 49 225 GDSC SMLM ImageJ Plugins parameters is not shown lt gdsc fitting batchSettings gt lt images gt lt string gt path to image tif lt string gt l
94. ata can be very noisy The data is smoothed using a LOESS smoothing procedure and the crossing points with the correlation cut off curve are computed Illustration 6 shows an example of an FRC curve The smoothed FRC line crosses the cut off curve at a frequency of approximately 0 02 nm The resolution is therefore 50nm Page 111 225 GDSC SMLM ImageJ Plugins Gaussian2D Create Data FRC Curve 0 00 0 01 0 02 0 03 0 04 0 05 0 06 Spatial Frequency nm 1 Save Copy Illustration 28 Example FRC curve from the Fourier Image Resolution plugin The raw FRC data are in black Smoothed FRC data are in red The resolution cut off threshold is in blue at a fixed value of 1 7 Page 112 225 GDSC SMLM ImageJ Plugins 8 PC PALM Plugins The following plugins are used to analyse the auto correlation of a set of localisations using Pair Correlation PC analysis This can provide information on whether the localisations are randomly distributed or clustered Sengupta et al 2011 Sengupta et al 2013 Puchnar et al 2013 The analysis uses a set of localisations assumed to represent single molecules or single fluorescent bursts The data is compared to itself and a curve is computed as a function of the distance from the centre of the localisation A flat curve is indicative that the distribution of localisations is no different from a random distribution Shaped curves can be fit using models that apply to various di
95. ation the fitting method and the initial guess for the fit to be configured The fitting process is performed and the fit rejected if the coordinates move outside the fitting region the signal is negative or the fitted width deviates more than 2 fold from the initial estimate All other results are stored for analysis The following parameters can be configured Parameter Description REGION SIZE The size of the region around the localisation used for fitting The actual region is a square of dimensions 2n 1 PSF wiptH The initial estimate for the 2D Gaussian FIT SOLVER The solver used for fitting The plugin will show a second dialog allowing the fitting to be configured that is specific to the selected solver Details of configuring each fit solver can be found in the section describing the Peak Fit plugin section 5 2 FIT FUNCTION The function used for fitting OFFSET FIT Select this to start fitting at a distance offset from the true localisation centre The fitting repeated 4 times using the Start oFFsET along each of the diagonals 1 1 1 1 1 1 1 1 START OFFSET The distance to offset the initial estimate INCLUDE CoM eit Perform fitting by starting at the centre of mass of the fit region BACKGROUND FITTING Select this to fit the background If false then fitting will fix the background parameter using the true background SIGNAL FITTING Select this to fit the signal If fal
96. aussian standard deviation using the microscope optics D amp PSF Calculator vy y X Pixel pitch nm 107 000 Wavelength nm pla Numerical Aperture NA 1 40 Proportionality factor 1 52 StdDev nm 115 265 StdDev pixels 1 077 OK Cancel Help The calculator uses the following formula SD pX1 323X IA Where SD The standard deviation of the Gaussian approximation to the Airy pattern A The wavelength in nm NA The Numerical Aperture p The proportionality factor Using a value of 1 gives the theoretical lower bounds on the peak width However the microscope optics are not perfect and the fluorophore may move on a small scale so the fitted width is often wider than this limit The factor of 1 52 in the calculator matches the results obtained from the PSF Estimator plugin on many calibration images made with the GDSC optical set up When the configuration wizard is finished the user is presented with the Simpce Fit dialog shown in Illustration 4 The settings are saved to the settings file If the wizard is cancelled at any point then the settings file is not created The user will be forced to go through the wizard again the next time they run the plugin 5 1 3 Advanced Settings The Simete Fit plugin is a simplified interface to the Peak Fit plugin that uses default values for fitting parameters All the fitting parameters can be adjusted only by using the Peak Fit plugin Since the Simpce Fit plugi
97. average number of photons m The EM gain multiplication factor c The observed pixel count 0 C The Dirac delta function 1 when c 0 O otherwise Bessell1 Modified Bessel function of the 1 kind Page 32 225 GDSC SMLM ImageJ Plugins Gp m C The probability of observing the pixel count c This is taken from Ulbrich and Isacoff 2007 The output of this function is subsequently convolved with a Gaussian function with standard deviation equal to the camera read noise and mean zero This must be done numerically since no algebraic solution exists However Mortensen et al 2010 provide example Python code that computes an approximation to the full convolution using the Error function to model the cumulative Gaussian distribution applied to the Poisson Gamma convolution at low pixel counts This approximation closely matches the correct convolution with a Gaussian but is faster to compute No gradient is available for the function and so non derivative based methods must be used during fitting Parameters Since MLE requires that we know the value of the data at each point the Peak Fit plugin requires the camera bias This is subtracted from the data before fitting so that the probability model can accurately return the likelinood of the pixel values given the expected values from the function The Maximum Likelihood Estimator requires the following additional parameters Parameter Description Camera Bias The value added to all p
98. case only the initial diffusion of the particles will be unconstrained The analysis should therefore fit the initial linear section of the MSD plot If the confinement radius is too small there may be no linear section to the MSD curve Page 197 225 GDSC SMLM ImageJ Plugins Note The asymptote of the curve for confined diffusion should be defined by the average distance to the centre of a random distribution of particles within a sphere This can be computed using the distance from the centre of all the points in a sphere divided by the number of points in a sphere The surface area SA of a sphere is equal to the number of points at distance r from the centre So SA x r is the sum of the distances of points at distance r from the centre If this is integrated from zero to R it produces the sum of all distances from any point within a sphere of radius R The number of points is the volume V of the sphere Therefore R R R Jsaxr_ J Amr xr fanr AR _3R V 4nR 3 4nR I3 4nR I3 4 Thus the mean distance to the centre for particles in a sphere is 3 4 R 10 7 5 2 Diffusion example If the SHow exampte option was selected the plugin will show an image of the track a single particle The track is shown on a black background The track is initialised at a value of 32 and ends with a value of 255 The movement can thus be followed using a color Lookup table LUT e g Inace gt Lookup Tastes gt FIRE The plugin will also show a
99. cel Help Illustration 4 Simple Fit dialog 5 11 Parameters The plugin offers the following parameters Parameter Description USE CURRENT CALIBRATION If selected use the current SMLM configuration Otherwise run the configuration wizard This option is only shown if a SMLM configuration file can be found If no file is found then the configuration wizard is run by default Page 19 225 GDSC SMLM ImageJ Plugins SHOW TABLE Show a table containing the localisations SHOW IMAGE Show a super resolution image of the localisations The image will be 1024 pixels on the long edge Note that the plugin will run if no output options are selected This is because the fitting results are also stored in memory The results can be accessed and manipulated using the Resutts plugins see section 6 It is possible to stop the fitting process using the Escare key All current results will be kept but the fitting process will end 5 1 2 Calibration The SMLM plugins require information about the system used to capture the images This information is used is many of the analysis plugins The information that is required is detailed below Information Description Pixel Pitch Specify the size of each pixel in the image This is used to set the scale of the image and allows determination of the distance between localisations This is used in many analysis plugins and for the localisation
100. ception of the last image which may be truncated The dialogue summarises at the bottom the total number of images and frames that will be read in the series Miu Sequence Options JURA Folder images storm tom S93 mEOS in cells Runl First image movie part1 tif Width 512 Height 512 Frames 300 Mumber of images 31 Starting image 1 Increment 1 File name contains or enter pattern 31 images 9300 frames OK Cancel Illustration 9 Peak Fit Series sequence options dialogue When different options are selected the plugin updates the count of the number of images Page 48 225 GDSC SMLM ImageJ Plugins and frames that will be processed The parameters that effect what images are loaded are show below Parameter Description NUMBER OF IMAGES Specify the maximum number of images to load STARING IMAGE The first image in the sequence The sequence begins at 1 INCREMENT The gap between images of the sequence Use a number higher than 1 to miss out images in a sequence FILE NAME CONTAINS Specify the text that the image filename must contain Or ENTER PATTERN Specify a pattern regular expression that the image filename must match If the user selects OK then the Peak Fit plugin is run and must be configured as described in section 5 2 The only difference is that the plugin is not running on a single image but on a series of images that are loaded sequentially and p
101. ch using active Covariance Matrix Adaptation Evolution Strategy CMA ES The CMA ES is a reliable stochastic optimization method which should be applied if derivative based methods e g conjugate gradient fail due to a rugged search landscape This is a bounded search and does not require derivatives http en wikipedia org wiki CMA ES Conjugate Gradient Search using a non linear conjugate gradient optimiser Two variants are provided for the update of the search direction Fletcher Reeves and Polak Ribi re the later is the preferred option due to improved convergence properties This is a bounded search using simple truncation of coordinates at the bounds of the search space Note that this method has poor robustness fails to converge on test data and is not recommended This method requires derivatives http en wikipedia org wiki Conjugate_gradient_method BFGS Search using a Broyden Fletcher Goldfarb Shanno BFGS gradient optimiser This method requires derivatives This is a good alternative to the Powell method for the Poisson noise model http en wikipedia org wiki Broyden E2 80 93FletchermE2 80 93Goldfarb E2 80 93Shanno_algorithm 5 2 4 4 Which Fit Solver to Choose The most general fit solver is the least squares estimator It does not require any specific information about the camera to perform fitting For this reason this is the default fitting engine It is also the fastest method Maximum Likelihood estimat
102. cking tif LVM 7923 Distance Threshold nm 800 Distance Exclusion nm 0 Min trace length 5 Save traces Multiple inputs OK Cancel Help The plugin has the following parameters Parameters Description INPUT Specify the input results set DISTANCE THRESHOLD The distance threshold for tracing DISTANCE EXCLUSION The exclusion distance If a particle is within the distance threshold but a second particle is within the exclusion distance then the trace is discarded due to overlapping tracks MIN TRACE LENGTH The minimum length for a track in time frames Longer tracks are truncated for analysis SAVE TRACES Save the traces to file in the Peak Fit results format MULTIPLE INPUTS Select this option to allow more than one input dataset If selected the plugin will show a second dialogue where additional datasets can be selected This allows analysis of data combined from multiple imaging experiments each dataset will be traced individually and the combined traces then analysed When all the datasets have been traced the plugin presents a second dialogue to configure the diffusion analysis The following parameters can be configured Parameters Description TRUNCATE TRACES Set to to true to only use the first N points specified by the minimum trace length INTERNAL DISTANCES Compute the all vs all distances Otherwise only compute dist
103. click action to open a file selection dialogue As with the Peak Fit plugin the results file suffix will be changed to xls for text results and bin for binary results One additional parameter is available for Image output Page 57 225 GDSC SMLM ImageJ Plugins Parameter Description Inace Winbow Applies to output images The Image Window specifies the number of consecutive frames from the results that should be plotted on a single ImageJ stack frame By default this parameter is zero All localisations are plotted on the same output frame If this is set to 1 then each frame will be output to a new frame in the output image Use this option to allow the input and output images to be directly compared frame by frame If set higher than 1 then N frames will be collated together into one output image Use this option to produce a time slice stack through your results at a specified collation interval This option is not available during live fitting since the result must be sorted This is not possible with multi threaded code as the results can appear out of order As with all of the SMLM plugins the Results Manacer is fully supported by the ImageJ macro recorder This allows the use of macros to bulk convert many results sets for example to render images and save them using the Fite gt Save As command 6 2 Summarise Results Shows a summary of all the results currently in memory The summary table shows the n
104. could not be joined are given a suffix Cluster Singles all clusters are given a suffix Clusters The Cluster Singles plus Clusters datasets equal the Clustered dataset 7 3 1 Clustering Algorithms The following table lists the available clustering algorithms Algorithm Description PARTICLE SINGLE LINKAGE Joins the closest pair of particles one of which must not be ina cluster Clusters are not joined and can only grow when particles are added CENTROID LINKAGE Hierarchical centroid linkage clustering by joining the closest pair of clusters iteratively PARTICLE CENTROID LINKAGE Hierarchical centroid linkage clustering by joining the closest pair of any single particle and another single or cluster Clusters are not joined and can only grow when particles are added PAIRWISE Join the current set of closest pairs in a greedy algorithm This method computes the pairwise distances and joins the closest Page 84 225 GDSC SMLM ImageJ Plugins pairs without updating the centroid of each cluster and the distances after every join centroids and distances are updated after each pass over the data This can lead to errors over true hierarchical centroid linkage clustering where centroid are computed after each link step For example if A joins B and C joins D in a single step but the new centroid of AB is closer to C than D PAIRWISE WITHOUT NEIGHBOURS A variant of Pair
105. cts localisations together with the same ID into clusters If localisations have no ID they are ignored The localisations in each cluster are then sorted by start frame to create an ordered trace Each cluster is then drawn on a selected image or a new empty image using an ImageJ overlay The size of the empty image can be specified but the plugin will Zoom a small image until the display window is 500 pixels on the long edge The overlay can be removed using Imace gt Overlay gt Remove OVERLAY The user has the option to draw the cluster as a series of points a cluster or as a connected line a trace Plotting points is appropriate when the clusters contain multiple localisations that do not represent a single molecule Plotting a line is appropriate when the cluster represents a single molecule s position through time If an input image is selected then the number of time frames in the image is compared with the maximum start frame in all the localisations If the image stack is large enough the plugin can draw each cluster on the specific frame containing the localisation In this case the entire cluster is drawn and the point contained in that particular frame is highlighted using a cross An example is show below Page 86 225 GDSC SMLM ImageJ Plugins Draw Clusters 2400 Y A PS 45 88 20x20 pixels 8 bit 34K The following options are available Parameter Description INPUT Select the input results to
106. cules are randomly positioned in a 3D volume These are then subjected to photoactivation laser illumination and readout laser illumination The illumination is not constant across the image but uses a radial fall off function to simulate the darkening towards the edges of a wide field microscope image The light fall off is 50 at the field edge Illumination light and background fluorescence are subject to Poisson noise The read out laser is a continuous light source The activation laser can be continuous or pulsed When pulsed mode is used all readout frames have a low level of activation light This is interspersed with pulses of the activation laser at set intervals The pulse is deemed to be a zero time event The ratio between the amount of energy a fluorophore can receive during the pulse and between pulses can be controlled This allows the simulation to vary the level of background activation i e molecules that activate in frames not directly following an activation pulse The amount of photons required for photo activation of each molecule is defined by sampling from a random exponential distribution The average for this distribution is set using the cumulative number of photons in the centre of the field at 30 of the simulation Page 129 225 GDSC SMLM ImageJ Plugins length Thus approximately 50 of the molecules should have activated by 1 3 of the simulation The simulation allows for a single dark state or dual dark state mo
107. d The filtering is then performed on each frame in the image candidates in the configured border are ignored and the combined list of spot candidates ranked This ranking depends on the filter but is usually done using the pixel value in the filtered image at the spot candidate position The ranking will be the same as that used when performing fitting within the Peak Fit plugin only on all the candidates at the same time and not on the candidates per frame since Peak Fit processes and fits frames individually The ranked spot candidates are then analysed to produce scoring metrics of the filter performance The following parameters can be configured Parameter Description SPOT FILTER TYPE The type of filter to use If a Dirrerence Or Jury filter is selected then the plugin will present an additional dialogue to configure each additional spot filter SPOT FILTER The name of the first spot filter SMOOTHING The smoothing parameter for the first filter SEARCH WIDTH Define the region within which to search for a local maxima The region size is 2n 1 This must be at least 1 Page 152 225 GDSC SMLM ImageJ Plugins Parameter Description BORDER Define the number of border pixels to ignore No maxima are allowed in the border ANALYSIS BORDER Define the number of border pixels to ignore during the analysis Any true or candidate maxima within this border are ignored MATCH DISTANCE The
108. d as _ E E c G ml cj e P5 c lo Besselt 2 P where p The average number of photons m The EM gain multiplication factor c The observed pixel count c The Dirac delta function 1 when c 0 O otherwise Besselll Modified Bessel function of the 1 kind Gp m C The probability of observing the pixel count c The output of this is subsequently convolved numerically no algebraic solution exists with a Gaussian function with standard deviation equal to the camera read noise and mean equal to the camera bias 10 5 1 1 Camera Bias Note that in order to observe the read noise of the camera a bias offset is added to the camera pixel values This allows a pixel to record negative read noise on very low counts which would not be possible using unsigned integer values as no value below zero is allowed The bias for the camera is set by the manufacturer and is set at a value far greater than the expected read noise of the system e g 100 400 500 or 1000 for a read noise of 3 30 ADUs Analogue to Digital Units or pixel values 10 5 2 Input image The plugin requires a white light image where each pixel has been exposed to the same number of photons This can be produced by imaging without a sample instead using white paper in front of the objective so that images are evenly illuminated The light can be adjusted by varying the exposure time and different calibration performed by using different camera gain settings The input imag
109. dates that do not match a true localisation where fitting failed i e the algorithm did not return a result TP The sum of the match score for fit results that can be matched to a localisation FP The sum of the remaining match score for fit results that can be matched to a localisation This will be zero if not using a ramped match score with March Distance above Lower DISTANCE RECALL The recall of the fitted candidates Page 161 225 GDSC SMLM ImageJ Plugins Field Description PRECISION The precision of the fitted candidates JACCARD The Jaccard of the fitted candidates F1 score The F1 score of the fitted candidates Mep DISTANCE The median of the histogram of the distance between fitted candidates and the localisations Mep DEPTH The median of the histogram of the z depth of localisations that were fitted Mep PRECISION The median of the histogram of the precision computed for all positive fit results 9 13 Benchmark Filter Analysis Run different filtering methods on a set of benchmark fitting results produced by Fit Spot Data outputting performance statistics on the success of the filter If these results are not available an error will be displayed The Benchmark Fitter Analysis plugin is designed to test the results filtering available in the Peak Fit plugin The principle is that simulated localisations are identified as candidates for fitting and then fitted using the same routines ava
110. del For the single dark state model the fluorophore can be either on or off dark state The number of time the fluorophore enters the dark state is selected from a probability distribution For the dual dark state model the fluorophore can be on or in either dark state 1 or dark state 2 The dark state can only transition between the on state There is no transition from dark state 1 to 2 or the reverse The number of time the fluorophore enters the 2 dark state is selected from a probability distribution For each time the molecule is in the on state the number of time the fluorophore enters the 1st dark state is selected from a probability distribution The dual dark state model can be used to simulate flickering of the fluorophore at a fast rate i e moving between the on state and dark state 1 broken by longer period of off time i e moving between the on state and dark state 2 The number of blinks is sampled from a Poisson or Geometric distribution and the length of time in the on state and off state s are sampled from exponential distributions The average for these distributions are set as simulation parameters Analysis of the signal of mEOS3 fluorophores in yeast show that the total signal and signal per frame can be modelled using a Gamma distribution Analysis of the signal per frame verses the time for the lifetime of the fluorophore shows that the signal is approximately constant i e the signal does not get weaker over time Con
111. density STORM data or low density PALM data 5 4 Fit Configuration This plugin allows the fitting engine to be configured The plugin dialogue has several sections controlling different parts of the fitting algorithm as shown in Illustration 8 These settings are the same as the Peak Fit plugin and are described in section 5 2 Ly Fit Configuration JOUR Configuration settings for the single molecule localisation microscopy plugins Gaussian fitting Config file ANIME Fit solver Maximum Likelihood Estimator MLE Calibration nm px 102 38 Fit function Circular Gain 37 70 Fail limit 3 y EM CCD Include neighbours Exposure time ms 100 00 Neighbour height b 30 Gaussian parameters Residuals threshold h oo Initial StdDevO 0 735 Duplicate distance 0 50 Initial StdDevi 0 735 ESE Sa Discard fits that shift are too low or expand contract Initial Angle 0 000 Shift factor 1 36 Maxima identification Signal strength 0 00 Spot filter type Single Min photons 30 Spot filter Mean Width factor 2 00 Smoothing j h 30 Precision threshold 40 00 Search width 1 00 Border 0 00 Fitting width 3 00 OK Cancel Help Illustration 8 The Fir CONFIGURATION dialogue As with the Peak Fit plugin the settings contained in the configuration file are loaded when the plugin is initialised If no file exists then a default set of settings will be created A different file c
112. ditions used to acquire the image The pixel size is used to define distances in nm The gain is used to convert the Analogue to Digital Units ADUs to photons Parameter Description CALIBRATION NM Px The size of the image pixels in nm Gain The total gain Used to convert the camera ADUs to photons EM CCD Select this if you used an EM CCD camera This is stored with the results and used in precision calculations EXPOSURE TIME ms This is the length of time captured by each frame in milliseconds Note that a bias offset zero level is not always needed since the fitting process fits the background which will include the bias offset The number of photons in the peak can then be calculated without needing to know the camera bias If Maximum Likelihood fitting is used then the bias is required and the plugin will prompt the user to enter it 5 2 2 Gaussian PSF Parameters The Point Spread Function PSF of the microscope is approximated using a 2D Gaussian function The Gaussian can have the same width in the X and Y dimensions or separate widths If the widths are different then the Gaussian will be elliptical in shape In this case the ellipse can be rotated by an angle The parameters allow the initial shape of the Gaussian PSF to be specified These parameters are only an initial guess and the Gaussian shape will be optimised to fit each identified spot in the image Note that the Gaussian function is defined in un
113. e The average density is shown in the summary table The density is the number of molecules within the specified radius 9 7 1 Fitting Limits The Create Benchmark Data plugin will report the theoretical limit precision for fitting the signal number of photons and the XY coordinates localisation These limits use the formulas of Thompson et al 2002 for the signal and Mortensen et al 2010 for the localisation See Appendix A Localisation Precision Note that these formulas are derived from modelling the point spread function PSF as a 2D Gaussian for both the simulation and the fitting Given that the true data will have a PSF defined by the microscope parameters these formulas only approximate the precision that can be obtained on image data However they are useful to allow demonstration that the fitting routines in the SMLM plugins can achieve the theoretical limit i e they are working as well as can be expected 9 8 Fit Benchmark Data Fit the image created by Create Benchmark Data and compute statistics on the accuracy and precision of fitting The Fit Benchmark Dara plugin will fit a stack image of localisations all created at the same coordinates This image must be created by the Create Benchmark Data plugin as the Page 146 225 GDSC SMLM ImageJ Plugins parameters used to create the image are stored in memory and used in the analysis The plugin allows the size of the fitting region around the localis
114. e and optionally signal factor of a true localisation and reject all other fit results If a candidate fails to be fitted but is close to a true localisation it will not be included in the assessment scores since the result is not available for filtering and so not relevant to benchmarking filters Note that the use of a ramped score function based on distance allows the comparison of scores between different fitting algorithms since some algorithms may fit the spots closer to the true localisation Also note that if it is not clear at what level to set the match distance then using a ramped distance score will produce the same results as repeating the analysis with multiple match distances and averaging the score 9 12 2 Parameters The following parameters can be configured Parameter Description FRACTION POSITIVES Set the limit in percent on the number of filter candidates that match true localisations that must be processed FRACTION NEGATIVES AFTER After the positive target has been reached set the limit in POSITIVES percent on the fraction of filter candidates that must be negatives i e how many of the candidates for fitting should be incorrect MIN NEGATIVES AFTER After the positive target has been reached set a minimum POSITIVES number of filter candidates that must be negatives i e how many extra incorrect candidates should be included in the fitting process MATCH DISTANCE The distance limit defining t
115. e sqrt 2D This step size can be used to simulate diffusion using a grid walk At each step a particle can move forward or backwards by the step size If the direction is random then the population of particles will have an average displacement of zero a mean displacement of the step size and a MSD of step size squared 2D Multi dimension diffusion is done by simulating the movement in each dimension separately 10 7 2 Random Move simulation Diffusion can also be simulated by moving particles on a random vector The distance moved should be sampled from a Gaussian distribution with a mean of zero anda standard deviation of sqrt MSD This is 2D 4D or 6D for 1 2 or 3 dimensions respectively However the unit vector must be directed in a random orientation For one dimension this is either forward or backward For higher dimensions a random vector can be produced by sampling the movement in each dimension from a Gaussian distribution with mean zero and standard deviation 1 This vector is normalised to unit length The generation of the unit vector and the movement distance can be combined into a single stage The random displacement is produced by sampling each dimension from a Gaussian distribution with mean zero and standard deviation of sqrt 2D 10 7 3 Confined Diffusion Particles may not be able to freely move in any direction for example when they collide with a barrier The Dirrusion Rate Test plugin allows particles to be confined
116. e ImageJ stack frame By default this parameter is zero All localisations are plotted on the same output frame Page 44 225 GDSC SMLM ImageJ Plugins If this is set to 1 then each frame will be output to a new frame in the output image Use this option to allow the input and output images to be directly compared frame by frame If set higher than 1 then N frames will be collated together into one output image Use this option to produce a time slice stack through your results at a specified collation interval This option is not recommended during live fitting since the results must be sorted This is not possible with multi threaded code and the results can appear out of order In this case any result that is part of a frame that has already been drawn will be ignored The option is also available using the Resutts Manacer plugin which can plot all results in order SHOW PROCESSED FRAMES Show a new image stack labelled Processed frames that show the images that were passed to the fitting engine This option is useful when using the InterLaceo Data Or INTEGRATE Frames options Each slice will be labelled with the start and end frame of the original image used to produce the image data 5 2 13 Interlaced Data The additional fitting options allow for interlaced data where not all the frames in the image should be analysed Interlaced data must follow a regular pattern where a repeating block of fr
117. e a per localisation K or L score as follows Y Haver Since the count of localisations is expected to be the area of the local region multiplied by Page 90 225 GDSC SMLM ImageJ Plugins the average sample density A then the Ki r score is expected to be the area of the local region The Ki r score can be normalised by the local region area and should be equal to 1 As before the Ki r score can be variance normalised to an L score L r K 1 1 In this case the L score is normalised by Tt If using a square approximation then the normalisation factor for the area of a square is 4 The Li r score should be equal to r The following scores are supported in the plugin Score Description DENSITY The count of the number of localisations in the region around a localisation K r K score Should be equal to the local region area K r Area Should be equal to 1 L r Should be equal to the radius L r r Should be equal to zero L mr Should be equal to one Scores should be comparable across different radii L r r r Should be equal to zero Scores should be comparable across different radii 7 5 2 Ripley s L plot If the Compute L pLot option is selected then the plugin will compute the L score for a range of radii A dialogue is presented allowing the user to select the Min rRaDius and Max Rabius and the Increment used to move between them A plot is produced showing the L r r r
118. e faster and both methods return very similar results The weighted least squares estimator provides a weight for each point using the estimated value The fit attempts to minimise SS O EV E Note that when the estimated value is small the weight will have a destabilising effect on the sum by significantly over weighting data The weight is thus limited to a minimum of 1 However weighted least squares is not recommended as it has not been proven in testing on simulated single molecule data to outperform the standard LSE Currently the quasi Newton LSE requires no additional parameters to be configured The GDSC Least Squares Estimator requires the following additional parameters Parameter Description Fit CRITERIA The fit uses a non linear least squares routine until convergence If convergence is not achieved by the maximum iterations then the fit fails Convergence can be defined using e Least squared error convergence of the least squared error of the fit to a given number of SIGNIFICANT DIGITS e Least squared error plus convergence of the least squared error of the fit to a given number of SIGNIFICANT DIGITS Convergence is also achieved if 3 consecutive improvements are the same relative improvement and half of the maximum iterations has passed This avoids slowly converging fits e Co ordinates convergence of the X Y centre coordinates to within a specified Coord DELTA e Parameters convergence of each of the
119. e is used to construct a histogram of the pixel values that are observed for the given camera settings and background number of photons This is then fit using the Poisson Gamma Gaussian probability mass function Ideally the input image should provide a minimum of 1000000 pixels for example 16 Page 190 225 GDSC SMLM ImageJ Plugins frames of a 256x256 pixel image This level of pixels is required to construct an even histogram that adequately samples the probability mass function The pixels should have the same mean i e a constant mean across the field of view If it is not possible to achieve a constant mean across the field for example in the instance of a gradient in the illumination then the plugin will support rectangular ROI crops of the image However the number of pixels should reach the minimum limit to construct a good histogram If the minimum pixel limit is not reached the plugin will log a warning but will continue to analyses the image 10 5 3 Parameters The following parameters can be configured Parameter Description Bias ESTIMATE The initial estimate for the camera bias The bias may be obtained from the camera manufacturer s specifications A guess can be made by selecting the darkest part of the image taking the mean and rounding usually down to the nearest hundred GAIN ESTIMATE The initial estimate for the total gain of the camera The total gain may be obtained from the camera manufacturer s spec
