Heterogeneous T cell motility behaviors emerge from a coupling between speed and turning in vivo
Abstract
T cells in vivo migrate primarily via undirected random walks, but it remains unresolved how these random walks generate an efficient search. Here, we use light sheet microscopy of T cells in the larval zebrafish as a model system to study motility across large populations of cells over hours in their native context. We show that cells do not perform Levy flight; rather, there is substantial celltocell variability in speed, which persists over timespans of a few hours. This variability is amplified by a correlation between speed and directional persistence, generating a characteristic cell behavioral manifold that is preserved under a perturbation to cell speeds, and seen in Mouse T cells and Dictyostelium. Together, these effects generate a broad range of length scales over which cells explore in vivo.
Introduction
Many immune cells migrate through tissue in search of antigen or pathogens. In some cases, such as during extravasation from blood vessels and homing to target organs, this migration is guided by chemokine gradients (Witt et al., 2005; Okada et al., 2005; Germain et al., 2012; Sarris and Sixt, 2015). However, for naive T cells within T cell zones, in situ imaging studies have found that unguided random walk processes dominate (Miller et al., 2002; Miller et al., 2003; Preston et al., 2006; Cahalan and Parker, 2008; Beltman et al., 2007; Banigan et al., 2015; Harris et al., 2012; Worbs et al., 2007; Textor et al., 2011; Beauchemin et al., 2007; Mrass et al., 2006; Katakai et al., 2013; Mrass et al., 2017, reviewed in Mrass et al., 2010; Krummel et al., 2016). This observation creates a conceptual challenge: T cells must dwell at scales of microns to make contact with antigen presenting cells (Wülfing et al., 1997; Krummel et al., 2000; Beltman et al., 2009a; Fricke et al., 2016), yet migrate over scales of millimeters to find rare targets. A conventional diffusive random walk struggles to access these varied scales efficiently, since a walker that dwells near another cell for 1 min would require several days to travel 1 mm. Several authors have suggested that T cells may have an intrinsic behavioral program that allows them to explore over different length scales (Harris et al., 2012; Krummel et al., 2016; Mempel et al., 2004). However, testing this hypothesis via in situ fluorescence microscopy raises inherent technical challenges: to observe a single cell accessing a broad range of spatial scales, it is necessary to have micron scale resolution over fields of view of millimeters, with low enough photodamage to observe the same cells at high spatiotemporal resolution over long periods. For example, one intriguing proposal is that T cells perform Levy flight (Harris et al., 2012), an anomalous random walk characterized by a powerlaw distribution of step sizes. Such random walks have been described in detail in the physics and ecology literature (Shlesinger et al., 1995; Bartumeus et al., 2005; Viswanathan et al., 2011), and their scalefree behavior provides a natural way for foragers to accelerate searches in many contexts (Bartumeus et al., 2002). However, observation over short periods cannot distinguish between Levy flight and heterogeneity amongst individual walkers (Petrovskii et al., 2011), both of which can create a broad distribution of displacements. More generally, we would like to understand whether there is a statisticallyconsistent behavioral program carried out by these cells.
To address this question, we used selective plane illumination microscopy (Pitrone et al., 2013; Power and Huisken, 2017) to observe the native population of T cells in the live larval zebrafish (Tg(lck:GFP, nacre^{/}) Langenau et al., 2004), over millimeter fields of view and periods of a few hours. We observed a population of motile cells in tissue in the tail of the zebrafish, primarily in the tail fin and larval fin fold (Figure 1A, Figure 1—video 1). We chose this population for further study because of the potential to measure the interstitial exploration behavior of the cells over long lengthscales, and to dissect the variation in behavior over a populations of cells.

Figure 1—source data 1
 https://cdn.elifesciences.org/articles/53933/elife53933fig1data1v1.txt

Figure 1—source data 2
 https://cdn.elifesciences.org/articles/53933/elife53933fig1data2v1.txt

Figure 1—source data 3
 https://cdn.elifesciences.org/articles/53933/elife53933fig1data3v1.txt
Rather than a single broad distribution of speeds sampled by all cells, as in Levy flight, we observed considerable heterogeneity in both speed and turning behavior across cells. This observation, together with prior literature (Maiuri et al., 2015), prompted us to analyze the distribution of cell behaviors in a space defined by speed and turning statistics. Surprisingly, cell behaviors fell on a one dimensional manifold in this space, characterized by a coupling between speed and directional persistence. Analysis of previouslypublished data in mouse T cells (Gérard et al., 2014) and Dictyostelium (Dang et al., 2013) within this framework showed that their migration statistics fell along a similar manifold. Our results show that a wide variation in speeds, combined with a coupling between speed and persistence, generate a broad distribution of length scales of exploration in vivo.
Results
Cell motility behavior is inconsistent with Levy flight
To investigate the statistical properties of T cell motility in our system, we measured cell trajectories within the tissue posterior to the anus (Materials and methods, Figure 1—video 1, Figure 2—video 1). This region is composed primarily of the tail fin and larval fin fold, which represent a millimeterscale tissue over which the cells can potentially migrate. We note that cells in circulation, while present, move orders of magnitude faster than those in tissue, and thus are not included in our observations or analysis. Note also that our observations were performed in the absence of an external perturbation such as an infection.
We first evaluated evidence for Levy flight behavior, as opposed to persistent random walks (Beauchemin et al., 2007; Beltman et al., 2007; Banigan et al., 2015; Harris et al., 2012), in our system. The distinction hinges on whether the statistics of individual trajectories are scalefree, so that superdiffusive behavior continues to long times; or if, alternatively, individual trajectories are diffusive at long times but there is heterogeneity across the population. To address this question, we performed a standard analysis of mean squared displacement as a function of time interval. Consistent with previous measurements (Beauchemin et al., 2007; Beltman et al., 2007; Banigan et al., 2015; Harris et al., 2012), we observed a fasterthanlinear increase in MSD at early times, indicating superdiffusive behavior, with a bestfit line in surprisingly good quantitative agreement with previous observations up through 10 min (Harris et al., 2012; Fricke et al., 2016; Figure 1C). However, we observed a transition at the scale of minutes, consistent with persistent random walks, and inconsistent with Levy flight (also note the straight line on a linear scale, Figure 1C inset, characteristic of diffusive behavior). Note that while we have examined the subset of longer trajectories to measure the behavior through an additional order of magnitude in time, this result also holds when examining all trajectories through 15 min (Figure 1—figure supplement 2). To further test for an intermediate timescale, we computed the velocityvelocity power spectrum, using secantapproximated velocities along each trajectory (Materials and methods). This quantity captures the timescale at which the velocities become decorrelated, if it exists; for a Levyflight process the same negative slope is observed at all frequencies (Viswanathan et al., 2005), while a persistent random walk model passes towards zero slope at low frequencies (Viswanathan et al., 2005; Pedersen et al., 2016). Consistent with the MSD analysis, we observe two regimes, with a clear timescale on the order of minutes (Figure 1D). Finally, we computed the distribution of lengths between direction changes (bout lengths) within a trajectory (Materials and methods), scaled by the average bout length as suggested in Petrovskii et al., 2011, and did not observe the characteristic Levyflight power law (Figure 1E).
Motility behavior is heterogeneous across cells
Since we did not find support for Levy flight in our system, we next evaluated evidence for celltocell heterogeneity. From examples of velocity traces (Figure 2A,C–E, Figure 2—video 1), we observed substantial variation in speed between cells, that can persist over spans of a few hours. These trajectories are not atypical: overall, 88% of trajectories have distributions of secantapproximated speeds that are inconsistent with the speed distribution pooled on all trajectories (KS test, $p<.01$). Interestingly, we also found significant heterogeneity in cell turning behavior: 67% of cells had turn angle distributions inconsistent with the overall distribution (KS test, $p<.01$).

