Help for Tme-Resolved Analyss TRI2 verson 2.4 P Barber, 22.01.10 Introducton Tme-resolved Analyss (TRA) becomes avalable under the processng menu once you have loaded and selected an mage that contans sutable mult-dmensonal data. Ths s typcally an cs fle. When such an mage s loaded the ntensty or sum mage s shown n the usual mage wndow. If the mage has been dentfed as a tme-resolved mage then the words Tme Resolved appear n the extra text below the ntensty mage. There are many processng optons avalable, please be aware that many of them may not be relevant to TRA and many only work on the 2D ntensty mage. One process that does work on 3D data s the arthmetc functon. TRA allows you to ft functons to sngle pxel or bnned data and also to perform functons to whole mages. Such as performng a ft at every pxel, or bn of pxels, or usng all pxels together n some form of global analyss. More detal can be found n the followng document, but for detals about the fttng functons please refer to: Tme Resolved Fttng (Detal).pdf NEW As of verson 2.4 we now have a Bayesan method for mono-exponental fttng and we hope bexponental wll follow soon. Ths analyss accounts for the Possonan nature of low photon count data and s more accurate and robust n these stuatons. Another beneft of ths technque s that the errors reported for the ftted parameters are now realstc error ntervals, gvng you drectly the confdence n the values. Unfortunately nothng s free, and the Bayesan algorthm s much slower to run than the Marquardt methods. Also parameter fxng and global methods are not avalable wth the Bayes method. 1
Contents Introducton... 1 Contents... 2 Tme-Resolved Analyss... 3 Inputs... 3 Pre-Processng... 4 Cursors... 4 Type of Ft... 5 Instrument Response/Exctaton/Prompt... 5 Parameter Freedom... 6 Fttng... 6 Outputs... 7 Errors... 7 Reduced Ch Square... 7 Iteratons... 8 Error... 8 Confdence Ellpsod... 8 Image Producton... 8 Support Plane Analyss... 10 Bayes Probablty Dstrbuton Analyss... 12 Macros... 12 Batch Processng... 14 Appendx B Global Fttng... 16 2
Tme-Resolved Analyss Inputs Select an mage that has tme resolved data n any workspace to make t the subject of TRA. Choose Processng->Tme-Resolved Analyss from the workspace f the TRA wndow s not vsble. Image Chosen va workspace Has Pre-Processng optons Instrument response/exctaton/prompt Chosen va menu Has cursor optons Ft Type Chosen on ths panel Has optons on ths panel Parameter Freedom Chosen on ths panel Has free/fxed/restraned optons Selected Pxel & Data Chosen by clckng on ths mage or usng the X and Y controls. 3
Pre-Processng Thresholdng: Ths allows you to excluded pxels wth a low and/or a hgh ntensty. You can choose to use a threshold based on a % of the ntensty or on a fxed value. A fxed value s useful for batch processng when you want to exclude a background below a fxed ntensty. The mage demonstrates excludng all pxels wth an ntensty n the bottom 10% of all pxels. Maskng: If there s a mask assocated wth the mage n the workspace t can be appled to TRA by checkng the Apply Mask box. Bnnng: The tme-resolved data of the pxels n the neghbourhood of the selected pxel can be added together. Use Bnnng to select a 3x3 or 5x5 pxel area, for example. Checkng the All Pxels box adds all the data of all the pxels that have not been excluded va thresholdng or maskng (N.B. f ths box s checked that selected pxel become rrelevant). Cursors The cursors panel allows you to manually change to cursor postons. It also allows you to lock the cursors together so that: the mpulse delta (tme dfference between the start of the prompt 4
(exctaton) and the start of the transent (tme-resolved data) and the mpulse wdth are mantaned f the transent start s moved, or the mpulse delta s mantaned f the prompt start s moved. Estmate Cursors: Places all the cursors (prompt and data cursors, except prompt baselne) n sensble postons. Type of Ft Choose the model functon wth the Type of Ft control and the mathematcal functon assocated wth t wll be dsplayed. Estmate Intal Values: Uses a three ntegral ft to the data to estmate startng parameters for the current model. The values calculated are placed n the value boxes of the Ftted Parameters. Estmate Cursors: Places all the cursors (prompt and data cursors, except prompt baselne) n sensble postons. Pre-ft Estmaton: Ths control determnes where the startng parameters arse from. Integral Ft Estmate performs the Estmate Intal values before each ft. Estmate from last ft uses the ftted parameters from the last ft