120. e localisations in the dataset If unselected the Search bistance is absolute in pixels FITTED POINTS The number of points to fit on the N tg curve Must be 4 or more RANGE OF FITTED POINTS The maximum number of additional points to fit for variation analysis Fit are computed from Fittep Points to Firreo Points Rance Set to zero to show the N tg curve Page 94 225 GDSC SMLM ImageJ Plugins Parameters Description TIME AT LOWER BOUND When constructing the dark time curve the number of frames used for tracing is converted to time in milliseconds Set to true to output time as nFrames x msPerFrame Set to false to output time as nFrames 1 x msPerFrame This setting will shift the time axis of the curve and will produce different curve fitting results Simulations using the Create Data plugin suggest that this should be TRUE A value of false is stating that localisations in consecutive frames may have blinked into a dark state of less than 1 frame D amp Blink Estimator Molecule Counts yD x 400 350 5 o o 300 td ms Save Copy Illustration 19 N t4 curve output from the BLinx Estimator The curve data is l plotted in black The red circles show the fitted points The blue crosses indicate where the fitted line will asymptote 7 8 Neighbour Analysis Saves all localisations paired with their neighbour if present to file The NeicHBour Anatysi
121. e offset Scale 10 00 zdepth 1000 00 nm Grid size 10 Recall limit lt m r 0 25 Region size 4 gt f5 Background fitting Fitsolver Least Squares Estimator LSE x Fitfunction Circular T V Offset fit Start offset 0 500 V Include CoM fit M Use sampling Photons 1000 Photon limit lt 10 25 Smoothing lt w gt fo 40 9 3 1 Drift Calculation The drift curve represents the centre of the PSF for each image in the PSF stack This is computed by drawing the PSF into an image at a specified scale and then fitting the image with a 2D Gaussian as per the Peak Fit plugin Note that the PSF rendering uses bilinear interpolation to scale the PSF before insertion The integral of the scaled PSF over each output pixel is then used to set the image pixel value Alternatively the PSF can be treated as a 2D probability distribution The coordinates from random sampling of this distribution are then mapped to the output pixels to generate the counts for each pixel The PSF is drawn multiple times to reduce bias The PSF is inserted into the image centre pixel at each point on an NxN grid so reducing bias from the fitting due to the location the PSF was inserted For example a grid of 10 would insert the PSF at 100 locations spaced at 0 1 pixel intervals starting from O in each dimension 100 fits would be computed and the recall number of successful fits recorded Page 123 225 GDSC SMLM ImageJ
122. e to be saved as a file SAVE IMAGE RESULTS Show a dialog allowing the image localisations to be saved as a PeakResults file Note that this does not contain the molecule Z position Page 151 225 GDSC SMLM ImageJ Plugins Parameter Description Save LOCALISATIONS Show a dialog allowing the localisations to be saved The file contains the time and X Y Z positions of each fluorophore when it was in an on state SHOW HISTOGRAMS Show histograms of the generated data CHOOSE HISTOGRAMS Set to true to allow the histograms to be selected otherwise all histograms are shown HISTOGRAM BINS The number of bins in the histogram REMOVE OUTLIERS Remove outliers before plotting histograms Outliers are 1 5 times the interquartile range above below the upper lower quartiles Outliers are always removed for the Precision data since low photon signals can produce extreme precision values 9 11 Filter Spot Data Filter the image created by Create Simpie Data or Create Spot Data and compute statistics on the accuracy and precision of identifying spot candidates The Fitter Spot pata plugin will filter a stack image of localisations to identify candidates for fitting This image must be created by the Create Simpte Data or Create Spot Data plugin as the parameters used to create the image are stored in memory and used in the analysis The plugin allows the spot filter and the analysis settings to be configure
123. eJ Plugins Field Name Description 6 Intensity The signal intensity The Loan Locatisarions plugin will ask the user to select a file The file is then read assuming the Create Dara localisations data format Any lines beginning with the character are ignored The units are assumed to be in pixels The plugin then presents a dialogue allowing the user to select a subset of localisations by z depth Illustration 35 The dialogue shows the minimum and maximum limits of the z coordinates and provides an option to limit the z depth The limits can then be adjusted using the sliders 2837 localisations with 0 11 z lt 0 26 Limit 2 depth minz 0 11 maxz k A 0 26 OK Cancel Illustration 35 Load localisations plugin dialogue The subset of localisations are saved to a results set in memory named Localisations The localisation results do not have a calibration or data on the peak width and amplitude Therefore the results cannot be used in many of the SMLM plugins However the XY coordinates can be used in compatible plugins for example within the Resutts March Catcutator plugin Thus the Loap Locatisations plugin can be used to load selected slices of data using the z depth filter and compute the match statistics to fitted results This allows benchmarking the performance of fitting spots that are both in and progressively out of focus Since the plugin is fully supported by the I
124. eans that it is possible to create a series of values from minimum to maximum using the increment Note that the increment Page 162 225 GDSC SMLM ImageJ Plugins does not have to be an exact factor of the range The value is just incremented from the minimum until the maximum is reached or exceeded If the filter set can be expanded the plugin will compute the number of combinations that will be created after expansion It will then ask the user if they would like to expand the filters Expanding filters is much faster that reading a large number of filters in from a file and so is the preferred method of loading a large evenly spaced filter set Any filter set that has been expanded is also available for a step search optimisation of the parameters see below 9 13 2 Analysis For each filter in the set the plugin runs the filter on the fit results The filter separates the results into those that are accepted positives and those that are rejected negatives Note that the results are processed in the order determined by the filter that identified the fit candidates As per the Peak Fit plugin a record is kept of the number of consecutive results that fail This includes any candidates that did not produce a fit and any results that are rejected by the filter As soon as the configured fail count is reached then the remaining results in that frame are all rejected The filtered results are then scored The scoring is designed to f
125. ecision Jaccard and F1 score See Appendix B for more details The first set of statistics are for the raw candidates before fitting These show how effective the filter was at identifying candidates that were processed and so set an upper limit on the performance of the fitted Page 159 225 GDSC SMLM ImageJ Plugins results The second set summarise the performance of the fitted results Note that the table does not show the False Negative score since this is equal to the number of simulated molecules minus the True Positives The analysis results are then reported in a summary table Field Description FRAMES The number of frames in the simulated image W The width of the simulated image minus the analysis border H The height of the simulated image minus the analysis border MoLecuLes The number of molecules that occur within the bounds of the analysis border DENSITY The molecule density within the analysis region N The average number of photons per localisation Ss The standard deviation of the Gaussian profile that matches the PSF A The pixel size DEPTH The z depth of the localisations FIXED True if the simulation used a fixed depth Gain The total gain of the simulation ReapNolse The read noise of the simulation B The background number of photons B2 The noise per pixel This is a combination of the read noise and the background number of photons SNR The signal to no
126. ed PSF image Each spot is extracted into a stack and enlarged using the configured settings The background is calculated for the spot using the N initial and M final frames and subtracted from the image A Tukey window is then applied to the spot so that the edge pixels approach zero If using interactive mode the user has a second chance to view the spot data and accept it A plot is produced of the total intensity within half of the region surrounding the spot against the z position see Illustration 32 At this stage the centre cannot be adjusted However it is possible to view when the profile does not smoothly fall away in intensity from the centre i e the spot is gradually defocussed from the centre and reject the spot Page 118 225 GDSC SMLM ImageJ Plugins 200000 100000 List Save Slice Copy Illustration 32 Spot intensity within half the region surrounding the spot The profiles is produced after the image has been scaled background normalised and windowed The centre is marked using a green line For all spots that are accepted the spots are then overlaid using their X Y and Z centres into an average PSF image It is assumed that the in focus spot can be modelled by a 2D Gaussian All the pixels with 3 standard deviations of the centre are summed as foreground pixels The image is then normalised across all frames so that the sum of the foreground is 1 9 2 3 Parameters Parameters Descript
127. ed into memory When the plugin is run the user is presented with a selection dialogue of the available results The user can select the results to filter The dialogue also contains a text area This is used to construct filters using eXtensible Markup Language XML A set of example filters can be shown by clicking on the SHow DEMO FILTERS Checkbox This will record the available filters to the ImageJ log Note To see the filters and copy them to the clipboard as examples you will first have to cancel the plugin dialogue The following filters are available Filter Description WIDTHFILTER Filters the results using an upper width factor Width is relative to the initial peak width WIDTHFILTER2 Filter the results using a width range Width is relative to the initial peak width SIGNALFILTER Filter results using a lower signal threshold The threshold is applied in photons SNRFILTER Filter results using a lower SNR threshold Page 62 225 GDSC SMLM ImageJ Plugins SNREI LTER2 Filter results using a lower SNR threshold and width range Width is relative to initial peak width PRECISIONFILTER Filter the results using an upper precision threshold SNRHysTERESISFILTER Filter results using a signal to noise SNR threshold Any results above the upper SNR limit are included Any results below the lower SNR limit are excluded Any results between the limits candidates are included only if
128. ed within a shell of radius r and a width dr at time At is given by 2 r pr At dr e PA dr This can be expanded to a mixed population of m species where each fraction f has a diffusion coefficient D 2 2 Y fi a 2 Atjdr md p r At dr 2 4D At e r For the purposes of fitting the integrated distribution can be used For a single population this is given by 2 r p r dr 1 e Ds P r At o gt The advantage of the integrated distribution is that specific histogram bin sizes are not required to construct the cumulative histogram from the raw data Note that the integration holds for a mixed population of m species where each fraction f has a diffusion coefficient D E m P r At 1 gt fje 0 j 1 Weimmann et al 2013 show that fitting of the cumulative histogram of jump distances can accurately reproduce the diffusion coefficient in single molecule simulations The performance is measured relative to the average distance a particle travels in the chosen time d and the average localisation precision o expressed as a ratio B d o When B is above 6 then jump distance analysis reproduces the diffusion coefficient as accurately as MSD analysis for single populations For mixed populations of moving and stationary particles the MSD analysis fails and the jump distance analysis yields accurate values when is above 6 Page 200 225 GDSC SMLM ImageJ Plugins The Trace Dirrusi
129. el imaging was performed or alternating white light and localisation imaging If selected the program will ask for additional parameters to specify which frames to include in the analysis see section below INTEGRATE FRAMES Combine N consecutive frames into a single frame for fitting This allows the Peak Fit plugin to simulate the result of running the image acquisition at a slower frame rate exposure time The results will be slightly different from a long exposure experiment due to the cumulative read noise of multiple frames differing from the read noise of a single long exposure frame Note that the results will be entered into the results table with a start and end frame representing all the frames that were integrated MIN ITERATIONS The minimum number of iterations to run the fitting optimiser Prevents the optimiser stopping too soon but may prevent the optimiser recognising convergence since later iterations may not improve the fit An experimental feature that should be used with caution Noise Set a constant noise for all frames in the image This overrides the per frame noise calculation in the default mode NOISE METHOD Specify the method used to calculate the noise See section 11 5 Noise Estimator plugin for details of the methods IMAGE WINDOW Applies to output images The Image Window specifies the number of consecutive frames from the results that should be plotted on a singl
130. elected for crossover and then new individuals are created by crossing their parent parameter values at random points along the genome These new individuals may also mutate to change parameters in their genome When enough new individuals have been created the fitness is evaluated again and the process repeated until no improvement can be made Note that the individuals selected for the subset are not changed and only new individuals can mutate This means that the population should not get worse if the top fraction is selected each iteration If selection is by sampling from the population then it is possible the population can get worse but the top individual is always retained Due to the use of mutation the genetic algorithm is able to produce parameter values that were not in the original filter set Step Search If a filter set has been expanded using 3 filters defining minimum maximum and increment parameters then the plugin can perform a step search All of the filters in a filter set are evaluated and then ranked If the best filter has a parameter value at the edge of the range of values for that parameter then new filters are created that use the increment to push the parameters to new values outside the original range The new filters are evaluated and this process is repeated until no improvement in score is made The Step searcu option is a fast method for taking an initial parameter range and producing an optimal set of paramete
131. emoved This means that the average off time increases as the short off times are removed The average on time increases as well since bursts that are joined by a short off time will be joined up to longer bursts Finally the number of blinks is reduced because very short blinks cannot be counted It should be possible to experimentally compute values close to the sampled statistics by using optimised fitting parameters within the Peak Fit plugin and then using the Brink Estimator plugin An approximate number of molecules and pulses can be estimated using the Trace Motecutes plugin 9 5 9 Memory Output The localisations that are created are stored as various results sets in memory Each molecule has a unique ID that is stored in each localisation The results are named as follows Page 141 225 GDSC SMLM ImageJ Plugins Suffix Description LocaLisation DATA Create Data A full set of localisations with each assigned the corresponding molecule ID Localisation Data Create Data PuLses A set of centroids each centroid is composed of the collection of localisations from a single molecule that were continuously visible in consecutive frames of the image The start and end frame of the pulse is stored Locatisation DATA Create Data No Density The set of localisations where there was no other localisation within the radius used to calculate the density LOCALISATION DATA Create Data Density The s
132. en a consecutive number of fits fail To account for high density samples neighbour peaks within the block region are included in the fit if they are within a fraction of the height of the candidate peak typically 30 If multiple peak fitting fails then single peak fitting is attempted Additionally the candidate can be fit using a two peak model if the fit residuals show an asymmetric distribution around the centre The doublet fit is selected if it improves the corrected Akaike Information Criterion AIC Hurvich amp Tsai 1989 To prevent over counting when fitting multiple peaks a check is made for duplicates using a distance criterion before adding to the results The method is applicable to all types of localisation microscopy data and results are suitable input for filtering methods using structural models Image frames are processed independently allowing multi threaded operation Results can be output to memory file or a rendered image using various methods Page 16 225 GDSC SMLM ImageJ Plugins 3 Installation The plugin is designed to run within ImageJ This can be the original ImageJ version 1 or any modified version of ImageJ such as ImageJ2 or Fiji 3 1 Install using ImageJ2 Fiji The SMLM plugins are distributed using an ImageJ2 Fiji update site This allows the plugins to be easily installed and kept up to date To install the plugins using Fiji just follow the instructions here http fiji sc How_to_follow_a_3rd_
133. entify many false positives the overall precision score is very low Thus the plugin also reports the precision at a fraction of the maximum recall This fraction Page 153 225 GDSC SMLM ImageJ Plugins can be configured and is shown on the plot using a magenta line In the example above the line is drawn at 98 of the maximum recall In addition the precision can be plotted directly against the recall The area under the precision recall curve AUC is the average precision at each possible recall value This provides a single score on how good the filter is at finding and ranking spot candidates An example precision recall chart is shown below The AUC2 score is computed using a modified precision curve that uses the the highest precision at that recall or above This smooths a noisy curve that may occur at low recall values The AUC2 score is always above the AUC score AUC 0 679 AUC2 0 6798 1 0 0 5 Precision 0 0 0 0 0 2 0 4 0 6 0 8 1 0 Recall An additional analysis is performed using the ranked candidates For each frame in the input image a count is made of the number of false positives failures before each additional true positive The counts are plotted as a histogram and a cumulative histogram if the Show FAILURE PLOTS option is selected The cumulative histogram is then used to determine the number of consecutive false positives to accept to achieve a set fraction of the maximum true positives The fractions are repo
134. entre width and height to a set number of significant digits Max ITERATIONS Stop the fit when this is reached SIGNIFICANT DiGITS When comparing two numbers defines the significant digit for equality e g specify 3 to recognise 1 and 1 001 as equal Note that Java floating points have a limited precision preventing comparisons to high numbers of significant digits Using a value over 6 will not work no convergence for the Gaussian or Parameter fitting criteria options and is not recommended for the LEAST SQUARED ERROR Option Page 55 225 GDSC SMLM ImageJ Plugins Parameter Description Coorp DELTA Define the smallest shift in pixels that specifies a movement of the X Y coordinates Used in the CoorbinaTes fit criteria SINGLE FIT Peaks are fit all at once using the entire ROI or can be fitted individually Single fit If using single fit then a region is drawn around the peak and fitted Individual fitting works well if the box does not include any other peaks otherwise a neighbour peak can interfere and it is best to fit all at once SINGLE REGION SIZE The size around each peak to use for fitting InrriaL StoDev The initial standard deviation in pixels for the Gaussian Set to zero to estimate this from the peak width Loc PROGRESS Write progress messages to the ImageJ log SHOW DEVIATIONS The show deviations output produces an estimated error for each of the parameters in the
135. ep of the same particle is given a new frame and Page 198 225 GDSC SMLM ImageJ Plugins particles are allocated a unique ID The current frame is incremented between particles so that each particle track is separated in time This allows the results set to be used within the Trace Dirrusion and Draw Cuusters plugins to verify their functionality 10 8 Trace Diffusion The Trace Dirrusion plugin will trace molecules through consecutive frames and then perform mean squared displacement analysis to calculate a diffusion coefficient The plugin is similar to the Dirrusion Rate Test plugin however instead of simulating particle diffusion the plugin will use an existing results set This allows the analysis to be applied to results from fitting single molecule images using the Peak Fit plugin 10 8 1 Analysis The plugin runs a tracing algorithm on the results to find localisations that occur in consecutive frames Details of the tracing algorithm can be found in section 7 2 Trace Molecules The distance threshold for the tracing algorithm can be specified but the time threshold is set to 1 frame i e only continuous tracks will be extracted Thus a pair of localisations within adjacent frames will be connected if they are within the distance threshold In addition the plugin allows the track to be excluded if a second localisation occurs within an exclusion threshold of the first localisation This effectively removes traces of particles that c
136. er gradients are more robust and those with higher gradients are the ones that cannot be varied very much for optimal performance of the filter 9 13 2 3 Optimisation Searching for the best parameters for a filter is an optimisation problem The more parameters there are in the filter the more combinations are possible It may not be feasible to enumerate all the possible parameter combinations to find the best parameters The plugin offers two methods for searching for the optimal parameters evolution using a genetic algorithm and a step search Once the optimal parameters are found for the filter set then the plugin produces the summary results as per normal Evolution using a Genetic Algorithm All the filters in a filter set are used to create a population of filters The parameters are listed in order to create a genome for each individual The fitness of each individual is the score that is achieved using the ranking metric If the criteria is not reached then the fitness is set to zero Optionally this can be relaxed to allow all filters achieving the criteria to be ranked ahead of all filters not achieving the criteria After computing the fitness of individuals in a population the population is allowed to change The population is first reduced to a subset of the individuals using a selection process the best scoring individual is always kept at each iteration The subset forms a new population that is expanded by breeding Pairs are s
137. estimated from the data using the Bunk Estimator plugin see 7 7 Blink Estimator Alternatively it can be measured by manual inspection of purified single fluorophores sufficiently spread on a slide to avoid two molecules in the same location Care must be taken to ensure that the imaging condition are the same as those used for in vivo experiments The optimisation method is adapted from Coltharp et a 2012 Optimisation is based on the following equation Observed pulses Expected molecules E Blinking rate The observed pulses is the number of single pulse events that are observed in the data i e continuous emission from the same fluorophore Dividing this by the average blinking rate of a fluorophore should give the number of molecules The observed pulses can be found by tracing the localisations using a time threshold of 1 and a distance threshold that will allow a match of the same molecule position This will only join localisations that are in adjacent frames into a single light pulse The distance to use is obtained from the data using 2 5x the average localisation precision For example if 10 000 pulses have been identified by tracing at t 1 d 2 5xPrecision and the blinking rate is known to be 2 then the expected number of molecules is 5 000 A score metric can be computed for a given tracing result Traces Expected molecules Score Expected molecules The closer the score to zero the more likely that the traci
138. et of localisations where there was at least one other localisation within the radius used to calculate the density It is possible to save these results to file using the Resutts Manacer plugin 9 6 Create Simple Data Creates an image by simulating single molecule localisations at a specified density The Create Simpce Data plugin is a modification of the Create Data plugin to remove the simulation of diffusing fluorophores The simulation draws localisations on frames ata specified density until enough frames have been created to reach the desired number of localisations Note that at least one localisation is drawn per frame so to achieve a very low density will require using a large image size The number of photons per localisation is randomly sampled from the range specified by the minimum to the maximum photons parameters The output of the plugin is an image and summary table as per the Create Data plugin The Create Simpce Data plugin records the details of the simulation in memory This data can be used with the Fitter Spot Dara plugin to filter the image to identify candidate localisations and report statistics on the recall and precision of the results The following parameters can be configured Parameter Description PIXEL PITCH The simulated size of the pixel in the image in nm SIZE The width and height of the image in pixels DEPTH The depth of the simulation in nm Molecules will only be sampled wit
139. eved by fitting The third is the histogram for all the fitted results that were accepted by the filter This is plotted in red An example is shown below Page 172 225 GDSC SMLM ImageJ Plugins Black Spots Blue Fitted Red Filtered 300 N o o Frequency Pp o o MN Mi da ial bulk 0 L 1000 500 500 1000 1500 este nm Since the number of localisations at different depths is highly variable the histograms are smoothed and then normalised by the number of localisations In the normalised plot only the fitted and filtered lines are shown the magenta lines represent the depth of field specified by the Summary DePTH field 1 0 Blue Fitted Red Filtered 0 8 _ 0 6 w o w x 0 4 0 2 0 0 1000 500 0 500 1000 Depth nm Page 173 225 GDSC SMLM ImageJ Plugins If the Score anatysis option was selected the plugin will compute a histogram of the distance and signal factor for all matches Two histograms are computed The first is for all the fitted results that match a localisation This is plotted in blue and provides the upper limit that can be achieved by filtering The second is the histogram for all the fitted results that were accepted by the filter This is plotted in red The label shows the mean of each histogram in braces 250 Blue Fitted 55 02 Red Filtered 53 88 Frequency 0 50 100 150 Distance nm If the SHow taBLE Or Show summary Options are selected then plugin wil
140. ferent for each method This means that a more robust fitting method that has a higher recall may not be fairly compared against a poor fitting method that fails on all the difficult targets The poor method may have an artificially inflated precision because the worst fits were discarded A fair comparison between fitting methods is to store all the fitting results in memory Then when several different fitting methods have been run the average and standard deviation statistics are recomputed only for those localisations that were successfully fit by every method The Benchmark Anatysis plugin requires that the Fit Benchmark Data plugin has been run at least twice for a given set of benchmark data If a new set of benchmark data is created then any results in memory will be discarded The plugin will analyse the data for all localisations successfully fit by each method and produce a summary table as per the Fit Benchmark Data plugin The only difference is an additional column after the Reca column that provides the original recall OricReca t The recall column should be the same for each fitting method and in some cases may be much lower than the original recall indicating that some of the fitting methods have performed much worse than others It is now possible to judge the accuracy and precision of each method in a fair comparison on an equivalent dataset 9 10 Create Spot Data Creates a sparse image by simulating zero or one localisation per
141. ffects the performance of fitting routines if it is not constant for example cell walls may be visible as a change in low level fluorescence over a distance of a few pixels This uneven background will not be modelled by a fitting routine which assumes the background is constant Any local gradients in the background can be eliminated by assuming that all real fluorescence over a short time frame will be much higher than the other values for the pixels in the same location Using the median value for the pixel will approximate the background This can be subtract from the image data prior to fitting so that only fluorescent bursts are left for fitting The Mebian Fitter plugin will compute the median for each pixel column through the image i e all Z positions of the pixel using a rolling window The median can be calculated at every pixel or at intervals In the case of interval calculation then the intermediate points have linearly interpolated medians The median image either replaces the input image or is subtracted from the input image to produce an image with only localisations A bias offset is added to this image to allow noise to be modelled i e values below zero The following parameters can be specified Parameters Description Rapius The number of pixels to use for the median The median is calculated using a window of 2 X radius 1 INTERVAL The interval between slices to calculate the median An interval of 1 wil
142. filtering on a set of categorised localisation results and computes match statistics for each filter The Fitter Anatysis Fite plugin is similar to the Fitter Anatysis plugin see section 7 9 The difference is that the plugin will not present options to create filters in the main dialogue Instead the filters are created from an input file that is selected following the main dialogue All other functionality is identical The filter file can specify thousands of different filters which are described using XML This allows combinations of filters to be specified using And and Or filters this is something that is not possible with the Fitter Analysis plugin A filter file can be generated from a filter template by enumerating the filter parameters using the Create Fitters plugin See section 7 10 7 12 Spot Analysis The Spot Analysis plugin is designed to allow analysis of fluorophore blinking kinetics using calibration images The plugin allows the user to extract an ROI outlining a fluorophore position from an image and manually mark the frames where a spot is visible A trace of the image intensity helps the user choose the brightest frames where a spot may be present The plugin records the signal on time and off time for the fluorophore to files for later analysis The plugin has been used to generate distributions for the signal per frame on times and off times for mEOS3 fluorophores captured at a frame rate of 50 frames a second 20
143. frame The Create Spot Data plugin is a modification of the Create Data plugin to remove the simulation of diffusing fluorophores The simulation draws localisations on 50 of the image frames Note that a maximum of one localisation is drawn per frame Each localisation is randomly positioned in the central 50 of the image The number of photons per localisation is randomly sampled from the range specified by the minimum to the maximum photons parameters The output of the plugin is an image and summary table as per the Create Dara plugin The Create Spot Data plugin records the details of the simulation in memory This data can be used with the Fitter Spot Data plugin to filter the image to identify candidate localisations and report statistics on the recall and precision of the results The following parameters can be configured Parameter Description PIXEL PITCH The simulated size of the pixel in the image in nm SIZE The width and height of the image in pixels DEPTH The depth of the simulation in nm Molecules will only be sampled within this volume Note that the output image is only 2D Set to zero to have no depth simulation Page 150 225 GDSC SMLM ImageJ Plugins Parameter Description FIXED DEPTH Select this to use the DeptH parameter as a fixed z coordinate This allows simulating out of focus spots BACKGROUND The background level in photons This is subject to Poisson noise Convert
144. g a fluorophore SNR The average signal to noise ratio SNR of a fluorophore SNR continuous The average signal to noise ratio SNR of fluorophores that were continuous for the entire frame DENSITY The localisation density calculated in the region defined by the Density Rabius parameter PRECISION The average precision in nm WIDTH The average PSF width in pixels 9 5 7 Compound molecules By default all the molecules are single particles However it may be desirable to simulate a collection of compound molecules for example dimers and hexamers This is possible using the Comrounb moLecuLes option If this option is selected the plugin will show a second dialogue where the user can input the molecule configuration using an XML specification The specification is a list of all the compounds that should be simulated Each compound has a fraction parameter The compound will be represented using the fraction divided by the total sum of all fractions to indicate the proportion of the compound Each compound also has a diffusion parameter When using compound molecules the Dirrusion parameter in the main plugin dialogue is ignored Note that the Fixen Fraction parameter is still used to fix a fraction of the compounds To gain more control over the moving molecules set the FIXED FRACTION parameter so zero Then simulate a mixed population of diffusing molecules and fixed molecules by specifying the same compounds twice one with