Figure 2—source data 1
 https://cdn.elifesciences.org/articles/53933/elife53933fig2data1v1.txt

Figure 2—source data 2
 https://cdn.elifesciences.org/articles/53933/elife53933fig2data2v1.txt

Figure 2—source data 3
 https://cdn.elifesciences.org/articles/53933/elife53933fig2data3v1.txt

Figure 2—source data 4
 https://cdn.elifesciences.org/articles/53933/elife53933fig2data4v1.txt
To evaluate the rate of speed switching in our system, we measured the average speeds of individual trajectories on nonoverlapping ~20 min intervals, and evaluated how the speed ranks change as a function of the time between intervals (Figure 2B). We found a high correlation between speeds on adjacent nonoverlapping intervals, which decays slowly on the timescale of the measurement. Thus each cell samples a characteristic distribution of speeds that is stable over one to two hours. For the remainder of the analysis, we will consider the average speed to be a property of the trajectory; we return to consider the implications of speed switching in the discussion.
We note that we observed variation in the distributions of cell speeds between samples: overall, 48% of the variance in cell speeds can be explained by the sample identity. Nonetheless, the distributions of cell speeds within each sample are broad and overlapping (Figure 2—figure supplement 1), accounting for the majority of the variance (52%). Amongst other effects, sample to sample variation could be the result of differences in antigen environment or global cytokine levels between fish.
Heterogeneous cell migration statistics fall on a behavioral manifold
Previous work (Maiuri et al., 2015) has suggested that actin flows may generate a coupling between speed and directional persistance in migrating cells. This study generates the hypothesis that cells, in general, are not free to pick any turn and speed statistics, but rather that there may be underlying biophysical constraints. To investigate this hypothesis in our system, we divided the cells into quintiles based on speed, which we refer to as speed classes. We observed strong variation in the distribution of turn angles amongst speed classes (Figure 3A): fast cells are most likely to turn shallowly, slow cells are most likely to turn around, and the distribution varies smoothly across the speed classes. This dependence could be driven by a local coupling between speed and turn angle: cells tend to go straighter whenever they go fast, which the faster cells do more often. Alternatively, it could be driven by an overall behavioral difference between fast and slow cells. To distinguish these possibilities, we measured the average turn angle as a function of the size of the steps surrounding it (Figure 3B). We found that both of these effects contribute: all cells go straighter during faster periods, but for a given step size, slow cells are more likely to turn sharply.

Figure 3—source data 1
 https://cdn.elifesciences.org/articles/53933/elife53933fig3data1v1.txt

Figure 3—source data 2
 https://cdn.elifesciences.org/articles/53933/elife53933fig3data2v1.txt

Figure 3—source data 3
 https://cdn.elifesciences.org/articles/53933/elife53933fig3data3v1.txt

Figure 3—source data 4
 https://cdn.elifesciences.org/articles/53933/elife53933fig3data4v1.txt
The relationship between speed and turning suggests that there may also be systematic differences in the scaling of the MSD at short times between cells. In particular, variation in speed alone amongst individuals would not change the shape of the MSD, which would collapse when appropriately scaled (Appendix 1). On the other hand, the systematically shallower turns of faster cells would be expected to boost the slope of their MSD at short times, an effect we observe in the data (Figure 3C).
The analysis at the level of speed classes suggested that there might be a single scalar variable, for which the cell’s average speed is a good proxy, that determines a number of higherorder statistics characterizing the cell’s migration behavior. To test this at the level of individual trajectories, we chose two summary statistics that capture the cell’s turning behavior: the average of the cosine of the turn angles along the trajectory, and the correlation between speeds and turn angles along the trajectory. The former is a summary of the overall distribution of turn angles for that cell, while the latter captures the degree of additional local coupling between speed and turn angle. Together with the cell’s speed, these two summary statistics form a threedimensional behavioral space. We observed that the cell trajectories fall close to a curve in this space (Figure 3D). In particular, 73% of the variance in the average cosine can be explained by cell speed, with some residual variance due to the stochasticity of the process (7%) and other unknown effects (20%) (Figure 3—figure supplement 1). Thus T cell migration statistics can be organized into a onedimensional behavioral manifold, characterized by a strong dependence between speed and turning behavior.
Model predicts wide variation in length scales of exploration across the population
Our observation of a behavioral manifold suggests that, despite the apparent heterogeneity in migration strategies, there may be a common program with a single underlying variable, consistent with the work of Mauri et al. In this view, a cell’s location on the manifold reflects its internal value of this control variable, which in turn dictates its random walk behavior. Given the results of our MSD analysis, to determine candidates for a singleparameter migration model, we started with the canonical persistent random walk (OrnsteinUhlenbeck) process (Uhlenbeck and Ornstein, 1930):
where v is the velocity, $\eta $ is a white noise term, and $i$ labels the velocity component. This model has two free parameters: the speed, S, and the persistence time, P, which is the average time before a cell turns. (Note that speeds inherently vary along trajectories in this model; S controls the average speed.) Our observations suggest that there may in fact only be one control parameter; in particular, because faster cells tend to make shallower turns, we expect P to increase with S. To determine the relationship between these two variables, we measured the persistence time, averaged along each trajectory, as a function of cell speed, and found a linear dependence (Figure 4A). This suggests the following simple model of cell motility:
where $\alpha $ is a constant with units of acceleration, $\beta $ is a constant with units of time, and both are constrained by the empirical relationship in Figure 4A. We call this the speedpersistence coupling model (SPC).
As in other persistent random walk models, SPC walkers are diffusive at long times; the MSD scales linearly with time, and the ratio between these quantities defines an effective diffusion constant (Appendix 1):
Due to the dependence of P on S, the SPC model predicts a strong scaling of the effective diffusion constant with cell speed. We tested this prediction at several time intervals $\tau $ and found good quantitative agreement between the model and the data (Figure 4B). In particular, heterogeneity in speeds creates a broad range of effective diffusion constants, spanning 2 orders of magnitude. The coupling between speed and persistence amplifies this effect, generating fivefold more variation in the effective diffusion constants across the cells than would be expected for a uniform persistence time model (UPT). We also note that the collapse of ${D}_{eff}$ measured at different time lags $\tau $ provides additional corroboration of diffusive (as opposed to Levy/superdiffusive) scaling.
The analyses in this and the previous section depend on measured cell speeds and turn angles, which are an imperfect proxy for the true instantaneous process (Beltman et al., 2009b). In particular, both noise in the cell locations and finite sampling intervals can introduce bias in the measured speeds, which could in principle generate spurious relationships between measured speed and turning behavior. We took two approaches to addressing the sensitivity of our conclusions to these issues. First, we addressed sensitivity to sampling rate by repeating the analyses above, subsampling timepoints by a factor of 2. This makes the turning behavior of the slowest two speed classes harder to distinguish, because they are rarely persistent over more than one timestep (Figure 4—figure supplement 1A,D), and introduces more noise in the local coupling and persistence relationships (Figure 4—figure supplement 1B–C), but otherwise does not alter the structure of the correlations (Figure 4—figure supplement 1A–F). Second, we assessed the potential biases introduced by mislocation noise and finite sampling to the speedpersistence relationship in simulations (Appendix 1, Appendix 1—figure 1). We found that mislocation noise can lead to spurious correlations between speed and persistence at the slow end of the speed spectrum, but cannot account for the consistent correlation we observe across speeds.
Additionally, we note that our measured trajectories stay predominantly within the tail fin and larval fin fold (Figure 1—figure supplement 1), suggesting a boundary between the fin fold and muscle region of the tail. Such a boundary could influence the MSD. However, we compared to the MSD calculated on one heldout sample not subject to these boundary effects and observed no difference (see Appendix 1—figure 2).
Finally, we note that the SPC Langevin model describes the effective diffusive behavior of the trajectories and their scaling at longer times, but may not capture all the details of the microscopic dynamics. In particular, the propensity of trajectories to turn backwards (peak at $\theta =\pi $ radians, Figure 3A) is not captured by this model.
Manifold is preserved under a drug perturbation to cell speeds, and in mouse T cells and Dictyostelium
We next asked about the robustness of the observed behavioral manifold under a perturbation to cell speeds. Given the role of actin nucleation and remodeling in leukocyte motility (VicenteManzanares et al., 2002), we chose the drug Rockout, a known Rho kinase inhibitor affecting this pathway (BarrosBecker et al., 2017), as a candidate for perturbing cell speed, and repeated the measurements and analysis of cell migration behavior in the presence of the drug (Materials and methods). We found that the distribution of cell speeds shifted downwards, but we still observed a quantitatively similar positive relationship between speed and turning behavior (Figure 5A,B). This is consistent with a model where the perturbation primarily shifted an internal cell state variable that determines location along the behavioral manifold, which in turn dictates both speed and turning behavior, although we note that there may be an additional small shift towards shallower turns in the drug condition.