as startng values for the next. Estmate from panel values always uses the values that are n the Ftted Parameters value boxes as the startng values for a new ft. N.B. for sngle fts the last two optons wll be dentcal because the values from the last ft wll always be dsplayed n the Ftted Parameters value boxes. Ths s not the case, however, for makng mages based on pxel fts. Target ChSq: The Target Ch Square control can be used to determne how strngent the fttng engne should be. Ths value s used to determne how many tres (re-fts) are made to try and mprove the ft (the lower the ChSq, the better the ft) Instrument Response/Exctaton/Prompt You are able to load a fle that descrbes the response of the nstrument used to acqure the mage. Ths s also often called the exctaton functon or the prompt functon. Ths fle can be n cs or sdt format and contans a sngle tme-resolved sgnal. Ths must have been captured wth the same nstrument settngs as the mage and so has the same number of tme-resolved ponts (number of channels) over the same tme perod. 5
The exctaton functon wll be convolved wth the pure ft functon before comparng the result to the raw data when determnng the goodness of ft. A better estmate of the model parameters can thus be acheved. You can choose to not use an exctaton functon by selectng ths menu opton. X10 expands the y-axs of the exctaton graph for better settng of the Exctaton Baselne cursor. Parameter Freedom The freedom of each model parameter can be set. In other words constrants can be appled to fx or restran the value of certan parameters. Fxed Value Red background Free Value Whte background Restraned Value Orange background Freedom Optons Constrants can be appled by clckng the freedom button to call up the freedom optons panel for each parameter. Here you can free the parameter, fx t to any value by changng the Value box and checkng the Fx button, or restran the parameter between mnmum and maxmum values. The +/- button and % box allow you to quckly set mn and max lmts based on the current parameter value (.e. Clckng +/- wth 10 % sets the mn at value-10% and the max at value+10%). There are shortcuts to free and fx parameters from the man TRA panel. Just type a new value n the parameter value box to fx that parameter. To free a parameter, rght-clck on the value box or the freedom button. Fttng The Ft transent button wll perform a ft based on all the nputs provded and wll perform an ntal pre-ft estmaton of the parameters for Marquardt fttng. The Ft w/o estmaton Auto-Ft Red = on Green = off button performs a ft based on all the nputs provded but wll not perform an ntal pre-ft estmaton (.e. the current panel values wll be used as the ntal estmate for Marquardt fttng). N.B. Integrals fttng does not requre any pre-estmate of the parameters. The Parameter Modfed ndcator nforms of when the currently dsplayed ft and parameter values are no longer vald because somethng has been manually changed and a new ft should be performed. If the auto-ft button s on (red) then a new ft wll be performed whenever somethng changes and so the current values should always be vald. 6
See Appendx A for more detal on the Integral and Marquardt fttng procedures. Outputs Save Ft Data The Ft Ftted Parameters Reduced Ch Squared, Iteratons and Error Resduals Errors Indcates estmated errors n all the determned parameters. Reduced Ch Square The Reduced Ch Square (or Ch sq. / d.f. ) s gven by: 7
2 n [ I( tk ) Ic ( tk )] I( t ) k=1 χ r = = χ 2 / (n - p) n p where: I(t k )= the data at tme pont k I(t k )= the ft at tme pont k n = number of tme ponts p = number of varable ft parameters n p = d. f. (degrees of freedom) and the lower the Reduced Ch Square the better the ft. In the absence of nose ChSq should approach zero; for Posson-lmted nose, expect a value around 1. k Iteratons The reported number of teratons (or # ters ) s, for Marquardt fttng, the total number of teratons of Marquardt fttng. If re-fts occur, the numbers of teratons of each ft are added together. For ntegral fttng the number of teratons ndcates the number of re-fts (See appendx A) Error Indcates f there was an error n the fttng. Confdence Ellpsod 2 The confdence ellpsod descrbes our confdence n the ftted values by ndcatng the shape of the Ch Square support plane around the mnmum (around the ftted soluton). Image Producton The drop-down menu lets you choose between pxel fts, a global ft or a mult-mage global ft. Pxel Fts allow you to use the nputs you have provded and perform a ft on every pxel n the mage that has not been excluded through thresholdng or maskng. Bnnng also apples to pxel fts. Take care snce bnnng All Pxels wll result n all the pxels beng the same! The ftted parameters and the ChSq values wll be used to form mages whch wll appear n a new mage workspace wndow. Global Ft performs a global ft usng all the pxels that have not been excluded through thresholdng or maskng. A Mult-Image Global Ft wll use all the tme-resolved mages n the current workspace 8
