The official SpotOn documentation.
SpotOn allows you to analyze single particle tracking datasets. SpotOn fits a realistic kinetic model to the jump length distribution of the observed trajectories and provides estimates of the fraction bound (\(F\)) and diffusion coefficients (\(D\)) for either a two state (boundfree) or a three state (boundfree1free2) model.
SpotOn is a libre/opensource software and exists both as a webapplication and a commandline version.
This project owes a lot to Davide Mazza, who initially developed the conceptual framework implemented in SpotOn (see Mazza et al, 2012).
Browse the documentation for various versions of SpotOn:
Within a cell, a DNAbinding factor diffuses and occasionally binds to DNA or forms complexes. Each of these states can be macroscopically characterized by an apparent diffusion coefficient and a fraction of the total population residing in this state. Thus, we are interested in extracting those parameters for each state. Note that even when the observed molecules are stably bound to DNA, they will still exhibit a nonzero diffusion coefficient (reflecting a mixture of the slow motion of chromatin (estimated to be around 0.010.02 µm²/s, Shinkai et al, 2016) , the motion of the cell itself, microscope drift and possibly other factors).
To infer those parameters, single particle tracking (SPT) approaches can be implemented. In single particle tracking of nuclear proteins, cells are typically engineered to express a protein of interest either fused to a fluorescent protein or to a tag that can be conjugated to a synthetic dye (e.g. HaloTag). When the density of dyes in the focal plane is sufficiently low (because the number of expressed proteins is low, because the depth of field is extremely small or because only a fraction of the molecules are visible at a time), individual molecules appear as isolated spots that can be localized with a subpixel accuracy by fitting a 2D (usually Gaussian) function and performing tracking between successive frames. This yields a series of trajectories, each corresponding to the motion of a single proteinconjugated fluorophore.
Although extremely powerful, single particle tracking of nuclear factors is subject to several methodological difficulties detailed below:
When a diffusing particle is observed, it will keep diffusing while one frame is acquired. In this case, particles exhibit "motion blur", that is that the photons emitted by a fastdiffusing molecule appear spread across a higher surface than bound molecules. This has several consequences:
Because of these two effects, fastdiffusing particles are harder to detect, especially if PSFfitting localization algorithms are used. Furthermore, because bound molecules are not affected by motion blur, molecules in the bound state tend to be overestimated because the fastdiffusing molecules are undercounted.
The picture below shows one frame containing two particles, one immobile particle appears as a very identifiable, Gaussian and symmetric spot (right red spot) whereas the fastdiffusing particle on the left is much harder to detect and very poorly resembles a pointemitter (spread out, left red spot).
Because motion blur results in underdetection of fastdiffusing particles, the amount of missed particles strongly depends on internal settings of the detection algorithm, and cannot readily be corrected after the acquisition. Section How to acquire a dataset details a few ways to circumvent these biases at the acquisition step.
In brief, the effect of motion blur can be mitigated by reducing the excitation pulse duration (to minimize the motion of the fastdiffusing population during one exposure) and the laser intensity (to keep the signaltonoise sufficient).
As single particle tracking is intrinsically a lowthroughput method, one may want to increase the density of tracked particles per frame in order to accelerate the data collection rate. However, as the density of particles increases, the tracking can become ambiguous. Furthermore, fastmoving particles are again more likely to be misconnected with other unrelated detections. This might result in a truncated jump length distribution, and thus a wrong estimation of the diffusion coefficient.
When imaging with a high density of particles, the nearest detection in the next frame might not be the same particle. In the limit of particles with high diffusion coefficients, it is likely that particles will "cross" each other and that one particle with be connected with another particle.
In practice, this leads to an underdetection of long jumps, because when a particle exhibits a long jump, the tracking algorithm is likely to pick another particle closer in space. This effect results in an underestimation of the fastdiffusing fraction and can be reduced by imaging at a low number of particles per frame. Section How to acquire a dataset details a few ways to circumvent those biases at the acquisition step.
In addition to motion blur biases, that leads to fastmoving particle to be missed by the detection algorithm, particles diffuse out of the detection volume (usually a slice of ~ 1 µm thickness). This effect is virtually zero for bound molecule, but becomes significant for fastmoving particles, leading to an undercounting of this population. The movie below highlight this effect. It depicts molecules belonging to two subpopulations, one free and one bound, randomly photoactivated in a nucleus. Due to the finite depth of field of the objective, only a thin slice across the nucleus can be imaged at one time (red slice). Whereas molecules activated infocus remain infocus until they bleach and contribute many jumps, free diffusing molecules continuously cross the focal plane, and thus contribute less jumps per trajectory.
This effect can be quantitatively examined in the animated graph below, which shows the jump length distribution of a molecule appearing in two states with respective diffusion coefficients \(D_1\) and \(D_2\) (expressed in µm²/s).
More precisely, the graph below displays the theoretical jump length distribution in case of an unlimited depth of field (solid line) and the simulation of the observed jump length distribution (dotted line) when particles are only observed within the depth of field of the objective (here set to 0.75 µm, see below for a method to measure it).
The cursors under the simulation allow tuning the diffusion coefficients of the two populations (\(D_1\) and \(D_2\)) and the proportion of the first population (\(p\)). From this graph, it appears (1) that as one increases the second diffusion coefficient (\(D_2\)), the discrepancy between the solid line and the dotted line increases, reflecting the fact that fastdiffusing particles tend to be undercounted in the observation through a setup with a finite depth of field.
In addition to \(D_1\), \(D_2\) and \(p\), this interactive graph allows you to play with the effect of the localization error \(\sigma\) and the exposure time \(\Delta t\). Note that this simulation does not take into account motion blur, so the undercounting of fastdiffusing particles is likely to be an underestimate.
Briefly, a reduced exposure time leads tends to limit the fraction of fastdiffusing particles moving outoffocus from one frame to another. On the other hand, when the frame rate becomes too high, the detections are dominated by the localization error and inference become less and less accurate. Thus, a tradeoff between the exposure time and the fastdiffusion coefficient has to be found.
D_{1} (μm²/s)  
D_{2} (μm²/s)  
P  
σ (nm)  
Δt (ms)  
Show model with no depth of field correction 

From this representation, one can derive the fraction of particles that will move out of focus in the next frame as a function of the fastdiffusion coefficient and the exposure time (in this case, allowing one gap so that a particle out of focus for one frame can still be reconnected in the following frame).
This graph shows that fastdiffusing molecules (\(D> 5 \mu m/s\)) are extremely hard to track, even at a relatively high frame rate. For instance, when imaging at 100 Hz (10 ms per frame) a factor moving at 10 µm²/s (such as Halo3xNLS), 40% of the particles move out of focus at each frame. This drastically limit the number of trajectories coming from the free population.
Furthermore, this graph only represents the fraction of particles remaining in focus after one frame. To get longer trajectories (more than two timepoints) is much harder, and is both limited by photobleaching and particles moving out of focus (detailed in section What limits the length of trajectories?.
This section of the SpotOn documentation will guide you through a sample analysis with a couple of demonstration files and will provide you with an overview of SpotOn features and options.
To access the demonstration files, go to the SpotOn homepage and scroll to the "Get Started section" (or alternatively click the Start spotting! button on the top menu. First fill in the "I'm not a robot" CAPTCHA. Then you have the option to either upload your own tracking files and start your analysis or start with demo files. We will use the demo files for the purpose of this tutorial.
This option will load the analysis page and will automatically import some demonstration file. Also, a custom and permanent URL is created. Your analyses will accessible from this URL until you choose to delete them. Do not share this URL if you want your datasets and analyses to remain private. You might want to bookmark it in order to reaccess the data later. Note that if you lose this address, there is no way for you to recover your files, since your upload is totally anonymous (we do not collect your identity or email address).
When you click on the "Start with a demo file" button, ten sample datasets are loaded. They are part of a bigger dataset described in details in the Datasets section that include single particle tracking of four nuclear proteins: histone H2B (H2B), Sox2, HaloTag3xNLS and CTCF. These four proteins were imaged through a range of conditions, leading to 1064 cells imaged in total.
By default, the ten imported files are five replicates of histone H2B (fused to both a HaloTag and a SNAPtag in U2OS cells, labeled with the HaloPAJF646 dye and imaged at 74 Hz (that is 1000/74 = 13.5 ms per frame).
The five other files are five replicates of the transcription factor Sox2 (fused to a HaloTag in mouse embryonic stem cells and imaged in comparable conditions: labeled with PAJF646 and imaged at 74Hz.
In this demo dataset, one of the goals is to get an idea of the dynamics of the Sox2 transcription factor. Indeed, an estimate of the fraction bound and diffusion coefficient of Sox2 provides a valuable insight into how this transcription factor regulates transcription. For instance, a low fraction bound and a high diffusion coefficient could suggest a highly dynamic regulation, but also a target search mechanism dominated by free diffusion. The H2B samples are provided as a reference for a protein that is known to be mostly bound to chromatin, in order to facilitate comparisons with more characterized systems.
First of all, SpotOn is organized into four successive tabs. These tabs are populated one after the other (that is, for instance, the "Kinetic modeling" tab remains blank as long as no dataset has been uploaded in the "Data" tab, etc). The four tabs are (① in the screenshot below):
Tab  Description 