Figure 5—source data 1
 https://cdn.elifesciences.org/articles/53933/elife53933fig5data1v1.txt

Figure 5—source data 2
 https://cdn.elifesciences.org/articles/53933/elife53933fig5data2v1.txt

Figure 5—source data 3
 https://cdn.elifesciences.org/articles/53933/elife53933fig5data3v1.txt

Figure 5—source data 4
 https://cdn.elifesciences.org/articles/53933/elife53933fig5data4v1.txt

Figure 5—source data 5
 https://cdn.elifesciences.org/articles/53933/elife53933fig5data5v1.txt

Figure 5—source data 6
 https://cdn.elifesciences.org/articles/53933/elife53933fig5data6v1.txt
Finally, we analyzed published data from two other species, mouse T cells in situ (Gérard et al., 2014) and Dictyostelium (Dang et al., 2013), in this framework. While some of the analyses that depend on longer time traces and larger cell numbers are not possible with these datasets, we tested the relationship between average turn angle and cell speed. We found that this correlation held amongst the control cells in both studies (Figure 5C–F). This suggests that, as for zebrafish T cells, there is heterogeneity in speed and turning behavior amongst the cells, and is consistent with a similar behavioral manifold. In the two published studies, genetic perturbations that knocked out or down one member of the actin remodeling machinery were used: a knockout of the noncanonical myosin Myo1g in one case, and a knockout of the Arp2/3 inhibitor Arpin in the other. In each case, the perturbation had a substantial effect on the distribution of cell speeds (Figure 5, EF). However, in both cases, a quantitatively similar positive relationship between the speed and turning behavior amongst the perturbed cells was preserved.
Single cell RNA sequencing suggests transcriptional heterogeneity in actin nucleation activity
Our observation that cells maintain characteristic distributions of speeds over periods of a few hours suggests that there may be variation in transcriptional state that underlies some of the heterogeneity in cell migration behavior. To investigate this possibility, we performed singlecell RNA sequencing on cells isolated from the tail of 15 dpf Tg(lck:GFP) zebrafish. To assess the fidelity of the marker, we sorted GFP+ cells from an unbiased FSC/BSC gate (Materials and methods). We used standard dimensional reduction and clustering methods (Materials and methods) to identify 330 putative T cells (Figure 6—figure supplement 1). Unexpectedly, we also identified a population of epithelial cells that may misexpress lck at low levels (Materials and methods, Figure 6—figure supplement 1, Figure 6—figure supplement 2).
We next used a selfassembling manifold algorithm designed to detect subtle variation (Tarashansky et al., 2019) to examine finerscale structure within the putative T cell cluster. This algorithm revealed a plate effect related to one of our sort plates (Figure 6—figure supplement 3), which we therefore excluded from the remainder of the analysis. We repeated the SAM analysis on the remaining (n = 237) cells, and identified two main subtypes (Figure 6A–B), consistent with a previous report (Tang et al., 2017). We note that the prior study identified the smaller subpopulation as NK cells; however, in addition to the previouslyreported marker genes, we find that these cells have moderate expression of the T cell receptor trac. We have therefore chosen not to annotate these as NK cells.

