Spot-On: robust model-based analysis of single-particle tracking experiments

Single-particle tracking (SPT) has become an important method to bridge biochemistry and cell biology since it allows direct observation of protein binding and diffusion dynamics in live cells. However, accurately inferring information from SPT studies is challenging due to biases in both data analysis and experimental design. To address analysis bias, we introduce “Spot-On”, an intuitive web-interface. Spot-On implements a kinetic modeling framework that accounts for known biases, including molecules moving out-of-focus, and robustly infers diffusion constants and subpopulations from pooled single-molecule trajectories. To minimize inherent experimental biases, we implement and validate stroboscopic photo-activation SPT (spaSPT), which minimizes motion-blur bias and tracking errors. We validate Spot-On using experimentally realistic simulations and show that Spot-On outperforms other methods. We then apply Spot-On to spaSPT data from live mammalian cells spanning a wide range of nuclear dynamics and demonstrate that Spot-On consistently and robustly infers subpopulation fractions and diffusion constants. IMPACT STATEMENT Spot-On is an easy-to-use website that makes a rigorous and bias-corrected modeling framework for analysis of single-molecule tracking experiments available to all.


INTRODUCTION 41
Advances in imaging technologies, genetically encoded tags and fluorophore 42 development have made single-particle tracking (SPT) an increasingly popular method for 43 analyzing protein dynamics (Liu et al., 2015). Recent biological application of SPT have 44 revealed that transcription factors (TFs) bind mitotic chromosomes (Teves et al., 2016), how 45 Polycomb interacts with chromatin (Zhen et al., 2016), that "pioneer factor" TFs bind 46 chromatin dynamically (Swinstead et al., 2016), that TF binding time correlates with 47 transcriptional activity (Loffreda et al., 2017) and that different nuclear proteins adopt distinct bias. Constant excitation during acquisition of a frame will cause a fast-moving particle to spread out its emission photons over many pixels and thus appear as a motionblur, which make detection much less likely with common PSF-fitting algorithms. In contrast, a slow-moving or immobile particle will appear as a well-shaped PSF and thus readily be detected. (B) Tracking ambiguities. Tracking at high particle densities prevents unambiguous connection of particles between frames and tracking errors will cause displacements to be misidentified. (C) Defocalization bias. During 2D-SPT, fast-moving particles will rapidly move out-of-focus resulting in short trajectories, whereas immobile particles will remain in-focus until they photobleach and thus exhibit very long trajectories. This results in a bias toward slow-moving particles, which must be corrected for. (D) Analysis method. Any analysis method should ideally avoid introducing biases and accurately correct for known biases in the estimation of subpopulation parameters such as D FREE , F BOUND , D BOUND . Table 1), but slightly underestimated the diffusion constant (-4.8%; Figure 3B; Table 1). 143 However, this underestimate was due to particle confinement inside the nucleus: Spot-On   Figure 3C). Spot-On and vbSPT accurately inferred 155 both D FREE and F BOUND . In contrast, MSD i (R 2 >0.8) greatly underestimated F BOUND (13.6% vs. 156 70%), whereas MSD i (all) slightly overestimated F BOUND . Since MSD i -based methods apply 157 two thresholds (first, minimum trajectory length: here 5 frames; second, filtering based on R 2 ) 158 in many cases less than 5% of all trajectories passed these thresholds and this example 159 illustrate how sensitive MSD i -based methods are to these thresholds. Second, we considered 160 an example with a slow frame rate and fast diffusion, such that the free population rapidly 161 moves out-of-focus (D FREE : 14.0 µm²/s; F BOUND : 50%; Δτ: 20 ms; Figure 3D). Spot-On again 162 accurately inferred F BOUND , and slightly underestimated D FREE due to high nuclear confinement 163   Figure Supplement 9. Comparison of Spot-On and MSDi estimates of D FREE and F BOUND to ground-truth simulation results inside a 4 µm radius nucleus using PDF-fitting. Figure Supplement 10. Sensitivity of Spot-On to state changes and comparison with vbSPT. Figure Supplement 11. Robustness of localization error estimates from Spot-On. bias is minimal), vbSPT strongly overestimated F BOUND in this case ( Figure 3D). Consistent 166 with this, Spot-On without defocalization-bias correction also strongly overestimates the 167 bound fraction (Figure 3 -Figure Supplement 5). We conclude that correcting for 168 defocalization bias is critical. The MSD i -based methods again gave divergent results despite 169 seemingly fitting the data well. Thus, a good fit to a histogram of log(D) does not necessarily 170 imply that the inferred D FREE and F BOUND are accurate. A full discussion and comparison of the 171 methods is given in Appendix 1. Finally, we extended this analysis of simulated SPT data to 3 172 states (one "bound", two "free" states) and compared Spot-On and vbSPT. Spot-On again Having established that Spot-On is accurate, we next tested whether it was also robust. Taken together, this analysis of simulated SPT data suggests that Spot-On successfully 188 overcomes defocalization and analysis method biases ( Figure 1C-D