145. ge 5 225 GDSC SMLM ImageJ Plugins A 210 1L5 N0lse ESTIMA A 211 11 5 1 Mage Residir ao io ARAE ALAA 212 11 5 2 Noise estimation within the Peak Fit plUQiN occcccccncccocccnnccnncncconnccononononss 212 TEO Media A E a a ee eadea deans a angina E E eae 213 TEC OVEN AY Image A A AA O A 214 12 TOOlSet PIDA ici erieou prado SEEN 215 12 1 Install SMLM TOO Set ica tias 215 12 2 STOW SMEM TOA Sa ISA EE O E doen a aie 215 12 3 Create SMLM Tools COM i 217 Appendix A Localisation PrecisiON oooommmooooconononcnnnonnnnonnonnnnonnnnnnnonnnaronnconcoronnannnos 218 A e ea E a e a a Ena 218 A 2 Localisation Precision for Least Squares FIittiNQ oooconncccnccnnnnnnnnnnnnnnnnnnncnnnnnonos 218 A 3 Localisation Precision for Maximum Likelihood Fitting cccceeeeeeeeseeeeeeeeeees 219 Appendix B Comparison Mets iii ad sia 221 BARA A arios 221 B2 PreCISION ee CPR Peter e err re tem errr e reer rere ete Ptr ernr rete errr ent rer teeter rt Pere 221 A A e intinnes e E a E A E E A 221 B4 ESOO O a aia 222 BS FNR aro A i 222 OIDO E 222 B 7 Defining the Actual or Predicted POINTS cccccccnnncnncnnccnnnnninnnonineninininenineninininininass 222 B 8 Metrics requiring the True Negative COUNt cccccccccncnnncnnnnnnnnnnnonnnnnonononanncnnncnnnnnans 222 TS RefereNteS oraina iia 224 Page 6 225 GDSC SMLM ImageJ Plugins 1 Introduction Super resolution microscopy can be used to obtain a higher level of resolutio
146. gnal precision Limit X The theoretical limit of localisation precision for Least Squares Fitting Limit X ML The theoretical limit of localisation precision for Maximum Likelihood fitting REGION The actual size of the region used for fitting WIDTH The PSF width used for fitting METHOD The method used for fitting OPTIONS Additional options for the fitting method RECALL The fraction of localisations that were successfully fitted This does not indicate that the fitting was good only that it returned a result Page 148 225 GDSC SMLM ImageJ Plugins Field Description DB amp The average and standard deviation of the difference of the fit to the actual background DB amp The average difference of the fit to the average signal DSIGNAL amp The average and standard deviation of the difference of the fit to the average signal DANGLE amp The average and standard deviation of the difference of the fit to the angle All simulations will use a circular PSF so the actual angle is assumed to be zero This is only reported for the Free fit function DX amp The average and standard deviation of the difference of the fit to the actual X position DY amp The average and standard deviation of the difference of the fit to the actual Y position DSx amp The average and standard deviation of the difference of the fit to the actual PSF standard deviation in the X dimension
147. h of the filter e the number of pixels around a point that are used in the filter The actual region width is 2w 1 This allows comparison of the size of different filters FILTER The name of the first filter PARAM The parameter of the first filter DESCRIPTION The full description of the filter For a Dirrerence or Jury filter the full set of filters will be listed A BORDER The analysis border D The match distance TP The overall number of true positives FP The overall number of false positives Page 155 225 GDSC SMLM ImageJ Plugins Field Description RECALL The overall recall PRECISION The overall precision JACCARD The overall Jaccard TP The number of true positives at the configured fraction of the maximum recall FP The number of false positives at the configured fraction of the maximum recall RECALL The recall at the configured fraction of the maximum recall PRECISION The precision at the configured fraction of the maximum recall JACCARD The Jaccard at the configured fraction of the maximum recall TP The number of true positives at the maximum Jaccard score FP The number of false positives at the maximum Jaccard score RECALL The recall at the maximum Jaccard score PRECISION The precision at the maximum Jaccard score JACCARD The maximum Jaccard score Time The total run time for filtering the image and ranking the candidates AUC The area
148. h record shows the ID centre X and centre Y of the ROI outlining the spot the total signal the number of blinks and then a chain of paired start and stop frames for each pulse This file contains all the information of the other files except the signal per frame see sicnaL TxT TON TXT Contains the on times for all the results TOFF TXT Contains the off times for all the results SIGNAL TXT Contains the signal for each frame The frame and signal are shown separated by a space A header line is added before the signal for each fluorophore showing the ID number of blinks and the total signal BLINKS TXT Contains the number of blinks for all the results Blinks are the number of dark times recorded for a fluorophore It is one less than the number of pulses on time events 7 13 Spot Analysis Add This plugin provides a named plugin command for the App button of the Spot Anatysis plugin Any named plugin command can be mapped to a hot key using ImageJ s PLucins gt SHORTCUTS gt CREATE SHORTCUT Command Thus the App button can be mapped by ImageJ to a keyboard shortcut This allows the user to scroll through an image generated by the Spot Analysis plugin using the standard left and right arrow keys to move between frames When a spot is present the user adds the spot to the list by clicking the App button on the Spot Anatysis window If the App command is mapped to a shortcut the user can perform the same ac
149. he analysis results This allows the plugin to be run Page 205 225 GDSC SMLM ImageJ Plugins with many different settings to view the effect on the calculated diffusion coefficient The following columns are reported Column Description DATASET The input dataset EXPOSURE TIME The dataset exposure time per frame D THRESHOLD The distance threshold Ex THRESHOLD The exclusion distance MIN LENGTH The minimum track length that was analysed TRUNCATE True if tracks were truncated to the min length INTERNAL True if internal distance were used FIT LENGTH The number of points fitted in the linear regression TRACES The number of traces analysed D The diffusion coefficient from MSD linear fitting JUMP DISTANCE The time distance used for jump analysis Jump D The diffusion coefficient s from jump analysis FRACTIONS The fractions of each population from jump analysis TOTAL SIGNAL The average total signal of each trace SIGNAL FRAME The average signal per frame of the localisations in a trace T ON The average on time of a trace This excludes the traces too short to be analysed The plugin will report the number of traces that were excluded using the length criteria and the fitting results to the ImageJ log This includes details of the jump analysis with the fitting results for each model e g 783 Traces filtered to 117 using minimu
150. he camera The local background will provide more contextual information about the localisation precision and may be preferred if fitting localisations where the image background is highly variable If using precision filtering the plugin will ask the user if they wish to perform the calculation using the local background If using a local background then the camera bias must be provided so that the background photons can be correctly determined 5 2 7 Results Parameters Control where the list of localisations will be recorded Parameters have been grouped in the following table by background colour for different outputs Table Image File and Memory Page 38 225 GDSC SMLM ImageJ Plugins Parameter Description Los PROGRESS Outputs a lot of logging information to the ImageJ log window Used for debugging the fitting algorithm Logging slows down the program and should normally be disabled SHOW DEVIATIONS Calculate the estimated deviations for the fitted parameters These are shown in the table output and saved to the results files Note that the deviations are not used for filtering bad fits so should be disabled to improve speed performance Table Results RESULTS TABLE Show all the fitting results in an ImageJ result table e None No results table e Calibrated Output the result positions and widths in nm and values in photons e Uncalibrated Output the result positions and widths in pixe
151. he difference can be so great that some localisations are not visible The Binary Display plugin converts all non zero pixels to the value 1 This allows the user to see any pixel that contains any level of localisation This mode may be useful for drawing regions of interest ROIs around dense sections of localisations Note that the data for the image are directly updated The data can be reset using the Reset DisPLay plugin 11 3 Reset Display Resets a binary image generated by Binary Display back to the standard display This will only work for stack images if the user remains at the same slice position Moving to a new slice and back will delete the information used to reset the image 11 4 Pixel Filter Perform filtering to replace hot pixels from an image The Pixel Fitter is a simple plugin that will replace pixels with the mean of the surrounding region if they are more than N standard deviations from the mean The filter is designed to remove outlier hot pixels that are much brighter then their neighbour pixels These pixels will be identified as candidate maxima by the Peak Fit plugin although they are not suitable for Gaussian fitting The filter operates on the currently selected image The preview option allows the results of the filter to be viewed before running the filter on the current frame or optionally the entire image stack The filter uses a cumulative sum and sum of squares lookup table to compute the region mean a
152. he minimum score for a match between a fitted localisation and the true localisation The distance is expressed relative to the PSF width used to generate the data LOWER DISTANCE The distance limit defining the maximum score for a match between a fitted localisation and the true localisation The distance is expressed relative to the PSF width used to generate the data Set to the same as the March pistance to ignore the ramped scoring function MATCH SIGNAL Define the limit for the difference between the fitted signal and the actual signal for a match A value of N 1 indicates the fit is allowed to be N fold different i e use 2 for a 3 fold difference Set to zero to ignore Page 158 225 GDSC SMLM ImageJ Plugins Parameter Description InrriaL StoDev The initial 2D Gaussian standard deviation for fitting The width is expressed in pixels By default it is set using the configured width of the PSF used to generate the data and should not need adjusting unless it is intended to benchmark an incorrectly calibrated fitting algorithm FITTING WIDTH Define the size of the region around a candidate to use for fitting The region size in pixels is set using the Fittinc wiotH multiplied by the Initia StpDev FIT SOLVER Define the solver used for fitting Depending on the chosen solver a second dialog box will be presented to allow further configuration See section 5 2 4 Fitting Parameters Fit
153. he wavelength of light used for the image lambda NUMERICAL APERTURE The objective numerical aperture NA PRoPORTIONALITY Factor The proportionality factor set to 1 to match the Gaussian to the Airy profile ADJUST FOR SQUARE PIXELS Perform square pixel adjustment set to false to match the Gaussian to the Airy profile Airy WibTH Nm The calculated PSF Airy width in nanometres Airy WibTH PIXELS The calculated PSF Airy width in pixels SToDev nm The calculated PSF Gaussian standard deviation in nanometres StoDev PIxELS The calculated PSF Gaussian standard deviation in pixels HWHM pixeLs The calculated PSF Gaussian HWHM in pixels Note that the first three fields are only used to calculated the image pixel pitch If this is already known then it can be entered into the PixeL pitcH um field note the use of micrometres and not nanometres and the Maenirication and Beam ExPANDER Can be set to 1 The Pixet pitcH in nanometres is then used to convert the calculated widths in nanometers to pixel dimensions Clicking OK will save the PSF standard deviation in pixels to the global properties This will be used in the Peak Fit plugin Please contact a herbert sussex ac uk if you have feedback on the calculated width from the plugin verses your measured PSF using quantum dots or other single point light sources on calibration images 10 2 PSF Estimator A plugin that estimates the PSF using a test im
154. hed average for the profile plots 7 12 2 1 Profiling a spot region The first action is to select a spot on the input image using a rectangular ROI It is difficult to see spots on the input image which has many frames and very few fluorescent bursts Consequently it is recommended that an overview image is created to allow the spots to be identified This could be a maximum or average intensity projection of the input image However it is best to identify spots using the Fino Peaks plugin and then reconstruct an image using the fitted PSFs If the image scale is set to 1 then the reconstructed image is the same size as the input image This allows spots to be outlined on the PSF image and then the ROI reapplied to the original image An example of this is show in Illustration 23 When a suitable spot has been outlined the region can be analysed using the ProriLe button The analysis extracts the region into a new image named Spot Anatysis Raw spot This is magnified to allow easier viewing The same region is subjected to a Gaussian blur and extracted to a new image name Spot Analysis Buur spot The blurred image can make it easier to See peaks in very noisy images In addition an average intensity projection is created for the spot region and named Spot Anatysis Averace spoT The average image can indicate if the spot is fixed and central moves around the image or overlaps with other signal An example of the raw blur and average images are
155. hin this volume Note that the output image is only 2D Set to zero to have no depth simulation Page 142 225 GDSC SMLM ImageJ Plugins Parameter Description FIXED DEPTH Select this to use the DeptH parameter as a fixed z coordinate This allows simulating out of focus spots BACKGROUND The background level in photons This is subject to Poisson noise Convert to actual ADU value by multiplying by the product of the camera gain EM gain and quantum efficiency EM Gain The EM gain of the simulated camera CAMERA GAIN The camera gain in ADU electron QUANTUM EFFICIENCY The efficiency converting photons to electrons in the camera READ NOISE The average Gaussian read noise to add to each pixel in electrons Bias The bias offset to add to the image Allows negative noise values to be displayed PSF MobeL Specify the PSF model to use The Imace PSF option is only available if a valid PSF image is open ENTER WIDTH Select this option to enter the PSF width in nm for the Gaussian Airy PSF A second dialog will prompt the user for the PSF SD Standard Deviation For an Airy PSF the SD is converted to the Airy pattern width by dividing by 1 323 If not selected a second dialog will prompt the user for the emission wavelength of the fluorophore and the numerical aperture of the microscope These will be used to define the PSF width DISTRIBUTION The random distribution of
156. hods Median Filter Compute the median of an image on a per pixel basis using a rolling window at set intervals Overlay Image Allow an image to be added as an overlay with a transparent background All of the plugins can be incorporated into ImageJ macros to allow automation of image analysis workflows Page 13 225 GDSC SMLM ImageJ Plugins 2 Background 2 1 Diffraction limit of light microscopy Light microscopy uses lens optics to focus light from a sample onto an imaging plane However even with a perfect set of optics it is not possible to bring all the light into perfect focus This is because light is diffracted when passing through an opening The diffraction pattern resulting from a uniformly illuminated circular aperture has a bright region in the centre known as the Airy disk which together with the series of concentric bright rings around is called the Airy pattern see Illustration 2 0 0 0 2 0 4 0 6 0 8 1 0 Illustration 2 A computer generated image of an Airy pattern Image taken from Wikimedia Commons The inability to perfectly focus light sets a limit on the resolution that can be achieved using conventional light microscopy The Rayleigh criterion for barely resolving two objects that are point sources of light is that the centre of the Airy disk for the first object occurs at the first minimum of the Airy disk of the second This separation can be calculated from the followi
157. hore enters dark state 2 from each repetition of the on state Set to zero to use a single dark state model Page 137 225 GDSC SMLM ImageJ Plugins Parameter Description Use GEOMETRIC DISTRIBUTION If true the blinks will be sampled from a geometric distribution otherwise a Poisson distribution is used MIN PHOTONS The minimum number of photons a fluorophore must emit to be included in a time frame Min SNR 71 The minimum signal to noise ratio for a fluorophore that is on in a single time frame Min SNR TN The minimum signal to noise ratio for a fluorophore that is on in consecutive time frames In theory it should be easier to see a spot that is on for consecutive frames and so this parameter should be lower than Min SNR T1 Raw IMAGE Select this option to output an image using 32 bit floating point numbers The default is to use 16 bit unsigned integers SAVE IMAGE Show a dialog allowing the image to be saved as a file SAVE IMAGE RESULTS Show a dialog allowing the image localisations to be saved as a PeakResults file Note that this does not contain the molecule Z position Save FLUOROPHORES Show a dialog allowing the fluorophores to be saved The file contains the number of blinks and the on and off times for each fluorophore to the thousandth of a second Save LOCALISATIONS Show a dialog allowing the localisations to be saved The file contains the time and X Y
158. ifications A good guess would be 25 50 NOISE ESTIMATE The initial estimate for the camera read noise The read noise in electrons may be obtained from the camera manufacturer s specifications This will have to be converted to ADUs by applying the camera gain not the total gain A good guess would be 3 10 SHOW APPROXIMATION Show on the final output plot a function that approximates the convolution of the Poisson Gamma distribution with a Gaussian distribution This approximate PMF is used to model the EM Gain when performing Maximum Likelihood Estimation fitting within the Peak Fit plugin Note that the plugin will remember the last values that were fitted for the bias gain and noise estimates Thus an initial guess can be used the image analysed and then the plugin repeated with updates to the estimates if appropriate to refine the fit 10 5 4 Simulation Mode Instead of using an input image to create a histogram of pixel values it is possible to simulate pixel values by generating a Poisson Gamma Gaussian random variable To run the plugin in simulation mode hold down the Shirr key when running the plugin The following additional parameters will be available Parameter Description SIMULATE Check this box to simulate the histogram of pixel values Page 191 225 GDSC SMLM ImageJ Plugins Parameter Description Bias The camera bias for the simulation Gain The total gain
159. ifications and various comparison metrics are generated allowing the best filter to be identified 7 9 1 Input Data The plugin requires a folder containing the results of running Peak Fit on one or more images The results will contain the X and Y coordinates X and Y standard deviations and amplitude of the Gaussian function The results will also contain the original pixel value of the peak candidate location This column must be updated to contain a zero for any result that is incorrect and a non zero value for any result that is correct The classification of spots can be performed using any method One successful data preparation method employed by the authors was to manually inspect a set of super resolution images and extract entire stacks from the image containing suitable spots These stacks should contain both on and off frames for the fluorophore and examples of good medium and poor spots that could still be identified manually The example spots were then manually scored by multiple researchers and a jury system used to score if the frame contained a spot or not The images were fitted using Peak Fit and the results files updated using the jury classification to mark results as correct incorrect When the plugin is run the user must select a directory The plugin will attempt to read all the files in the directory as PeakResults files The results are cached in memory If the same directory is selected the user can opt to re use the resu
160. ift correction SAVE DRIFT Save the drift curve to file The plugin will prompt the user for a filename The drift curve can later be loaded by the Drirt Calculator plugin using the Fite option for the MetHop parameter Note that if the drift correction is used to update the results then only the results held in memory will change Any derived output for example a table of the results or a reconstructed image will have to be regenerated from the new results Example images showing the original and drift corrected localisations following sub image alignment are shown in Illustration 14 The drift correction curve for the image data is shown in Illustration 12 Note how drift correction has removed the blur from the main image and resolved smeared spots into single points Page 71 225 GDSC SMLM ImageJ Plugins Illustration 14 Example of drift correction Left Original localisations Right Drift corrected localisations Details of the different drift calculation methods are shown below 7 AL Localisation Sub images If the localisations represent a structural image then a subset of the localisations will also represent the same structure Where there are a large number of localisations for example in STORM images it is possible to create sub images from sub sets of the data and align them The Locatisation sus imaces method performs the following steps Initialise the drift for each time point to zero Produce
161. ilable in Peak Fit This is done using the Fitter Spot Data and Fit Spot Data plugins The results can then be subjected to different filters to determine the best filter 9 13 1 Input Filters The plugin is able to process thousands of filters by loading the filters from a file The file describing the filters can be created using the Create Fitters plugin When all the parameters for the plugin are configured the plugin prompts the user for a filter file Loading filters may take a long time so if the filename selected for the filters is the same as the last set of loaded filters the plugin will ask if you would like to re use the filters that were previously loaded Filters are grouped into sets Each set is processed separately This allows results to be shown per filter and then as a summary of the best results per filter set This allows different types of filters to be compared in a summary table 9 13 1 1 Expanding Filter Sets Note that the plugin will detect if a filter set only contains 3 filters and determine if it can be expanded The criteria for expansion are that the second filter has a value for each parameter equal or above the first filter The first filter then forms the minimum value and the second filter the maximum value The third filter must then have a value that is positive for each parameter where the second filter value was above the first filter value The third filter then forms the increment for the parameters This m
162. ill be correctly adjusted to the next integer The score is recomputed using the new parameter value following a positive or negative change The average rate of change of the score is then computed The sensitivity is output for the Jaccard Precision and Recall scores Two scores are output a the raw average change titled Sensitivity betta or b the average change divided by the change in the parameter value titled Sensitivity unit 7 10 Create Filters The Create Fitters plugin can be used to prepare a large set of filters for use in the Fitter Anavysis Fite plugin see section 7 11 The purpose is to create a set of filters that can be applied to a testing dataset to identify the best filter The plugin dialog shows a text area where a filter template can be specified as shown in Page 100 225 GDSC SMLM ImageJ Plugins Illustration 22 If the SHow emo Fitters Checkbox is selected then several example filters will be recorded in the ImageJ log Ly Nis Create Alters Y A x Create a set of filters for use in the Filter Analysis plugin Attributes will be enumerated if they are of the form min max increment lt SNRFilter snr 10 20 1 gt lt PrecisionFilter precision 30 50 2 gt Y Enumerate early attributes first Show demo filters Cancel Help Illustration 22 Create Filters plugin dialogue The filter template must be valid XML elements Each element should take the format of
163. ilter Spot filter2 Mean Smoothing2 3 00 Y Preview OK Cancel Help b L 3 ij Eocalisal D amp Smooth Image Y A X 1 um 64x64 16 bit 80K 1 10 6 91x6 9 Smooth image Spot filter Mean Smoothing Y Difference filter Spot filter2 Mean Smoothing2 3 00 Preview Cancel Help k Illustration 43 Smooth image dialogue with the preview applied to the current image A Standard smoothing for a 16 bit image B Difference of smoothing for a 32 bit image Use the Preview button to see the effect of smoothing If you click OK the plugin will perform smoothing on the entire stack or optionally just the current frame 11 1 1 Smoothing within the Peak Fit plugin Note that the Peak Fit plugin calculates the smoothing window size using a factor of the PSF width This can result in a non integer value Algorithms that require integer window sizes e g Block mean median have the window size rounded down to the nearest integer to avoid over smoothing Page 209 225 GDSC SMLM ImageJ Plugins Most images analysed within the Peak Fit plugin will use a filter size less than 4 due to the small size of the PSF from single molecule microscopy 11 2 Binary Display Switches an image to binary white black to allow quick visualisation of localisations The SMLM plugins contain several methods for generating an image Often images are created with a large difference in value for pixels that contain localisations T
164. images to the frequency domain e Compute the FRC between the two images at all the available frequencies e Plot the FRC against the frequency This will gradually fall to zero as the frequency decreases see Illustration 28 e Use the FRC curve to look up the spatial frequency corresponding to a correlation cut off limit The spatial frequency at the correlation limit is the Fourier Image Resolution FIRE This can be interpreted as stating that there is no meaningful similarity information at any frequency higher than the resolution i e if the image was reconstructed using only frequencies at this level and above then it would be not be recognised as matching itself The plugin will display progress of the computation on the ImageJ status bar When the plugin has finished the FIRE number will be reported to the ImageJ log window The FRC plugin provides the following options Parameters Description INPUT The results set to analyse Ranpom SPLIT If true then the data is split randomly into two halves Otherwise the data is split by alternating frames simulating an image acquisition on the microscope FOURIER IMAGE SCALE Specify the image enlargement scale to create the super resolution image from the localisation data Auto will create an image that is 2048 pixels on the long edge this size should fit into memory SAMPLING FACTOR The FRC is calculated by sampling the circle at N points where N is equal to 271r x sampling
165. imation are described below Parameter Description Number or Peaks The number of fitted peaks to use to estimate the Gaussian parameters The parameters are estimated by averaging across all the fitted peaks P VALUE The p value to use for significance testing e are the parameters the same using a Student s T test at the given significance UPDATES PREFERENCES If selected the plugin will update the global configuration with the calculated PSF values Los PROGRESS Log progress of the estimator to the ImageJ log window Page 182 225 GDSC SMLM ImageJ Plugins Parameter Description ITERATE When the PSF parameters have converged and a Free fitting option was chosen a test is done to determine if the angle or Y width are significant If not then the estimator will restart ignoring the insignificant parameter from the modelled PSF The order of iterations is Free gt Free CIRCULAR gt CIRCULAR Note these statistics often don t work so unless you expect astigmatism you can choose to start with a Circular Gaussian and just find the estimated widths SHOW HISTOGRAMS Show a histogram of the estimated parameters from the final fitting run A histogram is shown for each parameter These can be used to verify the mean of the parameter distribution is a suitable estimate for the parameter HisTOGRAM BINS The number of bins to use on the histograms Page 183 225 GDSC SMLM ImageJ
166. imation is the processes of fitting a function expected values to a set of observed values The fit attempts to minimise the sum of the squared difference between observed O and expected E ss O EY The parameters for the expected function are updated until no improvement can be made The estimation process uses the popular Levenberg Marquardt LVM algorithm which uses the gradient of the function e how the function value will change with a change to the parameters to choose how to modify the parameters The Peak Fit plugin offers two version of the algorithm One version uses the Hessian matrix of partial derivatives i e it is a Full Newton method for finding roots of equations This is a matrix of the gradient of Page 29 225 GDSC SMLM ImageJ Plugins the function with respect to two parameters for all combinations of parameters The method must compute the matrix and invert it and this can lead to numerical instability with floating point numbers for example if one parameter has a very small gradient with respect to any of the other parameters The second uses only the Jacobian matrix of partial derivatives This is a matrix of the gradient with respect to each parameter at each data point The Jacobian is used to approximate and update the inverted Hessian i e it is a quasi Newton method and is less prone to instability This method is provided by an external library Apache Commons Maths The custom made GDSC routines ar
167. imulated localisations using everything that was passed through the filter Positives The results table indicates this by prefixing the score column titles with o for Original This score is comparable when a different spot candidate filter has been used and the total number of candidates is different e g Mean filtering vs Gaussian filtering Note that in this scheme there is no TN total and so the number of comparison metrics that can be computed are reduced to recall precision Jaccard and F1 score The original score metrics are used by default for selection and ranking 9 13 2 1 Ranking filters When all the scores have been computed for the filters in a filter set the filters are ranked Ranking is performed using two chosen scoring metrics The first metric is chosen as a minimum limit that must be achieved this is the Criteria metric The second metric is chosen to rank all the filters that pass the criteria this is the Score metric If no filters pass the criteria then a warning is written to the ImaceJ log window This ranking system allows filters to be restricted to those that function at a minimum desired level and then ranked For example assessing all filters that achieve 95 precision and then ranking by recall would pick the best filter for high confidence in the results and assessing all filters that achieve 80 recall and then ranking by precision would pick the best filter for returning a high number of localisations but pote
168. in a sphere In this case the diffusion step is calculated and if the step would move the particle outside the sphere the move is rejected Attempts are made to move the particle a set number of times until successful otherwise the particle coordinates are not updated This simulation produces good results when the average step size is at least an order of magnitude less than the sphere radius So allowing many steps inside the sphere to be valid Page 195 225 GDSC SMLM ImageJ Plugins 10 7 4 Analysis The Dirrusion Rate Test plugin simulated the random diffusion of many particles over a period of time Each diffusion path is then analysed The plugin has the following parameters Parameters Description PIXEL PITCH NM The pixel size for the simulation SECONDS The duration of the simulation STEPS PER SECOND The number of diffusion steps the particle makes per second PARTICLES The number of particles to simulate DIFFUSION RATE The diffusion coefficient D USE GRID WALK If true then simulate diffusion using a grid walk otherwise use a random move The grid walk simulation is approximately 3 times faster USE CONFINEMENT If true then use a sphere to confine the particle movement CONFINEMENT ATTEMPTS The number of times to attempt a confined move CONFINEMENT RADIUS The radius of the confinement sphere Fit N When using confined diffusion only fit the first
169. in the Peak Fit plugin and allows much faster fitting since the Poisson PMF a can be evaluated much faster than the Poisson Gamma Gaussian PMF and b has an analytical derivative allowing derivative based fitting methods Page 194 225 GDSC SMLM ImageJ Plugins 10 7 Diffusion Rate Test The Dirrusion Rate Test plugin will simulate molecule diffusion and fit a graph of mean squared displacement to determine the diffusion coefficient This is a test plugin to show that the simulated diffusion in the Create Data plugin generates correct moving particles When a molecule is diffusing it can move in any direction The total distance it moves and the track it took may not be visible due to the speed of movement However the diffusion of particles is a single dimension can be modelled as a population If the squared distances from the origin after a set time are plotted as a histogram they can be modelled using a Gaussian curve The average distance the particles will move is zero and the standard deviation of the Gaussian curve will be the mean squared displacement MSD This can be expressed by unit time The MSD is proportional to the diffusion coefficient D The relationship for a single dimension is MSD 2D This increases to 4D and 6D for two and three dimensional distances since the diffusion in each dimension is independent 10 7 1 Grid Walk simulation Since the MSD in a single dimension is 2D the mean distance a particle moves will b
170. in the image MetHop1 is shown in blue MetHop2 is shown in red If you click OK the plugin will compute all the estimation methods for the entire stack or optionally just the current frame and display the results in a table The following noise methods are available Method Description ALL PIXELS The standard deviation of the pixels Page 211 225 GDSC SMLM ImageJ Plugins Lowest PIXELS The standard deviation of a box region around the lowest intensity pixel in the image The box region can be adjusted using the Lowest rapius parameter This is the method used within QuickPALM Henriques et a 2010 and can produce inconsistent noise levels between frames due to the small sample size ResipuaLs Least MEDIAN OF SQUARES Calculate the median of the residuals Then use this to estimate the standard deviation of the residuals ResipuaLs LEAST TRIMMED SQUARE ESTIMATOR Square the residuals Sum the smallest half of the squared residuals Then use this to estimate the standard deviation of the residuals This is insensitive to high intensity pixels Resipuacs Least MEAN SQUARE ESTIMATOR Calculate the standard deviation of the residuals Quick ResipuaLs LEAST Mebian OF SQUARES As before but ignore pixels on the image boundary Quick ResipuaLs LEAST TRIMMED SQUARE ESTIMATOR As before but ignore pixels on the image boundary Quick ResipuaLs Least Mean Square ESTIMATOR