Data  This tab allows you to upload your datasets in various formats in a batch mode, to annotate them, and to see statistics both for individual datasets and for the ensemble of uploaded files. 
Kinetic modeling  Performs the fit of the kinetic model according to specified parameters, displays the jump length distribution and the corresponding fit. Allows to include or exclude files for analysis. Display and fits can be marked for download. 
Download  This tab allows you to download the files marked for download in various formats (PDF, SVG, EPS, PNG, and ZIP archive). The ZIP archive contains the raw data, the fitting parameters and the fitted coefficients. 
Settings  Allows you to erase the analysis (together with all the uploaded datasets). 
The "Upload dataset" region (② in the screenshot below), where you can upload from various file formats. Clicking on any of the format will display a box where you can enter additional upload parameters, and will ultimately display a draganddrop upload box. Accepted formats are described in more details in the Input formats section below.
The "Uploaded datasets" region (③ in the screenshot below), that displays the uploaded datasets, together with their status (uploading
, queued
, error
). The meaning of the descriptors in the "status" column in the upload box is detailed in the Status code of imported datasets section below. Clicking on the "eye" symbol () next to an uploaded dataset will display some statistics in the area ④. The meaning and details of the computation of each statistic is detailed in section Dataset statistics below. Finally, area ⑤ displays similar statistics as area ④, but for all the datasets pooled together.
To proceed with the tutorial, several files have been loaded, they are named. They might get imported in a different order:
These files correspond to a subset of an experimental series spanning ~1500 cells in several conditions for various transcription factors and DNAbinding proteins, acquired at various framerates and durations of stroboscopic illumination. This dataset is described in more details in the Datasets section.
Five of these correspond to the transcription factor Sox2, which has been endogeneously tagged with a HaloTag and observed with the PAJF646 organic dye (Grimm et al, 2016). The five other correspond to the Halotagged histone H2B imaged under the same conditions.
Since the naming convention of these files is a little bit cumbersome, let's first edit the description of each file to make it clearer. To do so, click on the "pencil" icon (, see ⑥) next to each uploaded dataset. An "edit" box will appear at the bottom of the "Uploaded datasets" area, and we can now either rename or add a more explicit description of the datasets. We choose to leave the name as is, but add a short description for each dataset, such as "H2B cell1", "H2B cell2", etc. (⑦)
Now that we see a little bit clearer through the datasets, let's inspect a little bit the datasets, and try to assess the quality of the dataset. SpotOn provides a few quality metrics (statistics), accessible for each dataset by clicking the "eye" button ().
Click on the "eye" button () next to the datasets and have a look at the metrics displayed. Make sure you familiarize yourself with those.
The table below summarizes the statistics computed for the first dataset (named mESC_C3_HaloSox2_PAJF646_1ms633nm_74Hz_rep2_cell01.mat).
Statistic  Value 

Number of traces  6103 
Number of frames  29997 
Number of detections  15692 
Longest gap (frames)  1 
Number of traces with >3 detections  1813 
Number of jumps  9589 
Length of trajectories (in number of frames)  median: 1, mean: 2.571 
Particles per frame  median: 0, mean: 0.523 
Jump length (µm)  median: 0.126, Mean: 0.236 
Although the number of jumps is not extremely high, we need to keep in mind that we plan to pool this dataset with four other datasets, which should overcome the limited size of this dataset. In case we encounter a dataset of unsuitable quality, we can exclude it by clicking the "cross" button () next to the dataset.
Once that we are confident about the quality of the uploaded data, we can proceed to the second tab, the "Kinetic modeling".
The "kinetic modeling" tab is divided in several sections:
#  Section  Description 

⑧  Dataset selection  This section lists all the uploaded datasets. For each fit of the model, you can choose whether to include one specific dataset for fitting or not. 
⑨ and ⑩  Parameters  Parameters used to compute the empirical jump length distribution (⑨) and to fit it (⑨). This includes the choice of a 2state vs. a 3state model, the range of the tested parameters, etc. 
⑪ and ⑫  Jump length histogram  This area contains the plot of the jump length distribution, overlaid with the fitted model (if evaluated). It also contains the option to either visualize single datasets or the pool of the selected datasets. Finally, it contains an option to save an analysis for download. 
For the purpose of this tutorial, we'll simply fit the H2B and Sox2 datasets separately, and compare the twostate and threestate models based on their goodness of fit (assessed by the Bayesian Information Criterion, BIC).
First, in the "Dataset selection" select the five Sox2 replicates. This is done by switching the "Include" toggle button to "On" next to the Sox2 datasets. Make sure that none of the H2B datasets are included.
We can then set the parameters to compute the jump length distribution. We will mostly leave the parameters as default. Section Jump length distribution computation parameters describe the role of each parameter in more details.
Then click the Compute! button. After a few seconds, the jump length distribution is computed for all the datasets and appears under the "Jump length distribution" section.
The table below summarizes some key principles to properly set those parameters
Parameter  Value  Default?  Comment 

Bin Width (µm)  0.01  Y  The size of the bin used to build the empirical histogram of jump lengths. 
Number of gaps allowed  1  Y  The number of gaps allowed by the tracking algorithm. This has to match the maximum number of gaps allowed by the tracking algorithm. 
Number of timepoints  8  Y  The number of \(\Delta t\) to consider when fitting the model. Usually, higher values provide better results, provided that the histogram are sufficiently populated. 
Jumps to consider  4  Y  The number of jumps per trajectory actually used to build the histogram. This is empirically useful to correct for overcounting of slowmolecules not accounted for by the corrections implemented in the algorithm (for instance for undercounting due to motionblur). Here, for each trajectory, the first 4 jumps for each \(\Delta t\) (if possible) will be used to build the jump length histogram. For example, if Number of timepoints=8 and JumpsToConsider=4, a trajectory of 9 frames will contribute 4 jumps to 1dT, 4 jumps to 2 dT, …, and 2 jumps to 7 dT. This is a semiempirical way of correcting for additional biases towards bound molecules. 
Max jump (µm)  3  Y  The range of distances to build the histogram of jump lengths. This parameter has to be set so that the tail of the distribution is properly captured. Conversely, a value too high will disturb the fitting, that will be very sensitive to this potentially noisy tail. 
The graph displayed should be read as follows:
Before moving to the fitting, compare the pooled jump length distribution for Sox2 and H2B. To compute the H2B jump length distribution, simply uncheck the Sox2 datasets and select the H2B datasets in the "Dataset selection" area. Then click the Compute! button in the "Jump length distribution parameters" box. The two histograms are displayed below. What can you tell from that? Does it match your knowledge of H2B and Sox2?
When looking at the two histograms sidebyside, the two look very similar at short time scales (up to 200 nm), suggesting that the two proteins show a bound fraction. The dispersion around ~70 nm is likely to be characteristic of a combination of localization error (similar at all time scales, from \(1\Delta t\) to \(7\Delta t\) and of slow diffusion of chromatin (that slowly spreads when looking at higher \(\Delta t\).
Then, when considering higher distances, the histograms differ significantly, with Sox2 exhibiting a "heavy tail" whereas H2B lacks it. This reflects the fact that H2B is mostly bound whereas Sox2 has a significant freelydiffusing fraction. The modeling approach presented in the next steps of the tutorial will allow us to better characterize this diffusing state.
Before moving to the fitting of the data, let's save this last plot. We will download it later (from the "Download" tab). To do so, click the Mark for download button at the bottom of the page. This will prompt a small form where you can enter a name and a description that will be used as a reminder when you download the file. Also, display again the jump length distribution for Sox2 (by selecting the appropriate files and clicking the and Compute! button in the "Jump length distribution parameters" box) and save Mark it for download too. We'd get back to these saved analyses later.
Now that we are familiar with the computation and display of the jump length distribution, let's now move to model fitting!
SpotOn fits the jump length distribution, as defined by the parameters of the "Jump length distribution" box. The fitting parameters are defined in the "Model fitting" box.
Let's first try to fit a twostate model. Click on the picture of the twostate kinetic model (BoundFree). Specific parameter for this model unfold. Let's take a minute to quickly review them (a more detailed description of each parameter is presented in Section Fitting parameters, a short description is shown below).
Having now reviewed the parameters, we can click the Fit kinetic model button. A "spinning wheel" will appear next to the button while the fit is being performed and will get displayed when the fit completes.
Parameter  Value  Default?  Description/Comments 

Kinetic model  2state model  N  
D_{bound} (µm²/s)  [0.005, 0.8]  Y  The range of diffusion coefficients for the bound fraction. It is based on a wide plausible range of chromatin diffusion coefficients. 
D_{free} (µm²/s)  [0.15, 25]  Y  The range of diffusion coefficients for the free fraction. These numbers encompass a wide range of freediffusion coefficients. Note that for diffusion coefficients > 10 µm²/s, motion blurring can become a very important issue. 
F_{bound}  [0,1]  Y  The range for the fraction bound. 
Localization error (µm)  0.035  Y  See How to measure the localization error? below. 
dZ (µm)  0.7  Y  The estimated detection range in z. 
Model Fit  CDF  N  Select whether the model will fit the jump length distribution (that is the probability density function, PDF), or the cumulative jump length distribution (CDF). 
Perform single cell fit  No  Y  If "Yes", each individual dataset will be fit. Since our uploaded files are replicates of the same experiment, we want to pool them together. 
Iterations  3  Y  The number of times the solver will independently be initialized. 
When adjusting the dZ parameter (in the fitting parameters box), you will notice that the mention next to the dZ box changes. The displayed values relate to precomputed coefficients required to perform the correction for particles moving out of focus (see the Methods section). These parameters are termed \((a,b)\) and were precomputed over a grid of depths of field (dZ) and exposure times (dT).
However, even though we tried to be as comprehensive as possible in our simulations to derive \((a,b)\), the condition that matches exactly the acquisition settings might be missing. The displayed parameters represent the closest match of the acquisition parameters (dT, dZ) in our simulated database. For most acquisitions setup, the closest precomputed value lies within 0.5 ms and 100 nm of the empirical value.
It is important to make sure that the set of displayed parameters is not too far from the real acquisition settings, else, the computed z correction might be biased.
Let's take some time to quickly look at the parameters returned by the fitting routine for the H2B datasets. Note that due to different initialization values, the returned parameter can differ from execution to execution:
Parameter  Value 