198 spaSPT minimizes biases in experimental SPT acquisitions 199
Having validated Spot-On on simulated data, which is not subject to experimental 200 biases ( Figure 1A-B), we next sought to evaluate Spot-On on experimental data. To generate 201 SPT data with minimal acquisition bias we performed stroboscopic photo-activation SPT 202 (spaSPT; Figure 4A), which integrates previously and separately published ideas to minimize 203 experimental biases. First, spaSPT minimizes motion-blurring, which is caused by particle 204 movement during the camera exposure time ( Figure 1A), by using stroboscopic excitation (Elf 205 et al., 2007). We found that the bright and photo-stable dyes PA-JF 549 and PA-JF 646 (Grimm et 206 al., 2016a) in combination with the HaloTag ("Halo") labeling strategy made it possible to 207 achieve a signal-to-background ratio greater than 5 with just 1 ms excitation pulses, thus 208 providing a good compromise between minimal motion-blurring and high signal ( Figure 4B).     all but the most lowly expressed nuclear proteins. Thus, this now makes it possible to study 240 biological cell-to-cell variability in TF dynamics. 241 242

Effect of motion-blur bias on parameter estimates 243
Having validated Spot-On on experimental SPT data, we next applied Spot-On to 244 estimate the effect of motion-blurring on the estimation of subpopulations. As mentioned, 245 bound fraction, motion-blurring caused a ~2-fold overestimate for rapidly diffusing Halo-257 3xNLS ( Figure 4K), but had a minor effect on slower proteins like H2B, CTCF and Sox2. 258 Importantly, similar results were obtained for both dyes, though JF 549 yielded a slightly lower 259 bound fraction for Halo-3xNLS ( Figure 4J-K). We note that the extent of the bias due to 260 motion-blurring will likely be very sensitive to the localization algorithm. Here, using the 261 MTT-algorithm (Sergé et al., 2008), motion-blurring caused up to a 2-fold error in both the 262 D FREE and F BOUND estimates. 263 Taken together, these results suggest that Spot-On can reliably be used even for SPT 264 data collected under constant illumination provided that protein diffusion is sufficiently slow 265 and, moreover, provides a helpful guide for optimizing SPT imaging acquisitions (we include 266 a full discussion of considerations for SPT acquisitions and a proposal for minimum reporting 267 standards in SPT in Appendix 3 and 4).  This platform can easily be extended to other diffusion regimes. Moreover, spaSPT provides 282 an acquisition protocol for tracking fast-diffusing molecules with minimal bias. We hope that 283 these validated tools will help make SPT more accessible to the community and contribute 284 positively to the emergence of "gold-standard" acquisition and analysis procedures for SPT.

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Competing interests 299 RT is a member of eLife's Board of Directors. JBG and LDL declare competing financial 300 interests. The other authors declare no competing interests.