171. in width lo Single region size 10 Block find algorithm Initial StdDev 0 000 Neighbour check Log progress Border A lo Show deviations Filter results W Preview OK Cancel Illustration 11 Gaussian Fit plugin with live preview of the candidate peaks on the active image The plugin is designed to work on rectangular regions of an image or the whole image It will work best in the following situation 1 The background level is constant across the image 2 The peaks are distinct and well separated e g over 40 of the peak height is clearly visible away from any other peak The plugin works using a two stage process 1 Identify peaks on a smoothed image using non maximal suppression 2 Fit all the peaks simultaneously using a 2D Gaussian with a global background Page 53 225 GDSC SMLM ImageJ Plugins 5 10 1 Maxima Identification Pixels are smoothed using a box filter of 2n 1 Square dimensions around each pixel Non integer smoothing sizes are supported using a weight for the edge pixels Peaks are selected if they are higher than all other pixels in a 2n 1 box region The box can be a different size from the smoothing window The peaks must also satisfy the criteria of minimum height above the defined background minimum width and a certain distance from the edge of the ROI When you run the plugin you can enable a preview checkbox at the bottom of the dialogue This will draw on the image the current
172. ince the matches of results to localisations are computed within that program Page 168 225 GDSC SMLM ImageJ Plugins Parameter Description PARTIAL MATCH DISTANCE The distance limit defining the maximum score 1 for a match between a fitted localisation and the true localisation The value is expressed relative to the match distance used with the Fit Spot Dara plugin since the matches of results to localisations are computed within that program Set to the same as the Upper march DISTANCE to ignore the ramped scoring function Otherwise matches at a distance between Partial and UPPER MATCH DISTANCE Will have a score between 0 and 1 UPPER SIGNAL FACTOR The signal factor defining the minimum score for a match between a fitted localisation and the true localisation The value is expressed relative to the signal factor used with the Fit Spot Data plugin since the matches of results to localisations are computed within that program PARTIAL SIGNAL FACTOR The signal factor defining the maximum score for a match between a fitted localisation and the true localisation The value is expressed relative to the signal factor used with the Fit Spot Data plugin since the matches of results to localisations are computed within that program Set to the same as the Upper sicnat pistance to ignore the ramped scoring function Otherwise matches with a signal factor PartiaL and Upper sIGNAL FACTOR Will have a score bet
173. ind the best fitter amp filter combination for the given spot candidates The ideal combination would correctly fit amp pick all the candidate positions that are close to a localisation and reject all other candidates The following scoring scheme is used Candidates TN Actual matches FN Fitted Spots Positives Negatives Where Candidates All the spot candidates Actual matches Any spot candidate or fitted spot candidate that matches a localisation Page 163 225 GDSC SMLM ImageJ Plugins Fitted spots Any spot candidate that was successfully fitted Positives Any fitted spot that was accepted by the filter Negatives Any fitted spot that was rejected by the filter TP True Positive A spot candidate that was fitted and matches a localisation and is accepted FP False Positive A spot candidate that was fitted but does not match a localisation and is accepted FN False Negative A spot candidate that failed to be fitted but matches a localisation or a spot candidate that was fitted and matches a localisation and is rejected TN True Negative A spot candidate that failed to be fitted and does not match a localisation or a spot candidate that was fitted and does not match a localisation and is rejected Classically a match is assigned if a predicted result and a localisation are within a distance threshold This makes the choice of distance threshold critical It also means that methods that ge
174. ined image composed of pixels that are maxima Analysis of simple Jury filters has shown that they have high recall but lower precision than single filters e g a Since Mean with smoothing 1 3 verses a Jury of Mean 1 Mean 2 and Mean 3 Page 28 225 GDSC SMLM ImageJ Plugins 5 2 4 Fitting Parameters Parameter Description Fit SoLveR Specify the method used to fit the maxima e LSE Use the GDSC Least Squares Estimator LSE fitting algorithm based on the Hessian matrix of partial derivatives e WLSE Use the GDSC Weighted Least Squares Estimation e LSEgqn Use the Apache Commons LSE fitting algorithm based on the Jacobian matrix of partial derivatives MLE Use Maximum Likelihood Estimation Note The LVM method is fastest MLE is the most precise smallest error Individual Fit Sowver methods may require further parameters which are detailed in the following section Fit FUNCTION Specify the type of 2D Gaussian function to fit e Fixed Fits X Y centre and amplitude e Circular Fits X Y centre combined X Y deviation and amplitude e Free Circular Fits X Y centre individual X Y deviation and amplitude e Free Fits X Y centre individual X Y deviation rotation angle and amplitude Fait Limit Stop processing the image frame when N consecutive fits fail This prevents attempting to fit the remaining candidates that have a lower signal 5 2 4 1 Least Squares Estimation Least squares est
175. ined in either result set 2 5 Total S otal Score ian pep The number of time points p is equal to the count of the number of individual localisations in the results before tracing p gt tEnd tStart 1 where tStart is the trace start time and tEnd is the trace end time The normalisation penalises the score if either result set contains many unmatched or partially matched traces The overall score should have a value between 0 and 1 The score metrics are shown in a results table Optionally a table of the matched pairs can be displayed showing the matched and unmatched localisations The pairs table supports interactive identification of the selected points on the source image This is the same functionality as the Resutts March Catcutator See 6 10 1 Any previous results in the pairs table will be cleared The plugin can compare one or two results sets to the same reference This allows the user to compare different tracing results to a benchmark for example the results of tracing raw localisations can be be compared to tracing filtered localisations If two test sets are input then the matched pairs table will contain additional columns to display triples The following parameters can be set Parameters Description Resuts1 The first results set the reference Resu_ts2 The second results set test set 1 ResuLTs3 The third results set test set 2 optional DISTANCE The minimum distance for a match
176. ing algorithm will not be expected to perform matches consistently below this limit In practice though it is usually fair to set the lower distance as 33 50 of the Abbe limit As well as matching the localisation position it is possible to assign matches using the fitted signal The signal factor is computed within the Fit Spot Data plugin and is a measure of how far the fitted signal was from the true localisation number of photons Matches can be rejected if they are above a threshold and as for the distance match a ramped score is available using a ramped scoring function In the case that ramped scoring is used for both distance and signal factor then the final match score is the product of the two ramped scores The remaining unmatched score is set so the total for the result is 1 Page 164 225 GDSC SMLM ImageJ Plugins The totals TP FP TN FN must equal the number of spot candidates This allows different fitting methods to be compared since the total number of candidates is the same The TP FP TN and FN totals can be used to compute scores as detailed in Appendix B Comparison Metrics As an alternative scoring system different fitting methods can be compared using the same TP value but calculating FN localisations TP and FP as Positives TP In this scheme FN represents any original spots that were missed and FP represents the number of accepted fits that do not match an original spot This creates a score against the original s
177. ing the same approximation formula as the PSF CaLcuLator plugin Alternatively the width can be specified explicitly in the plugin The width changes using a z defocussed exponential model The width is scaled using the following formula Scale 1 exp z In 2 zDepth where z is the z position relative to the focal plane z 0 and zDepth is the depth at which the width should be double The zDepth constant is set at 500nm This approximately matches the width spread of the PSF observed using quantum dots on the wide field super resolution microscope at the GDSC PSF sampling is done by drawing a Gaussian random variable for the X and Y coordinates and then adding this location to the image 9 5 2 2 Airy PSF The Airy PSF uses the Airy pattern to describe the PSF The width of the Airy pattern is obtained from the microscope parameters using the same formula as the PSF CatcuLator plugin The Airy PSF is valid for a z depth of zero However the software does not implement an advanced defocussed PSF model for the Airy pattern When defocussed the width changes using a z defocussed exponential model as per the Gaussian PSF PSF sampling is done by constructing a cumulative Airy pattern i e power of the Airy pattern for all distances up to the 4 zero ring This is approximately 95 2 of the entire Airy pattern power Note however that the pattern diminishes gradually to infinity so sampling beyond this ring is not practical Arandom sample
178. ion UPDATE FIT CONFIGURATION Run the Fit Conricuration plugin to allow the fitting parameters to be updated The WiTH Factor should be set to allow very wide out of focus spots e g 5 and the Sicnat sTrencTH Should allow poor spots e g 30 NM PER SLICE The z slice step size used when acquiring the calibration image Rapius The square radius around each marked point to use for analysis Any spot within 2 x radius will eliminate the spot from analysis AMPLITUDE FRACTION The fraction of the peak amplitude to use to mark the in focus spot START BACKGROUND FRAMES The number of initial frames to use to calculate the background Page 119 225 GDSC SMLM ImageJ Plugins Parameters Description END BACKGROUND FRAMES The number of final frames to use to calculate the background MAGNIFICATION The magnification to use when enlarging the final PSF image SMOOTHING The LOESS smoothing parameter CENTRE EACH SLICE Set the centre of each slice the to the centre of mass Note that using this option may cause consecutive frames to shift erratically A better approach is to disable this and compute a drift curve using the PSF Driet plugin CoM cur oFF The amplitude cut off for pixels to be included in the centre of mass calculation Any pixels below this fraction of the maximum pixel intensity are ignored as noise INTERACTIVE MODE Set to true to manually accept reject each spot ana
179. ion molecules The appearance of the fluorophore is modelled using a configurable point spread function PSF When the molecules have been simulated the results can be filtered to remove low signal spots This allows the Create Data plugin to generate images at a certain signal to noise ratio for benchmarking experiments The simulation creates an ImageJ image stack and the underlying data can be saved in various formats The raw localisations per frame are also written to a results set in memory Page 130 225 GDSC SMLM ImageJ Plugins allowing the results of fitting the simulated image to be compared to the actual underlying data The simulation computes the fluorophores using a single worker thread The time intensive rendering of the localisations as an image is multi threaded The number of threads uses the ImageJ setting under Ebir gt Options gt Memory amp THREADS 9 5 2 Point Spread Function The appearance of the fluorophore is modelled using a configurable point spread function PSF The number of photons in the fluorophore is used to create a Poisson random variable of the number photons N that are actually observed The PSF is then sampled randomly N times and each sample is mapped from the PSF coordinates on to the correct pixel in the image 9 5 2 1 Gaussian PSF The Gaussian PSF uses a 2D Gaussian function The width of the Gaussian is obtained from the microscope parameters wavelength and Numerical Aperture us
180. ion should return a solution that is more precise than least squares estimation i e has less variation between the fitted result and the actual answer MLE should be operating at the theoretical limit for fitting given how much information is actually present in the pixels This limit is the Cram r Roa lower bound which expresses a lower bound on the variance of estimators of a deterministic parameter MLE has also been proven to be robust to the position of the localisation within the pixel whereas least squares estimation is less precise the further the localisation is from the pixel centre Abraham et al 2009 Therefore MLE should be used if you would like the best possible fitting However it requires additional parameters which if configured incorrectly will lead to fitting results that are not as precise as the least squares estimators If you are fitting localisations with a high signal then the Poisson model will work This model also has the advantage of requiring only the camera bias If unknown then this can be guessed from a low light image using the darkest part of the frame The Poisson model allows use of the derivative based BFGS algorithm and is fast Page 35 225 GDSC SMLM ImageJ Plugins At low signal levels other sources of noise beyond shot noise become more significant and the fitting will produce better results if they are included in the model This would mean choosing the Poisson Gaussian function slow for a standard
181. ipulation Toolset For install of the SMLM Toolset and configuration of the SMLM Tools window Page 18 225 GDSC SMLM ImageJ Plugins 5 Fitting Plugins The following plugins use the SMLM fitting engine to find and fit spots on an image It is vital that the method used by the software is understood when adjusting the parameters from the defaults Please refer to section 2 3 Localisation Fitting Method for more details The plugins are described in the following sections using the order presented on the PLucins gt GDSC SMLM gt Fittinc menu 5 1 Simple Fit The Simeue Fit plugin provides a single plugin to fit localisations on an image and produce a table and image reconstruction of the results The fitting is performed using the fitting defaults i e no fitting options are presented This simplifies the fitting process to a single click operation The plugin must be run when a single molecule image is the currently active window in ImageJ Each frame of the image will be analysed and the localisations recorded in a table and or drawn on a high resolution image reconstruction The fitting is performed using multi threaded code with a thread analysing each frame Consequently results can appear out of order in the results table The plugin dialog has a simple appearance as shown in Illustration 46 i i PeakHt x Dy amp Fit single molecule localisations Y Use current calibration Y Show table Show image Can
182. ise ratio N sqrt b2 s Px The standard deviation of the Gaussian profile that matches the PSF in pixels FILTER The full description of the filter used to identify the fitting candidates For a Dirrerence Or Jury filter the full set of filters will be listed Spots The number of filter candidates Page 160 225 GDSC SMLM ImageJ Plugins Field Description NP The number of filter candidates that identify a true localisation positives Note This result is computed with the distance thresholds set in the Fitter Spot Data plugin NN The number of filter candidates that do not identify a true localisation negatives SOLVER The fit solve used for fitting FITTING The fit window size used for fitting NP The fraction of positive candidates that were processed NN The fraction of negative candidates that were processed TOTAL The number of candidates that were processed cTP The number of candidates that match a true localisation Candidate True Positives cFP The number of candidates that do not match a true localisation Candidate False Positives CRECALL The recall of the candidates CPRECISION The precision of the candidates CJACCARD The Jaccard of the candidates cF1 The F1 score of the candidates Fait cTP The number of candidates that match a true localisation where fitting failed i e the algorithm did not return a result Fait cFP The number of candi
183. its of pixels Parameter Description InrriaL StoDevO Set the initial parameters for the 2D Gaussian InrriaL StoDev1 Set the initial parameters for the 2D Gaussian Used for independent X Y width fitting Free Circular Free Page 26 225 GDSC SMLM ImageJ Plugins InrriaL ANGLE Set the initial parameters for the 2D Gaussian Used for elliptical fitting Free 5 2 3 Maxima Identification Parameters Note that the smoothing search border and fitting width parameters are factors applied to the Gaussian function width Initia StoDev They have no units Parameter Description SPOT FILTER TYPE The type of filter to use The default is a Since filter If a DirrerENCE Or Jury filter is selected then the plugin will present an additional dialogue to configure each additional spot filter More details are given in the next section SPOT FILTER The name of the first spot filter Mean Compute the mean in a square region The region can be any size as the final edge pixels are given a weight using the region width Block mean Compute the mean in a square region The region is rounded to integer pixels Circular mean Compute the mean in an approximate circular region The circle is drawn using square pixels To see the circle mask use Process gt Fitters gt SHow Circular Masks Gaussian Perform Gaussian convolution The convolution kernel standard deviation is set to the Sm
184. ixels by the camera MODEL CAMERA NOISE Select this option to model the camera noise read noise and EM gain if applicable If unselected the MLE will use the Poisson noise model READ NOISE The camera read noise in ADUs Only applicable if using MopeL CAMERA Noise Gain The total camera gain Only applicable if using Mopet Camera Noise EM CCD Select this if using an EM CCD camera The Poisson Gamma Gaussian function will be used to model camera noise The alternative is the Poisson Gaussian function Only applicable if using Move Camera Noise SEARCH METHOD The search method to use It is recommended to use the Powell algorithm for any model The BFGS algorithm is a good alternative for the Poisson noise model SEARCH METHODS are detailed in the following section RELATIVE THRESHOLD Define the relative threshold for convergence ABSOLUTION THRESHOLD Define the absolute threshold for convergence Page 33 225 GDSC SMLM ImageJ Plugins Parameter Description Max ITERATIONS The maximum number of iterations Note that in contrast to the least squares estimators the function is evaluated multiple times per iteration Max FUNCTION The maximum number of times to evaluate the model EVALUATIONS 5 2 4 3 Search Methods Brief notes on the different algorithms and where to find more information are shown below for completeness It is recommended to use the Powell or BFGS methods
185. ject to Poisson noise Convert to actual ADU value by multiplying by the product of the camera gain EM gain and quantum efficiency EM cain The EM gain of the simulated camera CAMERA GAIN The camera gain in ADU electron Quantum EFFICIENCY The efficiency converting photons to electrons in the camera READ NOISE The average Gaussian read noise to add to each pixel in electrons Bias The bias offset to add to the image Allows negative noise values to be displayed PSF MobeL Specify the PSF model to use The Imace PSF option is only available if a valid PSF image is open ENTER WIDTH Select this option to enter the PSF width in nm for the Gaussian Airy PSF A second dialog will prompt the user for the PSF SD Standard Deviation For an Airy PSF the SD is converted to the Airy pattern width by dividing by 1 323 If not selected a second dialog will prompt the user for the emission wavelength of the fluorophore and the numerical aperture of the microscope These will be used to define the PSF width PARTICLES The number of molecules to simulate X POSITION The X position relative to the centre of the image in nm To place the localisation in the centre of a pixel set the Size parameter to an odd number Y POSITION The Y position relative to the centre of the image in nm To place the localisation in the centre of a pixel set the Size parameter to an odd number Z POSITION
186. l be listed Spots The number of filter candidates NP The number of filter candidates that identify a true localisation positives Note This result is computed with the distance thresholds set in the Fitter Spot Data plugin NN The number of filter candidates that do not identify a true localisation negatives SOLVER The fit solve used for fitting TITLE The True field from the plugin dialog is copied here Name The name of the filter Fait The fail count Lower D The lower match distance Upper D The upper match distance LOWER FACTOR The lower match signal factor UPPER FACTOR The upper match signal factor TP The true positive score FP The false positive score Page 175 225 GDSC SMLM ImageJ Plugins Field Description TN The true negative score FN The false negative score Merrics Configured score metrics computed using TP FP TN and FN See Appendix B Comparison Metrics oFP The original false positives score This is equal to the number of results that were accepted by the filter minus the TP oFN The original false negatives score This is equal to the number of localisations that were simulated minus the TP oMerrics The original score metrics computed using TP OFP and oFN See Appendix B Comparison Metrics The summary table contains the same fields as the results table The following additional columns are present Field Description
187. l display the results in a table The following fields are shown in the results tables Note that for brevity not all the metrics that can be selected by the user are described here See Appendix B Comparison Metrics for details of the metrics Field Description FRAMES The number of frames in the simulated image W The width of the simulated image minus the analysis border H The height of the simulated image minus the analysis border MoLEcuLES The number of molecules that occur within the bounds of the analysis border DensITY The molecule density within the analysis region N The average number of photons per localisation Ss The standard deviation of the Gaussian profile that matches the PSF A The pixel size DEPTH The z depth of the localisations FIXED True if the simulation used a fixed depth Page 174 225 GDSC SMLM ImageJ Plugins Field Description Gain The total gain of the simulation READNoIsE The read noise of the simulation B The background number of photons B2 The noise per pixel This is a combination of the read noise and the background number of photons SNR The signal to noise ratio N sqrt b2 s Px The standard deviation of the Gaussian profile that matches the PSF in pixels FILTER The full description of the filter used to identify the fitting candidates For a Dirrerence Or Jury filter the full set of filters wil
188. l produce a true rolling median Larger intervals will require interpolation for some pixels BLock SIZE The algorithm is multi threaded and processes a block of pixels on each thread in turn Specify the number of pixels to use ina block Larger blocks will require more memory due to the algorithm implementation for calculating rolling medians The number of threads is set in Epit gt Options gt Memory amp THREADS SUBTRACT Subtract the median image from the original image Bias If subtracting the median add a bias to the result image so that negative numbers can be modelled i e when the original image data is lower than the median Page 213 225 GDSC SMLM ImageJ Plugins 11 7 Overlay Image Allow an image to be added as an overlay with a transparent background Using a transparent background is not possible with the standard ImageJ Imace gt Overtay gt App IMAGE Command For example the super resolution image created from fitting localisations can be overlaid on the average z projection of the original image to show where the localisations occur The Overtay Imace plugin must be run after selecting the image to overlay The following parameters can be specified Parameters Description IMAGE TO ADD Select the image to use as the overlay The list only shows the images that are valid Overlay images must be equal or smaller in width and height than the target image X LO
189. language The following parameters are available Page 170 225 GDSC SMLM ImageJ Plugins Parameter Description POPULATION SIZE The size of the population to reach when producing new individuals A higher number will slow down the optimisation but may allow a better solution to be found FAILURE LIMIT The limit on the number of failed attempts to create a new individual before stopping growing the population Note that new individuals are checked to be unique so it is common in a highly similar population that many crossovers will no create unique combinations TOLERANCE The relative difference below which two fitness scores are equal CONVERGED COUNT The number of iterations with no change in fitness for convergence Warning If this is set to zero then convergence checking is disabled and the algorithm must be stopped using the ImaceJ interrupt by pressing the Escape button MUTATION RATE The mean fraction of the genome positions that will mutate The number of mutations is a Poisson variable sampled using a mean equal to the mutation rate multiplied by the genome length Note that the same position can mutate multiple times CROSSOVER RATE The mean fraction of the genome positions that will crossover The number of crossovers is a Poisson variable sampled using a mean equal to the crossover rate multiplied by the genome length It is not possible to crossover more times than the number of par
190. le EN Plot top n Calculate sensitivity Deta KM 10 EN Illustration 20 Filter Analysis plugin dialogue The following filters are available Filter Description SNR Fitter Remove all results with a Signal to Noise Ratio SNR below a set value Additionally remove peaks where the width has expanded above a Set ratio from the estimated PSF width The SNR ratio used is from Min SNR to Max SNR in integer increments The width used is from Min WiptH to Max WiptH in increments of INcREMENT WIDTH PRECISION FILTER Remove all results with a precision below a set value The precision used is from Min Precision to Max Precision in integer increments Page 97 225 GDSC SMLM ImageJ Plugins Filter Description TRACE FILTER Remove all results that do not form part of a molecule trace using the specified time and distance threshold See Trace MoLecuLes for details of the tracing algorithm The minimum and maximum time and distance threshold can be configured along with the increments used to move between the min and max HysTERESIS SNR FILTER Mark all results with a Signal to Noise Ratio SNR above an upper level as valid Remove all results with a Signal to Noise Ratio SNR below a lower level Any result with a SNR between the upper and lower levels is a candidate result Candidates are retained if they can be traced directly or via other candidates to a valid result
191. lisation Precision for Least Squares Fitting From Mortensen et al 2010 Page 218 225 GDSC SMLM ImageJ Plugins s 16 8msib Var FX xl Ti E where Var The variance of the localisation position in the X dimension when fitting a Gaussian 2D function to a Gaussian 2D PSF F The noise scaling factor 2 for an EM CCD camera 1 otherwise Sa The standard deviation of the Gaussian function s adjusted for square pixels The adjustment is computed as S Vs a 12 N The number of photons in the localisation b The expected number of photons per pixel from a background with spatially constant expectation value across the image a The pixel size in nm A 3 Localisation Precision for Maximum Likelihood Fitting From Mortensen et al 2010 2 s Var F XX r E f tln t de o tp where Var The variance of the localisation position in the X dimension when fitting a Gaussian 2D function to a Gaussian 2D PSF F The noise scaling factor 2 for an EM CCD camera 1 otherwise Sa The standard deviation of the Gaussian function s adjusted for square pixels The adjustment is computed as S vs a 12 where a is the pixel size in nm N The number of photons in the localisation l 2ns b The integration factor an a b The expected number of photons per pixel from a background with spatially constant expectation value across the image Note that since the formula for Maximum Likelihood fitting involves an integral with no analytic s
192. ll be plotted in yellow Page 204 225 GDSC SMLM ImageJ Plugins 3 Cumulative Probability Save Trace Diffusion Jump Distance wy YY amp 2 4 6 8 10 12 Distance um 2 second Copy X 7 94 Y 0 4255 Illustration 42 Jump distance cumulative probability histogram The best fit l for the single species model is shown in magenta 10 8 5 3 Histograms If the Show Histocrams option is selected the plugin presents a second dialog where the histograms can be configured The number of bins in the histogram can be specified and outliers can optionally be removed Outliers are any point more than 1 5 times the interquartile range above or below the upper and lower quartile boundaries The following histograms can be chosen Parameters Description TOTAL SIGNAL The total signal of each trace SIGNAL PER FRAME The signal per frame of the localisations in a trace T ON The on time of a trace This excludes the traces too short to be analysed MSD MoLecuLe The average mean squared distance per molecule Plots of the all vs all and adjacent MSD are shown If the particles contain molecules moving with different diffusion rates or a fixed fraction of molecules then the histogram may be multi modal D MoLecuLe The apparent diffusion coefficient per molecule Plots of the all vs all and adjacent D are shown 10 8 5 4 Summary table The plugin shows a summary table of t
193. ll scores will be reversed However the F score will remain identical because it is the harmonic mean of the two scores The F score is consequently a good measure of the similarity of two sets of points that have been aligned for matches B 8 Metrics requiring the True Negative count Note that when comparing point coordinates that can only ever exist the definition of the true negative is invalid However there are cases where a Set of results have two classifications either absent or present and a set of predictions aim to predict those values In this case the TN count can be obtained and used to compute scores TNR True negative rate tn TNR fp tn Page 222 225 GDSC SMLM ImageJ Plugins NPV Negative predictive value NPV tn fn FPR False positive rate FPR fp fp tn ACC Accuracy _ tp tn ANUE pa fp tn n MCC The Matthews Correlation Coefficient is used in machine learning as a measure of the quality of binary two class classifications introduced by biochemist Brian W Matthews in 1975 It takes into account true and false positives and negatives and is generally regarded as a balanced measure which can be used even if the classes are of very different sizes The MCC is in essence a correlation coefficient between the observed and predicted binary classifications it returns a value between 1 and 1 A coefficient of 1 represents a perfect prediction O no better than random prediction and 1
194. ls and values in ADUs Image Results Page 39 225 GDSC SMLM ImageJ Plugins Parameter Description IMAGE Show a reconstructed image using the localisations e None No image e Localisations Use a value of 1 for each spot e Signal intensity Use the signal strength for each spot e Frame number Use the frame number for each spot e PSF Plot the fitted Gaussian PSF e Localisations width precision Plot a Gaussian at the centre of each spot using the localisation precision for the width e Signal width precision Plot a Gaussian at the centre of each spot using the localisation precision for the standard deviation and the signal intensity for the height e Localisations width av precision Plot a Gaussian at the centre of each spot using the configured image precision for the width e Signal width av precision Plot a Gaussian at the centre of each spot using the configured image precision for the standard deviation and the signal intensity for the height Fit error Use the fitting error for each spot WEIGHTED If selected the exact spot coordinates are used to distribute the value on the surrounding 2x2 integer pixel grid using bilinear weighting If not selected the spot is plotted on the nearest pixel EQUALISED Use histogram equalisation on the image to enhance contrast Allows viewing large dynamic range images IMAGE PRECISION The Gaussian standard deviation to use for the average precision plotting o
195. lts Click No to re read the results for example if the files have been modified with new classifications 7 9 2 Available Filters When the results have been loaded the user is presented with a dialogue as shown in Illustration 20 There are several filters available with parameters to control them Enable the filter by using the checkbox for the filter name Each filter typically has a set of parameters that control the filter The plugin allows the parameters to be enumerated so that the performance of the filter can be tested The plugin dialogue will allow the minimum and maximum value for the filter to be set along with an increment used to move between them The filter will be run for each combination of parameters that is to be enumerated to produce a filter set Page 96 225 GDSC SMLM ImageJ Plugins Du SNR filter Min SNR Max SNR Min Width Max Width Increment Width Y Precision filter Min Precision Max Precision Trace filter Min distance Max distance Increment distance Min time Max time Increment time 20 files 597186 results 12880 True Positives 1 50 2 00 0 50 20 80 0 30 1 20 0 30 _OK Cancel Help Filter Analysis Hysteresis SNR filter Min SNR gap 10 40 Max SNR gap Increment SNR gap Hysteresis Precision filter Min Precision gap 10 Max Precision gap 40 Increment Precision gap 10 Save filters Show tab
196. ly constant X drift or can vary during the course of the image acquisition Y drift Page 69 225 GDSC SMLM ImageJ Plugins 0 5 0 0 Drift px 0 5 10000 20000 30000 40000 50000 6000C Frame 0 4 Drift px o N o o 10000 20000 30000 40000 50000 6000C Frame Illustration 12 Plot of the calculated X drift top and Y drift bottom following drift calculation using the localisation sub images method The STORM dataset consisted of 410 000 results over 60000 frames Sub images were produced using 2000 frames raw drift calculated blue and smoothed using LOESS with a maximum of 4 points before interpolation to the drift curve red Page 70 225 GDSC SMLM ImageJ Plugins When the drift analysis is complete the plugin will present a dialog asking the user what to do with the drift curve Apply drift correction to in memory results Update method New dataset Save drift OK Cancel illustration 13 Drift calculator curve options dialogue The following options are available Parameter Description UPDATE METHOD None Do not use the drift curve Update Update the input results coordinates using the drift New dataset Create a new dataset with updated coordinates using the drift New truncated dataset Create a new dataset with updated coordinates but truncate the results to the interpolation range of the drift curve points outside this range may have a poor dr