D_{bound}  0.021 µm²/s 
D_{free}  3.929 µm²/s 
F_{bound}  0.733 
l_{2} error  0.00009489 
AIC  194578 
BIC  194554 
A few comments arise. First, the estimated fraction bound is about 70 %, which is expected from a strongly DNAassociated protein such as H2B. The associated coefficient with the bound population is close to zero (0.021 µm²/s) whereas the diffusion coefficient for the free population (3.93 µm²/s) matches previous knowledge of the dynamics of the protein.
Furthermore, the \(\ell_2\) error (the mean square error) is \(\lt 10^{4}\), which can be considered as acceptable (note that this value is not a hard limit and depends on several parameters, including the bin width and the max jump parameters), even though significant misfit appear at low and high \(\Delta t\): at \(1\Delta t\), the fitted distribution is fading faster than the empirical one, whereas at \(7\Delta t\), the opposite effect happens. This might be a sign that the protein of interest exhibits anomalous diffusion, or more generally that the model does not fully explain the dynamics of the molecule.
Finally, the AIC (Akaike Information Criterion) and BIC (Bayesian Information Criterion) criteria are provided to allow model comparison. These are two criteria that can be used to compare models and to get hints about which model fits the data best while penalizing for the number of parameters, in order to avoid overfitting.
More specifically, the 3state model provided by SpotOn has more free parameters than the twostate model (two extra parameters: the "slow" diffusion coefficient and the fraction of the slowmoving fraction). This additional degrees of freedom almost always a better fit than the 2state model. The AIC and BIC criteria take this difference in the number of parameters and establish a tradeoff between the quality of fit (that increases with the number of model parameters) and the number of parameters, in our case penalizing the possible overfitting of the 3state model.
Although these criteria are useful when comparing the fit of one dataset compared to various models, they cannot be used to assess the quality of fit per se.
Then, we can save the displayed fit by clicking the Mark for download button.
We can now proceed similarly to derive the fit for the Sox2 datasets. The resulting fit is shown below, next to a fit using a threestate model. Notice in this plot that significant misfit occurs: at high \(\Delta t\) the model estimates predicts that the bound fraction should have bigger displacements than what actually is. This characterizes a model mismatch and suggest the use of a threestate model.
Finally, we can now see how the quality of the fit increases by running the fit again, but with a 3state model. Select the 3state model icon (SlowBoundFast) on the "Model fitting" box. New parameters appear, very similarly as with the twostate model. We will leave the parameters to their default values, except for the CDF fit. Then click the Fit kinetic model button and wait a until the fitting completes. Observe how the quality of fit evolves, and the parameters and estimated fractions.
Parameter  Value 

D_{bound}  0.030 µm²/s 
D_{free}  2.410 µm²/s 
F_{bound}  0.340 
l_{2} error  0.00039589 
AIC  164571 
BIC  164547 
Parameter  Value 

D_{bound}  0.012 µm²/s 
D_{slow}  0.595 µm²/s 
D_{fast}  4.016 µm²/s 
F_{bound}  0.256 
F_{slow}  0.258 
l_{2} error  0.00014930 
AIC  185061 
BIC  185021 
Based on the information criteria, it is clear that the 3state model provides a better fit to the data, even when penalizing for the number of parameters.
Let's then fit the H2B data with a twostate model, as described in Step 10 for Sox2 (make sure that you select the right datasets before clicking the Fit button). Once the fit has completed, compare the fitted coefficients between the two proteins:
Parameter  Value 

D_{bound}  0.030 µm²/s 
D_{free}  2.410 µm²/s 
F_{bound}  0.340 
Parameter  Value 

D_{bound}  0.023 µm²/s 
D_{free}  3.84 µm²/s 
F_{bound}  0.70 
Notice that the bound diffusion coefficient are very similar, likely reflecting the diffusion coefficient of DNA/chromatin itself, while the free diffusion coefficients are different, and are likely to reflect different exploration modes of the two proteins. Also notice that the fraction bound are widely different: whereas H2B is mostly bound (70%), Sox2 appears mostly free.
Finally move to the "Download" tab, where all the analyses we marked for download are stored. The view should look as below:
For each analysis marked for download, the following fields are displayed, in addition to the time of the analysis and the name and description we provided in the previous tab:
Column  Description 

Name & description  The name & description we provided in the previous tab. 
Datasets  The list of datasets included for this plot. Hovering over the numbers displays the full name and description of the dataset. 
Display  Descriptor corresponding to the type of plot displayed. Hover over the descriptor to see a short description:
P : display of the probability density function,
JP : display the pooled jump length distribution,
F : pooled fit displayed 
Download  Download the corresponding analysis in various formats. The ZIP archive contains all the formats, the raw data, the display parameters and the fitted coefficients (if any). 
Delete  To delete this analysis. 
This section describes in detail the function of all the features and options implemented into SpotOn.
SpotOn accepts tracking files from the following software and raw CSV (column naming below): TrackMate (for which a dedicated importer exists, see below), MOSAIC suite, evalSPT (a variant of MTT) and an additional custom Matlab format. Sometimes, the importer can be a little bit picky. We provide sample files for these formats so that you can potentially study them. In case you have a problematic file, do not hesitate to contact us and email us the problematic file.
Files can be uploaded as raw CSV files. Make sure that the separator indeed is a comma (,). Importing from a tabseparated or semicolonseparated file will not work. The CSV file should have a header line and contain the following columns. Any other column will be ignored. The order of the columns does not matter. Note that the header naming convention is case sensitive. This importer assumes that tracking has been performed already and that sets of detections were assigned a numerical index (or trajectory id).
frame  t  trajectory  x  y  

Format  (integer)  (float)  (integer)  (float)  (float) 
Description  Frame number  Time (in s)  The trajectory id  x position of the particle (in µm)  y position of the particle (in µm) 
The 4D nucleome consortium, together with many labs across the world, agreed on a common format to share single particle tracking data. The format is mostly a tabseparated format with standardized headers and column names. A full description of the format is available online. Opendata datasets should be put online in 2018 on the 4DN data portal.
So far, SpotOn only supports one acquisition per file (although the 4DN format can multiplex several acquisitions in one file). SpotOn will issue an error if you try to import such multiplex 4DN file. Please use the 4DN splitter tool to convert a multiplex file to a series of 4DN files with only one acquisition per file.
TrackMate is an ImageJ/Fiji plugin that can perform various types of tracking and export the traces to various file formats. SpotOn can interact with TrackMate in two manners:.
The SpotOn↔TrackMate connector is a small TrackMate plugin that takes care of uploading the tracked datasets from TrackMate to SpotOn. It takes the form of a button that you can click at the end of the TrackMate wizard (see below).
The installation instructions of the SpotOn↔TrackMate and the plugin to download are available on Gitlab:
Note that the file has to be exported from the last panel of the wizard (clicking the "Save" button at the bottom of the window will produce a XML file that cannot be read by SpotOn). A screenshot of TrackMate's export interface is displayed below.
TrackMate saves the framerate and the units of the movie in the exported XML file. However, for some reasons, this can be unproperly set. See the ImageJ documentation about how to set up the framerate. The framerate has to be set in 'ms' (milliseconds) to be recognized by SpotOn, and the spatial unit should be 'um' or 'µm' or 'micron' (micrometers).
In the .xml file exported by TrackMate, the recorded framerate is indicated in the frameInterval
field, and the saved unit in the timeUnits
field. You can safely manually edit those values in case they were not saved when performing the tracking.
Again, the export can be performed by selecting either "Export tracks to a XML file" or "Export all spot statistics" followed by File > Save as. Clicking on "Save" directly in the TrackMate interface will not work.
Download sample file (CSV) Download sample file (XML)utrack is an Matlab software that can perform various types of tracking and export the traces to a custom Matlab format. SpotOn can import it provided that no branching was allowed in the settings. Below are some suggested parameters:
gapCloseParam.timeWindow = 1; %maximum allowed time gap (in frames) between a track segment end and a track segment start that allows linking them. gapCloseParam.mergeSplit = 0; %1 if merging and splitting are to be considered, 2 if only merging is to be considered, 3 if only splitting is to be considered, 0 if no merging or splitting are to be considered. gapCloseParam.minTrackLen = 1; %minimum length of track segments from linking to be used in gap closing.
Note that if gapCloseParam.mergeSplit
is set to 1, SpotOn will not be able to read the format and will silently fail.
We are very grateful to Khuloud Jaqaman (UT Southwestern) and Gaudenz Danuser (UT Southwestern) for precisions about this file format.
Download sample file (mat)MOSAIC suite is an ImageJ/Fiji plugin that can perform tracking and export the traces as an ImageJ table. This table can be further exported to CSV. The table is displayed by clicking the "All Trajectories to table" and "Selected Trajectories to table" at the end of the wizard.
evalSPT
(software mentioned in Normanno et al, 2015) produces a TSV format (tabseparated values), with no header, with the first columns ordered as follows. Additional columns might be present but will be ignored. An example file is provided below.
Column 1  Column 2  Column 3  Column 4  Column 5 and more 

x position of the particle (in pixel) 
x position of the particle (in pixel) 
frame number  trajectory number  These columns are ignored 
SpotOn also accepts a custom Matlab file format. An example is provided below. The trackedPar
variable is a structured array. Each element of this array corresponds to one trajectory. Each trajectory contains several fields: xy
, t
, frame
. Each of these fields is a 2Dmatrix with 2, 1 and 1 columns, respectively and a number of rows corresponding to the number of detections for this trajectory.
Note that this format (in particularx the shape of the objects) has to be followed rigorously for SpotOn to be able to import it. In particular, a \(N\times 1\) matrix is different from a \(1\times N\) matrix.
Download sample fileStatus code  Meaning 