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Spot-On model 312 Spot-On implements and extends a kinetic modeling framework first described in Mazza et al. 313 (Mazza et al., 2012) and later extended in Hansen et al. (Hansen et al., 2017). Briefly, the 314 model infers the diffusion constant and relative fractions of two or three subpopulations from 315 the distribution of displacements (or histogram of displacements) computed at increasing lag 316 time (1∆ , 2∆ , ...). This is performed by fitting a semi-analytical model to the empirical 317 histogram of displacements using non-linear least squares fitting. Defocalization is explicitly 318 accounted for by modeling modeling the fraction of particles that remain in focus over time as 319 a function of their diffusion constant. 320 Mathematically, the evolution over time of a concentration of particles located at the origin as 321 a Dirac delta function and which follows free diffusion in two dimensions with a diffusion 322 constant D can be described by a propagator (also known as Green's function). Properly 323 normalized, the probability of a particle starting at the origin ending up at a location r = (x,y) 324 after a time delay, ∆ , is given by: 325 Here N is a normalization constant with units of length. Spot-On integrates this distribution 327 over a small histogram bin window, Δr, to obtain a normalized distribution, the distribution of 328 displacement lengths to compare to binned experimental data. For simplicity, we will 329 therefore leave out N from subsequent expressions. Since experimental SPT data is subject to 330 a significant mean localization error, , Spot-On also accounts for this ( Here, the quasi-immobile subpopulation has diffusion constant, BOUND , and makes up a 341 fraction, BOUND , whereas the freely diffusing subpopulation has diffusion constant, FREE , 342 and makes up a fraction, FREE = 1 − BOUND . To account for defocalization bias ( Figure 1C), 343 Spot-On explicitly considers the probability of the freely diffusing subpopulation moving out 344 of the axial detection range, ∆ , during each time delay, ∆ . This is important. For example, 345 only ~25% of freely-diffusing molecules will remain in focus for at least 5 frames (assuming 346 ∆ =10 ms; ∆ =700 nm; 1 gap allowed; D=5 µm²/s), resulting in a 4-fold undercounting if 347 uncorrected for. If we assume absorbing boundaries such that any molecule that contacts the 348 edges of the axial detection range located at MAX = ∆ 2 and MIN = −∆ 2 is permanently 349 lost, the fraction of freely diffusing molecules with diffusion constant, FREE , that remain at 350 time delay, ∆ , is given by (Carslow and Jaeger, 1959 However, this analytical expression overestimates the fraction lost since there is a significant 355 probability that a molecule that briefly contacted or exceeded the boundary re-enters the axial 356 detection range. The re-entry probability depends on the number of gaps allowed in the 357 tracking ( ), ∆ , and ∆ and can be approximately accounted for by considering a corrected 358 axial detection range, ∆ corr , larger than ∆ : ∆ corr > ∆ : Although ∆ corr depend on the number of gaps (g) allowed in the tracking, we will leave it out 361 for simplicity in the following. We determined the coefficients a and b from Monte Carlo 362 simulations. For a given diffusion constant, D, 50,000 molecules were randomly placed one-363 dimensionally along the z-axis drawn from a uniform distribution from MIN = −∆ 2 to 364 MAX = ∆ 2. Next, using a time-step ∆ , one-dimensional Brownian diffusion was 365 simulated along the z-axis using the Euler-Maruyama scheme. For time delays from 1∆ to 366 15∆ , the fraction of molecules that were lost was calculated in the range of D=[1;12] μm 2 /s. 367 ∆ , ∆ , and ∆ , ∆ , were then estimated through least-squares fitting of 368 remaining ∆ , ∆ corr , to the simulated fraction remaining. The process was repeated over a 369 grid of plausible values of (∆ , ∆ , ) to derive a grid of 134,865 (a,b) parameter pairs. This 370 pre-calculated library of (a,b) parameters enables Spot-On to perform model fitting on nearly 371 any SPT dataset with minimal overhead. 372 Thus, the 2-state model Spot-On uses for kinetic modeling of SPT data is given by: 373 Where CORR ∆ , ∆ corr , is as described above.

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Numerical implementation of models in Spot-On 390 Spot-On calculates the empirical histogram of displacements based on a user-defined bin 391 width. Spot-On allows the user to choose between PDF-and CDF-fitting of the kinetic model 392 to the empirical displacement distributions; CDF-fitting is generally most accurate for smaller 393 datasets and the two are similar for large datasets (Figure 3 -Figure Supplement S9). The 394 integral in CORR ∆ , ∆ corr was numerically evaluated using the midpoint method over 200 395 points and the terms of the series computed until the term falls below a threshold of 10 -10 . 396 Model fitting and parameter optimization was performed using a non-linear least squares 397 algorithm (Levenberg-Marquardt). Random initial parameter guesses are drawn uniformly 398 from the user-specified parameter range. The optimization is then repeated several times with 399 different initialization parameters to avoid local minima. Spot-On constrains each fraction to 400 be between 0 and 1 and for the sum of the fractions to equal 1.