197. ly identified maxima This will update as you adjust the parameters such as the smoothing and the minimum peak height The following parameters are available Parameter Description SMOOTHING The size of the smoothing window Box Size Identify maxima within a 2n 1 box BackGROUND Set the background for the image Min HEIGHT Set the minimum height above the background FRACTION ABOVE BACKGROUND Set the minimum height above the background as a fraction of the total peak height MIN WIDTH The minimum peak width at half maxima BLOCK FIND ALGORITHM Use the block find algorithm for non maximal suppression Neubeck and Van Gool 2006 This is much faster than a standard search of each 2N 1 region around every pixel The algorithm finds the maximum in each of the non overlapping N 1 sized blocks in the image Only the single maxima from each block is compared to the remaining pixels in the 2N 1 region NEIGHBOUR CHECK The block find algorithm defines a maxima as any pixel with no other higher pixels within a radius This can over count maxima if they are equal height Check adjacent blocks for equal height maxima eliminating any maxima with neighbours that are already a maxima BORDER The border size in pixels to ignore when identifying maxima PREVIEW Draw on the image the currently identified maxima 5 10 2 Gaussian Fitting When peaks have been identified they are fit using a 2D Gaussian
198. lysis result This allows the parameters to be fine tuned until successful and then they can be applied in batch analysis INTERPOLATION Set the interpolation mode to use when enlarging images 9 2 4 Output The plugin will log details of each spot analysed to the ImaceJ log window e g centre and width When complete the plugin will record the z centre scale and standard deviation of the final PSF image to the log The plugin also fits a 2D Gaussian to the combined PSF image and records the fitted standard deviation at the z centre as a measure of the PSF width The final PSF image is shown as a new image The z centre is selected as the active slice The PSF image has an XML tag added to the image info property containing the z centre image scale number of input images used and the PSF width This will be saved and reloaded when using the TIFF file format in ImaceJ This information is used in the PSF Drirt PSF comser and Create Data plugins The information can be viewed using the IMAGE gt SHow InFo Command e g lt gdsc smlm ij settings PSFSettings gt lt zCentre gt 453 lt zCentre gt lt nmPerPixel gt 11 428571428571429 lt nmPerPixel gt lt nmPerSlice gt 20 0 lt nmPerSlice gt lt nImages gt 1 lt nImages gt lt gdsc smlm ij settings PSFSettings gt Page 120 225 GDSC SMLM ImageJ Plugins When the final PSF image has been constructed the plugin will show the Amplitude and PSF plots for the fi
199. m length 5 Linear fit 5 points evaluations Gradient 2 096 D 0 5239 um 2 s SS 0 047595 2 Jump Distance analysis N 151 Time 6 frames 0 6 seconds Mean Distance 1371 0 nm Precision 38 55 nm Beta 35 57 Estimated D 0 4698 um 2 s Fit Jump distance N 1 D 0 0498 um 2 s SS 0 433899 IC 453 1 12 evaluations Fit Jump distance N 2 D 1 655 0 0346 um 2 s 0 1832 0 8168 SS 0 014680 IC 960 3 342 evaluations Page 206 225 GDSC SMLM ImageJ Plugins Fit Jump distance N 3 D 1 655 0 0346 0 0346 um 2 s 0 1832 0 1204 0 6964 SS 0 014680 IC 956 1 407 evaluations Coefficients are not different 0 0346 0 0346 1 0 Best fit achieved using 2 populations D 1 655 0 0346 um 2 s Fractions 0 1832 0 8168 Page 207 225 GDSC SMLM ImageJ Plugins 11 Tools Plugins The following plugins contain utilities for image manipulation The plugins are described in the following sections using the order presented on the PLucins gt GDSC SMLM gt Toots menu 11 1 Smooth Image Provides a filter plugin for smoothing an image see Illustration 43 The filter uses the same methods as the Peak Fit plugin for identifying local maxima However only a single or difference filter is available no Jury filter so that a single dialog can display all the options A single filter applies a single smoothing operation to the image A difference filter applies two sm
200. m the image to prevent identification of false candidate maxima that waste time during the fitting process and may create bad localisation data A Since filter will process the image once with the selected filter A DIFFERENCE filter will process the image twice with the two configured filters The second filtered image is then subtracted from the first This acts as a band pass filter that allows any frequency between the two filters to pass but remove the other frequencies For example a PSF with an approximate standard deviation so of 1 could be filtered with a difference of Gaussians filter using a filter standard deviation of 0 5 and 2 The Dirrerence filter is useful when there is a large background variation in the image since the subtraction of the second image is performing a local background subtraction The spots are then ranked using their relative height over background This would rank a spot with a height of 10 over a background of 50 as lower than a spot with a height of 30 over a background of 20 The Since filter would put the height 10 spot first as its total height is 60 compared to 50 for the other brighter spot A Jury filter will apply many filters to the image Each filtered image is used to identify maxima The pixel value from the filtered image from each maxima is added to a sum image When all filters have been processed the maxima are then identified in the sum image The Jury filter is therefore finding maxima in a comb
201. m the localisation PC PALM Save Results Saves all the PC PALM results held in memory to a results folder PC PALM Load Results Load all the PC PALM results from a results folder to memory PC PALM Fitting Combine multiple Pair Correlation curves and fit them using models for random or clustered distributions PC PALM Clusters Find clusters of molecules using a partial centroid linkage hierarchical clustering algorithm 1 4 Model plugins PSF Creator Extracts the PSF from a Z stack image of markers e g quantum dots or fluorescent beads PSF Drift Computes the drift in a PSF image PSF Combiner Combines several PSF images into a single average PSF Create Data Creates an image by simulating single molecule localisations using a model of photoactivated diffusing fluorophore complexes The PSF can be simulated or real using an input PSF image Create Simple Data Creates an image by simulating single molecule localisations at a specified density Create Benchmark Data Creates an image by simulating single molecule localisations in a fixed location Fit Benchmark Data Fit the image created by Create Benchmark Data and compute statistics on the accuracy and precision of fitting Benchmark Analysis Compute statistics on the accuracy and precision of fitting using different methods Statistics are only computed for all the localisations that were fit successfull
202. ma distribution with the shape parameter equal to the input electrons and the scale parameter as 1 le EMgain 1 _ aa gain electrons The amplified electrons are converted to ADUs using the camera gain The read noise calculated earlier for use in the per localisation noise calculation is then added to the image along with the camera bias The bias offset above zero ensures that the final output image using unsigned integers can record negative noise values Note Accurate values for the read noise gain and EM gain for a camera can be obtained using the Mean Variance Test plugin See section 10 3 or the EM cain Analysis plugin see section 10 4 4 9 5 4 Particle distribution The simulation can distribute the particle using the following methods Page 133 225 GDSC SMLM ImageJ Plugins Method Description UniFormM RNG The particle are randomly positions in the 3D volume defined by the Size and DeptH parameters The coordinates are drawn using a random number generator Uniform HALTON The particle are randomly positions in the 3D volume defined by the Size and DeptH parameters The coordinates are drawn using a Halton sequence that very uniformly distributes the particles Unirorm SoboL The particle are randomly positions in the 3D volume defined by the Size and DeptH parameters The coordinates are drawn using a Sobol sequence that very uniformly distributes the particles Mask The
203. mageJ macro recorder this analysis can be automated in a macro script Page 178 225 GDSC SMLM ImageJ Plugins 10 Calibration Plugins The following plugins contain functionality to estimate the width of the Point Spread Function PSF for an imaging set up and analyse the noise and gain of the imaging camera The plugins are described in the following sections using the order presented on the PLucins gt GDSC SMLM gt CAaLIBRATION Menu 10 1 PSF Calculator A simple plugin that estimates your Gaussian approximation to the PSF using the microscope imaging parameters and the wavelength of light x lt gt Ly an PSF Calculator Pixel pitch um 3 15 Magnification 63 Beam Expander 1 00 Pixel pitch nm 102 381 wavelength inm h 500 RP un D o Numerical Aperture NA E Account for optical aberations and focus error Proportionality factor gt h 52 Adjust for square pixels Airy Width nm 56 841 Airy Width pixels 0 555 StdDev nm 114 305 StdDev pixels 1 153 HWHM pixels 1 358 Save StdDev pixel width to the fitting properties OK Cancel Help Illustration 36 The PSF Catcutator dialogue The calculator uses the following formula Page 179 225 GDSC SMLM ImageJ Plugins Airy Width 2m NA Where Airy Width The width of the Airy pattern A The wavelength in nm NA The Numerical Aperture The Airy profile can be approximated by a Gaussi
204. maximum allowed distance between a true and candidate maxima to be classed as a match RECALL FRACTION The fraction of the maximum recall to use for calculating the second set of recall and precision scores SHow PLOTS Select this option to show plots of the results the match statistics verses the spot candidate rank and the precision recall curve SHOW FAILURE PLOTS Select this option to show a histogram of the count of false positives before each true positive i e failures 9 11 1 Data Summary The Fitter Spot Data plugin will compare the spot candidates to the actual localisation positions in each frame Any spot candidate that is within the March Distance of an actual localisation is marked as a match true positive The comparison is done using a closest pairs algorithm where the first pair are eliminated from subsequent pairings All other spot candidates that fail to match an actual localisation are false positives The recall precision and Jaccard score see Appendix B Comparison Metrics are computed for the entire collection Given that the spot candidates are ranked it is possible to compute the scoring metrics for each additional spot added to the collection starting from the highest ranked spot A plot is shown of the recall precision and Jaccard score against the rank Precision Blue Recall Red Jaccard Black 50000 100000 150000 200000 250000 Spot Rank Since the spot filter will id
205. mmon parameters used are Catisration and Exposure TIME Page 60 225 GDSC SMLM ImageJ Plugins 6 7 Show Results Header Shows the header information from any supported localisation results file format This is particularly useful for reading the header from GDSC SMLM binary format results files When the plugin is run the user is presented with a dialog where the results file can be selected Show Results Header Show the results header double click the string field to open a file chooser Filename Raw The Filename field can be double clicked to open a file selection window When the plugin runs it will attempt to open the selected file and read it as a localisation results file The header will be extracted and reported to the ImaceJ log window If the Raw option is selected then the header will be written directly Note that the ImaceJ log window does not show tab characters However if a line containing tab characters is copied from the log window and pasted into a text editor these characters are maintained If the Raw option is not selected then the plugin will attempt to extract the standard information stored ina GDSC SMLM results file header Field Description FORMAT The GDSC SMLM file format code Name The name of the results Bounps The bounds of the results data minx miny width height CALIBRATION The calibration nm pixel exposure time etc CONFIGURATION
206. ms exposure time At this rate the fluorophore emissions are very faint but frames can be manually labelled as on or off By analysing hundreds of spots it is possible to extract distribution parameters that allow the fluorophores to be modelled using the Create Data plugin 7 12 1 Input Images The purpose of the plugin is to mark the fluorescent bursts from a single fluorophore Consequently the input images should ideally be of single fluorophores spread evenly on the image and fixed in position Overlapping fluorophores can be excluded from analysis by only selecting spots that appear distinct An example input image with a simulated PSF image generated using the Peak Fit plugin is shown in Illustration 23 A single spot has been selected with an ROI on the PSF image The selection has been applied to the Original image to select the region for analysis Page 102 225 GDSC SMLM ImageJ Plugins EJES 20ms_4 tif 200 Yes 81 500 189x131 pixels 16 bit 24MB 189x131 pixels 16 bit 48K a k Illustration 23 Example Spot Analysis input image of mEOS3 expressed in S pombe fixed and activated at a low power to produce non overlapping fluorophore bursts The super resolution image is a simulated PSF image of localisations with a SNR above 100 A single fluorophore is selected for analysis 7 12 2 Plugin Interface The Spot Analysis plugin displays a window as shown in Illustration 24 The window contains a drop do
207. n The distribution is specified using an input file of photon values one per line The photons will be sampled using a probability distribution based on these values but with a mean of the photon rate specified by the PHotons parameter If not selected the photon distribution is sampled from a gamma distribution with the specified PHoton shape parameter The scale parameter of the gamma distribution will be equal to the photons divided by the shape PHOTON SHAPE The shape parameter for the photon gamma distribution If no shape parameter is provided then the photon distribution is fixed using the PHotons parameter CORRELATION If non zero the total photon budget of a fluorophore will be proportional to the total on time using this correlation The average photon budget will still be defined by the PHotons parameter The Custom PHOTON DISTRIBUTION and PHOTON SHAPE parameters are ignored ON TIME The average on time of a fluorophore OFF TIME SHORT The average off time of a fluorophore in dark state 1 short OFF TIME LONG The average off time of a fluorophore in the dark state 2 long N BLinks SHORT The average number of times the fluorophore enters dark state 1 from each repetition of the on state Note that a blink is caused by the dark state Set to zero to prevent blinking and all fluorophores will only activate and then bleach N BLinks LONG The average number of times the fluorop
208. n be used in simulations to draw diffraction limited spots that appear the same as those taken on the microscope These simulations can be used to optimise localisation analysis Page 115 225 GDSC SMLM ImageJ Plugins 9 2 1 Input image The input image must be a z stack of diffraction limited spots for example quantum dots or fluorescent beads The spot must be imaged through a large z range in small increments from out of focus through focus to out of focus This will allow the entire PSF to be captured The first and last frames are used to set a background level for the image intensity so ideally the spot should not be visible at all An example spot imaged at 1000nm intervals is shown in Illustration 29 It can be seen that the spot disappears when 3um out of focus Ideal input images should cover a similar range but using a smaller step size for example 20nm Illustration 29 Fluorescent bead imaged at 1000nm intervals The central frame is in focus Contrast levels have been set to show the PSF when out of focus When preparing a calibration image not all the spots are ideal due to problems with sample preparation The spots should be inspected and only those that show a small in focus spot and a smooth transition to out of focus should be selected for analysis The spots may have their focal point in different z slices In addition there should be no surrounding spots that will contribute overlapping PSFs to the image The spots sh
209. n from an image than conventional light microscopy In conventional light microscopy the subject is illuminated and all the light interacting with the subject is captured simultaneously into an image The resolution is limited since the optics of the microscope cannot focus the light perfectly Super resolution microscopy uses small molecules that can be activated to emit light Ifa single molecule is activated its position can be localised using software analysis Using thousands of localisations it is possible to reconstruct a virtual image of the subject This increases the image resolution to the precision of the localisation method The improvement depends on the imaging conditions but is often 5 10 times higher Illustration 1 shows the increased resolution of single molecule localisation microscopy The difference is most noticeable where structures meet since the single molecules have a cleaner signal when activated individually than the combined signal of all the molecules together Page 7 225 GDSC SMLM ImageJ Plugins A Standard image B Super resolution image C Standard image 8x Illustration 1 Example images of standard and single molecule localisation microscopy The GDSC Single Molecule Light Microscopy SMLM plugins provide various tools for single molecule localisation analysis The following plugins are available 1 1 Fitting plugins Simple Fit Performs fitting on an image to genera
210. n resets the SMLM configuration file to the fitting defaults when the Peak Fit plugin is run immediately after the Simpe Fit plugin the results will be the same This allows the user to reset the fitting parameters with Simpe Fit and then Page 24 225 GDSC SMLM ImageJ Plugins repeatedly make changes to the parameters with the Peak Fit plugin to see how the results are affected This can be a useful learning tool to experiment with the fitting parameters 5 2 Peak Fit Finds all the candidate maxima in an image and fits them using a 2D Gaussian The Peak Fit dialog is shown in Illustration 5 Ed Peak t Y O ey Peak filtering A ERs ne Discard fits that shift are too low or expand contract Config file home ah403 gdsc smlm settings xml Shift factor E 1 Calibration nm px 108 Signal strength 70 Gain ADU photon 37 70 Min photons 30 EM CCD width factor 1 5 Exposure time ms 100 00 Precision 40 00 Initial StdDevo 1 2 Results Initial StdDevl 1 2 Log progress Initial Angle 0 000 Show deviations Spot filter type Single 1 Results table None Spot filter Mean Image output Smoothing K 1 T 1 30 Image Localisations Search width 1 00 Weighted Border _ lo 00 Y Equalised Fitting width 3 00 Image Precision nm 0 Gaussian fitting Image Scale El a Fit solver Least Squares Estimator LSE 1 File output Fit function Circular J
211. n the a pulse boundary into separate traces Use this setting if your imaging conditions use pulsed activation and you have imaged for long enough between pulses to be sure that all fluorophores have photo bleached OPTIMISE If selected the plugin will provide a second dialogue that allows a range of distance and time thresholds to be enumerated see section 7 2 3 SAVE TRACES When the tracing is complete show a file selection dialogue to allow the traces to be saved SHOW HISTOGRAMS Present a selection dialog that allows histograms to be output showing statistics on the traces e g total signal on time and off time SAVE TRACE DATA Save all the histogram data to a results directory to allow further analysis A folder selection dialog will be presented after the tracing has finished REFIT OPTION Provide the option to extract all the frames corresponding toa single trace from the source image into a combined image and perform PSF fitting The plugin will trace the localisations and store the results in memory with a suffix Traced Two additional datasets are created all single localisations which could not be joined are given a suffix Trace Singles all traces are given a suffix Traces The Trace Singles plus Traces datasets equal the Traced dataset A summary of the number of traces is shown on the ImageJ status bar The results are accessible using the Resutts Manacer plugin 7 2
212. n using a single image Single image mode cannot compute the camera bias or read noise and the gain values are not as accurate as the full test using multiple images Hold the Shirr key down when running the plugin and the analysis will be performed on the currently active image The image must have more than one slice to allow difference images to be computed and be a white light image with a constant uniform exposure across the image field e no significant image features In single image mode the plugin will compute the pairwise comparison of consecutive frames in the image and for each pair compute the approximate camera gain variance EM gan A a mean bias 2 x gain The bias must be provided since there is no input bias image the plugin will ask the user to input the camera bias and camera gain Using a camera gain of 1 will calculate the total gain of the system The results will be displayed in a table as described above The plugin provides a plot of gain verses slice and a histogram of the values These can be used to determine if the gain is constant throughout the image and so is a good estimate 10 5 EM Gain Analysis Analysis a white light image from an EM CCD camera construct a histogram of pixel intensity and fit the histogram to obtain the bias EM gain read noise and photons per pixel see Ulbrich amp Isacoff 2007 Supplementary Information 10 5 1 EM CCD Probability Model The EM Gain Anacysis plugin u
213. nal PSF image A dialogue is then presented allowing analysis of the PSF to be done interactively 17 a PSF Creator Yes SuperPlot the cumulative signal verses distance from the PSF centre Z centre 117 PSF width 125 4 nm slice EJ Wha Distance 21376 Normalise OK Cancel The Suice parameter controls the current slice from the PSF image that will be analysed The Distance parameter controls the distance used for the cumulative signal analysis Two additional plots are displayed and updated interactively when the Suce and Distance parameters change One shows the percentage of the PSF signal at different z depths that is within 3 times the standard deviation of the fitted PSF SD for the z centre This shows that as the spot moves out of focus less of the signal is captured within the same area The green line shows the currently active slice Total 75 84 z 80 0 nm 1 60 Signal D o 20 100 200 300 400 500 600 Z A plot is also shown of the cumulative signal as the distance from the centre of the PSF increases This plot is drawn using data for the currently active slice in the PSF Page 121 225 GDSC SMLM ImageJ Plugins Total 0 9652 376 3 nm z 80 0 nm 1 0 Signal 0 0 0 500 1000 1500 Distance nm The green line shows the current distance selected and the total is shown in the plot label If the Normatise parameter is selected then the cumulative signal up to the distance is normali
214. nal for the localisation The relative signal factor is simply the fitted signal divided by the true signal The relative signal factor rsf above or below the true signal which has 1 for a perfect match is adjusted so that the new signal factor sf score is O for a perfect match sf rsf lt 1 P 1 raf The matches are then assigned a score The score is created using a ramped function between the Lower Distance and the March bistance Any distance below the Lower pistance iS 1 Anything above the March pistance is O The match score is then used to accumulate a score for how accurate the fitting was performed If the match is between a fitted candidate and a true localisation then the score is a positive This score can be set to a negative if the signal factor is above the defined limit i e the fitted signal is not close to the true signal If the match is between a unfitted candidate and a true localisation then score is a negative When using a ramped distance function to create the score the remaining score is calculated as 1 score The performance is then calculated by summing Page 157 225 GDSC SMLM ImageJ Plugins e The true positives TP as the sum of the score for the positives e The false positives FP as the sum of the remaining score for the positives The TP and FP totals thus represent the score that can be achieved for a perfect filter that is able to correctly allow any fit results that are within the match distanc
215. nce plot produced by the Mean Variance Test plugin The best fit line is shown in red The plugin reports the final calculated gain and read noise to the ImageJ log e g Mean Variance Test Directory images CameraCalibration CameraGain 2 EmGain 0 Bias 515 4 7 4 ADU Variance 21 78 0 1557 mean Read Noise 47 53 e Gain 1 6 422 ADU e The parameters for the best fit line are shown as Variance a b mean The parameter b is the gain The read noise is shown in electrons The units for the gain are Analogue to Digital Unit ADU per electron Page 186 225 GDSC SMLM ImageJ Plugins Note that the gain can be expressed as electrons per ADU and so the output shows the gain using 1 over the reciprocal of the fit parameter to allow comparison with manufacturer gain values E g in the example above 1 6 422 1 1 0 1557 and the gain would be 6 422 e ADU 10 3 4 Single Image Mode The plugin can be run using a single image Single image mode cannot compute the camera bias or read noise and the gain values are not as accurate as the full test using multiple images Hold the Shirr key down when running the plugin and the analysis will be performed on the currently active image The image must have more than one slice to allow difference images to be computed and be a white light image with a constant uniform exposure across the image field e no significant image features In single image mode the
216. nd photons Thus it is possible to store a calibration within the results This calibration is added automatically when the results are generated inside the SMLM plugins However the results may be loaded from file where a calibration is not present or the calibration was incorrect when the results were generated This plugin allows the calibration to be updated When the plugin is run it presents a selection of the current result that are held in memory If no results are available then an error is displayed The user must select the results to update The following options are then available Parameter Description UPDATE ALL LINKED When new results are created from existing results they copy the RESULTS calibration from the source results Select this to update all the results in memory that share the same calibration If unselected then the other results will remain unchanged CALIBRATION Nm Px The size of the pixels in nanometers Gain ADU PHoTON The number of Analogue to Digital Units ADU that represent one photon EM CCD A flag to indicate if the image was taken using an EM CCD camera Exposure TIME Ms The exposure time for a single frame in milliseconds Camera Blas ADUs The bias offset added to each pixel by the camera Reap noise ADUs The camera read noise in ADUs Note that not all the calibration parameters have to be configured Not all the plugins require every parameter The most co
217. nd standard deviation This allows fast computation in constant time regardless of the size of the neighbourhood region The following parameters can be set Parameters Description Rapius The radius of the square neighbourhood region ERROR The number of standard deviations above the mean that identifies a hot pixel PREVIEW Preview the filter on the image The number of pixels replaced will be shown in the dialogue Page 210 225 GDSC SMLM ImageJ Plugins 11 5 Estimates Noise Estimator noise in an image This plugin can be used to compare noise estimation methods Note that estimating the noise in an image is important when setting the signal to noise ratio SNR for use in filtering localisation fitting results When loaded the plugin provides a plot of the noise estimate of the next 100 frames of a stack from the current frame as shown in Illustration 46 Two noise estimation methods can be chosen see table below Changing an estimation method will dynamically update the noise plot EJ y Noise Estimator YU ey Method blue ResidualsLeastMeanOfSquares Method2 red QuickResidualsLeastTrimmedOfSquares Lowest radius La l6 Click OK to compute noise table using all methods OK Cancel sequence Noise 20 40 60 80 100 List Save Copy Illustration 44 Noise Esimator plugin showing the noise plot for the next 100 frames
218. ng formula sin 9 122 d where is the angle at which the first minimum occurs A is the wavelength of the light and d is the diameter of the aperture Therefore the resolution that can be achieved is a function of the wavelength of the light and the size of the aperture used in the optical system Page 14 225 GDSC SMLM ImageJ Plugins 2 2 Approximation using a Gaussian The Airy pattern falls rather slowly to zero with increasing distance from the centre such that the outer rings contain a significant portion of the integrated intensity As a result the spot size is undefined i e infinite when using the entire pattern An alternative measure of the spot size is to ignore the relatively small outer rings of the Airy pattern and to approximate the central lobe with a Gaussian profile This is shown in Illustration 1 normalized PSF amplitude 0 1 2 3 radial coord in units of A Fnum Illustration 3 Approximation of the Airy pattern solid line using a Gaussian dashed line Image taken from Wikimedia Commons The Gaussian profile closely approximates the profile of the Airy pattern in the plane of focus This allows the location of a point source of light to be found by 2D Gaussian fitting However this approximation breaks down if the focal plane is above or below the imaging plane In this instance the pattern still exists as a series of rings but the relative strength of central spot is reduced Consequently the Ga
219. ng parameters are correct In addition a negative score indicates over clustering a positive score is under clustering Consequently a plot of the distance and time thresholds verses the score will indicate the parameters that are best suited to achieving a zero score The zero score can be more easily seen on such a plot by using the absolute value of the score Page 78 225 GDSC SMLM ImageJ Plugins The following table describes the parameters used during the optimisation Parameter Description Min Distance THRESHOLD Px The minimum distance threshold Px Max Distance THRESHOLD The maximum distance threshold Min Time THRESHOLD SECONDS The minimum time threshold Max Time THRESHOLD SECONDS The maximum time threshold STEPS The number of steps to use between the minimum and maximum Steps intervals are chosen using a geometric not linear scale to bias sampling towards lower threshold values BLINKING RATE The average blinking rate of the fluorophore Must be above 1 otherwise no occurrences of repeat molecules are expected Note that the blinking rate is equal to the number of blinks 1 PLot Produce a plot of the score against the time distance threshold None No plot Nearest Neighbour Output only the calculated values Bilinear Interpolate between calculated values to produce a smoother plot When the optimisation option is selected it is preferable
220. ng the appropriate slice from the image using the z depth The z centre is specified using the middle of the slice so if the slice depth is 30nm then both 10 and 10 will be sampled from the centre slice Arandom sample from 0 to 1 is taken and used to look up the appropriate pixel within the cumulative image for that slice This sampled PSF pixel is then mapped to the output and the location added to the image Note that if the cumulative total for the slice is below 1 then the sample may be ignored This is allowed since the Image PSF has a limited size Missed samples are unlikely to effect the output image as the pixels are very far from the PSF centre 9 5 3 Noise model The simulation aims to match the data produced by the pixel array of an EM CCD camera Photons are generated in a random process modelled by the Poisson distribution Photons are captured on the sensor and converted to electrons The conversion is subject to the quantum efficiency of the camera sensor modelled as a binomial distribution The electrons are amplified through an Electron Multiplying device to increase the number This process is subject to gamma noise The electrons are read from the camera and digitised to Analogue to Digitial Units ADUs Reading the electrons is subject to Gaussian read noise The simulation models the camera CCD array as a set of photo cells that will be read into pixels The photons emitted by fluorophores are spread onto the photo cells using a
221. ng workflow will provide statistics on the recall and precision that can be achieved when fitting localisations of a given photon signal strength throughout the depth of field of the point spread function The plugins are described in the following sections using the order presented on the Piucins gt GDSC SMLM gt Mone menu 9 2 PSF Creator Produces an average PSF image using selected diffraction limited spots from a sample image The PSF Creator plugin can be used to create a Point Spread Function PSF image for a microscope The PSF represents how a single point source of light passes through the microscope optics to be captured on the camera Due to physical limits the wavelength of light cannot be focussed perfectly and will appear as a blurred spot The spot will change size with z depth as the light will be captured as it is converging to or diverging from the focal point Additionally since the spot is actually composed of a series of waves it may appear as a ring due to diffraction More details on the PSF can be found in section 2 1 Diffraction limit of light microscopy The exact shape of a PSF can be calculated using various models that account for the diffraction of various immersion media water oil etc used to image samples However individual microscope optics are unique and the PSF may vary from one set up to another even if the hardware is duplicated The PSF Creator allows an image model of the PSF to be created that ca
222. not occur if the molecule is part of the fixed fraction but will be allowed if the molecules is not fixed but the diffusion rate is zero The compound molecules dialogue contains a Show examples checkbox If this is selected the plugin will output a set of examples to the ImageJ log Cancel the dialogue to allow the ImageJ log to be selected and use the examples as the basis for new compounds When the simulation is run the molecules are created and placed randomly in the 3D volume Each atom in the compound is then modelled as a separate fluorophore The total lifetime of the compound is computed using the first and last time any fluorophore was active The entire compound is then subject to the diffusion and rotation over the lifetime of the compound 9 5 8 Sampled Statistics The simulation computes the on and off times for each fluorophore using fractions of a second However the image is reconstructed using a specified exposure time into image frames Thus it is possible for a fluorophore to turn off and then back on in the same frame or in consecutive frames This will be seen on the image as a less intense spot since the fluorophore is emitting for less time However it will not be possible to see these fast off times since the spot emission will appear continuous The sampled statistics recompute the number of blinks on and off times for integer frame sampling Any off time than does not completely span a frame cannot be viewed and is r