Uploading  The dataset is being transferred to the server. 
Queued  The dataset has been uploaded, and will be checked for import. 
Ok  The dataset was successfully imported. 
Error  Something went wrong with the import process, and the file could not be imported. The file has been deleted from our servers and you might want to check the file format and upload it again. 
Note that once the dataset is marked as "ok", the jump length distribution might still be computing in the background. The content of the second tab only appears when this computation is done, which might take a few seconds.
Once a dataset has been successfully imported, several statistics are displayed and allow you to get a quick overview of the data, and spot dubious datasets or datasets that might likely need to unreliable analyses. We detail below how theses statistics are computed and what are suggested reference values.
Statistic  Meaning  Why it matters? 

Number of traces  The number of trajectories in the dataset. Trajectories can be singletons (one detection) and arbitrary long.  A low number of traces will cause the jump length histograms to be noisy and limit the accuracy of modelfitting 
Number of frames  The duration of the acquisition (in frames). This is inferred as the maximum index of the "frame" field. If you do not have detections at the end of the movie, this number can be lower than the true number of frames.  This number should more or less match the number of frames for the acquisition of this dataset. 
Number of detections  The number of particles detected.  Too low a number of detections is problematic since background noise will make a bigger contribution, whereas too high may suggest tracking errors. 
Longest gap (frames)  The maximum number of frames during which a particle disappeared before being tracked again by the tracking software.  A number of gaps >2 frames is very likely to yield significant tracking errors. 
Number of traces with ≥ 3 detections  Number of trajectories that contain three detections or more  This indicates whether histograms can be populated for \(\Delta t > 1\). 
Number of jumps  The number of tracked translocations (only \(1\Delta t\) translocations are reported)  Jumps are used to build the histogram of jump lengths, so this is probably one of the most relevant metrics to evaluate the quality of the dataset. 
Length of trajectories (in number of frames)  Provides the mean and median length of trajectories.  Useful also for assessing dataset quality. 
Particles per frame  The mean and median number particles per frame.  A median number higher than one indicates the risk of tracking errors. 
Jump length (µm)  The mean and median translocation distance  In general, the mean translocation should be significantly bigger than the localization error. 
Parameter  Meaning 

Bin width (µm)  how finely to do binning for PDF fitting and plotting in units of micrometers. Generally, 0.010 μm or 10 nm is reasonable, but if you have very small amounts of data you may want to increase it. 
Number of timepoints  How many time points to consider. If you allow \(N\) time points, this corresponds to considering displacements with a maximal timedelay of \((N1)\Delta t\). Generally, we do not recommend going much above 5060 ms unless you have an a very large number of trajectories and/or very long trajectories, since otherwise, the displacement histograms at longer \(\Delta t\) tend to be undersampled. 
Jumps to consider  The number of jumps per trajectory actually used to build the histogram. This is emppirically useful to correct for overcounting of slowmolecules not accounted for by the corrections implemented in the algorithme (for instance for undercounting due to motionblur). Here, for each trajectory, 4 jumps (if possible) will be used to build the jump length histogram. For example, if Number of timepoints=8 and JumpsToConsider=4, a trajectory of 9 frames will contribute 4 jumps to 1dT, 4 jumps to 2 dT, …, and 2 jumps to 7 dT. This is a semiempirical way of correcting for additional biases towards bound molecules. This parameter is ignored if "Use entire trajectories" is set to Yes. 
Use entire trajectories?  If "Use entire trajectories" is set to "Yes", the previous parameter ("Jumps to consider" is being ignored. If set to "Yes", all displacements will be used from each trajectory. If set to "No", then the number of displacements is determined by the "Jumps to consider" variable. A trajectory of \(N\) frames, will contribute \(N1\) displacements to the \(1\Delta t\) histogram, \(N2\) displacements to the \(2\Delta t\), histogram, ..., \(Nk\) displacements to the \(k\Delta t\) histogram. This parameter was called "Use all trajectories" in v0.11 and earlier. 
Max jump (µm)  this parameter affects dataprocessing. For binning displacements, a maximum displacement has to be set, so this parameter should be set to a large value that should be at least as big as the largest displacement. Generally, 5.05 μm is reasonable for singlemolecule tracking data in mammalian cells. 
dT (ms)  Time delay between frames in units of milliseconds. 
It is posisble to constrain the diffusion constants and relative fractions of the model by setting the same value to the upper and lower bound of the interface.
Parameter  Meaning  Why it matters? 

Kinetic model  The number of diffusive states in the model. SpotOn supports 2 or 3state. In most singlemolecule tracking experiments of molecules that can engage scaffolds (e.g. transcription factors, which may bind chromatin), one of these states will correspond to a bound state. In the case of HaloCTCF in human U2OS cells, this will manifest itself as the chromatinbound state of CTCF exhibiting a very small \(D\) for the bound state which likely corresponds to slow diffusion of chromatin. The other states will correspond to freely diffusive states.  
D_{free}, D_{bound}, D_{slow}, D_{fast}  Allowed lower and upper bound for the faster diffusion constant for the modelfitting in units of μm²/s for the free (2state model), bound (all models), slow (3state model) or fast (3state model), respectively.  
F_{bound}, F_{fast}  The range of possible values for the bound fraction (all models) and the fastdiffusing fraction (3state model), respectively.  
Localization error (µm)  If "Fit from data" is set to "No", you can provide the localization error with which singlemolecules were localized. If "Fit from data" is set to "Yes", SpotOn will try to infer this from the modelfitting. In that latter case, you need to provide an exploration range for these values. In the datasets provided with SpotOn, the localization error was around 35 nm. If the localization error parameter is set inaccurately, this will generally show up through poor fitting of the bound state and will cause the estimation of the bound diffusion constant to be inaccurate.  
dZ (µm)  Axial observation slice in units of micrometers. This parameter will depend somewhat on signaltonoise conditions and imaging modality. But for a typical setup (HiLo or epi illumination, HaloTag or SNAPTag dyes), this is likely to be around 0.7 μm. The parameters tell SpotOn how far outoffocus a molecule can be before it fails to be detected and it is important for accurately correcting for diffusing molecules gradually moving outoffocus and thus being undersampled at longer timeintervals. In most cases 0.7 μm is reasonable, but for details on how to measure this please see (Hansen et al. (2017).  
Perform single cell fit  When set to "Yes", each single uploaded file will be analyzed and fitted separately. This is useful for assessing how much celltocell variability there is and for determining whether a single outlier is biasing the results, but also very slow, since fitting merged data takes about the same amount of time as fitting a single cell.  
Model Fit  Determines whether fitting will be performed to the displacement histograms (PDF) or to the cumulative distribution function of displacements (CDF). We have performed Monte Carlo simulations and CDFfitting is always more precise, whereas PDFfitting tends to slightly underestimate the fraction bound and the diffusion constant, likely because PDFfitting is more prone to binning artifacts and undersampling. Thus, for all quantitative analysis, CDFfitting should be performed. However, displacement histograms often seem more intuitive, and for this reason SpotOn also allows PDFfitting for making figures etc.  
Iterations  SpotOn fits a mathematical model to the data using leastsquares fitting. Since this algorithm may occasionally get trapped in local minima in parameter space, for each iteration of the fitting SpotOn generates a random initial guess of the parameters, which differs between each iteration. Thus, increasing the "Iterations" parameter, increases the probability that the globally optimal fit will be generated, but comes at the cost of slowing down the fitting. In practice, for all singlemolecule tracking data we have tested so far, the globally best fit is always obtained in the first or second iteration of fitting, so we generally recommend keeping this parameter to 23. 
These parameters affect how the graphs are displayed, and which features are to be plotted. It does not affect how the fits or the jump length distribution are computed. These settings are located under the graph region.
These parameters are only displayed when a graph has been processed. This is either done automatically after datasets have been successfully uploaded or by clicking the "Compute!" button in the "Jump length distribution parameters" box. Some of the settings only appear for specific combination of parameters.
Parameter  Meaning  Only displayed if... 