and ft them all smultaneously. In short, global analyss s a powerful technque n whch some parameters of the fttng functon are restraned to be the same for every pxel (globally ftted parameters) and others are free to be dfferent for each pxel (locally ftted parameters). All the tmeresolved mage data are consdered smultaneously when the best ft s determned (see appendx B for a more detaled descrpton of how ths global fttng s performed). The table below detals whch parameters are consdered global and local for the current software: Parameter Mono-exponental B-exponental Tr-exponental Stretched Exponental Z Local Local Local Local A 1 Local Local Local Local Tau 1 Global Global Global Global A 2 Local Local Tau 2 Global Global A 3 Local Tau 3 Global h Global The locally ftted parameters and the local ChSq values wll be used to form mages whch wll appear n a new mage workspace wndow. The globally ftted values and global ChSq wll appear as extra text on approprate mages n the workspace. Example workspace outputs: The global Reduced ChSq s defned as the sum of all the local ChSq s dvded by the global degrees of freedom: df global = [N.(n p l free)] - p g free, where: N = number of transents (pxels); p l free = number of free local parameters; p g free= number of free global parameters. 9
Support Plane Analyss Once we have a ft, wth resultng ftted parameters and a ChSq value, we can nvestgate the local map of ChSq and ask questons lke (for example): What s the ChSq f tau was forced to be 1.9 rather than 1.8? What s the lkely error n tau? How lkely s t that tau s 1.9 rather than 1.8? Ths s where support plane analyss (SPA) s useful. Support plane analyss s avalable from the wndow menu of TRA. SPA for: allows you to choose between SPA for the sngle transent on the TRA panel or global fttng on the whole mage. Global SPA may tme some tme snce a global ft must be performed at every pont on the graph. Analyse: selects one (1D support plane) or two (2D support plane) parameters to vary. Parameter1 and Parameter 2: allow you to choose whch parameters to vary, over what range and n how many steps. Normalse to mnma: dvdes every pont on the graph by the mnmum ChSq calculated. Add Plot: Performs the calculatons and add a plot to the graph. Many plots can be added each wth the same or dfferent range, or from dfferent pxels (select a dfferent pxel on the man TRA panel 10
and then clck Add Plot. If you change the parameters to vary n between plots you may get some strange results. You can change each plot s appearance by clckng Propertes to access the propertes panel. Clear Graph: Clears all plots from the graph. : Orentate the graph : Change the vew of the graph to orthographc or to perspectve, respectvely. Hnt: For a more usual vew of a 1D support plane, clck and then. Hnt: For a contour map of a 2D support plane, clck and then. Propertes: Opens the graphs propertes panel. Help: Informs about how to control the vew of the graph. Copy Graph: Copes the current vew of the graph to the wndows clpboard for pastng n other applcatons (e.g. MS Word or PowerPont). Save Data: Saves a text fle contanng the last plot s data ponts n a format that can be mported nto MS Excel to use t s 3D graphng functons. 11
Bayes Probablty Dstrbuton Analyss Smlar to the Support Plane Analyss, the Bayes Probablty Dstrbuton Analyss panel can be used to vew and explore the resultng probablty densty functon when Bayesan fttng s performed. Most functon on ths work n the same way as the SPA panel. The numbers reported are the maxmum a posteror (MAP) value,.e. the most probable, peak value, of the dstrbuton, the average (AVE) or frst moment of the dstrbuton and the error nterval (ERR), whch s the second moment or standard devaton of the dstrbuton. Macros From the man workspace menu several macros are avalable for TRA. These macros wll search for sutable mages n the current workspace on whch to perform the operaton (.e. those named A1, tau1 etc.). New mages wll be created n the workspace from the result(s). You wll be told f a sutable set of mages could not be found. Fractonal Intensty: Produces a F mage for every A found (to a max of 3) accordng to: 12