223. ntially also returning many false positives Note that some scores are better as they get lower In this case the plugin reverses the ordering to pick the best filter The original score metrics are used by default for selection and ranking The precision is used to set the Criteria Limit The results are then ranked using the Jaccard score Using the Jaccard ensures that the best possible filter is chosen since this score maximises the overlap between predicted and actual results Note that when ranking filters if the score is the same then the rank is determined by the criteria metric The use of the Criteria filter can be disabled by setting the Criteria Limit to a value achievable by any filter e g Precision 0 The best filter from each filter set is recorded to the summary table 9 13 2 2 Sensitivity Analysis The sensitivity analysis aims to show how much the scores will change when the filter parameters are adjusted An ideal filter would be one with low sensitivity i e changing the parameters away from the optimal does not alter performance Sensitivity can be calculated for the best filter from each filter set This is done by altering the parameters of the filter by a small change delta and recomputing the scores This can be used to express the relative change in the score with a change in the parameters i e Page 165 225 GDSC SMLM ImageJ Plugins the gradient The gradient of each parameter is reported those with low
224. nts of the curve The Bunk Estimator computes the N tg curve and fits the curve to the specified formula By default the plugin fits the curve and shows a plot of the N t curve with the fitted line see Illustration 19 The fit parameters are reported to the ImageJ log window Alternatively the plugin can fit the curve multiple times using a different number of points for each fit In this case the output is a set of plots showing the values of each of the fitted parameters against the number of fitted points Note that tracing localisations through time also requires a distance threshold to determine if the two coordinates are the same molecule The distance threshold used for the analysis is computed using the average precision of the localisations multiplied by a search factor The average precision is determined by fitting a skewed Gaussian to a histogram of the localisation precision This fit can optionally be displayed The following parameters can be set within the plugin to control the output Parameters Description INPUT Select the input results set Max DARK TIME The maximum dark time to use for the N t plot HISTOGRAM BINS The number of histogram bins SHOW HISTOGRAM Show the histogram of the precision along with the fitted skewed Gaussian curve SEARCH DISTANCE Define the distance threshold for trace analysis RELATIVE DISTANCE If selected the Search pistance is relative to the average precision of th
225. o far the diffusion can be confined using the following methods Page 134 225 GDSC SMLM ImageJ Plugins Method Description Mask Confine the movement to a mask defined using an input image The plugin will ask the user to select a mask image The image must be square but width height dimensions are scaled to match the simulation The boundaries are specified by non zero pixels If a single slice is used then the z depth uses the Depth parameter Any stack image must have the z depth of each slice defined so the plugin asks for the slice depth in nm SPHERE Confine the movement to a sphere with the origin at the diffusion start location The plugin will ask for the sphere radius in nm 9 5 5 Parameters The following parameters can be used to control the simulation Parameter Description PIXEL PITCH The simulated size of the pixel in the image in nm SIZE The width and height of the image in pixels DEPTH The depth of the simulation in nm Molecules will only be sampled within this volume Note that the output image is only 2D Set to zero to have no depth simulation FIXED DEPTH Select this to use the DeptH parameter as a fixed z coordinate This allows simulating out of focus spots SECONDS The duration of the simulation EXPOSURE TIME The exposure time for the output image STEP PER SECOND The number of simulation steps per second ILLUMINATION The type of
226. of the PSF to use when calculating the localisation density around each molecule The average density is shown in the summary table The density is the number of molecules within the specified radius 9 7 Create Benchmark Data Creates an image by simulating single molecule localisations in a fixed location The Create Benchmark Dara plugin is a modification of the Create Data plugin to remove the simulation of diffusing fluorophores The simulation draws a single localisation on each frame at a fixed position relative to the image centre The number of photons per localisation is randomly sampled from the range specified by the minimum to the maximum photons parameters The output of the plugin is an image and summary table as per the Create Data plugin If the minimum and maximum photon limits are the same the Create Benchmark Data plugin records the details of the simulation in memory This includes the exact number of photons for each localisation This data can be used with the Fit BencHmark Data plugin to fit the localisations and report statistics on the accuracy and precision of the fit results The following parameters can be configured Parameter Description PIXEL PITCH The simulated size of the pixel in the image in nm Page 144 225 GDSC SMLM ImageJ Plugins Parameter Description SIZE The width and height of the image in pixels BackGROUND The background level in photons This is sub
227. olution the formula is evaluated using numerical integration This is slow to compute The formula can be used to demonstrate that for any given set of parameters the precision Page 219 225 GDSC SMLM ImageJ Plugins of Maximum Likelihood fitting is lower i e better than Least Squares fitting Page 220 225 GDSC SMLM ImageJ Plugins Appendix B Comparison Metrics Several plugins within the SMLM package compute matches between points One set of points can be labelled as the actual result the second can be labelled as the predicted results When comparing actual and predicted points the following combinations are possible Actual Point Predicted Point Classification Label PRESENT PRESENT True Positive tp PRESENT ABSENT False Negative fn ABSENT PRESENT False Positive fp ABSENT ABSENT True Negative tn The classification counts can be used to compute binary scoring statistics as described below B 1 Recall Recall measures the number of actual points that are correctly predicted It is also known as the True Positive Rate TPR or sensitivity tp tp fn A score of 1 indicates that all the points were predicted lower scores indicate that some points were missed recall Recall can be interpreted probabilistically as the chance that a randomly selected actual point will be predicted B 2 Precision Precision measures the confidence of the predicted points It is also known as the Po
228. on plugin performs jump distance analysis using the jumps between frames that are n frames apart The distances may be from the origin to the nth frame or may use all the available internal distances n frames apart A cumulative histogram is produced of the jump distance This is then fitted using a single population and then for mixed populations of j species by minimising the sum of squared residuals SS between the observed and expected curves Alternatively the plugin can fit the jump distances directly without using a cumulative histogram In this case the probability of each jump distance is computed using the formula for p r At and the combined probability likelinood of the data given the model is computed The best model fit is achieved by maximising the likelihood MLE Maximum Likelihood Estimation When fitting multiple species the fit is rejected if a the relative difference between coefficients is smaller than a given factor or b the minimum fraction f is less than a configured level The result must then be compared to the previous result to determine if increasing the number of parameters has improved the fit see 10 8 3 Selected the best fit Optimisation is performed using a fast search to maximise the score by varying each parameter is turn Powell optimiser In most cases this achieves convergence However in the case that the default algorithm fails then a second algorithm is used that uses a directed random walk
229. on surrounding each localisation This value is biased by the total number of localisations and the total area sampled The number can be normalised using the sample size and sample area to produce different scores The scores are based on the Ripley s K and L functions Ripley s K function describes the fraction of points within a distance threshold r normalised by the average pues of points A 1 d lt r n Aj where is the indicator function di is the Euclidean distance between the and jP points in a data set of n points and A is the average density of points generally estimated as n A where A is the area of the region containing all points Note that the indicator function has a value of 1 for all elements di that are a member of a set in this case di lt r otherwise it is zero If the points are randomly distributed then K r should be equal to nr The K function can be variance normalised to the L function L r K r x The L function should be equal to r if the points are randomly distributed and its variance should be approximately constant in r A plot of L r r should follow the horizontal zero axis if the data are dispersed using a homogeneous Poisson process A plot of L r r r_ will also be zero but should have equal variance at any r thus the magnitude of deviations from zero can be directly compared for any r Note that the K and L functions apply to an entire dataset However it is possible to produc
230. on to save the curve to the PSF image The curve is added to the PSFSettings XML stored in the Image Info data field If the entire stack is not covered by the calculated drift curve then the plugin provides the user with the option to average the last n frames of the drift curve in each direction and store this average drift for the terminal frames P Save the drift to the PSF Slices 26 1000 0 nm 112 720 0 nm above recall limit Optionally average the end points to set drift outside the limits Selectzero to ignore Number of points lt m ti fa Yes No Click Yes to save the curve or No to discard the results The saved drift can be used to offset the centre of each frame of the PSF when reconstructing images This can be done when running the PSF Drirr plugin to check the curve is correct The following example shows a re run of the plugin using the recently computed drift curve Note that the maximum drift has been reduced from 87nm to 7 4nm and most of the drift is below 0 5nm Page 127 225 GDSC SMLM ImageJ Plugins d PSF Drift Drift Y MI The saved drift curve is used by default in the Create Data plugin when reconstructing images This allows benchmarking data to be constructed by placing the localisation data at the average centre that would be found by idealised fitting of that PSF 9 4 PSF Combiner The PSF Coweiner plugin produces an average PSF image from multi
231. ooth parameter The total region width around each point that is used will be 2n 1 with n 2 80 where x is the ceiling function Median Compute the median in a square region The region is rounded to integer pixels SMOOTHING Controls the size of the first smoothing filter Smooth InitiAL StDDeEv SMOOTHING Filtering can be disabled using a SmootHinG value of 0 Search WIDTH Controls the size of the region used for finding local maxima Width integer IniriaL StoDev Search Note that ideally localisation spots should be well separated over 5 pixels and so increasing this parameter will reduce the number of false maxima identified as fitting candidates by eliminating noisy pixels Page 27 225 GDSC SMLM ImageJ Plugins Parameter Description BORDER Define the number of border pixels to ignore No maxima are allowed in the border Width integer InrriaL StoDev Fittinc FITTING WIDTH Controls the size of the region used for fitting each peak Width integer InrriaL StoDev Fittinc The width should be large enough to cover a localisation spot so the function can fit the entire spot data 3 standard deviations should cover 99 of a Gaussian function 5 2 3 1 Spot Filter Type The Peak Fit plugin can perform initial filtering on the image using a Since DiFFERENCE Or Jury filter The filtered image is then analysed for local maxima The purpose is to remove noise fro
232. oothing operations and the second smoothed image is subtracted from the first This produces a difference of smoothing image As can be seen by comparing Illustration 46 A and B the difference filter is beneficial when there is a variable background across the image The filter reduces the contribution the background has to the brightness of the spots by performing local contrast enhancement The following algorithms are available Algorithm Description MEAN Compute the mean in a square region The region can be any size as the final edge pixels are given a weight using the region width BLock MEAN Compute the mean in a square region The region is rounded to integer pixels CIRCULAR MEAN Compute the mean in an approximate circular region The circle is drawn using square pixels To see the circle mask use Process gt Fitters gt SHow Circular Masks GAUSSIAN Perform Gaussian convolution The convolution kernel standard deviation is set to the SmootH parameter The total region width around each point that is used will be 2n 1 with n 2 80 where x is the ceiling function MEDIAN Compute the median in a square region The region is rounded to integer pixels Page 208 225 GDSC SMLM ImageJ Plugins A B y Y Localisation Data 400 O amp IIa amp Smooth Image Y Y As 1 10 6 91x6 91 um 64x64 16 bit 80K Smooth image Spot filter Mean Smoothing 1 5 Difference f
233. ould be marked using the ImaceJ Point ROI tool Right clicking on the toolbar button will allow the tool to be changed to multiple point mode Clicking the image will add a point Points can be dragged using the mouse and a point can be removed by holding the Att key down while clicking the point marker 9 2 2 Analysis Each marked spot will be analysed in turn Spots will only be used when there are no other spots within a specified distance to ensure a clean signal is extracted i e no overlapping PSFs For each frame the plugin will run the Peak Fit algorithm to fit the amplitude centre and width of the peak Fitting will begin to fail when the peak is very out of focus as the PSF may not resemble a 2D Gaussian The amplitude is smoothed using a LOESS smoothing algorithm and plotted against the Z position The amplitude should be highest when the peak is in focus This point from the smoothed data is taken as the initial centre slice The range of the in focus spot is marked by moving in either direction from the center slice until the smoothed amplitude is below a set fraction of the highest point The width and centre X and Y positions are then extracted for the in focus range and smoothed using the LOESS algorithm Since the amplitude is not a very consistent marker the centre slice is moved to the point with the lowest width The spot centre is then recorded for the centre slice using the smoothed centre X and Y data Page 116 225 GD
234. ould overlap with another moving particle Once the tracks have been identified the tracks are filtered using a length criteria and shorter tracks discarded Optionally the tracks can be truncated to the minimum length which ensures even sampling of particles with different track lengths The plugin computes the mean squared distance of each point from the origin Optionally the plugin computes the mean squared distance of each point from every other point in the track These internal distances increase the number of points in the analysis Therefore if the track is not truncated the number of internal distances at a given time separation is proportional to the track length To prevent bias in the data towards the longer tracks the average distance for each time separation is computed per track and these are used in the population statistics Thus each track contributes only once to the mean displacement for a set time separation The Mean squared distance MSD per molecule is calculated using two methods The ALL vs ALL Method uses the sum of squared distances divided by the sum of time separation between points The value includes the all vs all internal distances if selected The ADJACENT Method uses the average of the squared distances between adjacent frames divided by the time delta At between frames The MSD values are expressed in um22 second and can be saved to file or shown in a histogram The average mean squared distances for all the t
235. ound in section 12 Toolset Plugins Page 17 225 GDSC SMLM ImageJ Plugins 4 ImageJ Plugins The various ImageJ plugins allow the processing of single molecule light microscopy images and analysis of the results This includes finding and fitting spots on the image reconstructing an image from the list of localisations analysis of the blinking rate of fluorophores and tracing of fluorophore molecules through time The plugins used to analyse a set of localisations only require that the localisations be loaded into memory The localisations do not have to be computed by the SMLM fitting plugins and can be generated by another program For example it is possible to read the following file formats for analysis e RapidSTORM Nikon NSTORM The plugins have been divided into the following sub sets which are detailed in the remaining sections Jar File Description Fitting For identification of localisations on an image Results Allow loading and saving results in different formats Results can be filtered to subsets and compared to a reference set e g for benchmarking Analysis Perform analysis on localisations for example blinking rate estimation molecule tracing and Fourier image resolution PC PALM Plugins for Pair Correlation PC analysis Model Simulate single molecule images Calibration Estimate PSF widths and allow calibration of the imaging camera noise and gain Tools Utility plugins for image man
236. ow The following workflow is recommended when using the Spot Analysis plugin 1 Open the next input image Magnify the image if necessary Imace gt Zoom gt In Run the Peak Fit plugin to identify peaks with a SNR above 100 or other criteria to show clear spots Create a PSF image output with a scale of 1 Select a spot on the PSF image using a new rectangle ROI or moving the previous one It is recommended to maintain the same ROI size throughout the analysis Choose a spot that does not overlap any other spots Select the input image and press Crr_ Suirt E to restore selection apply the same ROI to the input image This will outline the spot location on the input image Press the Profe button This will produce a profile of the image intensity and standard deviation per frame for the spot Any localisation results from the Peak Fit plugin are marked on the profile The Prorie command will also extract the ROI to a new detail image and zoom in for easier viewing A blurred version of the image will also be shown using a Gaussian blur to make the spots more uniform Contrast may have to be adjusted in these images The images will be set to the first frame containing a localisation fitting result or frame 1 if none are available Scroll left and right through the image using the left right keys to locate spots The original and blurred images will be synchronised Click the App button when a spot is visible
237. ows results held in memory to be calibrated Show Results Header Shows the header information from any support localisation results file format Filter Results Filters a list of localisations using signal strength coordinate shift and PSF width Free Filter Results Filters a list of localisations using a custom filter specified using a text description Multiple filters can be combined with AND OR operators Results Match Calculator Calculate the match statistics between two results sets Trace Match Calculator Calculate the match statistics between two sets of traced molecules Spot Inspector Extracts the fitted spots from an image into a stack ordered by Page 9 225 GDSC SMLM ImageJ Plugins the user selected score 1 3 Analysis plugins Drift Calculator Corrects stage drift using sub image alignment fiducial markers within an image reference stack alignment or a drift file Trace Molecules Traces molecules through time using time and distance thresholds using a type of single linkage clustering Cluster Molecules Clusters molecules through time using time and distance thresholds using centroid linkage clustering Draw Clusters Draws collections of localisations with the same ID on an image for example the output from Trace MoLecuLes Or CLusteR MoLECULES Density Image Calculates the local density around localisations and displays
238. party_update_site and add the GDSC SMLM update site Fiji will automatically check for a new version during start up and install it if desired All the plugins will appear under the Plugins gt GDSC SMLM menu 3 2 Install using ImageJ version 1 The plugin is designed to run within ImageJ You can obtain the latest version of ImageJ from http rsbweb nih gov ij download html To get the plugins you can download the latest Jar files from the update site and put them in your ImageJ plugins folder The jars can be found here http sites imagej net GDSC SMLM You will also need to install the additional Apache Commons Math library This is already included in Fiji so is not on the update site You can get the jar file here http www sussex ac uk gdsc intranet files commons math3 3 2 jar Place all of the following Jar files into the ImageJ plugins directory Jar File Description GDSC SMLM Contains the SMLM plugins Apache Commons Math 3 Contains Math routines EJML Efficient Java Matrix Library for linear algebra Jtransforms Library for multi threaded Fourier transforms Xstream A library for reading writing XML The plugins will be visible under the PLucins gt GDSC SMLM menu An ImageJ toolset can be installed using the GDSC SMLM gt Tootset gt Insta SMLM Tootset plugin When selected the toolset adds a set of buttons on the ImageJ toolbar for commonly used plugins More details can be f
239. peaks within the fitting region in the fit multiple peak fitting NEIGHBOUR HEIGHT Define the height for a neighbour peak to be included as a fraction of the peak to be fitted The height is taken relative to an estimate of the background value of the image the image mean If the target peak is below the background then only higher neighbour peaks are included Since neighbours that are higher than the maxima may cause the fit procedure to drift to a different position this setting allows higher peaks to be included and lower neighbour peaks to be ignored A value of 1 will only include peaks higher than the target peak A value of 0 will include all neighbours Page 36 225 GDSC SMLM ImageJ Plugins Parameter Description RESIDUALS THRESHOLD Set a threshold for refitting a single peak as a double peak A value of 1 disables this feature The residuals difference of the fitted function to the data are analysed to determine if there is a skewed arrangement around the centre point The skew is calculated by dividing the region into quadrants clockwise labelled ABCD summing each quadrant and then calculating the difference of opposite quadrants divided by the sum of the absolute residuals A B C D sum r If this value is zero then the residuals are evenly spread in each quadrant If it is one then the residuals are entirely above zero in one pair of opposing quadrants and below zero in the other i
240. per resolution microscopy Nat Methods 7 5 377 81 Neubeck A Van Gool L 2006 Efficient Non Maximum Suppression Pattern Recognition 2006 ICPR 2006 18th International Conference on vol 3 pp 850 855 Nieuwenhuizen R P J Lidke K A Bates M Puig D L Grunwald D Stallinga S Rieger B 2013 Measuring image resolution in optical nanoscopy Nature Methods 10 557 Puchnar E M Walter J M Kasper R Huang B Lim W A 2013 Counting molecules in single organelles with superresolution microscopy allows tracking of the endosome maturation trajectory PNAS 110 16015 16020 Schneider C A Rasband W S Eliceiri K W 2012 NIH Image to ImageJ 25 years of image analysis Nature Methods 9 671 675 Sengupta P Jovanovic Talisman T Lippincott Schwartz J 2013 Quantifying spatial resolution in point localisation super resolution images using pair correlation analysis Nature Protocols 8 345 354 Sengupta P Jovanovic Talisman T Skoko D Renz M Veatch S L Lippincott Schwartz J 2011 Probing protein heterogeneity in the plasma membrane using PALM and pair correlation analysis Nature Methods 8 969 975 Snyder D L Helstrom C W Lanterman A D Faisal M White R L 1995 Compensation for readout noise in CCD images Journal of the Optical Society of America 12 272 283 Tubbs RN 2004 Lucky exposures Diffraction limited astronomical imaging through the atmosphere Obse
241. ple PSF images PSF images can be created using the PSF Creator plugin see section 9 2 When the plugin is run it searches all the open images for valid PSF images These will be tagged in the image info property with the z centre image scale and number of input images used to create the PSF The plugin then presents a dialogue where the user can select the images to combine Illustration 33 The dialogue is presented iteratively to allowing only one image to be selected from the available images each time Select the first image from the dialogue and click OK to include the image The list of available images is then updated and the dialogue reshown Click Cance to stop adding images Note that the iterative addition of images allows the plugin to be fully supported by the ImageJ macro recorder D PSF Combiner yy a Select the next input PSF image Each PSF must have the nm pixel scale PSF 1 scan_beads 20nm_step1 tif Cancel to finish OK Cancel Illustration 33 PSF Combiner image selection dialogue Page 128 225 GDSC SMLM ImageJ Plugins When the input images have been selected the plugin checks that each PSF has the same image scale Note that input PSFs can have different X Y and Z dimensions If the scales are not the same then the images cannot be combined and an error is shown Otherwise the plugin then presents a dialogue where the z depth of the combined PSF can be selected This allows the size of
242. ple if the plugin is set to fit 2 out of 3 frames but integrate 4 frames then any fit results from the first processed image will have a start frame of 1 and an end frame of 5 5 3 Template Configuration Allows the user to load custom configuration templates from a directory The GDSC SMLM configuration is stored in a configuration file This file is used by many of the plugins to save and load settings Copies of this file can be edited and saved as templates to a directory This allows settings to be applied from pre configured templates within various plugins for example the fitting configuration of the Peak Fit plugin Page 46 225 GDSC SMLM ImageJ Plugins To load a set of saved templates run the TemrLare Conricuration plugin The user will be asked to select a template directory By default this is a directory inside the user s home directory named gdsc smim When the directory is selected all files with the XML extension will be processed If the file can be successfully loaded as a GDSC SMLM settings file then the template will be added to the list of available templates The template will be named using using the filename without the xml file extension Any existing templates with the same name will be replaced When finished the number of templates successfully loaded will be displayed Templates can be used to pre configure settings for the software for different microscope equipment or different fitting scenarios e g high
243. pley s L plot shown for two datasets with 99 confidences intervals upper limit blue and lower limit red A Data showing a significantly non random distribution Data was generated by simulating randomly placed fixed position fluorophores with average t on times of 3 frames Localisations are expected to be non random B The same data following tracing with t 10 frames d 0 3 pixels Localisations have been collated into single molecules and the traced data do not show deviation from a random distribution 7 6 Dark Time Analysis The Dark Time Anatysis plugin computes a dark time histogram for blinking fluorophores and then outputs the time threshold required to capture a specified percentage of the blinks Fluorophores can be inactive dark for a variable amount of time between fluorescent bursts If tracing is to be used to connect all separate bursts from the same fluorophore into a single molecule then the tracing must be done using the maximum dark time expected from the fluorophore This can be estimated using the Dark Time Anarys s plugin ideally on an image sample of fluorophores captured under the same imaging conditions as will be used for in vivo experiments The most success will be obtained using fixed fluorophore samples The plugin performs tracing or clustering on the localisations using a specified search distance and the maximum number of frames in the results for the time threshold This allows the algorithm to connect
244. plot shows a very similar width for the fibres as the original image However there has been a significant reduction in background noise since any signals not identified as a localisation are removed The Locatisations image method can be used to directly count localisations in an area for example counting localisations in regions of a cell This is only valid if the image has not been rendered using equalisation since that adjusts the pixels values to increase contrast A region can be marked on the image using any of ImageJ s area ROI tools The localisation count can be measured by summing the pixel intensity in the region This is performed using the Anatyze gt Measure command Ctr_ M Note Ensure that the INTEGRATED DENSITY Measurement is selected in the ImageJ Anatyze gt Ser MEASUREMENTS dialogue Page 42 225 GDSC SMLM ImageJ Plugins A Original average intensity projection B Localisations the C Signal intensity weighted and equalised D PSF equalised A Illustration 6 Example super resolution images using different rendering methods Images were generated from a sequence of 2401 frames using the Tubulins 1 dataset from the Localisation Microscopy Challenge 2013 http bigwww epfl ch smim challenge The original image has been enlarged using 8x magnification and part of the image has been extracted using a region of 256x256 pixels at point x 1348 y 1002 The region contains 3855
245. plugin is running the Peak Fit plugin with an argument indicating that it should only find the spot candidates Page 215 225 GDSC SMLM ImageJ Plugins The SMLM Toots window is a series of buttons arranged in columns Each button on the window has the name of the plugin The buttons are ordered using the order of the configuration file Any separator entries in the file using the plugin name will result in padding being applied between buttons a separator row Separator rows are also added for empty lines 2 or more successive separator entries will result in a new column Illustration 46 shows an example of the SMLM Toots window Page 216 225 GDSC SMLM ImageJ Plugins Ed Simple Fit GDSC SMLM Image Plugins Drift Calculator v A x POF Creator Peak Fit Trace Molecules PSF Combiner Fit Configuration Density Image Dark Time Analysis Create Data Peak Fit Series Blink Estimator Create Data Image PSF Batch Fit Neighbour Analysis Image Background Spot Finder Filter Analysis Load Localisations Spot Finder Series Fit Maxima Create Filters Filter Analysis File Install SMLM Toolset Gaussian Fit Spot Analysis Show SMLM Tools Results Manager Summarise Results Spot Analysis Add Create SMLM Tools Config Fourier Image Resolution PSF Calculator Clear Memory Results Rename Results Smooth Image Filte
246. posure Time The fourth dialog of the wizard requests the exposure time Ly uy PeakHt K x PeakFit Configuration Wizard Enter the exposure time Calibration of the exposure time allows correct reporting of on and off times This is the length of time for each frame in the image Exposure time ms so OK Cancel Help 5 1 2 5 Configuration Wizard 5 Peak Width The fifth dialog of the wizard requests the expected peak width for the 2D Gaussian gw PeakFit Configuration Wizard Enter the expected peak width in pixels A point source of light will not be focussed perfectly by the microscope but will appear as a spread out peak This Point Spread Function PSF can be modelled using a 2D Gaussian curve An optimised optical system lens and camera sensor should have a peak standard deviation of approximately 1 pixel when in focus This allows the fitting routine to have enough data to identify the centre of the peak without spreading the light over too many pixels which increases noise The peak width can be estimated using the wavelength of light emitted by the single molecules and the parameters ofthe microscope Use a PSF calculator by clicking the checkbox below JRun PSF calculator Gaussian SD 11 000 OK Cancel Help Page 23 225 GDSC SMLM ImageJ Plugins A checkbox is provided which allows the user to run the PSF Calculator The calculator will compute an expected G
247. ptions IMAGE SCALE The factor used to enlarge the image File Results RESULTS DIR The directory used to save the results The result file will be named using the input image title plus a suffix Leave empty for no results file Page 40 225 GDSC SMLM ImageJ Plugins Parameter Description BINARY RESULTS If selected save the results in binary format The suffix is results bin If not selected save the results in text format The suffix is results xls The results are tab delimited and can be opened in a spreadsheet application Saving the results in binary format provides very fast read and write performance It is preferred when using large datasets The data can be read using the Resutts Manacer plugin Memory Results RESULTS IN MEMORY Store all results in memory This is very fast and is the default option applied when no other results outputs are chosen preventing the loss of results Results in memory can be accessed by other plugins for example the Resutt Manacer can convert them to file or images The memory results will be named using the input image title If a results set already exists with the same name then it will be replaced 5 2 8 Interactive Results Table The results table will show the coordinates and frame for each localisation To assist in viewing the localisations the table supports mouse click interaction If the original source image is open in
248. put EM gain will be the total gain of the system 10 4 1 Multiple Input Images Input images requirements are the same as the Mean Variance Test plugin images should be taken of the same view using different exposure times Each image must have at least two frames All images must be taken with the camera in the same gain mode and EM gain mode A bias image zero exposure must be provided If all the images are valid the plugin will show a dialogue asking for the camera gain Illustration 39 This will be the last entered value or the value computed by the Page 187 225 GDSC SMLM ImageJ Plugins Mean VARIANCE Test plugin dy o Mean Variance Test lt 2 gt YD Xx Estimating the EM gain requires the camera gain without EM readout enabled Camera gain ADU e 0 1557 _OK Cancel Illustration 39 EM gain dialogue of the Mean Variance Test EM CCD plugin 10 4 2 Analysis The images are analysed as per the Mean Variance Test plugin However the analysis of the difference image is used to approximate the camera EM gain variance mean bias 2 x gain EM gain This is recorded in a Summary table A graph is then produced of the mean verses the variance This data is fitted with a straight line The gradient of the line is the EM gain multiplied by twice the camera gain therefore the EM gain can be computed as gradient eee 2x gain 10 4 3 Output The plugin summary table and mean variance plot are the same as