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Theoretical characteristics and limitations of the model 403 Although Spot-On performs well on both experimental and simulated SPT data, the model 404 implemented by Spot-On has several limitations. First, the kinetic model assumes diffusion to 405 be ideal Brownian motion, even though it is widely acknowledged that the motion of most 406 proteins inside a cell shows some degree of anomalous diffusion. Nevertheless, Figure 4G-H 407 and Figure 4 - Figure Supplement 2 shows that the parameter inference for experimental data 408 of proteins presenting various degrees of anomalous diffusion is quite robust. 409 Second, Spot-On models the localization error as the static mean localization error and this 410 feature can be used to infer the actual localization error from the data. However, the 411 localization error is affected both by the position of the particle with respect to the focal plane 412 (Lindén et al., 2017) and by motion blur (Deschout et al., 2012). Even though a high signal-413 to-background ratio and fast framerate/stroboscopic illumination help to mitigate these 414 disparities, it is likely that the localization error of fast moving particles will be higher than 415 the bound/slow-moving particles. In that case, one would expect Spot-On to infer a 416 localization error that is the weighted mean of the "bound/static" localization error and the 417 "free" localization error. However, in many situations D free ∆ >> 3 (even assuming a 2µm²/s 418 particle imaged at a 5 ms framerate with a ~30 nm localization error, there is still an order of 419 magnitude difference between the two terms). As a consequence, the estimate of reflects the 420 static localization error (that is, the localization error of the bound fraction), and the 421 localization error estimate becomes less reliable if the bound fraction is very small ( causes the parameter inference to fail unless the timescale of state changes is at least 10-50 432 times longer than the frame rate. spaSPT experiments and analysis 488 The spaSPT experimental settings for Figure 4G-H were as follows: 1 ms 633 nm excitation 489 (100% AOTF) of PA-JF 646 was delivered at the beginning of the frame; 405 nm photo-490 activation pulses were delivered during the camera integration time (~447 μs) to minimize 491 background and their intensity optimized to achieve a mean density of £1 molecule per frame 492 per nucleus. 30,000 frames were recorded per cell per experiment. The camera exposure times 493 were: 4.5 ms, 5.5 ms, 7 ms, 9.5 ms, 13 ms and 19.5 ms.

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For the motion-blur spaSPT experiments ( Figure 4I-K), the camera exposure was fixed to 9.5 495 ms and photo-activation performed as above. To keep the total number of delivered photons 496 constant, we generated an AOTF-laser intensity calibration curve using a power meter and 497 adjusted the AOTF transmission accordingly for each excitation pulse duration. We developed a utility to simulate diffusing proteins in a confined geometry (simSPT). 513 Briefly, simSPT simulates the diffusion of an arbitrary number of populations of molecules 514 characterized by their diffusion coefficient, under a steady state assumption. Particles are 515 drawn at random between the populations and their location in the 3D nucleus is initialized 516 following a uniform law within the confinement volume. The lifetime of the particle (in 517 frames) is also drawn following an exponential law of mean lifetime . Then, the particle 518 diffuses in 3D until it bleaches. Diffusion is simulated by drawing jumps following a normal 519 law of parameters 0, 2 ∆ , where D is the diffusion coefficient and ∆ the exposure time. 520 Finally, a localization error ( 0, ) is added to each (x,y,z) localization in the simulated 521 trajectories. For this work, we parameterized simSPT to consider that two subpopulations of 522 particles diffuse in a sphere (the nucleus) of 8 µm diameter illuminated using HiLo 523 illumination (assuming a HiLo beam width of 4 µm), with an axial detection range of ~700 524 nm, centered at the middle of the HiLo beam. Molecules are assumed to have a mean lifetime 525 of 4 frames (when inside the HiLo beam) and of 40 frames when outside the HiLo beam. The 526 localization error was set to 25 nm and the simulation was run until 100,000 in-focus 527 trajectories were recorded. More specifically, the effect of the exposure time (1 ms, 4 ms, 7 528 ms, 13 ms, 20 ms), the free diffusion constant (from 0.5 µm²/s to 14.5 µm²/s in 0.5 µm²/s 529 increments) and the fraction bound (from 0 % to 95 % in 5 % increments) were investigated, 530 yielding a dataset consisting of 3480 simulations. More details on the simulations, including 531 scripts to reproduce the dataset, are available on GitLab as detailed in the "Computer code" 532 section. Full details on how the simulations were analyzed by Spot-On, vbSPT and MSD i are 533 given in Appendix 1. 534 535 Data availability 536 All raw 1064 spaSPT experiments (Figure 4) as well as the 3480 simulations (Figure 3)