Max jump displayed (µm)  The range of distances to be plotted. This parameter varies between 0 µm and "Max Jump". It allows to zoom on the origin of the plot.  For any plot 
Display PDF/CDF  Either display the PDF or the CDF  For any plot. 
Show pooled jump length distribution  Tell whether single datasets should be displayed or if the selected datasets should be pooled together.  For any plot. 
Displayed group  The list of datasets displayed in the pooled graph  Show pooled jump length distribution is set to "Yes" 
Display dataset  Sets the dataset to be displayed  Show pooled jump length distribution is set to "No" 
Show pooled fit  Tell whether fit for individual datasets or the fit for all the selected datasets has been computed  a fit has been computed 
Display residuals  If set to "Yes", the residual between the fit and the empirical jump length distribution is overlaid on the graph.  a fit has been computed 
Mark for download  This button allows to mark the current plot for download. When doing so, all the current settings are saved and will be available in the download section. You have the possibility to add a few annotations to the download for easier sorting.  For any plot 
To obtain a good and reliable singlemolecule tracking dataset, a series of requirements have to be met.
First of all, it must be possible to image singlemolecules at a high signaltonoise ratio. This is now relatively straightforward due to developments in fluorescence labeling strategies and imaging modalities. The development of the HaloTag proteinlabeling system and bright, photostable organic Halodyes such as TMR and the JF dyes developed by Luke Lavis and coworkers now make it possible to easily visualize single protein molecules inside live cells. Moreover, imaging modalities such as highly inclined and laminated optical sheet illumination (Tokunaga et al, 2008) are relatively straightforward to implement and combined with a highquality EMCCD camera make it possible to image singlemolecules at high signaltonoise suitable for generating highquality 2D singlemolecule tracking data. For details of our imaging setup which combines HaloTaglabeling with HiLoillumination and which is relatively common and easy to operate, please see Hansen et al., 2017. But we note that many other imaging modalities, e.g. lightsheet or even epifluorescence imaging can generate highquality singlemolecule tracking data.
Thus, in the following we will assume that the above condition is met: namely, that single protein molecules can be tracked inside live cells at high signaltonoise ratio. Nevertheless, even if this condition is met, there are at least 4 other major sources of bias:
SpotOn addresses point 3 and 4, as described elsewhere, but point 1 and 2 must be addressed in the experimental design. We discuss strategies to minimize these biases below (spaSMT).
Almost all localization algorithms achieve subdiffraction localization accuracy (“superresolution”) by treating individual fluorophores as pointsource emitters, which generate blurred images that can be described by that PointSpreadFunction (PSF) of the microscope. Modeling of the PSF (typically as a 2dimensional Gaussian) then allows extraction of the particle centroid with a precision of 10s of nm. But as illustrated in the above section (“Motion blur”), while this works extremely well for bound molecules, fastdiffusing molecules will spread out their photons over many pixels during the microscope exposure and thus appear as “motionblurs”. Thus, most localization algorithms will reliably detect bound molecules, but fail to detect fastmoving molecules. Clearly, the extent of the bias will depend on the exposure time and the diffusion constant: the longer the exposure and higher D, the worse the problem. Assuming Brownian motion, we can calculate the fraction of molecules that will move more than some number, \(r_{max}\), during an exposure time, \(t_{exp}\), given a free diffusion constant of \(D_{free}\) using the following equation:
$$\mathbb{P}\left(r\gt r_{max} \right) = e^{\frac{r_{max}^2}{4D_{free}t_{exp}}}$$For example, if we define motionblurring as moving more than 2 pixels (> 320 nm assuming a 160 nm pixel size) during the excitation, an exposure time of 10 ms and a typical free diffusion constant of 3.5 µm²/s (e.g. Sox2), we get:
$$\mathbb{P}\left(r\gt r_{max} \right) = e^{\frac{(0.32 \mu m)^2}{4 \times 3.5 \mu m^2s^{1} \times 0.010 s}} \simeq 0.481$$Thus, even for a relatively slowly diffusing protein, with a 10 ms exposure we should expect almost half (48%) of all free molecules to show significant motionblurring. The most straightforward solution is therefore to limit the exposure time: in the limit of an infinitely short exposure time, there is no motionblur. In practice, most EMCCD cameras can only image at ~100200 Hz for reasonably sized ROIs. Moreover, it is generally desirable for the mean jump lengths to be significantly bigger than the localization error, thus for most nuclear factors in mammalian cells it is not desirable to image at above > 250 Hz.
Accordingly, a reasonable solution is therefore to use stroboscopic illumination. That is, using brief excitation laser pulses that last shorter than the camera frame rate (e.g. 1 ms excitation pulse, 10 ms camera exposure time for a 100 Hz experiment): this achieves minimal motionblurring while maintaining a useful framerate. However, this highlights a key experimental tradeoff: shorter excitation pulses minimize motionblurring, but also minimize the signaltonoise. Therefore, a reasonable compromise has to be determined. Here we use 1 ms excitation pulses: this achieves minimal motion blurring (0.067% > 320 nm using \(D=3.5 \mu m^2/s\)) and still yields very good signal (signaltobackground > 5).
But users will need to decide this based on their expected \(D\) and their experimental setup (signaltonoise). As we show here, the estimation of \(D\) is quite sensitive to motionblurring, but the estimation of the bound fraction is less sensitive as long as the diffusion constant is < 5 µm²/s. Generally speaking, we do not recommend imaging at a signaltobackground < 3 and do not recommend using excitation pulses > 5 ms, but the optimal conditions will need to be determined on a casebycase basis.
In conclusion, experimentally implementing stroboscopic excitation makes it possible to minimize the bias coming from motionblurring, while still achieving a sufficient signal for reliable localization.
It is necessary to minimize tracking errors in order to obtain highquality singlemolecule tracking (SMT) data. Tracking errors bias the estimation of essentially all parameters we could want to estimate from SMT experiments including diffusion constants, subpopulations, anomalous diffusion etc.
While many different tracking algorithms exist, it is fundamentally impossible to perform tracking, that is connecting localized molecules between subsequent frames, at high densities without introducing many tracking errors. Thus, the simplest solution is to image at low densities: in principle, if there is only one labeled molecule per cell, there can be no tracking errors. However, because dyes generally bleach quite quickly, this has traditionally lead to a series tradeoff between data quality and the number of trajectories which can be obtained.
However, with the recent development of bright photoactivatable JFdyes (PAdye;Grimm et al, 2016), it is now possible to combine the superior brightness of the HaloJF dyes with photoactivation SMT (Manley et al, 2008). That is, a large fraction of Halotagged proteins in a cell can be labeled with HaloPAJF dyes and then photoactivated one at a time: this allows imaging at extremely low densities (< 1 fluorescent molecule per cell per frame) and nevertheless obtain tens of thousands of trajectories from a single cell. Thus, PAdyes now make it possible to nearly eliminate tracking errors without compromising on signaltonoise or amount of data.
In fact, imaging at extremely low densities generally also improves signaltonoise since outoffocus background is reduced and overlapping point emitters are avoided.
Nevertheless, even with paSMT it is still necessary to decide on an optimal density. The key parameters are size of the ROI (ideally the whole nucleus for studies in cells) and \(D\): a large nucleus and a slow \(D\) can support a higher density than can fastdiffusing molecules in a small nucleus. As a general rule of thumb we recommend a density of ~1 fluorescent molecule per ROI per frame. This will keep tracking errors at a minimum and still support rapid acquisition of large datasets. All data acquired for this study was acquired at this density.
In practice, keeping an optimal density will require some trialanderror optimization of the 405 nm photoactivation laser intensity. 405 nm excitation does contribute background fluorescence, so we prefer to pulse the 405 laser during the camera “deadtime” (~0.5 ms in our case) to avoid this. Moreover, this also makes it easier to keep the photoactivation level constant when changing the frame rate. However, the optimal photoactivation power will depend on the expression level of the protein, protein halflife and the dye concentration and will therefore have to be optimized in each case. We recommend recording initial datasets and then analyzing them using SpotOn which reports the mean number of localizations per frame and then using this information to determine the optimal photoactivation level. However, even then some celltocell variation may be unavoidable: especially in transient transfection experiments where there is huge celltocell variation in expression level or when studying proteins expressed from stably integrated transgenes (e.g. Halo3xNLS and H2bHalo in our case). In these cases, some cells will likely exhibit too high a density. To deal with this, SpotOn includes the option to analyze datasets from individual cells first and then excluding a cell with too high a density before analyzing the merged dataset.
In the sections above, we have discussed how to minimize common experimental biases in SMT experiments and proposed spaSMT as a general solution. However, many 2D SMT datasets recorded under different conditions are also appropriate for SpotOn. For example, SMT experiments without photoactivation or with continuous illumination may also be appropriate for analysis with SpotOn. But since SpotOn uses the loss of fastdiffusing molecules over time to correct for bias and to estimate the free population, it is essential that all trajectories are included in SpotOn for analysis. For example, some tracking and localization algorithms ignore all trajectories below a certain length (e.g. 5 frames), but this will cause SpotOn to misestimate the loss of molecules moving outoffocus and thus it is imperative that trajectories of all lengths be included when analyzing data using SpotOn.