249. r Results Binary Display PSF Estimator Mean Variance Test Reset Display Mean Variance Test EM CCD Free Filter Results Pixel Filter Diffusion Rate Test Results Match Calculator Trace Match Calculator Spot Inspector Noise Estimator Illustration 46 SMLM Tools window 12 3 Create SMLM Tools Config Create a configuration file allowing the SMLM Toots window to be customised PC PALM Molecules PC PALM Analysis PC PALM Fitting This plugin extracts the plugins config file from the SMLM jar file and writes it to ImageJ Pathl plugins smim config Optionally the file can be edited before installation to customise the plugins that appear on the SMLM Toots window see 12 2 Show SMLM Tools If the file cannot be written the plugin will report an error If the file already exists the user will be informed that they will overwrite the file and the option to remove the existing file is also provided If removed the SMLM Toots window will revert to showing the default plugins If the plugin is run and the SMLM Toots window is currently open then it will be closed and re opened to update to the new configuration Page 217 225 GDSC SMLM ImageJ Plugins Appendix A Localisation Precision The theoretical limit precision for fitting the signal number of photons and the XY coordinates localisation can be computed using the formulas of Thompson et al 2002 for the
250. race will be stored together under a Trace entry The Trace entry will have the format Trace x y sd n n b n on f off f signal f where e x amp yare the coordinates of the centroid e sd is the standard deviation of distances to the centroid e nis the size of the cluster e bis the number of pulses bursts of continuous time frames e onis the average on time of each pulse e off is the average off time between each pulse e signal is the total signal for all the localisations in the trace The prefix character allows the clusters to be ignored as comments for example when the cluster file is loaded as a results file Note that the number of bursts is equal to the number of blinks 1 It is equivalent to the blinking rate of the molecule Page 81 225 GDSC SMLM ImageJ Plugins 7 2 6 Refit option Provides the option to extract all the frames corresponding to a single trace from the source image into a combined image and perform PSF fitting The refit option is only available if the plugin can successfully load the original input source for the results This may be an image open within ImageJ or could be the image file or series located on disk The plugin must also be able to recover the original fitting configuration used when generating the results This should be stored by default as part of the results set The fitting configuration is used to set the standard fitting options in the dialogue The fitting options
251. races are plotted against the time separation and a best fit line is calculated The Mean squared distances are proportional to the diffusion coefficient D MSD nAt 4DnAtt 4o where n is the number of separating frames At is the time lag between frames and O is the localisation precision Thus the gradient of the best fit line can be used to obtain the diffusion coefficient Note that the plugin will compute a fit with and without an explicit Page 199 225 GDSC SMLM ImageJ Plugins intercept and pick the solution with the best fit to the data see 10 8 3 Selected the best fit Given that the localisations within each trace are subject to a fitting error or precision 0 the apparent diffusion coefficient D can be calculated accounting for precision Uphoff et al 2013 2 D max 0 pon 4At At The plugin thus computes the average precision for the localisations included in the analysis and reports the apparent diffusion coefficient D If the average precision is above 100nm then the plugin prompts the user to confirm the precision value 10 8 2 Jump Distance analysis The jump distance is how far a particle moves is given time period Analysis of a population of jump distances can be used to determine if the population contains molecules diffusing with one or more diffusion coefficients Weimann et al 2013 For two dimensional Brownian motion the probability that a particle starting at the origin will be encounter
252. re neighbour region with edges of 2 x radius If disabled use a circular neighbour region with the specified radius Using the square approximation avoids computation of pairwise distances by assigning localisations to a grid and summing the counts within the grid neighbourhood It is very fast when using extremely large datasets SQUARE RESOLUTION Define how many grid points will be used per pixel A larger resolution provides more accurate counting results at the cost of computational speed and memory size Page 89 225 GDSC SMLM ImageJ Plugins Parameter Description SCORE Define the score that will be output in the density image See 7 5 1 Available Density Score functions FILTER LOCALISATIONS Remove all localisations that have a score below the specified value The remaining localisations will be stored in a new results set in memory The results will be name using the source results name plus the suffix Density Filter FILTER THRESHOLD Define the filter threshold Most score functions will be either zero or 1 if the density matches that expected for randomly distributed particles Compute Ripley s L pLot Analyse the data using a range of distance thresholds and compute the Ripley s L score for each Show a plot of the L score against the distance threshold See 7 5 2 Ripley s L plot 7 5 1 Available Density Score functions The plugin computes the number of localisations in a regi
253. results table FILTER RESULTS Removes fits that are far away from the initial guess of the Gaussian Only valid for single fitting as peaks are filtered individually Peaks are removed if they drift more than half the width of the smoothing window or if the width changes more than 3 fold from the initial estimate Click OK to start the fitting The fit uses a non linear least squares routine until convergence If convergence is not achieved by the maximum number of iterations the fit fails The fitted results are output to a results table Page 56 225 GDSC SMLM ImageJ Plugins 6 Results Plugins The following plugins allow localisation results to be opened converted and saved using various formats The plugins are described in the following sections using the order presented on the PLucins gt GDSC SMLM gt Resutts menu 6 1 Results Manager Allows results to be output to a results table an image or to file The Resutts Manacer allows the Peak Fit plugin to be run in the fastest mode with no output results results are saved to memory The results can then be visualised with different options using the Resutts Manacer and saved to file Reconstructed images can be saved using the standard ImageJ Fite gt Save As options The plugin can be used to convert text results to binary results and vice versa Binary results save and load very fast but are not human readable They are a good option for storing large res
254. riginal source cannot be located then the plugin will fail with an error message The following parameters can be configured Parameters Description INPUT Select the input results set RANKING Select the score used to rank the results Rapius Select the pixel radius around the localisation centre to extract CALIBRATED TABLE Show the localisation sizes in nm default is pixels PLOT SCORE Show a plot of the score against the rank PLOT HISTOGRAM Show a histogram of the score HISTOGRAM BINS The number of bins to use for the histogram REMOVE OUTLIERS Remove any localisation from the plots that lies more than 1 5x the interquartile range above or below the 25 and 75 percentile quartile boundaries This can remove poor scoring results that skew the plot visualisation Page 67 225 GDSC SMLM ImageJ Plugins 7 Analysis Plugins The following plugins perform analysis on localisation results The plugins are described in the following sections using the order presented on the Piucins gt GDSC SMLM gt Analysis menu 7 1 Drift Calculator Stabilises the drift in the image by calculating the drift for each frame and applying it to correct the positions of the localisations Drift can be calculated using e Sub image alignment Subsets of the localisation data are used to build images that are aligned to the global image e Fiducial markers within an image The positions of fiducial markers
255. rs that may not be within that range If the range and increment for the parameters is well chosen then the optimal parameters can be found without computing the results for a large set of filters Page 166 225 GDSC SMLM ImageJ Plugins 9 13 3 Parameters When the plugin is run a dialog is present allowing parameters to be configured The dialog message shows a summary of the results computed by Fit Spot Dara that will be analysed The number of results is shown along with the number of true positives within the results if they are scored with the current values for the match distances If the match distances are altered then the number of true positives will be recomputed when the plugin is run but will not update in the plugin message until it is next displayed The expected signal and localisation precision of the simulation localisations is computed using the formulas of Thompson for signal and Mortensen for localisation see Appendix A Localisation Precision for more details Note that the match distance parameters are expressed relative to those used in the Fit Spot Data plugin This is because the matches are assigned within that program and cannot be recomputed A lower distance is allowed as it will change a match to a non match However higher values are not allowed The distances that were used by the Fit Spot Data plugin are shown in a message above the section where the distances are configured to remind the user of the value
256. rted for 95 99 and 100 This value can be used to determine the Fait timit parameter for the Peak Fit plugin for different imaging conditions i e how many failures to allow before processing of fit candidates is stopped The analysis results are then reported in a summary table Field Description FRAMES The number of frames in the simulated image W The width of the simulated image minus the analysis border H The height of the simulated image minus the analysis border MoLEcuLES The number of molecules that occur within the bounds of the analysis border DensITY The molecule density within the analysis region Page 154 225 GDSC SMLM ImageJ Plugins Field Description N The average number of photons per localisation Ss The standard deviation of the Gaussian profile that matches the PSF A The pixel size DEPTH The z depth of the localisations FIXED True if the simulation used a fixed depth Gain The total gain of the simulation ReaoNoIse The read noise of the simulation B The background number of photons B2 The noise per pixel This is a combination of the read noise and the background number of photons SNR The signal to noise ratio N sqrt b2 s Px The standard deviation of the Gaussian profile that matches the PSF in pixels TYPE The type of filter SEARCH The search width BORDER The border WIDTH The effective widt
257. rvatory 124 Page 224 225 GDSC SMLM ImageJ Plugins Ulbrich Isacoff 2007 Subunit counting in membrane bound proteins Nature Methods 4 319 321 Uphoff S Reyes Lamothe R Garza de Leon F Sherratt D J Kapanidis A N 2013 Single molecule DNA repair in live bacteria PNAS 110 8063 8068 Veatch S L Machta B B Shelby S A Chiang E N Holowka D A Baird B A 2012 Correlation Functions Quantify Super Resolution Images and Estimate Apparent Clustering Due to Over Counting PLoS One 7 Issue 2 e31457 Weimann L Ganzinger K A McColl J Irvine K L Davis S J Gay N J Bryant C E Klenerman D 2013 A Quantitative Comparison of Single Dye Tracking Analysis Tools Using Monte Carlo Simulations PLoS One 8 Issue 5 e64287 Wolter S Sch ttpelz M Tscherepanow M Van De Linde S Heilemann M And Sauer M 2010 Real time computation of subdiffraction resolution fluorescence images Journal of Microscopy 237 12 22 Page 225 225
258. s Re run the Fit Spot Dara plugin if you wish to use higher values The following parameters can be adjusted Parameter Description FAIL COUNT The number of failures to accept before rejecting the remaining results from the current frame FAIL COUNT RANGE If specified the filter will be evaluated using each fail count from Fait COUNT tO FaiL COUNT FAIL COUNT RANGE This setting significantly slows down computation as the filters must be evaluated multiple times and results pre processing is not performed RANK BY SIGNAL By default results are ranked using the order determined by the spot filter that identified the candidates Choose this option to rerank the results using the fitted signal Note that ranking spot candidates by fitted signal is not possible in the Peak Fit plugin since fitting results have not been computed This option allows the user to test if fitting every possible candidate spot re ranking and then filtering would improve results SHOW TABLE Show a result table with the scores of each filter SHOW SUMMARY Show a result table with the best filter s from each filter set CLEAR TABLES Remove any results in results tables that are already open Page 167 225 GDSC SMLM ImageJ Plugins Parameter Description SUMMARY TOP N Show the top N filters from each filter set in the summary table Set to zero to disable show only the top 1 filter SUMMARY DEPTH Specify
259. s plugin searches for the neighbour within the given time and distance thresholds with the highest signal These are then saved to file as a series of clusters Each cluster has either one or two entries The first contains the details of the localisation the optional second entry contains the details of the neighbour This plugin was written to allow off line analysis of the neighbours of localisations for example investigation of how average distance signal strength and frequency of neighbours vary when localisations are categorised using their own signal strength Page 95 225 GDSC SMLM ImageJ Plugins 7 9 Filter Analysis Performs filtering on a set of categorised localisation results and computes match statistics for each filter The Fitter Anacysis plugin is used to benchmark different methods for filtering the results of fitting a 2D Gaussian to an image When a Gaussian peak is fitted to an image it has many parameters that are changed in order to optimise the fit of the function to the data For example the centre of the spot the width of the spot etc It can be difficult to know if the parameters have been adjusted too far and the Gaussian function is no longer a fair representation of the image This plugin requires the user to prepare input data with fitting results identified as correct or incorrect The plugin will load the results and then filter them with many different settings The filtered results are compared with the class
260. s shown on the ImageJ task bar When tracing clustering is complete the plugin produces a histogram and cumulative histogram of the dark time for all traces The dark time corresponding to the specified percentile is then reported to the ImageJ log window 7 7 Blink Estimator Estimate the blinking rate of fluorophores in a results set The Buink Estimator uses the method of Annibale et al 2011 to estimate the blinking rate of a fluorophore The method is based on performing trace analysis of the localisations using different time thresholds The distance threshold used for the trace analysis is set using a factor of the average precision of all the localisations in the sample When the time Page 93 225 GDSC SMLM ImageJ Plugins threshold is 1 then the number of traces will be equal to the total number of flourescent bursts in the sample As the time threshold is increased the number of traces should asymptote at the number of molecules in the sample assuming that no missed localisation counts occur The curve of traces against time threshold can be fitted using the following formula 1 t N tg N 1 Mine i where ta is the dark time of the fluorophore time threshold N t is the number of traces at ta Nbiinx iS the average number of blinks per fluorophore t r is the average off time for fluorophores To avoid the problems associated with missed counts Annibale et al only fit this formula to the first five data poi
261. s then used to create an image of the density of localisations The following options are available Parameter Description INPUT Select the input results to analyse Rapius Specify the radius of the local region around each localisation Use ROI If selected the user will be presented with a dialogue allowing the selection of an image with an area ROI drawn on If only one image has an area ROI it will be chosen automatically The ROI will be scaled to the dimensions of the input results and only localisations within this region analysed This option allows the user to construct density images using only part of the input image results ADJUST FOR BORDER Localisations that are close to the edge of the analysis region will have a local area that extends outside the region This will result in under counting of neighbours This can be compensated for by scaling the count of neighbours using the proportion of area sampled e g if 40 of the area is sampled 60 missing the count is multiplied by 100 40 IMAGE SCALE Specify the scale of the output image relative to the input results CUMULATIVE IMAGE The output image may contain several localisations on the same pixel If CumuLarive mace is enabled each pixel will be the combined sum of all the localisation scores at that point If disabled each pixel will be highest score of any localisation score at that point Use SQUARE APPROXIMATION If enabled use a squa
262. score for each radius The score should be equal to zero for homogeneous data and is comparable across radii If the ConFIDENCE INTERVALS parameter is enabled the plugin will create 99 random simulations of the given sample size in the same sample area The L r r r score is computed for each simulation and the upper blue and lower red bounds of the confidence intervals are shown on the chart If the actual data values lies outside the confidence intervals then it is a non random distribution with 99 confidence An example of Ripley s L plot is shown in Illustration 46 The figure shows the L plot for simulated localisations of fluorophores The raw data show significant deviation from a random distribution 46A Tracing of the localisations with a suitable time and distance threshold collates the individual localisations into single molecule traces These do not show any deviation from a random distribution 46B Page 91 225 GDSC SMLM ImageJ Plugins r r L r Gaussian2D Create Data Ripley s L r r r yy a 5 D r L r Gaussian2D Create Data Traced Ripley s Lir r r JU Bee Pe ae x XXX x Ky XK XK x x x xxx xx ae dE 0 delo AN 1 0 1 2 1 4 0 A x 0 4 0 6 0 8 Radius 1 4 0 0 0 2 0 4 0 6 0 8 1 0 1 2 Radius List List Save X 0 66 Y 1 67 Save Copy Copy X 0 75 Y 34 3 Illustration 17 Ri
263. se then fitting will fix the signal parameter using the true signal SHOW HISTOGRAMS Show histograms of the results the difference between the fit results and the true answer If selected a second dialogue is shown allowing the user to choose which histograms to display 9 8 1 Data Summary The Fit Benchmark Data plugin will compute the difference between the fit result and the true answer for each parameter that was fitted Histograms of the differences can be shown using the SHow Histocrams options The average and standard deviation are then reported in a summary table Page 147 225 GDSC SMLM ImageJ Plugins Field Description MoLecuLEs The number of localisations in the benchmark data N The average number of photons per localisation Ss The standard deviation of the Gaussian profile that matches the PSF A The pixel size SA The standard deviation adjusted for square pixels computed as S Vs a 12 X The X position of the localisations relative to the centre of the image Y The Y position of the localisations relative to the centre of the image Gain The total gain of the simulation READNoIsE The read noise of the simulation B The background number of photons B2 The noise per pixel This is a combination of the read noise and the background number of photons SNR The signal to noise ratio N sqrt b2 Limit N The theoretical limit of si
264. section Image Background JE x z Creates a background and mask image from a sample input stack using a median projection Bias 500 Blur EF l2 OK Cancel Help illustration 34 Image background plugin dialogue 9 14 1 Image analysis The Imace Backcrouno plugin first computes a median intensity projection of the input image A Gaussian blur is then applied to the projection to smooth the image The blur parameter controls the size of the Gaussian kernel The bias is subtracted from the blurred image The bias is an offset that may be added to the pixel values read by the camera so that negative noise values can be observed It is a constant level that can be subtracted What remains should be the background level This can be ignored using a bias of zero Two output images are then displayed 1 Background the blurred projection 2 Mask the blurred projection subjected to the ImageJ default thresholding method 9 15 Load Localisations Loads the localisation file created by Create Data into memory The Create Data plugin simulates fluorophores in a 3D volume and then creates an image representation of the localisations The localisations are saved to file using a simple tab delimited format The records have the following fields Field Name Description 1 T Time frame 2 lo The identifier 3 X The x coordinate 4 Y The y coordinate 5 Z The z coordinate Page 177 225 GDSC SMLM Imag
265. sed to 1 on the chart but the label is unchanged This plot visualises how much of the PSF signal is missed at a given distance and how the focal depth changes how the signal is distributed The interactive dialogue is a blocking window It must be closed before the plots can be saved Finally the Centre of Mass CoM of the PSF is computed and shown on a plot The CoM is computed using all pixels within a fraction of the maximum pixel intensity of the image The default is 5 This should avoid including noise in the CoM calculation If the PSF is symmetric about the fitted centre then the CoM drift should be low In the example shown below the red line X drift is approximately flat but the blue line Y drift shows that the PSF is skewed in the Y direction as the CoM moves past the centre determined by the fitting algorithm Drift nm Slice 9 3 PSF Drift The PSF Drirt plugin computes the drift in a PSF image The drift can be stored as a correction factor applied to the PSF centre when reconstructing images using the PSF Page 122 225 GDSC SMLM ImageJ Plugins When the plugin is run it searches all the open images for valid PSF images These will be tagged in the image info property with PSFSettings XML containing details of the PSF The plugin then presents a dialogue where the user can configure how to compute the drift curve FE PSF Drift Select the input PSF image PSF PSF3tif v l Us
266. sequently the signal is modelled by sampling from a Gamma distribution with an average photon emission rate per second Alternatively a custom distribution can be used for example inputting a set of photon budgets extracted from real data An additional observation from real data is that the signal per frame of a molecule is negatively correlated with the total on time i e molecules that are on for a shorter amount of time have a brighter signal This may be because the release of more photons per second causes the molecule to expend the total photon budget and then photo bleach ina shorter time Thus the simulation allows the total on time of the fluorophore to be correlated with the average photon emission rate Molecules can move using diffusion The diffusion is modelled using a random walk as described in the Dirrusion Rate Test plugin see section 10 7 The diffusion can be random or confined to a specified volume The diffusion can be limited to a fraction of the molecules by fixing a random sample of the molecules The simulation runs for a specified duration at a given time interval per simulation step At each step the simulation calculates the new position if diffusing and fluorescence of the molecules These are then drawn on an image at a specified exposure rate The simulation interval does not have to match the exposure time of the output image Using a shorter simulation step than the exposure time is useful when simulating diffus
267. ses an analysis that assumes that the EM CCD camera has three main sources of noise 1 Photon shot noise occurs when light is emitted from an object Although the average rate of light from an object is constant for a given time e g 30 photons second each photon will arrive at a different time and the gaps between them will vary This will leads to changes in the number of photons counted each second This noise follow a Poisson distribution with a mean of the average photon emission rate 2 The photons are converted to electrons on the camera sensor These electrons are then multiplied in the Electron Multiplication EM gain register This multiplication increases the number of electrons to be read and reduces the relative size of any Page 189 225 GDSC SMLM ImageJ Plugins error introduced when reading the value However the EM gain process is random and introduces noise that is modelled using a Gamma distribution with a shape parameter equal to the number of input electrons and the scale parameter equal to the gain 3 Read noise occurs when the values stored on the camera chip for each pixel are read and converted to numbers This noise follows a Gaussian distribution with mean zero and variable standard deviation The probability of observing a pixel value given an input number of photons is therefore a convolution of a Poisson Gamma and Gaussian distribution The convolution of the Poisson and Gamma distribution can be expresse
268. set to O ID ANALYSIS If the results in the results set have an Id label for each localisation the plugin will compute the number of molecules that were matched The TP FN and recall for each results set will be added to the results table as additional columns Note Ids are added to the results by various plugins e g Trace MoLecuLes Create Data 6 10 1 Interactive Results Table The results SHow pairs table will show the coordinates and distance between matched pairs Unmatched paris will be added to the table at the end of the matches for the same time frame To assist in viewing the localisations that are matches the table supports mouse click interaction The table is linked to the results source for the Resutts1 input If this is an image open in ImageJ the table can draw ROI points on the image e Double clicking a line in the results table will draw a single point ROI at the coordinates identified The stack position will be set to the correct frame e Highlighting multiple lines with a mouse click while holding the shift key will draw multiple point ROI on the coordinates identified The frame will be set to the last identified frame in the selection The coordinates for each point are taken from the X1 amp Y1 columns or if they are unavailable the X2 amp Y2 columns 6 11 Trace Match Calculator Calculate the match statistics between two sets of traced molecules The Trace March Catcutator allows sets of tr
269. signal and Mortensen et al 2010 for the localisation Note that these formulas are derived from modelling the point spread function PSF as a 2D Gaussian for both the simulation and the fitting Given that the true data will have a PSF defined by the microscope parameters these formulas only approximate the precision that can be obtained on image data The photon count N is computed using the volume of the fitted 2D Gaussian function the signal divided by the camera gain _ Amplitude 21 0 0 o Gain The background noise b is estimated by the Peak Fit plugin during the fitting process either using a global noise estimate per frame or the local background level This is also adjusted by the camera gain to provide the noise in photons Note that the precision of the localisation is the square root of the variance Warning Without a correctly calibrated camera gain and bias the precision estimates in the SMLM code will be inaccurate A 1 Signal Precision From Thompson et al 2002 2 2 Var FX N ar 5 b a where Varn The variance of the signal a Gaussian 2D function to a Gaussian 2D PSF F The noise scaling factor 2 for an EM CCD camera 1 otherwise s The standard deviation of the Gaussian function N The number of photons in the localisation b The expected number of photons per pixel from a background with spatially constant expectation value across the image a The pixel size in nm From Thompson et al 2002 A 2 Loca
270. sitive Predicted Value PPV tp tp fp A score of 1 indicates that all the predicted points were correct lower scores indicate that some points are not correct precision Precision can be interpreted probabilistically as the chance that a randomly selected prediction is correct B 3 Jaccard The Jaccard measures the similarity between two sets and is defined as the size of the intersection divided by the size of the union Page 221 225 GDSC SMLM ImageJ Plugins _ ANB _ tp A as pe hi A score of 1 indicates that the overlap is perfect Zero indicates no overlap B 4 F score The precision and recall can be combined in a weighted score the Fg measure or F score F 1 B __precision recall 2 o B precision recall A weight of 1 produces the balanced F score where precision and recall are weighted equally Fos puts more emphasis on precision and F2 puts more emphasis on recall However the weight B can be any non negative real value The score was derived so that it measures the effectiveness of retrieval with respect to a user who associates 3 times as much importance to recall as precision B 5 FNR False negative rate FNR fn tp B 6 FDR False discovery rate EDR 1 Precision P tp fp B 7 Defining the Actual or Predicted Points Note that the categorisation of the actual and predicted points can be arbitrary If the categorisation is reversed then the precision and reca
271. ssing by ignoring many of the candidates Since the spots were simulated it is known which candidates are correct positives and which are incorrect negatives The Fit Spot Data plugin allows the user to specify the fraction of positives in each frame that will be processed This sets a target limit for the positives When this target has been reached the plugin will continue processing candidates until 1 a set fraction of the total number of candidates processed are negatives and 2 a minimum number of negatives after the positive target have been processed The rest of the candidates are then ignored and marked as not fitted The algorithm used to fit the spots can be configured in the plugin options However all fit results are accepted as long as the fitted signal is above zero There is no filtering performed by the plugin on the fit results This provides an upper limit for the recall that is possible using this fitting configuration Filtering of the results using limits on the signal peak width precision etc is done using the Benchmark FILTER Anarys s plugin When all the fitting has been done the fitted coordinates and any candidates coordinates that were not fitted or failed to fit are compared with the actual coordinates that were simulated The two sets of coordinates are assigned as matches if they are within a configured distance In addition the fitted candidates can be set as matches if they are within a factor of the true sig
272. stration 46 The chart shows a clear improvement and then fall off in performance as the lower threshold is increased Page 99 225 GDSC SMLM ImageJ Plugins 1 0 0 8 0 6 0 4 Jaccard 0 2 0 0 20 30 40 50 60 70 80 Precision Save Copy lllustration 21 Plot of the Jaccard score verses lower precision limit for the l Hysteresis Precision filter The upper limit for hysteresis thresholding is 20nm higher than the lower limit 20 7 9 4 3 Sensitivity analysis If CALCULATE sensitivity IS selected the plugin produces a table of the sensitivity of each parameter for each unique filter identified by name The sensitivity is calculated for the filter parameters that produce the highest Jaccard score The sensitivity is the partial gradient of the score with respect to each parameter If the sensitivity is low then the filter will perform well using a range of parameter values If the sensitivity is high then the filter performance will rapidly fall off as the optimum parameter value is changed Ideally a good filter will have good performance metrics and low sensitivity across all the parameters It may be better to choose a filter that does not have the highest Jaccard score but has the lowest sensitivity This filter should perform better on a range of input data The sensitivity is calculated by altering each parameter by a relative amount The delta parameter controls the update magnitude Note that integer parameters w
273. stributions of localisations random fluctuations or an emulsion The plugins are described in the following sections using the order presented on the PLucins gt GDSC SMLM gt PC PALM menu Note The PC PALM plugins are under development and should be considered experimental The plugins are subject to change and so no documentation has yet been produced to describe them They are included in this package to assess interest from the community If you wish to use the plugins please contact a herbert sussex ac uk for more information 8 1 PC PALM Molecules Prepare results held in memory for analysis using pair correlation methods This plugin either simulates results or filter results from a results set to a set of coordinates with time and photon signal information The localisations are drawn on a binary image to allow regions of the data to be selected for analysis 8 2 PC PALM Analysis Perform pair correlation analysis in the frequency domain as per the paper by Sengupta et al 2011 Sengupta et al 2013 to produce a g r correlation curve 8 3 PC PALM Spatial Analysis Perform pair correlation spatial analysis as per the paper by Puchnar et al 2013 This methods plots the molecule density around each localisation as a function of distance from the localisation 8 4 PC PALM Save Results Saves all the PC PALM results held in memory to a results folder 8 5 PC PALM Load Results Load all the PC PALM results from a res
274. sub images from N consecutive frames using the coordinates from the localisations plus the drift for that time point 3 Combine all sub images to a master projection 4 Aligns each sub image to the master projection using correlation analysis The drift time point is set using the average frame from all the localisations in the sub image 5 Smooth the drift curve 6 Calculate the change to the drift and repeats from step 2 until convergence The following parameters can be specified Parameter Description FRAMES The number of consecutive frames to use to construct each sub image MINIMUM LOCALISATIONS The minimum number of localisations used for a sub image If the frames for a sub image do not contain enough localisations then Page 72 225 GDSC SMLM ImageJ Plugins they will be combined with the next set of frames until an image is produced with the minimum number of localisations FFT size Specify the size of the reconstructed image Large images will a be slow to process b if there are not enough localisations the image density will be spread out and the correlation between images may not work and c may produce a better drift estimate if the number of localisations per sub image is very high 7 1 2 Drift File The drift can be loaded directly from file The file must contain delimited records of Time X Y The fields can be delimited with tabs spaces or commas Any line not starting with