Figure 6—source data 1
 https://cdn.elifesciences.org/articles/53933/elife53933fig6data1v1.txt

Figure 6—source data 2
 https://cdn.elifesciences.org/articles/53933/elife53933fig6data2v1.txt

Figure 6—source data 3
 https://cdn.elifesciences.org/articles/53933/elife53933fig6data3v1.txt

Figure 6—source data 4
 https://cdn.elifesciences.org/articles/53933/elife53933fig6data4v1.txt

Figure 6—source data 5
 https://cdn.elifesciences.org/articles/53933/elife53933fig6data5v1.txt
Both subpopulations of cells express high levels of genes canonically involved in actin nucleation and remodeling in the leukocyte cytoskeleton (VicenteManzanares et al., 2002; Takenawa and Suetsugu, 2007) (WASP/ARP2/3 pathway; Figure 6B); indeed, these genes are amongst the top differentially expressed between the T cells and putative epithelial cells in our sample (Figure 6—figure supplement 1, Figure 6—figure supplement 2). To analyze variation in this pathway amongst the T cells, we chose arpc1b, a subunit of the ARP2/3 complex, as a reference gene because ARP2/3 directly nucleates actin during ameboid cell migration, and its inhibition is known to modulate cell speed (Dang et al., 2013). We tested the rank correlation of expression of all other moderate to high expressed genes with arpc1b (Figure 6C). We found that 3 of the four top correlated genes (those that are statistically significant after Bonferonni correction) are also canonically involved in this pathway: the actin monomer genes act2b and act1b, as well as the upstream activator cdc42l. Unexpectedly, the fourth gene encodes a lincRNA whose biological function is unknown. Thus we detect real, although not strong, covariation in genes involved with actin nucleation, which may create longlived cellintrinsic variation in motility.
While the two T cell subpopulations separate in some dimensions of gene expression space, including, for example, the marker genes shown in Figure 6B, both groups express arpc1b and its correlates. Indeed, the distributions of expression for the two subtypes overlap for these genes (Figure 6D). This is consistent with a single continuous motility axis, without two distinct subgroups, as in our microscopy data.
We have observed transcriptional heterogeneity in actin nucleation genes, which may underly variability in motility states. This observation suggests that cells may vary along a ‘nucleation high’ to ‘nucleation low’ axis, generating a range of longlived speed states. However, it remains technologically infeasible to directly associate a cell trajectory with a gene expression profile, so a direct test awaits future work. Additionally, we note that regulation that occurs at the protein level, for example through phosphorylation states, is likely very important to shorter timescale variation in cell motility behavior, and is not reflected in gene expression.
Discussion
We have measured and analyzed the variability in cell motility amongst the T cells of the zebrafish tail. We found that cell motility statistics are inconsistent with Levy flight; rather, speeds are heterogeneous from cell to cell. We note that a previous study that reported modified Levy flight in T cells (Harris et al., 2012) was carried out in a very different biological context (adoptively transferred CD8+ T cells in mouse CNS in the presence of an infection), which could drive differences in motility behavior. However, we note that the statistics of our trajectories closely resemble those measured by Harris et al. up through the 10 min time lag analyzed in that study.
We also found that migration statistics from zebrafish T cells as well as mouse T cells and Dictoystelium fell on a behavioral manifold, characterized by a coupling between speed and directional persistence. We note that, in general, heterogeneity of motility behavior across a population could be caused by the tissue context rather than by cellintrinsic factors. However, the effects of the drug perturbation, as well as the effects of the genetic perturbations from Gérard et al., 2014 and Dang et al., 2013, support a cellintrinsic basis for the behavioral manifold we observe here. In particular, we performed trials in which the same regions of tissue were imaged and cells tracked before and after addition of the drug (Figure 5—figure supplement 1); the observed changes in migration statistics must then be caused by the drug’s effect on the cell’s internal state, not by the tissue context.
The drug perturbation experiment and analysis of data from the other species suggests that there is one underlying cellintrinsic variable that jointly controls speed and directional persistence. Maiuri et al. also observed a coupling between speed and directional persistence across multiple cell types, and performed elegant in vitro work to demonstrate that actin retrograde flow speed is correlated both with cell speed and persistence time (Maiuri et al., 2015). Using single cell RNA sequencing, we observed covariation amongst T cells in a group of genes involved in actin nucleation. This suggests that cells vary transcriptionally in their actin nucleation activity. Levels of these genes may represent an underlying cell control variable that determines actin retrograde flow speeds and hence both cell speed and persistence. A direct test of this hypothesis awaits development of techniques to link a single cell’s trajectory and its gene expression profile.
In two previous studies, genetic perturbations were performed that made cells faster and more persistent on average (Gérard et al., 2014; Dang et al., 2013). Our results suggest that this connection may be general to the cells rather than specific to the perturbation. In particular, shifts in the average turning behavior have been used to argue that Arpin and Myo1g control cell steering. Our analysis suggests that increasing cell speed may in many cases increase straightness, and vice versa, so that the effect on cell steering may be indirect.
We have analyzed cell migration in the context of a speedpersistence coupling model, which is a modified OrensteinUhlenbeck model where the speed and persistence time parameters are explicitly codependent. We chose this as the minimal model that captures both the diffusive behavior at long times and the coupling between speed and persistence, allowing for a prediction of the range of effective diffusion constants, and hence length scales of exploration, amongst the cells (Figure 4). Another feature of measured trajectories, in previous studies and in our work, is variation in speed along the trajectory, sometimes referred to as intermittency. We note that the Langevin dynamics of the SPC model inherently generate variation in speed, including pauses, along trajectories: the speed parameter sets the distribution of instantaneous speeds sampled by the cell. Other approaches have included adding pauses to a model with a fixed distribution of step sizes (Harris et al., 2012). Maiuri et al. considered an explicitly active model where actin dynamics within the cell generated motility. While slightly more complex, this model has several interesting features, including that the cell motility emerges from internal biophysical mechanisms, and also that it produces multiple phases of migratory behavior, including one with additional intermittency (Maiuri et al., 2015). Future work could use transgenic methods to label actin in the zebrafish to directly test this active matter model in vivo. Another mechanistic basis for intermittency was demonstrated by Dong et al., 2017, who showed that spontaneous cytosolic calcium signaling generates pauses during basal T cell motility. Investigation of this mechanism and its potential role in producing the speed fluctuations observed in our system would also be an interesting subject for further work.