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"Motion-blur" bias. Constant excitation during acquisition of a frame will cause a fast-moving 558 particle to spread out its emission photons over many pixels and thus appear as a motion-559 blur, which make detection much less likely with common PSF-fitting algorithms. In contrast, 560 a slow-moving or immobile particle will appear as a well-shaped PSF and thus readily be 561 detected. (B) Tracking ambiguities. Tracking at high particle densities prevents unambiguous 562 connection of particles between frames and tracking errors will cause displacements to be 563 misidentified. (C) Defocalization bias. During 2D-SPT, fast-moving particles will rapidly move 564 out-of-focus resulting in short trajectories, whereas immobile particles will remain in-focus 565 until they photobleach and thus exhibit very long trajectories. This results in a bias toward    [1,4,7,10,13,20] ms.

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Each experiment was then fitted using Spot-On, using vbSPT (maximum of 2 states allowed)

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As can be seen, correcting for defocalization bias slightly improves the D FREE -estimate, but is 723 essential for an accurate F BOUND -estimate. As expected, the longer the lag time, the more 724 important it is to correct for defocalization bias.                shown. We note that the numbers depend somewhat on the threshold set and differ a bit 856 between U2OS and mES cells. As an approximate average, we used 700 nm here.

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Importantly, we note that Spot-On is relatively robust to the axial detection range estimate    To systematically evaluate the performance of Spot-On as well as other common 908 analysis tools such as MSD i and vbSPT (Persson et al., 2013), we developed simSPT, a 909 simulation tool to generate a comprehensive set of 3480 realistic SPT simulations spanning 910 the range of plausible dynamics (almost a billion trajectories were simulated in total). simSPT 911 is freely available at GitLab: https://gitlab.com/tjian-darzacq-lab/simSPT. simSPT simulates 912 3D SPT trajectories arising from an arbitrary number of subpopulations confined inside a 913 sphere under HiLo illumination and takes into account a limited axial detection range, 914 realistic photobleaching rates and optionally state interconversion. The simulation methods 915 are described in detail at GitLab. All 3480 simulated datasets are also available (see Data 916 Availability section). 917 Briefly, we parameterized simSPT to consider that particles diffuse inside a sphere 918 (the nucleus) of 8 µm diameter illuminated using HiLo illumination (assuming a HiLo beam 919 width of 4 µm), with an axial detection range of ~700 nm with Gaussian edges, centered at 920 the middle of the HiLo beam. Molecules are assumed to have a mean lifetime of 4 frames 921 (when inside the HiLo beam) and of 40 frames when outside the HiLo beam. The localization 922 error was set to 25 nm and the simulation was run until 100,000 in-focus trajectories were 923 recorded. More specifically, the effect of the exposure time (1 ms, 4 ms, 7 ms, 13 ms, 20 ms), 924 the free diffusion constant (from 0.5 µm²/s to 14.5 µm²/s in 0.5 µm²/s increments) and the 925 fraction bound (from 0% to 95% in 5% increments) were investigated, yielding a dataset 926 consisting of 3480 simulations. The advantage of simulations is that the ground truth is 927 known.