Moreover, SpotOn does not currently support 3D SMT data. Furthermore, SpotOn assumes diffusion to be Brownian. This is a reasonable approximation even for molecules exhibiting some levels of anomalous diffusion, but SpotOn is not appropriate for molecules undergoing directed motion. Finally, the correction for molecules moving outoffocus assumes that molecules are not fully confined within small compartments, that prevent molecules from moving outoffocus.
SpotOn extracts kinetic parameters by fitting the jump length distribution of the tracked particles while taking into account that a significant fraction of the particles might be moving out of focus during the imaging process. This approach is based on the initial work by Mazza et al. (2012), further simplified by Hansen et al. (2017).
Transcription factors (or DNAbinding factors in general) can be envisioned (in an oversimplified manner) as proteins alternating between several states in the nucleus:
In this context, identifying the fraction of proteins present in each state and its diffusion coefficient is of biological relevance.
In such a context, the kinetic parameters mentioned above (fraction of the observed population and diffusion coefficient of each of the states) can be inferred by fitting a model to the histogram of jump lengths derived from single particle data (SPT). In a histogram of jump lengths, several populations can overlap with various diffusion coefficients. The slowmoving fraction tends to show short displacements, possibly dominated by localization error while the fastmoving fraction shows bigger jumps. Such fractions can be estimated using adequate modeling.
Such model has to account for two extra parameters: localization error and particles moving out of focus.
The evolution over time of a concentration of particles located at the origin as a Dirac delta function and which follows free diffusion in two dimensions with a diffusion constant \(D\) can be described by a propagator (also known as Green’s function). Properly normalized, the probability of a particle starting at the origin ending up at a location \(r = (x,y)\) after a time delay, \(\Delta t\), is then given by:
$$P(r, \Delta t) = N \frac{r}{2D\Delta t}e^{\frac{r^2}{4D\Delta t}}$$Here, \(N\) is a normalization constant with units of length. In practice, this distribution is compared to binned data: we integrate this distribution over a small histogram bin window \(\Delta r\), to obtain a normalized distribution and to compare to the empirically measured distribution. For simplicity, we therefore leave out this normalization constant of subsequent expressions.
Furthermore, in practice, we are unable to determine the precise localization of a single molecule. Instead, it is associated with a certain localization error \(\sigma\). Correcting for localization errors is important because it will other wise appear as if molecules move further between frames than they actually did. Thus, we obtain the following expression for the jump length distribution taking localization error, \(\sigma\), into account (Matsuoka et al., 2009)
$$P(r, \Delta t) = \frac{r}{2\left(D\Delta t + \sigma^2\right)}e^{\frac{r^2}{4\left(D\Delta t + \sigma^2\right)}}$$Next, we assume that the protein of interest exists in two states, one bound (characterized by a specific diffusion coefficient, \(D_{bound}\), and a fraction bound, \(F_{bound} \in [0,1]\)) and one "free" (characterized by a specific diffusion coefficient, \(D_{free}\), and a fraction free, \(F_{free} = 1F_{bound}\)). Thus, the distribution of jump length \(P(r, \Delta t)\) reflects this mixture of two populations:
$$P(r, \Delta t) = F_{bound} \frac{r}{2\left(D_{bound}\Delta t + \sigma^2\right)}e^{\frac{r^2}{4\left(D_{bound}\Delta t + \sigma^2\right)}} + \left(1F_{bound}\right)\frac{r}{2\left(D_{free}\Delta t + \sigma^2\right)}e^{\frac{r^2}{4\left(D_{free}\Delta t + \sigma^2\right)}}$$Then, fastmoving molecules are more likely to move out of the focal plane or axial detection window (\(\Delta z\)) during 2D image acquisition than slowmoving or bound molecules. Even though for short lag times (e.g \(\Delta t \sim 530 \text{ ms}\)), this is still long enough for a large fraction of the free population to be lost. As a consequence, bound molecules tend to have much longer trajectories than do free molecules. Again, this means that we are oversampling the bound population and undersampling the free population.
To correct for this, we consider the probability that a freely diffusing molecule with diffusion constant \(D_{free}\) will move out of the axial detection window \(\Delta z\) during a lag time \(\Delta t\). This problem has also been previously considered (Kues and Kubitscheck, 2002). If we consider the extreme case of a population of molecules equally distributed onedimensionally along an axis \(z\), with an absorbing boundary at \(z_{max} = \Delta z/2\) and \(z_{min} = \Delta z/2\), the fraction \(P_{remaining}\), of molecules remaining at lag time \(\Delta t\), is given by:
$$P_{remaining}(\Delta t) = \frac{1}{\Delta z}\int_{\Delta z/2}^{\Delta z/2} \left\{ 1\sum_{n=0}^{\infty}(1)^n \left[ \text{erfc}\left(\frac{\frac{(2n+1)\Delta z}{2}z}{\sqrt{4D_{free}\Delta t}} \right) + \text{erfc}\left(\frac{\frac{(2n+1)\Delta z}{2}+z}{\sqrt{4D_{free}\Delta t}} \right) \right]\right\}dz$$However, this expression significantly overestimates how many freely diffusing molecules are lost since it assumes absorbing boundaries: any molecules that comes into contact with the boundary at \(\pm \Delta z/2\) are permanently lost. In reality, there is a significant probability that a molecule, which has briefly contacted or exceeded the boundary, reenters the axial detection window, \(\Delta z\), during a lag time \(\Delta t\). Moreover, since trajectory gaps can be allowed in the tracking algorithm (i.e. a molecule present in frame \(n\) and \(n+2\) can still be tracked even if it was not localized in frame \(n+1)\), we must consider the probability that a lost molecule reenters the axial detection window during twice the lag time, \(2 \Delta t\). This results in the somewhat counterintuitive effect, which was also noted by Kues and Kubitscheck, that the decay rate depends on the microscope frame rate. In other words, the fraction lost depends on how often one 'looks'. One approach (Mazza et al, 2012) of accounting for this is to use a corrected axial detection window larger than the true axial detection window: \(\Delta z_{corr} > \Delta_z\).
\(\Delta z_{corr}\) was computed from the true \(\Delta z\) as:
$$\Delta z_{corr}(\Delta z, \Delta t, D) = \Delta z + a(\Delta z, \Delta t)\sqrt{D} + b(\Delta z, \Delta t)$$where compute the coefficients \(a\) and \(b\) were fitted based on Monte Carlo simulations. Indeed, for a given diffusion constant, \(D\), 50,000 molecules were uniformly placed onedimensionally along the zaxis from \(z_{min} = \Delta z/2\) to \(z_{max} = \Delta z/2\). Next, using a timestep \(\Delta t\), we simulated onedimensional Brownian diffusion along the zaxis. For time gaps from \(1 \Delta t\) to \(15 \Delta t\), we calculated the fraction of molecules that were lost, allowing for one missing frame as the default setting in our tracking algorithm. We repeated these simulations for particles with diffusion constants in the range of \(D = 1 \mu\text{m}^2/s\) to \(D = 12 \mu\text{m}^2/s\) to generate a comprehensive dataset over a range of biologically plausible diffusion constants. From this series of simulation, a pair of coefficients \(\left(a(\Delta z, \Delta t), b(\Delta z, \Delta t) \right)\) was estimated. The process was repeated over a grid of plausible values of \((\Delta z, \Delta t)\) to derive a grid of \((a,b)\) parameters.
Having derived an analytical expression for the probability of a free molecule being lost due to axial diffusion during the imaging time, we can now thus write down the final equations used for fitting the raw jump length distributions:
$$P(r, \Delta t) = F_{bound} \frac{r}{2\left(D_{bound}\Delta t + \sigma^2\right)}e^{\frac{r^2}{4\left(D_{bound}\Delta t + \sigma^2\right)}} + Z_{corr}(\Delta t)\left(1F_{bound}\right)\frac{r}{2\left(D_{free}\Delta t + \sigma^2\right)}e^{\frac{r^2}{4\left(D_{free}\Delta t + \sigma^2\right)}}$$where:
$$Z_{corr}(\Delta t) = \frac{1}{\Delta z}\int_{\Delta z/2}^{\Delta z/2} \left\{ 1\sum_{n=0}^{\infty}(1)^n \left[ \text{erfc}\left(\frac{\frac{(2n+1)\Delta z_{corr}}{2}z}{\sqrt{4D_{free}\Delta t}} \right) + \text{erfc}\left(\frac{\frac{(2n+1)\Delta z_{corr}}{2}+z}{\sqrt{4D_{free}\Delta t}} \right) \right]\right\}dz$$Finally, some questions arise about how to build the empirical jump length distribution.
One of them is whether to use the entire trajectory or not. One bias against moving molecules is that frequently, freely diffusing molecules will translocate through the axial detection window, \(\Delta z\), yielding only a single detectable localization and thus no jumps to be counted. Conversely, one bias against bound molecules, is that moving molecules can reenter the axial detection window multiple times resulting in the same molecule appearing as multiple distinct trajectories and thus being overcounted. Clearly, the extent of the bias will depend on the photobleaching rate – in the limit of no photobleaching, a single freely diffusing molecule could yield a very high number of different trajectories, leading to large overcounting of the free population. However, in practice, using the current dyes and high laser illumination, the average dye lifetime is quite short. Thus, the number of jumps to consider should be chosen accordingly with the estimated diffusion coefficient and the exposure time.
Another free parameter is the number of \(\Delta t\) used to fit the model. The default parameter is 7 \(\Delta t\), but this has to be adjusted so that the histograms for the longer time intervals remain populated.
Having introduced the theory for the inference of a twostate kinetic model, derivation of a threestate is straightforward.
First, we assume that the observed factor exists in three distinct populations, characterized by their diffusion coefficients \(D_{bound}\), \(D_{slow}\), \(D_{fast}\) and by their fractions: \(F_{bound}\), \(F_{slow}\), \(F_{fast}\), and the relationship \(F_{bound}+F_{slow}+F_{fast}=1\) holds, describing a model with five free parameters. From that, we can derive the (uncorrected) jump length distribution \(P_3(r, \Delta t)\):
$$\begin{align} P_3(r, \Delta t) = & F_{bound} \frac{r}{2\left(D_{bound}\Delta t \sigma^2\right)}e^{\frac{r^2}{4\left(D_{bound}\Delta t + \sigma^2\right)}}\\ + & F_{slow} \frac{r}{2\left(D_{slow}\Delta t + \sigma^2\right)}e^{\frac{r^2}{4\left(D_{slow}\Delta t + \sigma^2\right)}}\\ + &\left(1F_{bound}F_{slow}\right)\frac{r}{2\left(D_{fast}\Delta t + \sigma^2\right)}e^{\frac{r^2}{4\left(D_{fast}\Delta t + \sigma^2\right)}} \end{align}$$Then, as described in the two states model, this derivation is biased against fastmoving molecules, that tend to move out of focus whereas slowmoving and bound molecules remain in the focal plane for more frames. This results into slowmoving molecules exhibiting more jumps than the fast moving molecules. This distribution is thus corrected by a factor taking into account the fraction of molecules lost by moving out of focus:
$$\begin{align} P_3(r, \Delta t) = & F_{bound} \frac{r}{2\left(D_{bound}\Delta t \sigma^2\right)}e^{\frac{r^2}{4\left(D_{bound}\Delta t + \sigma^2\right)}}\\ + & Z_{corr}(\Delta t, D_{slow})F_{slow} \frac{r}{2\left(D_{slow}\Delta t + \sigma^2\right)}e^{\frac{r^2}{4\left(D_{slow}\Delta t + \sigma^2\right)}}\\ + & Z_{corr}(\Delta t, D_{fast})\left(1F_{bound}F_{slow}\right) \frac{r}{2\left(D_{fast}\Delta t + \sigma^2\right)}e^{\frac{r^2}{4\left(D_{fast}\Delta t + \sigma^2\right)}} \end{align}$$where \(Z_{corr}(\Delta t, D)\) is unchanged compared to the twostate model:
$$Z_{corr}(\Delta t, D) = \frac{1}{\Delta z}\int_{\Delta z/2}^{\Delta z/2} \left\{ 1\sum_{n=0}^{\infty}(1)^n \left[ \text{erfc}\left(\frac{\frac{(2n+1)\Delta z_{corr}}{2}z}{\sqrt{4D_{free}\Delta t}} \right) + \text{erfc}\left(\frac{\frac{(2n+1)\Delta z_{corr}}{2}+z}{\sqrt{4D_{free}\Delta t}} \right) \right]\right\}dz$$The modeling approach described above does not explicitely incorporate the exchange rates between the different states (the apparent \(k^*_{on}\) and \(k_{off}\)), but defines rather the fraction in each of the states, and assumes that:
$$F_{bound} = \frac{k^*_{on}}{k^*_{on}+k_{off}}$$However, our approach assumes that state exchange is rare when compared to the imaging framerate: that is that one observed jump likely belongs to one molecule either in one state or the other, rather than an average between the two states due to state exchange. In case this assumption is violated, then the estimate of diffusion coefficients and fraction bound might be wrong.
Although an analytical formula exists to estimate the fraction of molecule that reach the limit of the detection volume after a time \(\Delta t\), this formula does not take into account the fact that molecules can exit the detection volume for a very short time, or can exit for the duration of ~ 1 frame and reenter one frame later, a behavior that can be captured if the tracking algorithm is configured to allow for a gap. To take into account those effects, the corrected detection volume \(\Delta z_{corr}\) is estimated from Monte Carlo simulations. SpotOn relies on a database of ~16000 Monte Carlo simulations for a wide range of \(\Delta t, \Delta z, D\) values. Several limitations apply:
Here is a little bit more detail about how this model is implemented and fitted in SpotOn.
The empirical jump length distribution is computed as follows: first, the MaxJump
and BinWidth
parameters determine the range to build the histogram, and ulitmately the number of bins it will contain. Also, the input file is filtered for trajectories that contain more than three localizations.
Then, the histogram in itself is built. For each trajectory, the JumpsToConsider
parameter determines how many of the first jumps will be taken into account for the building of the histogram. If the UseAllJumps
is set to "Yes", then all jumps (and not the first few ones) will be used to build the histogram. Note that this later option is likely to bias the histogram towards bound molecules. For this procedure, the number of gaps in the data is extracted.
Since the diffusion coefficient (\(D\)) and the localization error always appear together in the equations, the model is not identifiable as it. However, when the model is fitted over several \(\Delta t\), then the localization error and the diffusion coefficient are properly separated and can be distinguished. Thus, SpotOn consider several time points to perform the model fitting. In addition, this increases the robustness of the fit. In practice, several histograms are built with increasing time lags \(\Delta t\). The number of histograms to be built is determined by the Number of time points
parameter.
Parameter optimization of \((D_{free}, D_{bound}, F_{bound})\) (or \((D_{fast}, D_{slow}, D_{bound}, F_{fast}, F_{bound})\) for a 3state model) is performed using a nonlinear leastsquare algorithm. In practice, the
LevenbergMarquardt solver implemented wrapped by the lmfit
library is used. Userprovided bounds are enforced and the algorithm provides estimates of the uncertainty for each estimated parameter. The routine is initialized with parameters drawn uniformly from the specified parameter range. The optimization is repeated several times with different initialization parameters. This number of initializations is determined by the Iterations
parameter.
The threestate model is fitted similarly as the twostate model. The only difference is the parameter bounds cannot be easily specified. Indeed, the optimization is performed under the following constraints:
$$\begin{align} D^{MIN}_{bound} \leq D_{bound} \leq D^{MAX}_{bound} \\ D^{MIN}_{slow} \leq D_{slow} \leq D^{MAX}_{slow} \\ D^{MIN}_{fast} \leq D_{fast} \leq D^{MAX}_{fast} \\ 0 \leq F_{bound} \leq 1\\ 0 \leq F_{slow} \leq 1\\ 0 \leq F_{fast} \leq 1\\ F_{bound} + F_{slow} + F_{fast} = 1 \end{align}$$The first six constraints are easy to enforce since they constrain the optimization inside an hypercube, and is builtin the solver. However, the last constraint, \(F_{bound} + F_{slow} + F_{fast} = 1\) is a triangular constraint for which a specific cost function was written. Indeed: \(F_{bound} + F_{fast} \leq 1\). Thus the cost function was modified to penalize parameters sets where \(F_{bound} + F_{fast} > 1\).
In practice, denoting \(X_i, i \in [0,N]\) the bins of the empirical histogram with \(N\) the number of bins (\(N = \lfloor \frac{\text{MaxJump}}{\text{BinWidth}}\rfloor\), and \(X^*_i, i \in [0,N]\) the model resulting a set of candidate parameters, the algorithm minimizes the cost function \(L(X,X^*)\):
$$L(X,X^*) = \sum_{i=0}^N \left(X_iX^*_i\right)^2 + 10^4\left(F_{bound}+F_{fast}1\right)\mathbf{1}_{F_{bound} + F_{fast} > 1}$$where \(\mathbf{1}\) denotes the indicator function. This in practice constrains the optimization to the halfplane where \(F_{bound} + F_{fast} \leq 1\).
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Normanno, Davide, Lydia Boudarène, Claire DugastDarzacq, Jiji Chen, Christian Richter, Florence Proux, Olivier Bénichou, Raphaël Voituriez, Xavier Darzacq, and Maxime Dahan. “Probing the Target Search of DNABinding Proteins in Mammalian Cells Using TetR as Model Searcher.” Nature Communications 6 (July 7, 2015): 7357.
Tokunaga, Makio, Naoko Imamoto, and Kumiko SakataSogawa. “Highly Inclined Thin Illumination Enables Clear SingleMolecule Imaging in Cells.” Nature Methods 5, no. 2 (2008): 159–161.
Grimm, Jonathan B, Brian P English, Jiji Chen, Joel P Slaughter, Zhengjian Zhang, Andrey Revyakin, Ronak Patel, et al. “A General Method to Improve Fluorophores for LiveCell and SingleMolecule Microscopy.” Nature Methods 12, no. 3 (January 19, 2015): 244–50.
Manley, Suliana, Jennifer M Gillette, George H Patterson, Hari Shroff, Harald F Hess, Eric Betzig, and Jennifer LippincottSchwartz. “HighDensity Mapping of SingleMolecule Trajectories with Photoactivated Localization Microscopy.” Nature Methods 5, no. 2 (February 2008): 155–57.
Shinkai, Soya, Tadasu Nozaki, Kazuhiro Maeshima, and Yuichi Togashi. “Dynamic Nucleosome Movement Provides Structural Information of Topological Chromatin Domains in Living Human Cells.” Edited by Alexandre V Morozov. PLOS Computational Biology 12, no. 10 (October 20, 2016): e1005136.
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SpotOn is a free/opensource software, feel free to contribute by reporting bugs, helping us to write the documentation or proposing new features. The code of SpotOn is available on the software forge GitLab, in the SpotOn repository. A bugtracker is also available for bug reports and feature requests.
SpotOn is divided in several packages:
The webinterface is released under the AGPL license. The backend is released under the GNU GPL version 3+
To comprehensively test SpotOn over many different conditions, we conducted 1064 spaSPT experiments. The raw data is freely available and the purpose of this section is to describe the organization, acquisition parameters and format of the data. The data is for 4 different cell lines imaged over 15 different conditions yielding a total of 60 different conditions. The four cell lines were:
The cell lines were constructed in different ways.
U2OS C32 HaloCTCF was made by homozygous endogenous Nterminal tagging of CTCF in human osteosarcoma U2OS cells using CRISPR/Cas9mediated genomeediting as described (C32 refers to clone number 32). We note the CTCF is an essential gene and that Nterminal tagging did not appear to affect CTCF function or expression level according to a series of control experiments (see Hansen et al, 2017). Moreover, C32 HaloCTCF has been authenticated using Short Tandem Repeat (STR) profiling (performed by Dr. Alison N. Killilea at the UC Berkeley Cell Culture Facility) against the following loci: THO1, D5S818, D13S317, D7S820, D16S539, CSF1PO, AMEL, vWA and TPOX. The C32 HaloCTCF cell line showed a 100% match with U2OS.
U2OS H2BHaloSNAP was made through random integration of a H2BHaloTagSNAPTag transgene expressed using the EF1a promoter with an IRESNeoR gene for drug selection. After transfection, cells were selected using G418 until a pure cell population was obtained. This cell line has also been described previously. The wildtype U2OS cell line used to make this cell line was also authenticated using STR profiling against the same loci as C32 and also showed a 100% match with U2OS.
U2OS Halo3xNLS was made through random integration of a FLAGHalo3xNLS (3x SV40 NLS: PKKKRKV) transgene expressed using the EF1a promoter. NeoR for drug selection was separately expressed using an SV40 promoter. After transfection, cells were selected using G418 until a pure cell population was obtained. This cell line has also been described previously. The wildtype U2OS cell line used to make this cell line was also authenticated using STR profiling against the same loci as C32 and also showed a 100% match with U2OS.
mESC C3 HaloSox2 was made through homozygous Nterminal tagging of Sox2 in JM8.N4 mouse embryonic stem cells using CRISPR/Cas9mediated genome editing as previously described (C3 refers to clone number 3). The functionality of the C3 HaloSox2 knockin was validated through control experiments and pluripotency through teratoma assays as described previously (see Teves et al, 2016).
Each file contains singlemolecule trajectories from a single cell imaged over 30,000 frames. Localization and tracking was performed using a customwritten Matlab implementation of the MTTalgorithm and the following settings:
Parameter  Value 