Our results show that across the population, cells explore over a very broad range of length scales, covering orders of magnitude of variation in effective diffusion constants. This variability is driven primarily by differences in average speed between cells, which is amplified by the observed coupling between speed and persistence. However, analysis of the effectiveness of this variation as a search strategy, as compared with modified Levy flight (Harris et al., 2012) or models with additional intermittency (Maiuri et al., 2015), would require a detailed knowledge of the distribution of targets in the tissue as well as an additional order of magnitude in time of observation of the cell trajectories in our system, to fully characterize the slow timescale speed switching. We additionally note that several studies (Dustin et al., 1997; Mempel et al., 2004; Kawakami et al., 2005; Castellino et al., 2006; Moreau et al., 2015; Dong et al., 2017; Negulescu et al., 1996) have indicated that T cells react to local chemical signals by changing speed–in particular, that calcium signaling can cause cell arrest, and this is important to contact with antigen presenting cells and antigen recognition. This suggests that the local signaling environment may also be important to shifting the cell behavior along the manifold. Detecting these signaling and recognition events in vivo in real time would be an exciting avenue for future work.
Materials and methods
Zebrafish lines and procedures
Request a detailed protocolTg(lck:GFP, roy^{/}, nacre^{/}) zebrafish (Danio rerio) (Langenau et al., 2004) were obtained as a generous gift from Dr. Leonard Zon and Dr. Aya LudinTal. Imaging was performed on Tg(lck:GFP) zebrafish crossed into a nacre^{/} background, at between 9 and 13 dpf. All adult and larval zebrafish were maintained according to protocols approved by the Stanford Administrative Panel on Laboratory Animal Care.
Microscopy
Request a detailed protocolImaging was performed on a singleplane illumination microscope constructed as specified in Pitrone et al., 2013, with the exception that a Prior ProScan XY stage (Prior Scientific) coupled to a Zaber TLLS 105 stage (Zaber Technologies) was used for sample movement. The light sheet was generated using an Olympus UMPLFLN10XW objective (NA = 0.3) and detection was performed with an Olympus UMPLFLN20XW objective (NA = 0.5) and an achromatic doublet tube lens (AC508180AML, Thorlabs). Images were recorded either on a Retiga 2000R camera (Qimaging) or an Ace acA2040 (Basler). For the Ace ac2040 camera, a meniscus lens (LE1418A  O2’ NBK7, Thorlabs) was added as a zoom lens, to match the image pixel width between the two cameras at $.37\mu m$. The fluorescence source was an Obis LS 488 nm laser (Coherent), and the microscope was controlled by MicroManager.
Zebrafish between 9 and 13 dpf were anesthetized with TricaineS (MS222, Pentair; .008% w/v, buffered to pH 7) and embedded in 2% low melting point agarose (Lonza SeaPlaque, #50100) with .004% w/v Tricaine. For imaging, the agarose was submerged in E3 with .008% w/v Tricaine and 50 mM Hepes. With the exception of Figure 2 and Figure 2—video 1, tiled zstacks were obtained every 45 s for at least 180 timepoints, with a field of view of at least 592 $\mu m$ (dorsalventral axis) by 1200 $\mu m$ (anteriorposterior axis), in the tail region posterior to the anus. For Figure 2A and Figure 2—video 1, a zstack was obtained every 12 s for 1100 timepoints, with a field of view of 757 × 568 µm (the first 900 timepoints are shown). For statistical comparison with the remainder of the data, trajectories from this final dataset were subsampled in time to give 48 s timesteps. Data was acquired with 2 × 2 binning, for an image pixel width of .74 µm.
For imaging in the presence of Rockout, embedded fish were submerged in E3 with .008% w/v Tricaine and 50 mM Hepes plus 12 µM Rockout (Sigma Aldrich #555553). For paired control/Rockout trials, fish were imaged for 2.5 hr in control conditions, followed by 2.5 hr in Rockout conditions over the same field of view.
Singlecell RNA sequencing
Request a detailed protocolThirty 15 dpf Tg(lck:GFP) zebrafish were euthanized using .04% w/v Tricaine and transected posterior to the anus. Tail portions were pooled into HBSS (ThermoFisher #14025092) on ice. Tails were dissociated by incubating with 100 $\mu g/mL$ LiberaseTL (Sigma Aldrich #5401020001) at room temperature for 20 min, followed by trituration with a 23 gauge needle. The cell suspension was filtered through a 40 $\mu m$ filter and washed once in HBSS. GFP+ cells were sorted from an unbiased FSCSSC gate on a Sony SH800 cell sorter into 384well hardshell PCR plates (BioRad HSP3901) containing .4 µl of lysis buffer, prepared as described previously (Tabula Muris Consortium et al., 2018). Reverse transcription following a SmartSeq2 protocol, and Illumina library preparation, were carried out as described previously (Tabula Muris Consortium et al., 2018), except that following cDNA amplification, cDNA was diluted uniformly to a mean target concentration of $.4ng/\mu l$ for library preparation. Libraries were sequenced on the NovaSeq 6000 Sequencing System (Illumina) using 2 × 100 bp pairedend reads.
Image processing and cell tracking
Request a detailed protocolTiles were assembled based on recorded stage coordinates and a Maximum Z projection was applied to Z stacks. Sample drift in x and y was subtracted by identifying and tracking autofluorescent pigment spots. In particular, the coordinates of 1–3 isolated pigment spots were identified manually at the first timestep; at each timestep, the brightness centroid was computed for a circle with a 25 pixel radius around the previous centroid, and the average trajectory of the pixel spots was rounded to the nearest pixel and subtracted from the timeseries. Prior to cell segmentation, the average image across the whole timecourse was subtracted from each timestep. For data recorded on the Retiga 2000R camera, prior to segmentation the image was thresholded at the 30th pixel percentile and the maximum pixel value was fixed so that .4% of pixels were saturated. For data recorded on the Basler Ace acA2040 camera, no lower threshold was used and the maximum pixel value at each timepoint was fixed so that .2% of pixels were saturated. Ilastik software (Sommer et al., 2011) was used for cell segmentation and tracking: the Ilastik pixel classification module was used to classify foreground and background, and the manual tracking module was used to identify and track cells. Tracks were terminated if two segmented cells collided and it was not possible to disambiguate, or if a segmented cell was lost due to passing into an autofluorescent region or due to imperfections in segmentation and/or illumination. To define trajectories, the brightness centroid of each cell in x and y at each timestep was computed from Ilastik tracking masks and the Maximum Z projection. Processing steps not using Ilastik were performed using Python 3.6 (code available at: https://github.com/erjerison/TCellMigration; Jerison, 2020; copy archived at https://github.com/elifesciencespublications/TCellMigration).
Trajectory analysis
Request a detailed protocolTrajectories with at least 30 consecutive steps were included in the analysis; for MSD calculations, trajectories that included all time intervals were included. For calculations of power spectra, single missing timesteps were linearly interpolated based on the two adjacent positions, and computations were performed on the longest consecutive segment for each trajectory. For the M. musculum data, the time interval was 30 s. For the Dictyostelium data, timesteps were subsampled from the original to give an interval of 20 s. Unless otherwise noted, statistics are reported as the median of the statistic on a bootstrap over trajectories.
Meansquared displacements were computed along each trajectory as:
where $N$ is the total number of timesteps and ${t}_{int}$ is the time interval. The overall MSD was computed by averaging the MSDs for each trajectory, and 95% confidence intervals were calculated via a bootstrap over trajectories.
The overall MSD was fit to:
which we note is the common formula for mean squared displacement in both the OrnsteinUhelnbeck model (see Appendix 1) and in the KratkyPorod wormlike chain model. Unless otherwise noted, fitting was performed using the scipy.optimize.curvefit function in scipy 1.3.0; fitting was performed in log space and weighted by computed confidence intervals.
The velocity power spectrum was computed based on the vector of secantapproximated velocities for each trajectory. Velocity vectors were zeropadded to 400 timesteps, and the fourier transforms of the velocity components were computed using the the fft function in numpy (1.16.4). Letting the fouriertransformed velocity components for trajectory $m$ be ${v}_{x}(k,m)$, ${v}_{y}(k,m)$, the power spectrum for each trajectory was computed as:
where $N=400$ and ${N}_{m}$ is the length of trajectory $m$. The overall PSD was computed as the average over the PSDs for each trajectory:
where $n$ is the number of trajectories. For Figure 1D, a piecewise linear function was fit to the PSD in log space; we plot the highfrequency fitted line and a line with slope 0.
Following (Petrovskii et al., 2011), we calculated the distribution of bout lengths within a trajectory as the distribution of x displacements between reversals in direction in x, divided by the average of these displacements within each trajectory. The distribution was calculated using the numpy.histogram function on percentile bins with the option density = True; the x locations of points were determined based on the average value of points in each bin. We fit the distribution to a stretched exponential function $f(x)=A{e}^{\gamma {x}^{\beta}}$; the fitted value of the stretch parameter $\beta $ was .9.
The overall speed distribution was computed by collecting secantapproximated speeds across all trajectories and timepoints; similarly, the overall turn angle distribution was computed by collecting all relative angles between consecutive segments. For the KolmogorovSmirnov (KS) test, the overall CDFs of speeds and turn angles were estimated by measuring the cumulative frequency over 25 percentile bins and performing linear interpolation to yield a continuous function. A twosided KS test (scipy.stats.kstest) was performed for the sets of speeds and turn angles of each trajectory.
We evaluated the fraction of the variance in cell speeds that can be explained by sample identity by fitting a linear model with indicator variables on the sample identity as predictor variables. We used the LinearRegression function of sklearn.linear_model to fit the model, and the ‘score’ method to evaluate ${R}^{2}$, the fraction of the variance explained by this model.
Turn angle distributions for each speed class were computed by collecting all relative angles between consecutive segments amongst cells in that speed class; the distributions were symmetric about θ = 0 and so were folded to be between 0 and $\pi $ radians. 95% confidence intervals were calculated based on a bootstrap over trajectories in each speed class. For the relationship between local speed and turn angles (Figure 2B), the local speed was estimated as the average speed of the two consecutive steps surrounding a turn. Turns were binned based on the local speed, and the average of the cosine of the turn angles was computed for each bin. For this and other binned statistics, the x location of the bin was fixed to be the average value for the points in that bin.
To estimate the rate of speed switching, all trajectories of at least 117 min in length were used. The average speed of each trajectory was measured on 19.5 min intervals; 19.5 min was chosen to minimize the biasvariance tradeoff. Specifically, because every cell samples speeds from a distribution, there is tradeoff between measuring speeds on intervals that are too short, which may not give a good estimate of the mean, and intervals that are too long, where cells may switch during the interval. To minimize this tradeoff, the interval that maximized the rank correlation between adjacent nonoverlapping blocks was used. The average speed of each cell was measured on nonoverlapping intervals, and the Spearman rank correlation coefficient between all pairs of intervals was computed. The correlation as a function of time was calculated as the average over all pairs of intervals with the same difference in start times. We computed 95% confidence on a bootstrap over trajectories. For the null model, we permuted speeds amongst the trajectories on each interval; we calculated 95% confidence intervals over the permutations.
For Figure 3, the average of the cosine of turn angles between adjacent steps was calculated for each trajectory, as well as the average over all adjacent steps of the secant approximated speeds. For Figure 3D, the correlation between local speed and turns was computed as the Pearson correlation coefficient between the local speed, as defined above, and turn angles across the set of adjacent steps in the trajectory.
To estimate the fraction of the variance in turning behavior explained by the cell speed, we fit a spline curve (UnivariateSpline class of scipy 1.3.0; default parameters) to the relationship between speed and the average of the cosine of the turn angles (Figure 3—figure supplement 1A). Letting the spline function be $f$, we estimated the variance accounted for by the speed as ${V}_{s}=Var(f({S}_{m}))$, where the index $m$ labels trajectories. We estimated the variance in the means due to variation within trajectories, which we called stochasticity, as ${V}_{st}=\frac{1}{n}{\sum}_{m=1}^{n}\frac{1}{{k}_{m}1}Va{r}_{j}(\mathrm{cos}{\theta}_{jm})$, where $n$ is the total number of trajectories, ${k}_{m}$ is the number of turn angles within trajectory $m$, and $\mathrm{cos}{\theta}_{jm}$ is the cosine of the turn angle $j$ in trajectory $m$. Remaining variance we classified as other (Figure 3—figure supplement 1B); this may be due to imperfections in the spline model, other experimental noise, or additional biological variability.
The persistence time was defined to be the time elapsed before the trajectory turns at least $\frac{\pi}{2}$ radians, averaged along the trajectory. Specifically, letting the displacement between timepoints $s$ and $s+1$ be $\overrightarrow{x}(s)$, the persistence time along each trajectory was calculated as:
where $m>s$ is the first timestep for which $\overrightarrow{x}(s)\cdot \overrightarrow{x}(m)<0$, ${t}_{int}$ is the time interval, and $n$ is the final base point for which $m\le N$, where $N$ is the final timepoint. For Figure 4A, trajectories were binned into mean speed deciles, and the average persistence time was calculated over trajectories in the bin; error bars represent 95% confidence intervals on a bootstrap over trajectories. We also repeated this analysis to measure the average time elapsed before the trajectory turns at least $\frac{\pi}{6}$ radians (Figure 4—figure supplement 2).
The effective diffusion coefficient at time $\tau $ was measured as:
To measure ${D}_{eff}(\tau )$ as a function of $S$, cells were divided into speed bins (with 5% of the speed distribution per bin); ${D}_{eff}(\tau )$ for each speed bin was measured by averaging the ${D}_{eff}(\tau )$ across trajectories, and error bars were computed based on a bootstrap over all trajectories. Note that ${D}_{eff}(\tau )$ will be independent of $\tau $ only if diffusion scaling is respected, so that the collapse of the data in Figure 4B is additional corroboration that the trajectories behave diffusively at long times.
As shown in the models section of the SI below, under the UPT model:
whereas under the SPC model,