275. t more images gt lt images gt lt parameters gt lt parameter gt lt name gt signalStrength lt name gt lt value gt 30 0 lt value gt lt parameter gt lt more parameters gt lt parameters gt lt resultsDirectory gt G Temp lt resultsDirectory gt lt runPeakFit gt true lt runPeakFit gt lt gdsc fitting batchSettings gt lt images gt The lt images gt tag is used to specify the full path to the input images Each image should be within a lt string gt tag lt parameters gt The lt parameters gt tag can contain any named parameter for the Peak Fit plugin Generating a new configuration file will create all the valid parameters with the default values Multiple values for a parameter are specified using a comma delimited list in the lt value gt tag e g lt parameter gt lt name gt signalStrength lt name gt lt value gt 30 40 50 lt value gt lt parameter gt will run the Peak Fit plugin using a signal strength of 30 40 and 50 If a parameter is removed then the default value will be used This allows redundant parameters to be removed from the batch file for simplicity Page 50 225 GDSC SMLM ImageJ Plugins The values that are allowed for each parameter can be deduced from the Peak Fit dialogue as follows Field Type Allowed values Example Field Example Value NUMBER WITH Any floating point number InrriaL StToDevO 1 2 DECIMAL PLACES NumBer wi
276. t are a member of that trace are assigned the same ID The results are then saved into memory The results are named using the input results set name plus a suffix as follows Page 80 225 GDSC SMLM ImageJ Plugins Suffix Description TRACED A full set of localisations with each assigned the corresponding trace ID TRACE CENTROIDS The localisations of each trace combined into a centroid Centroids have a signal equal to the sum of the localisations the coordinates are set using the signal weighted centre of mass of the localisations The background is averaged and the noise combined using the root of the sum of squares The Gaussian standard deviation of the localisation is set using the average precision of the localisations calculated using the Mortensen formula TRACE SINGLES Contains the localisations that were not part of a trace i e are a single localisation Trace Centros Mutt The localisations of each trace combined into a centroid Only traces with multiple localisations are included It is possible to save these results to file using the Resutts Manacer plugin 7 2 5 File output If the Save traces option is selected then the plugin will show a file selection dialogue allowing the user to choose the location of the clusters results file The results will use the same format as the plain text file results option in the Peak Fit and Results MAnacer plugins However all the localisations for each t
277. t very close to the answer are not scored better than methods that get just close enough to the answer This can be overcome by repeating the analysis multiple times with different distance thresholds and averaging the scores An alternative is to use a ramped scoring function where the degree of match can be varied from O to 1 When using ramped scoring functions the fractional allocation of scores using the above scheme is performed i e candidates are treated as if they both match and unmatch and the scores accumulated using fractional counts This results in an equivalent to multiple analysis using different thresholds and averaging of the scores but it can be preformed in one iteration The choice of the distance thresholds for benchmarking a microscope setup can be made using the wavelength of light A and the expected number of photons The upper threshold can be set using the Abbe limit a Resolution 2 NA where NA is the numerical aperture of the microscope Abbe 1873 Any match below this distance is within the standard resolution of an optical microscope and so can be classed as a super resolution match The lower threshold can be set using the Mortensen formula for the precision of fitting a 2D Gaussian to 2D Gaussian data corrupted by Poisson noise see Appendix A Localisation Precision Although only an approximation of fitting to a microscope PSF the formula provides an estimate of the limit of super resolution fitting Any fitt
278. tain more than one localisation This can take a long time for large results sets since no heuristics are performed to rank traces and stop if fitting continuously fails A summary of the results of fitting each trace is shown in the ImageJ log e g Trace fitting 32 singles 92 208 fitted 880 separated Note that singles are traces that contain one localisation These are not fitted The separated score shows the number of localisations that were part of traces that could not be fitted These are judged to be from poor tracing through non identical molecules and Page 82 225 GDSC SMLM ImageJ Plugins are thus split apart Fitting results are stored in memory The results set is named using the input results set name plus the suffix Trace Fit Note that the results will be a composite of the successful fits and the remaining localisations All the traces that were a single molecule are included the positions of successfully fitted traces are included and all the localisations that were traced but not successfully fitted are included as single localisations 7 2 6 1 Use case for Trace Fitting When using Peak Fit all frames are processed individually This excludes the possibility of using adjacent frames to improve the signal to noise ratio of spots It is possible to run an off line analysis of an image by e Identification of candidates using Spot FinDER e Tracing neighbouring candidates using Trace Motecutes with t 1 and
279. te a table of molecule localisations and an image reconstruction Provides a step through guide for initial configuration of microscope parameters Peak Fit Performs fitting on an image to generate a list of molecule localisations Template Allows the user to load custom configuration templates from a Configuration directory Page 8 225 GDSC SMLM ImageJ Plugins Fit Configuration Allows setting the fitting parameters and saving them to file Peak Fit Series Performs fitting on folder of images to generate a list of molecule localisations Batch Fit Runs the Peak Fit analysis on an image for each configuration option in the batch Spot Finder Identifies candidate maxima in an image Spot Finder Series Identifies candidate maxima in a folder of images Fit Maxima Performs PSF fitting on candidate maxima Gaussian Fit Allows interactive identification of maxima and 2D Gaussian fitting 1 2 Results plugins Result Manager Allows conversion of the localisation results into different formats e g files or images Summarise Results Displays a summary of the results held in memory Clear Memory Results Removes all results held in memory Rename Results Allows the results sets to be renamed Resequence Results Allows the frame number of results to be rebuilt assuming a repeating pattern of data and non data frames Calibrate Results All
280. ted A different file can be selected by double clicking in the text box This will open a file selection dialogue Page 52 225 GDSC SMLM ImageJ Plugins If the file name is changed and the new file exists the plugin will provide the option to reload the settings from the new configuration file When the plugin runs all the settings will be saved to the configuration file overwriting any existing file 5 10 Gaussian Fit Uses the Gaussian fitting code to fit peaks Since it requires no calibration parameters the least squares estimation is used It is currently not possible to use Maximum Likelihood estimation The plugin identifies peaks on a smoothed image using non maximal suppression and a set of size filters It supports an interactive preview of the candidate peaks see Illustration 11 These are then fitted using a 2D Gaussian and the results are output to a table e y Sim_1200Phot Y amp BY B WY Gaussian Ft YU Y Y 1 100 104x126 pixels 32 bit SME Fit 2D Gaussian to identified maxima Gaussian Fitting Image smoothing s P Within a 2n 1 box ginenon mel Smoothing Ah Fit background Maxima identification Mido da stops Fit criteria Least_squared_error Box size al Max iterations 20 Background 1154 Significant digits 4 Min height a 171 Coord delta 0 0100 ET gt Fraction above background 0 00 Single fit M
281. tes 5 1 2 1 Configuration Wizard 1 Introduction The first dialog of the wizard warns the user that no configuration file could be loaded D amp PeakHt Y E x PeakFit Configuration Wizard No configuration file could be loaded Please follow the configuration wizard to calibrate Cancel Help Page 21 225 GDSC SMLM ImageJ Plugins 5 1 2 2 Configuration Wizard 2 Pixel Pitch The second dialog of the wizard request the pixel pitch D WY Peak t k x PeakFit Configuration Wizard Enter the size of each pixel This is required to ensure the dimensions of the image are calibrated E g a camera with a 6 45um pixel size and a 60x objective will have a pitch of 6450 60 107 5nm Calibration nm px 107 00 OK Cancel Help 5 1 2 3 Configuration Wizard 3 Gain The third dialog of the wizard requests the total gain Du PeakFit Configuration Wizard Enter the total gain This is usually supplied with your camera certificate The gain indicates how many Analogue to Digital Units ADUs are recorded at the pixel for each photon registered on the sensor The gain is usually expressed using the product of the EM gain if applicable the camera gain and the sensor quantum efficiency A value of 1 means no conversion to photons will occur Gain ADU photon 57708 OK Cancel Help Page 22 225 GDSC SMLM ImageJ Plugins 5 1 2 4 Configuration Wizard 4 Ex
282. the output PSF to be limited to N frames above and below the z centre The combined PSF is created by overlaying the x y z centres and summing the individual PSF images Each PSF is weighted using the number of images used to created the PSF divided by the total number of images 2 n The combined PSF image is shown as a new image The z centre is selected as the active slice The PSF image has an XML tag added to the image info property containing the z centre image scale and number of input images used This information is used in the Create Data plugin The information can be viewed using the Imace gt SHow InFo command weight 9 5 Create Data Creates an image by simulating single molecule localisations using a model of photoactivated diffusing fluorophore complexes The simulation is partly based on the work of Colthorpe et al 2012 9 5 1 Simulation Fluorophores initialise in an inactive state where they do not fluoresce The switch to an active state is caused by subjecting the fluorophore to an activation laser Once in an active state the molecule can fluoresce when subjected to a readout laser The amount of fluorescence is proportional to the intensity of the readout laser The active molecule can reversibly switch into a dark state where it does not emit fluorescence Switching on and off causes the molecule to blink Eventually the molecule will irreversibly bleach to a state where it no longer fluoresces Mole
283. ther localisation within 0 5 pixels and 1 time frame using the following combined filter lt OrFilter gt lt filterl class AndFilter gt lt filterl class SNRFilter snr 10 0 gt lt filter2 class PrecisionFilter precision 30 0 gt lt filter1 gt lt filter2 class TraceFilter d 0 5 t 1 gt Page 63 225 GDSC SMLM ImageJ Plugins lt OrFilter gt Note how the combined filters require that the contained filters are specified in a lt ritteR gt tag and the type of filter is specified using the cass attribute The filter parameters are specified using attributes 6 10 Results Match Calculator Calculate the match statistics between two results sets The Resutts March Catcutator allows two sets of localisations to be compared The results are processed per time frame The plugin can identify results that span multiple time frames e g trace results produced by the Trace Motecutes plugin These will be split into a single localisation for each frame all with identical coordinates Localisations are identified as a match if they are within a set distance The plugin computes matches iteratively allocating the closest pairs first until no more matches can be made The matches are used to compute comparison score metrics to show the similarity between the two results sets The available metrics are Precision Recall F score and Jaccard Details of the comparison metrics can be found in Appendix B
284. tially set to the defaults which should work in most cases See the Peak Fit plugin for details of how to configure the solver FIT FUNCTION The function used to fit the data OFFSET FIT Fit each image with the initial guess for the centre shifted by an offset The guess is shifted in each of the 4 diagonal directions from the true centre START OFFSET The offset to use with the Orrser rit option Page 124 225 GDSC SMLM ImageJ Plugins Parameters Description INCLUDE CoM eit Fit each image with the initial guess for the centre as the centre of mass of the pixels Use SAMPLING Draw the PSF by sampling it as a 2D probability distribution The alternative is to draw it exactly using bilinear interpolation to scale the PSF PHOTONS The signal to draw in photons PHOTON LIMIT The lower fraction of the actual photons where fits will be rejected Fits are always rejected when the photons are 2 fold higher than the actual value SMOOTHING The smoothing parameter used to smooth the fit curve using the LOESS smoothing algorithm 9 3 3 Output The drift for each frame is computed as the mean of all the fit centres The curve represents the average centre of the PSF following idealised fitting of the data with the chosen Fit sotver and Fit Function i e no noise other than Poisson noise if Use sampuine is enabled The drift curves for each dimension X amp Y are then plotted
285. ting the plugin to continue with the same population PARAM NAME The mutation range The dialog will present a field for each named parameter of the filter The mutation range is the standard deviation of the Gaussian distribution used to mutate the parameter Note If the filter set was created using expansion from min max increment values then the range defaults to zero for any parameter that was not expanded It is assumed that the user does not want to explore this parameter Otherwise the value is a default for the filter parameter adjusted by the Detta parameter Once the genetic algorithm is started a results table is created named Benchmark Filter Analysis Evolution This table contains the same columns as the main results table with an extra column for the iteration of the algorithm The results from the best filter per iteration are added to the table This table can be used to track the progress of the algorithm If desired the algorithm can be stopped manually by pressing the Escare character 9 13 4 Results If the DEPTH RECALL ANALYSIS Option was selected the plugin will compute a histogram of the recall verses z depth Three histograms are computed The first is for all the localisations This is plotted in black and provides the upper limit for performance The second is the histogram for all the fitted results that match a localisation This is plotted in blue and provides the upper limit that can be achi
286. tion using the hotkey This allows faster analysis of images using only simple keyboard commands 7 14 Fourier Image Resolution Calculate the resolution of an image using Fourier Ring Correlation FRC This plugin is based on the FIRE Fourier Image REsolution plugin produced as part of the paper by Niewenhuizen et al 2013 The plugin was rewritten for speed optimisation and to improve the determination of line crossing points on the computed curves Fourier Ring Correlation computes the correlation between the features of two images ata certain spatial frequency A 2D image is transformed into the frequency domain using a Fourier transform The frequency image represents the amplitude and phase of the original data at different frequencies These can be visualised as a 2D image the centre of the image represents the highest frequencies moving to the lowest frequencies at the edge of the image Points taken from a ring drawn around the centre will represent all the Page 109 225 GDSC SMLM ImageJ Plugins amplitude and phases present at a single frequency Two images can be compared at a given frequency by measuring the correlation of the data sampled from the same ring on both images This is the Fourier Ring Correlation To compute the image resolution of a set of localisations requires the following steps e Split the data into two halves e Produce a super resolution image using each half of the localisation data e Transform the two
287. to choose a plot option An ideal plot will show an inverted L shape as shown in Illustration 16 The parameters that achieve a score close to zero are shown in black The scale of the image has been calibrated to use the scale of the distance and time thresholds Therefore hovering over a part of the image will show the time X axis and distance Y axis threshold required for the given score Page 79 225 GDSC SMLM ImageJ Plugins Ly a Find Clusters N N_actual N_actual y 80 00x5 00 sec 400x400 32 bit 625K Illustration 16 Output plot from the Trace Molecules optimisation algorithm The plot shows the absolute score against the time X coordinate and distance Y coordinate thresholds Note that at the end of optimisation the thresholds are automatically set using the zero score that is closest on the plot to the origin This should be a compromise point between the two thresholds The values used will be written to the ImageJ log window The tracing algorithm then runs and the traces are stored in memory If the optimised thresholds are not suitable it is left to the user to interpret the plot of the scores and select the best values For example this could be done by assuming the distance threshold calculated using 2 5xPrecision is correct and looking up the corresponding time threshold when the score is zero 7 2 4 Memory Output The tracing algorithm assigns a unique ID to each trace All the localisations tha
288. to select a folder containing source images This works using the same method as the Peak Fit Series plugin More details on the selection options can be found in section 5 5 Peak Fit Series 5 9 Fit Maxima Fits a 2D Gaussian to identified maxima This plugin uses the same algorithm as the Peak Fit plugin to fit maxima Candidates are taken from any results set held in memory with a valid image source i e fitting a list of selected maxima can be performed on the original data Candidates are collated per time frame and processed in ranked order until a number of successive fits fails or no candidates remain Candidates can be identified using the Spot Finper plugin Running the Spot Finner and Fit Maxima plugins will produce the same results as using the Peak Fit plugin However separating the two steps allows processing to be performed on the candidates For example the Trace Motecutes plugin can be used to join up candidates in successive frames and fit the combined stack These are identified internally as spanning multiple frames by tagging an end frame onto the result The Fit Maxima plugin will not fit any results that span multiple frames these will be send directly through to the result output The fit configuration is the same as in the Peak Fit plugin As with the Peak Fit plugin the settings contained in the configuration file are loaded when the plugin is initialised If no file exists then a default set of settings will be crea
289. tput image is selected then the stack must contain enough frames to plot all the localisations If no output image is selected then the default output image will be created as a stack of the required size LUT Specify the look up table i e the colour used to plot the clusters Each cluster is a single colour The colour is varied according to the order the clusters are processed Note Single colour LUTs vary the intensity of the colour from 50 to 100 to provide identification of the order 7 4 1 Drawing cluster centroids Note that the Draw Cuusters plugin will draw all the members of a cluster on the image If you wish to draw only the centroids then you should either e Load the centroids from a pre processed file as a single localisation with a unique ID e Run a clustering algorithm Trace Motecutes Cluster Motecutes and then select an appropriate centroids dataset that is stored in memory If you wish to draw the cluster centroid on each frame that contains a member of the cluster then you can use the ExPanD To sincLes and Use stack position options 7 5 Density Image Analyses the local density around each localisation and outputs an image using the Page 88 225 GDSC SMLM ImageJ Plugins density score Can optionally filter localisations based on the density score into a new results set The Density Imace plugin counts the number of localisations in the neighbourhood of each localisation The score i
290. tted data should allow the user to decide if a fluorophore is on in the selected frame The frame can be added to the on frames list using the App button This can also be performed using a shortcut key mapped to the Spot Anatysis App plugin see section 7 13 The frame is added to the list in the Spot Anatysis window along with the current estimate of the signal for that frame Note that LOESS smoothing only uses frames that have not been selected as on frames Consequently the background and the noise are updated as more on frames are added to the list 7 12 2 3 Saving a fluorophore sequence When all the on frames have been marked the fluorophore sequence must be saved using the Save button This will record the sequence to a summary window as shown in Illustration 27 The window shows the fluorophore signal on and off times and number of blinks Su Spot Analysis Results Y y x File Edit Font E 1 153 5 1035 3242 80 0 5800 0 3 20 0 1930 0 20ms_4 tif Illustration 27 Spot Analysis summary window The Save button can only be pressed once to prevent duplicates in the window If the sequence list is updated by adding or removing on frames then the listed can be re saved Note that the old sequence will remain in the summary window and the new sequence will have a new ID The old sequence should be removed using the summary tables Epit gt CLEAR command Page 107 225 GDSC SMLM ImageJ Plugins 7 12 3 Analysis Workfl
291. ue to blinking it is possible to trace the localisations through time Any localisation that occurs very close to another localisation from a different frame may be the same molecule The distance between localisations can be spatial or temporal Using two parameters it is possible to trace localisations using the following algorithm Any spot that occurred within time threshold and distance threshold of a previous spot is grouped into the same trace as that previous spot When all frames are processed the resulting traces are assigned a spatial position equal to the centroid position of all the spots included in the trace The molecule tracing algorithm is based on the work of Coltharp et al 2012 7 2 2 Trace Molecules Plugin The Trace Mo ecutes plugin allows temporal tracing to be performed on localisations loaded into memory Illustration 15 shows the plugin dialogue Page 75 225 GDSC SMLM ImageJ Plugins Input movie part2 tif LVM 77475 Distance Threshold nm 150 00 Distance Exclusion nm 0 00 Time Threshold seconds 6 00 Trace mode LatestForerunner Pulse interval frames 0 Pulse window frames 0 Split pulses Optimise Save traces Show histograms Save trace data Refit option OK Cancel Help Illustration 15 Trace Molecules dialogue The following parameters can be configured Parameter Description INPUT Specify the localisations to use Distance THRESHOLD Nm Maximum distance in
292. ultiplied by the fraction of the step that the fluorophore was active The number of photons is then sampled from the Poisson distribution with the given mean for the step This models the photon shot noise at a per simulation step basis The photons are then sampled onto the photo cells using a point spread function When the localisation is drawn on the image the variance of all the background pixels in the affected area is computed to be used to compute the localisation noise The variance of the background image is combined with the variance of the read noise image to produce the total variance The background image variance is in photons the read noise is in electrons The units are converted to ADUs using the appropriate gain factors The square root of the sum of the variances is the fluorophore noise Note that the noise value calculated is the noise that would be in the image with no fluorophore present This is the true background noise and it is the noise that is estimated by the Peak Fit plugin during fitting This noise therefore IGNORES THE PHOTON SHOT NOISE of the fluorophore signal Once all the localisations have been processed the captured photons are converted to electrons by sampling from a binomial distribution with the probability set to the quantum efficiency The electrons are amplified using the Tubbs model Tubbs 2004 for EM noise where the number of addition electrons generated in the EM amplification are sampled from a gam
293. ults folder to memory Page 113 225 GDSC SMLM ImageJ Plugins 8 6 PC PALM Fitting Combines multiple correlation curves calculated by PC PALM Analysis into an average curve and fits the curve using various models 8 7 PC PALM Clustering Clusters localisations using a distance threshold and produces a histogram of cluster size This can be fit using a zero truncated negative Binomial distribution with parameters n p to calculate the size of the clusters n and the probability of seeing a fluorophore p Page 114 225 GDSC SMLM ImageJ Plugins 9 Model Plugins The following plugins allow single molecule images to be simulated This can be used for benchmarking fitting parameters by comparing the results of fitting the simulation to the actual known positions Note that comparison of two sets of localisations can be done using the Resutts March Catcutator plugin see section 6 10 9 1 1 Benchmarking The benchmarking system provides the means to optimise the SMLM tools to produce the best results on data that is typical of a microscope setup e Create an ideal PSF of the microscope PSF Creator and PSF Drirt e Draw spots on an image using a defined camera noise model at configured XY positions and z depths Create Spot Data e Identify candidates for fitting Fitter Spot Data e Fit candidate spots Fit Spot Data e Filter the fitting results l e accept or reject fitting results BencHmark FILTER ANALYSIS The benchmarki
294. ults sets 10 000 or more localisations for repeat analysis 6 1 1 Input options Input can be from results in memory or a result file Using the result file option allows the user to load results that were generated in a previous session The plugin can load data generated by the Peak Fit plugin and saved as results file It also loads results that have been saved from the Peak Fit results table to a text file External file formats are also supported Currently the following alternative formats are supported e rapidSTORM e Nikon NSTORM 6 1 1 1 Image calibration The SMLM plugins require that an image have a calibration to allow certain plugins to function This calibration includes the pixel pitch the total gain and the exposure time as described in section 5 1 2 Certain file types do not have an image calibration In this case the plugin will present a dialog where the user can enter the calibration for the results This is added to the results and will be saved if using a SMLM file format 6 1 2 Output options The output options are the same as in the Peak Fit plugin The only difference is that the file output requires that the name of the output file be provided In the Peak Fit plugin only the results directory was specified and the filename was taken from the image Allowing the full filename to be specified provides greater flexibility in saving results Note that the Input Fite and Resutts rite fields support a mouse double
295. used to specify the probability likelinood of the observed value O given the expected value The total probability is computed by multiplying all the probabilities for all points together likelihood p Ol E or by summing their logarithms loglikelihood gt gt In p O E The maximum likelihood returns the fit that is the most probable given the model for the data Poisson noise model This model is suitable for modelling objects with a lot of signal The standard model for the image data is a Poisson model This models the fluctuation of light emitted from a light source photon shot noise This is based on the fact that gaps between individual photons can vary even though the average emission rate of the photons is constant The Poisson model will work when the amount of shot noise is much higher than all other noise in the data e when the localisations are very bright If the other noise is significant then a more detailed model is required The Poisson probability model is e with k equal to the pixel count and A equal to the expected pixel count Note that when we take a logarithm of this we can remove the factorial since it is constant and will not affect optimising the sum Page 31 225 GDSC SMLM ImageJ Plugins In p klA mt e k In amp In e In A In k1 2 kin A A The final log likelinood function is fast to evaluate and since it can be differentiated the formula can be used with
296. ussian fit will be poor or not possible and the localisation precision will be reduced 2 3 Localisation Fitting Method The single molecule localisation method used in the GDSC Single Molecule Light Microscopy SMLM plugins is based on 2D Gaussian fitting For each frame candidate spots are identified and then fit using a local region surrounding each candidate Wolter et al 2010 An estimate of the PSF width is required which can be obtained from the wavelength and optical system used for acquisition or estimated from the image Candidates are identified using a smoothing filter on the image followed by non maximal suppression Smoothing is done using a single filter such or a difference filter where the Page 15 225 GDSC SMLM ImageJ Plugins second smoothed image is subtracted from the first Various filters are available such as mean median or Gaussian Local maxima are identified within a configured search region which is at least 3x3 pixels Peak candidates are processed in descending height order and a 2D Gaussian is fit to the peak using a region around the candidate of typically 2 to 5 times the estimated Gaussian standard deviation Fitting is performed using a either non linear least squares Levenberg Marquardt method or Maximum Likelihood fitting until convergence or the maximum iterations is exceeded Fitted spots are filtered using signal to noise width precision and coordinate shift criteria Processing is stopped wh
297. ween O and 1 DEPTH RECALL ANALYSIS Produce a histogram of the recall verses z depth of the original localisations This option is only available if the simulation had variable z depth SCORE ANALYSIS Produce a histogram of the distance and signal factor for all fit matches to the original localisations Evolve Perform evolution optimisation with a genetic algorithm Step SEARCH Perform step search optimisation TITLE Add a title for the analysis to the results tables This can be used when running multiple repeats of the plugin with results from different filters and fitting algorithms Page 169 225 GDSC SMLM ImageJ Plugins Once the main parameters have been chosen a second dialog is presented where the scoring metrics that are recorded in the results table can be specified This allows the user to remove many of the results from the table if they do not need them to save space dy y Benchm Y y QS Select the results SmE TP FP TN FN TPR TNR PP NPY ER FNR FDR ACC MCC Informedness Markedness Y Recall Y Precision OF1 Y Jaccard Y oFP OFN Y oRecall Y oPrecision loF1 Y ojaccard OK Cancel Help If the Evotve option is selected a dialog will be presented for each filter set to be optimised The parameters are all prefixed with the filter set number This allows the settings for each filter set to be saved and used in the ImaceJ macro
298. wiseWithoutNeighbours is to join the closest pairs only if the number of neighbours for each is 1 In the event that no pairs has only a single neighbour then only the closest pair is joined This algorithm should return the same results as the CLosest algorithm but with different run time performance CENTROID LINKAGE DISTANCE PRIORITY Hierarchical centroid linkage clustering by joining the closest pair of clusters iteratively Clusters are compared using time and distance thresholds with priority on the closest time gap within the distance threshold CENTROID LINKAGE TIME PRIORITY Hierarchical centroid linkage clustering by joining the closest pair of clusters iteratively Clusters are compared using time and distance thresholds with priority on the closest distance gap within the time threshold PARTICLE CENTROID LINKAGE DISTANCE PRIORITY Hierarchical centroid linkage clustering by joining the closest pair of any single particle and another single or cluster Clusters are not joined and can only grow when particles are added Clusters are compared using time and distance thresholds with priority on the closest time gap within the distance threshold PARTICLE CENTROID LINKAGE TIME PRIORITY Hierarchical centroid linkage clustering by joining the closest pair of any single particle and another single or cluster Clusters are not joined and can only grow when particles are added Clusters are
299. wn selection list allowing the input image to be selected and various parameters for the analysis can be set The centre of the window shows the analysis of the current frame from the spot regions The window then has several buttons allowing different actions The final region of the window is a list of the currently selected on frames Page 103 225 GDSC SMLM ImageJ Plugins with the calculated signal in photons y a Spot Analysis BONES 20ms_4 tif j PSF width 1 2 Blur relative to width 1 Gain 37 7 ms Frame 20 Smoothing 0 25 Frame 81 Signal 81 42 SNR 87 8 Raw fit Signal 126 6 SNR 137 0 Blur fit Signal 58 24 SNR 62 8 Profile Add Remove Save Save Traces 81 81 42 84 26 01 177 98 53 374 118 27 Illustration 24 Spot Analysis plugin window The following parameters can be set Parameters Description PSF wiDTH The estimated peak width of the spots in pixels This is used to fit the spot region using Peak Fit BLUR The Gaussian blur to apply to create the blurred spot image The width is relative to the PSF width GAIN The total gain of the system ADUs photon This is used to convert the counts to photons MS FRAME The exposure time Used to calculate the on off times in milliseconds Page 104 225 GDSC SMLM ImageJ Plugins Parameters Description SMOOTHING The LOESS smoothing parameter used to create the smoot
300. y by each method Create Spot Data Creates a sparse image by simulating zero or one localisation per frame Filter Spot Data Filter the image created by Create SimeLe Data Or CREATE Spot Data and compute statistics on the accuracy and precision of identifying spot candidates Fit Spot Data Fits all the candidate spots identified by the Fitter Spot Data Page 11 225 GDSC SMLM ImageJ Plugins plugin Benchmark Filter Analysis Run different filtering methods on a set of benchmark fitting results outputting performance statistics on the success of the filter Image Background Produces a background intensity image and a mask from a sample in vivo image This can be used to simulate realistic fluorophore distributions Load Localisations Loads the XYZ location file from Create Data into memory for analysis 1 5 Calibration plugins PSF Calculator Allows calculation of the Point Spread Function PSF size given the microscope imaging parameters PSF Estimator Estimates the PSF by performing fitting on a sample image Mean Variance Test amp Mean Variance Test EM CCD Opens a folder of images and computes a Mean Variance test to determine the gain and read noise of the microscope camera Gain can be calculated for standard or Electron Multiplying EM cameras EM Gain Analysis Analysis a white light image from an EM CCD camera and fits a model to obt

Single Molecule Light Microscopy ImageJ Plugins

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