Localization error  10^{6.25} 
Deflation loops  0 
Blinking (frames)  1 
Max competitors  3 
Max \(D\) (µm²/s)  20 
The same 15 conditions were used for each of the 4 cell lines.
The purpose of this experiment was to test the effect of “motionblurring” on the SpotOn estimated \(D_{FREE}\) and \(F_{BOUND}\).
Experiment with PAJF549 dyesFive different experimental conditions were considered. Briefly, cells were grown overnight on plasmacleaned 25 mm circular coverslips either directly (U2OS) and MatriGel coated. Cell were labeled with 550 nM PAJF549 for around 1530 min, washed twice and medium exchanged to phenolred free medium. 30,000 frames were collected at a camera exposure time (Andor iXon Ultra 897; frametransfer mode; vertical shift speed: 0.9 μs; 70°C) of 9.5 ms which together with a ~447 μs camera integration time gave a frame rate of ~100 Hz. PAJF549 dyes were photoactivated during the ~447 μs camera integration time using 405 nm pulses and the 405 nm pulse intensity optimized to achieve a mean density of ~1 molecule per frame per nucleus. The JF549 dye was excited using a 561 nm laser and the total number of excitation photons kept constant but either delivered during a 1 ms pulse, a 2 ms pulse, a 4 ms pulse, a 7 ms pulse or with constant illumination. For each cell line and condition, 4 replicates were performed. We count a replicate as an independent experiment performed on a different day. For each replicate around 5 cells were imaged. Occasionally, fewer than 5 cells are available. To avoid tracking errors, we removed cells with too high a localization density from the analysis.
Experiment with PAJF646 dyesThis experiment was exactly identical to the “ExpA_PAJF549” experiment except cell were labeled with PAJF646 and excited using a 633 nm laser. The file names and data organization was otherwise the same and the same five excitation conditions were considered.
The purpose of this experiment was to test if the SpotOn estimated \(D_{FREE}\) and \(F_{BOUND}\) values would depend on the frame rate. In particular, all four proteins exhibit some levels of apparent anomalous diffusion, which could cause a dependence on the frame rate.
Cells were labeled with PAJF646 and grown and imaged as described above. Photoactivation took place during the ~447 μs camera integration time and JF646 dyes were excited using 1 ms stroboscopic 633 nm excitation pulses. To change the frame rate, the camera exposure time was set to 4.5 ms (~201 Hz), 5.5 ms (~167 Hz), 7 ms (~134 Hz), 13 ms (~74 Hz) and 19.5 ms (~50 Hz) when also counting the ~447 μs camera integration time.
SpotOn is an online tool to extract kinetic parameters from fast single particle tracking experiments. It does it in a manner that takes into account the finite depth of field of the objective and proposes corrections for that. SpotOn can fit twostate (BoundFree) and threestate (BoundFree1Free2) models.
SpotOn takes a set of trajectories as input (multiple formats supported) and outputs a fitted jump length distribution, together with goodnessoffit metrics and the corresponding fitted coefficients.
SpotOn is not a tracking algorithm, thus you need to perform the tracking of your single particle tracking datasets using a separated algorithm. SpotOn accepts inputs from a range of popular tracking softwares, and you can either add your own or write a converter towards a standard tablefile import.
See also the section Which datasets are appropriate for SpotOn?.
All tracking softwares are very sensitive to the input parameters, but also to the experimental acquisition conditions, such as the signaltobackground ratio and the presence/absence of motion blur.
Thus, in all cases, a tracking software and the associated parameters have to be chosen carefully based on analysis of the data. A consequence of that is there is to our knowledge no universal tracking software. However, the guidelines presented in section How to acquire a "good" dataset? are supposed to minimize the impact of the choice of the algorithm/tracking parameters by ensuring a high signaltobackground ratio and low levels of motion blur thanks to stroboscopic illumination.
All the data presented in this document was analysed using SLIMfast/evalSPT, a Matlabbased, modified version of MTT (Sergé et al.). A version of SLIMfast is available on the eLife website.
See this section of the documentation.
If the format of the tracking algorithm you use is not supported by SpotOn, here are a few things you can try:
/SPTGUI/parsers.py
file. Do not forget to open an issue on the bugtracker so that we are aware that you are working on a specific file format.Two factors limit the length of trajectories than one can obtain from a singleparticle tracking experiment.
Photobleaching: First, the dyes used do not have an infinite lifetime, and bleach eventually. When highpower lasers are used, this can happen in a few frames. The datasets analyzed above have a median length of trajectories of 4 frames, mostly limited by fluorophore lifetime.
Particles moving out of focus: As described above, free particles diffuse in 3D and can move out of focus extremely quickly. Thus, for a fastdiffusing particle, it is extremely unlikely to observe a "long" trajectory, just because the probability of being lost at some point in the tracking process increases exponentially.
The figure below shows for different diffusion coefficients and constant framerate (10ms) the fraction of particles that have remained in focus (allowing for one gap, that is to track a particle that has moved out of focus for at most one frame). One can see that it is extremely unlikely to follow a fast protein for 100 ms (10 frames), simply because the particles tend to move out of focus.
This is slightly more complicated, for several reasons presented in details in the methods section:
Two (orthogonal) approaches can be undertaken to measure the localization error \(\sigma\), measured as the standard deviation of the detection positions for a bound molecule. The first one consists into measuring it in a context where all molecules are bound (fixed cells). In the second approach, \(\sigma\) is fitted together with SpotOn's kinetic model.
Method 1: measurement on fixed cells
Method 2: estimation from SpotOn
Below is a short protocol to measure the empirical axial detection range:
During our tests that included up to 1 million detections, the computation of the jump length distribution and the fitting of the most complicated kinetic model (3 states with estimation of the localization error from the data) usually takes about one minute.
That said, the fitting speed depends on many parameters (load of the server, range of the parameters, shape of your jump length distribution, etc.). If the online version of SpotOn is performing too slowly for your needs, feel free to get either the offline version of SpotOn, or the command line version.
Sure! SpotOn is fully free/opensource and detailed download and installation instructions can be retrieved from our Gitlab page.
There is! SpotOn uses an independent commandline Python backend that is available in our Github repository. It implements most of the features of SpotOn, comes with simple wrapper functions that can quickly be implemented in your scripting framework. There is also a Matlab command line version of SpotOn available from our Gitlab repository.
SpotOn is written in Python. The backend relies on the lmfit library. The server is based on Django and uses Celery to run an asynchronous queue to perform jobs. The frontend is written in AngularJS and the graphs are rendered through D3.js.
Yes. The Matlab version gives equivalent results to the online version or Python command line version and can be downloaded from our Gitlab repository. Please note that the Matlab version accepts only one input format.
SpotOn is twofolds:
We'd love to hear it! You can either:
We only collect minimal information when you upload your datasets (your IP is saved somwhere in the logs but we don't use it), we do not ask for email or identification: no account is required to use SpotOn. Furthermore, you can erase your analysis anytime by going to the Settings tab in the analysis page. Finally, we provide an offline and a commandline version that you can run on your own machine. We can find more details on the Privacy page. If you have any concern, feel free to write to us.
You can use the following citation:
Robust modelbased analysis of singleparticle tracking experiments with SpotOn.
Hansen, A.S.*, Woringer, M.*, Grimm, J.B., Lavis, L.D., Tjian, R., and Darzacq, X.
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Thanks a lot for letting us know, this is really important to us! You can either open an issue on our Gitlab bugtracker or drop us a message.