F Fractonal Contrbuton: Produces a f mage for every A and tau par found (to a max of 3) accordng to: Aτ f = A τ = j Average Lfetme: Produces one mage show the contrbuton-weghted average lfetme from all A and tau mage pars found (max of 3) accordng to: 2 Aτ τ = fτ = Aτ Lfetme-Weghted Quantum Yeld: Produces one mage from all A and tau mage pars found (max of 3) accordng to: τ A τ j = j FRET Effcency: Produces one mage from the tau 1 and tau 2 mages accordng to: A A j j j τ E = 1 2 τ where tau 1 wll be the longer lfetme (.e. the lfetme of the FRET donor) and tau 2 the shorter (.e. the lfetme of the FRET donor n the presence of the acceptor). All defntons are from: Lakowcz, J. R. Prncples of Fluorescence Spectroscopy (Plenum Publshers, New York, 1999). j 1 j 13
Batch Processng Batch processng allows you to form a lst of mage fles and leave the computer to process them one by one. You must frst setup all the nputs to your TRA on any mage so the computer knows the startng pont for each mage. Ths ncludes any mask but currently only one mask per batch can be specfed. Hopefully, the operaton of batch processng panel s obvous so I wll not go nto t here, except to say The output of batch processng wll be a number of fles. These may be mages and/or text fles of data. They can be saved nto the drectory whence the mage came or nto another specfed drectory. If your mages are read from a CD, the computer may not be able to wrte the output fles to t, so you must specfy a dfferent drectory n that case. Dfferent batch operatons may appear n future. At the tme of wrtng, there s only one TRA batch operaton whch performs the followng: Load the tme resolved mage Copy any mask from the startng mage to ths mage Do a ft on the mage of the chosen type Save all resultng mages Save raw ft data Close/dscard the pxel ft workspace created Do a sngle nvarance ft where all the pxels are bnned together Save raw ft data Close/dscard the tme resolved mage It s possble to select whch parameters to output data on but you must have processed an example mage for the system to know what outputs are avalable to choose from. 14
Appendx A The Fttng Engnes Trple Integral Fttng Engne Dvdes the data n three and does a 3-ntegral ft. If the chsq target s not met the ft s repeated untl t s OR tres => 10 WHILE the chsq contnues to mprove Wth each reft the data s dvded more (nto 4, 5, 6 etc.) and the frst three dvsons taken Checks that the last ft was not worse than the prevous best Returns the number of fts performed. Marquardt Fttng Engne Does a ft startng from the ntal parameters gven If the chsq target s not met, the ft s repeated untl t s OR tres => 10 WHILE the chsq contnues to mprove The prevous ft s used as a startng pt for the next one whch should never be worse. Returns the total number of teratons from all the refts added together. More detal can be found on the fttng functons n the document: Tme Resolved Fttng (Detal).pdf 15
Appendx B Global Fttng The steps nvolved n global fttng are: 1) Estmate the global parameters. Sum all the pxels together. Trple ntegral estmate of Z est, A est, tau est. (If ths fals Z est =0, A est =max of summed data, tau est =2.0) Set sutable values for mult-exp fts, e.g.: Parameter Mono-exponental B-exponental Tr-exponental Stretched Exponental Z Z est Z est Z est Z est A 1 A est ¾ x A est ¾ x A est A est Tau 1 tau est tau est tau est tau est A 2 ¼ x A est 1/6 x A est Tau 2 2/3 x tau est 2/3 x tau est A 3 1/6 x A est Tau 3 1/3 x tau est h 1.5 2) Perform Marquardt ft to get good values for the global parameters. 3) Fx these parameters for every pxel. 4) Estmate ntal values for all the ndvdual transents. Trple ntegral estmate of Z est, A est, tau est. (If ths fals Z est =0, A est =max of transent) 5) Calculate the exponental functons and convolve wth the nstrument response whch only needs to be done once. (Local fts are now lnear fts f all the taus are global!) 6) For each transent (pxel) call perform a Marquardt ft. One re-ft s tred f chsq s partcularly bad. 7) Do the actual global ft. Julan Glbey says, It s bascally smlar to a sngle Marquardt ft, except that now we handle the extra ntrcaces nvolved n global fttng, n partcular, the much larger alpha matrx s handled n a specal way. 8) Calculate the number of degrees of freedom and report the global reduced ChSq. More detal can be found on the fttng functons n the document: Tme Resolved Fttng (Detal).pdf 16