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For more specific simulations, extra parameters were varied, such as the width of the In the case of the main 3480 simulation SPT datasets, we analyzed the data using the 933 Matlab version of Spot-On (either using JumpsToConsider=4 or all), MSD i (either R 2 >0.8 or 934 all) or vbSPT. We describe the analysis in details below. 935 936 Spot-On (4 jumps) 937 Rational and parameters: Spot-On allows a user to use the entirety of each trajectory 938 or to use only the first n jumps by adjusting the parameter, JumpsToConsider.  Performance evaluation: Spot-On (4 jumps) performs slightly worse than Spot-On 980 (all) when it comes to estimating BOUND as expected and essentially identically to Spot-On 981 (all) for estimating FREE . The mean error (bias) for estimating BOUND was -6.4%, the inter-982 quartile range (IQR) was 5.9% and the standard deviation 3.6%. The origin of the error is the 983 undercounting of the bound population due to considering only the first 4 jumps. Since bound 984 molecules remain in focus until they bleach, they always yield only a single trajectory, 985 whereas a single freely diffusing molecule has a probability of yielding multiple trajectories 986 by diffusing in-focus for a while, then moving out-of-focus for a while and then moving back 987 in-focus. For estimating FREE the bias for Spot-On (4 jumps) was -5.4%, the IQR 3.6% and 988 the standard deviation 3.2%. However, as shown in Figure 3 - Figure Supplement 2,4, the 989 slight underestimate of the free diffusion constant is not due to a limitation of Spot-On, but 990 instead due to confinement inside the nucleus (Figure 3 -Figure Supplement 4). For example, 991 a diffusing molecule close to the nuclear boundary moving towards the nuclear boundary will 992 "bounce back" resulting in a large distance travelled, but only a smaller recorded 993 displacement. We validated that this indeed is the origin of the underestimate of FREE by 994 considering a nucleus with virtually no confinement (20 μm radius) and found that the FREE -995 underestimate was now minimal (Figure 3 -Figure Supplement 4). Finally, Spot-On always 996 estimated the bound diffusion constant, BOUND , with minimal error unlike MSD i or vbSPT, 997 which were not able to accurately estimate BOUND . However, since there is generally less 998 interest in BOUND , we did not use this further for evaluating the performance of the different 999 methods. 1000 1001 BOUND . Finally, we note that these two biases somewhat compensate for each other: not 1192 considering localization errors causes a small overestimate of the free population, whereas not 1193 correcting for defocalization bias causes an underestimate of the free population. 1194 In summary, for conditions where the mean jump length of the free population can be 1195 distinguished from the localization error, vbSPT performs reasonably well, while being 1196 slightly outperformed by Spot-On. 1197 1198 Figure Supplement 8). As a rule of thumb we generally do not recommend setting timepoints 1246 above 10 or considering ∆ beyond 80 ms. 1247 1248 Iterations for fitting 1249 Spot-On almost always converges optimally in the first iteration, so generally 2 or 3 is 1250 more than sufficient when using the 2-state model. For the 3-state model, the parameter 1251 estimation is more complicated and here we recommend 8 iterations as a starting point. 1252 1253 PDF or CDF fitting 1254 Although for large datasets PDF-and CDF-fitting perform similarly as shown in 1255 Figure 3 - Figure Supplement S9, CDF-fitting tends to provide more reliable estimates of 1256 FREE and BOUND when the number of trajectories decreases, likely because PDF-fitting is 1257 more susceptible to binning noise. Thus, for quantitative analysis we always recommend 1258 CDF-fitting, though PDF-fitting can be convenient for making figures since most people find 1259 histograms more intuitive. 1260 1261 Fitting localization error 1262 Spot-On can either use a user-supplied localization error or fit it from the data. As 1263 long as there is a significant bound fraction, Spot-On will infer this with nanometer precision 1264 ( under different conditions or e.g. between different mutants of the same protein, we 1270 recommend fitting to obtain a mean localization error and then keeping it fixed in the 1271 comparisons.

1273
Choosing allowed ranges for diffusion constants 1274 Spot-On comes with default allowed ranges. For example, for the 2-state model, 1275 FREE = 0.5; 25 and BOUND = 0.0001; 0.08 . These ranges are generally reasonable, but 1276 may not be appropriate for all datasets. Whenever Spot-On infers a diffusion constant that is 1277 equal to the min or max, caution is needed and it may be necessary to change these limits. In 1278 particular, a molecule is bound to an unusually dynamic scaffold, BOUND =0.08 µm²/s is 1279 almost certainly too high. Thus, we recommend imaging a protein that is overwhelmingly 1280 bound, such as histone H2B or H3, fitting the histone data with Spot-On and then use the 1281 inferred BOUND for histone proteins or a slightly larger value as the maximally allowed 1282 BOUND value. 1283 1284 2-state or 3-state model 1285 Spot-On considers either a 2-state or 3-state model. Since the 3-state model contains 2 1286 additional fitted parameters, the 3-state fit is almost always better. While there are many cases 1287 where a 2-state model would be inappropriate (e.g. a transcription factor that can exist as 1288 either a monomer or tetramer, thus exhibiting two very different diffusive states), generally 1289 speaking, we prefer fitting a 2-state model for most transcription factors or similar nuclear 1290 chromatin-interacting proteins. In part, deviations from the 2-state model will be due to 1291 anomalous diffusion and confinement inside cells, which cause deviation from the ideal 1292 Brownian motion model implemented by Spot-On. For this reason, traditional model-1293 > max = +, max -./ FREE l exp