where $\alpha $ and $\beta $ are fixed across all trajectories. We fixed $\alpha $ and $\beta $ by fitting a line to the persistence time relationship in Figure 1C; note that this is a shorttime statistic and need not a priori predict the effective diffusion constant at longer times. We fit the UPT model (dashed line) and the SPC model (solid) to the measured ${D}_{eff}$ as a function of $S$; in both cases, there was one fitting parameter which was the constant of proportionality, which allows for an offset on the yaxis in log space but does not change the shape of the curve.
Analysis of scRNAseq data
Request a detailed protocolReads were aligned to the Zebrafish reference genome (genome release: GRCz10; annotations: GRCz10.85) using STAR (2.5) Dobin et al., 2013; reads aligned to each gene were counted using the htseqcount function of HTseq (0.8.0) Anders et al., 2015, with the options m intersectionnonempty and –nonunique all. Note that the final option counts reads that align to a location with more than one annotated feature (e.g. overlapping ORFs) as belonging to both features. This is necessary because of misannotation of the T cell receptor light chain constant region in the zebrafish reference genome; both ENSDARG00000075807 (traj39) and ENSDARG00000104132 (traj28) contain the trac, so that reads mapping to trac would otherwise be discarded.
Cells were filtered if they expressed fewer than 650 genes or more than 3250 genes, and if more than 8% of reads were of mitochondrial origin. We used UMAP (0.3.1) with the default options to embed the logtransformed counts table in two dimensions, including all genes expressed in at least 10% of cells; and HDBSCAN (0.8.22) with min_samples = 10 to call clusters (Figure 6—figure supplement 1A). Comparison with the index sort data (Figure 6—figure supplement 1B) showed that cells from the larger cluster had FSCBSC consistent with lymphocytes, whereas cells from the other cluster had higher FSC and BSC. We called the major cluster as the first cell group, excluding the 4 cells with $\text{BSC}>2\times {10}^{5}$, and other cells as the second group. We measured differential expression of genes between the two clusters as: $D=\frac{1}{n}{\sum}_{i=1}^{n}{\mathrm{log}}_{2}({E}_{1i})\frac{1}{m}{\sum}_{i=1}^{m}{\mathrm{log}}_{2}({E}_{2i})$, where ${E}_{1i}$ are expression values, in counts per million (CPM) + 1, for the first cluster, $n$ is the number of cells in this cluster, ${E}_{2i}$ are expression values (in CPM+1) for the second cluster, and $m$ is the number of cells in this cluster. (Note that this is the log of the ratio of the geometric means within each cluster.) In Supplementary file 2, we report the genes with $D>{\mathrm{log}}_{2}10$ and $p<.01$ (Wilcoxon ranksum test, Bonferonnicorrected.) Genes enriched in the larger cluster included the T cell and immunerelated genes tagapa, tagapb, ccr9a, tnfrs9b, il2rb, and ptprc (Tabula Muris Consortium et al., 2018); we also tested for expression of the T cell receptor light chain constant region (trac; expression estimated based on the expression of ENSDARG00000075807). Based on these markers, we identified the larger group (n = 330) as T cells. The significantly differentially expressed genes enriched in this group also included arpc1b, wasb, arhgdig, coro1a, scinlb, and capgb, which we classified as belonging to the WASP/ARP2/3 pathway based on the literature (VicenteManzanares et al., 2002). Finally, we observed very little expression of markers associated with other types of immune cells (the B cell light chain igic1s, the B cell marker ccl35.2, and the neutrophil and macrophage markers mpeg1 and mpx (Tang et al., 2017) in either group (Figure 6B, Figure 6—figure supplement 2). The genes most significantly enriched in the nonT cell group include keratin proteins (krt8, KRT1), as well as ahnak (Figure 6—figure supplement 2, Supplementary file 2). Based on these markers, we identified these cells as epithelial cells, possibly keratinocytes (Tabula Muris Consortium et al., 2018). We note that we observed GFP signal in the somite region of the Tg(lck:GFP) tail via microscopy (see, e.g., Figure 1A and Movie S1) which we did not observe in wildtype nacre^{/} zebrafish, suggesting that these cells may misexpress the marker.
To analyze finerscale variation within the T cell cluster, we used the selfassembling manifold algorithm method from Tarashansky et al., 2019. We first used the SAM algorithm with parameters thresh = 0.1 and k = 10 to perform dimensional reduction. Visualization of a UMAP projection together with the labels from our sort plates (Figure 6—figure supplement 3) showed that there was a plate effect related to p1; we excluded this plate from the remainder of the analysis. We reran the SAM algorithm using the remaining (n = 237) T cells, with parameters thresh = 0.1, k = 10, to produce the dimensional reduction shown in Figure 6A. Cluster labels were assigned using the KMeans class in sklearn.cluster. We measured differential expression of genes between the two subtypes as described above. In Supplementary file 1, we report the genes with $D>{\mathrm{log}}_{2}10$ and $p<.01$ (Wilcoxon ranksum test, Bonferonnicorrected), for the two subtypes. In Figure 6B, we show a subset of markers associated with the whole T cell cluster, as well as selected marker genes between the two subtypes.
To identify potential covariation with arpc1b expression amongst the T cells, we computed the Spearman rank correlation between expression of arpc1b (in counts per million) and all other genes expressed in at least 20% of cells. In each calculation of pairwise correlation coefficient, we excluded cells with zero counts for both genes to avoid biasing correlations upwards due to spurious points at the origin. We calculated p values using a permutation test: we permuted cell labels and recalculated all correlation coefficients; pvalues were calculated as the proportion of observations of a correlation coefficient higher than the observed coefficient, multiplied by the number of genes tested (Bonferonni correction).
Appendix 1
Persistent random walks: the uniform persistence time (UPT) and the speedpersistence coupling (SPC) models
The infinitesimal model most commonly used to describe metazoan cell migration is the OrensteinUhlenbeck model (OU) (Uhlenbeck and Ornstein, 1930), which has also been called the persistent random walk model (PRW) in the context of cell migration (Wu et al., 2014). While we have chosen this model for concreteness, the statistical features discussed below are also in common to a number of other models that include some directional persistence but are diffusive at long times, including the KratkyPorod wormlike chain model (Doi and Edwards, 1988). We briefly review some of the standard results which we use to compare to data below.
Under the OU model, the dynamics of a cell are described by:
where S is the speed parameter; P is the persistence time parameter; ${\eta}_{t}$ is a Gaussian white noise term; and $i=x,y,z$. This model, considered the prototypical noisy relaxation process, produces two main qualitative features: trajectories that turn smoothly (i.e. directional persistence), and diffusive behavior at times $t\gg P$. We note that fluctuations in velocity and speed along the trajectory are also features of this model. In particular, the velocityvelocity autocorrelation function is given by:
Setting $t=s$, we see that the speed parameter $S$ is proportional to the rootmean squared speed: $S=\sqrt{\u27e8\frac{1}{n}{\sum}_{i}^{n}{v}_{i}{(t)}^{2}\u27e9}$, where $n$ is the number of dimensions. Because the distribution of velocities generated by the model is Gaussian, $S$ is also proportional to the mean speed. The decay of the velocity autocorrelation in each component sets the turning timescale at $P$; at long times the directions of motion are uncorrelated.
The meansquared displacement (MSD) after a time interval $\tau $ is given by:
where n is the number of dimensions. The MSD scales advectively, as $n{S}^{2}{\tau}^{2}$, in the limit of $\tau \ll P$, and diffusively, as $2n{S}^{2}P\tau $, in the limit of $\tau \gg P$. Thus the model predicts that $\frac{\u27e8{(\overrightarrow{x}(\tau )\overrightarrow{x}(0))}^{2}\u27e9}{\tau}$ will approach a constant value of $2n{S}^{2}P$ at long times, which defines the effective diffusion constant to be $\frac{1}{2}{S}^{2}P$.
We refer to the OU model with fixed persistence time parameter $P$ (but potentially variable speed parameters $S$) as the uniform persistence time (UPT) model. We note that under the OU model, the MSD and PSD depend on the speed parameter $S$ only through the constant scale factor ${S}^{2}$: for fixed $P$, the quantities $\frac{\u27e8{(\overrightarrow{x}(\tau )\overrightarrow{x}(0))}^{2}\u27e9}{{S}^{2}}$ and $\frac{\u27e8{v}_{i}{(f)}^{2}\u27e9}{{S}^{2}}$ are independent of speed, as are the normalized quantities $\frac{\u27e8{(\overrightarrow{x}(\tau )\overrightarrow{x}(0))}^{2}\u27e9}{\u27e8{(\overrightarrow{x}({\tau}_{0})\overrightarrow{x}(0))}^{2}\u27e9}$ and $\frac{\u27e8{v}_{i}{(f)}^{2}\u27e9}{\u27e8{v}_{i}{({f}_{0})}^{2}\u27e9}$, where ${\tau}_{0}$ and ${f}_{0}$ are a chosen time interval and frequency, respectively. (Note that this is also true of the full dynamics: we can eliminate the dependence on $S$ by transforming to the variable $\stackrel{~}{v}=\frac{v}{S}$, or measuring distance in units proportional to $S$.) In particular, the effective diffusion constant ${D}_{eff}=\frac{1}{2}{S}^{2}P$ scales with ${S}^{2}$.
Our observation of a linear relationship between measured mean speeds and correlation times suggests the following constrained form of the OU model, which we have called the speedpersistence coupling (SPC) model:
where $\alpha $ is a constant with units of acceleration; $\beta $ is a constant with units of time; and both are fixed across all cells.
In this model, the effective diffusion constant is:
Under the SPC model, the control parameter $S$ is proportional to the cell’s mean speed, so that this observable fully specifies its dynamics.
Finally, we note that with fixed $S$ and $P$, these models still produce variation in both local speed and turning behavior along trajectories; the control parameters, together with Equation 14, set the distributions of these quantities.
Effects of finitelength trajectories, sampling intervals, noise, and distributions of persistence time on speedpersistence coupling
Measurements of speed and persistence time are imperfect estimators of the underlying continuous process. Here we address whether statistical artifacts could generate the observed correlations between speed and persistence time. In particular, the finite sampling interval introduces a bias downwards in all speed estimates, because some turns are missed. Because this effect is stronger for lesspersistent cells, which turn more, we expect it to introduce a correlation between the measured speed and the measured persistence time.
To evaluate the influence that this may have had on our data, we simulated a collection of cells with the same speeds as our measured cells under the OU model. Simulations were performed using the velocity update rule in Equation 14 (Gillespie, 1996), with 20 simulated intervals $dt$ per sampling interval. Position coordinates were determined by numerical integration of the velocities along the simulated trajectories. Noise in centroid locations was included by adding a Gaussian random variable to x and y positions. We conservatively set the noise parameter at $\sigma =3\mu m$ per sampling interval; this was chosen as an estimate of the combined effects of true technical noise and changes in cell shape during the interval. Each simulated trajectory was 50 sampling intervals (1000 microscopic timesteps) in length. To match the measurement, sampling intervals were assigned to be 45 s in length. We measured both mean speeds and correlation times on the simulated trajectories as defined in Materials and methods.
We first assessed whether the SPC model, defined in the previous section, with the addition of noise in the centroid locations, gave the expected dependence of measured persistence time on measured cell speed (Appendix 1—figure 1B). Next, we simulated a collection of cells with the same set of speeds as in the data, with a constant persistence time parameter $P$ (the UPT model), to check whether the finite length of the trajectories induced a correlation between measured speeds and persistence times (Appendix 1—figure 1C). We did not observe a significant effect. Next, we added centroid location noise to the UPT model. The addition of noise does induce a correlation at the slow end of the speed spectrum (Appendix 1—figure 1D); this is because cells that happen to have turned more will appear slower. However, this effect becomes negligible for cells with speeds above the noise level. We note that this likely contributes to the measured propensity for sharp turns amongst the slowest cells, and may lead to misassignment between the two lowest speed classes.
We next evaluated whether a model where both $S$ and $P$ varied in a manner consistent with the data, but were uncorrelated with each other, could induce a correlation between measured speed and persistence time. Such a correlation could appear on the faster end of the speed spectrum due to variable $P$, because the fastest measured cells are biased to having been both fast and particularly persistent. We evaluated the size of this effect in our data by simulating a collection of cells with the observed speed distribution, as before, permuting the predicted $P$ parameters from the SPC model amongst the simulated cells. We found that this did not measurably bias the speedpersistence relationship (Appendix 1—figure 1E). Finally, we simulated the uncorrelated $S$ and $P$ model with the addition of centroid location noise (Appendix 1—figure 1F).
From this analysis, we concluded that noise in the locations creates a spurious correlation between measured speed and measured persistence time at the slow end of the speed spectrum, but that this effect cannot account for the consistent correlation across speeds that we observe; and that a model with variable $P$ that is uncorrelated with $S$ also cannot account for our observations.
Potential effects of fin fold boundary on MSD
As noted in the text, we observed that trajectories tended to stay within the tail fin and larval fin fold (Figure 1—figure supplement 1), without crossing into the interior muscle region, suggesting a partial barrier between these zones. In principle, such a barrier could lead to saturation of the MSD. If present, this effect would be strongest for trajectories in the regions of the fin fold on the margins of the fish (Figure 1—figure supplement 1). To assess whether this effect could be driving the observed transition away from advective/superdiffusive behavior, we took two approaches. First, we note that the typical timescale between turns (Figure 4A) is 2 min, and diffusive scaling is reached by $\tau =9$ min (Figure 1C inset, Figure 4B). Over 9 min, the median cell experiences an average displacement of 15 $\mu m$, while the 80th percentile cell experiences an average displacement of 40 $\mu m$. Given that the width of the fin fold is about 200 $\mu m$ (although sometimes narrower, Figure 1—figure supplement 1), we would not expect boundary effects to be significant at the transition timescale. To further assess this, we calculated the MSD as a function of time lag on the control sample shown in Figure 2A–B and Figure 2—video 1. This sample includes only the tail fin region, without fin fold boundary effects. Data for this sample was acquired at a slightly different time interval (see Materials and methods), and so it was not pooled into the overall MSD calculation. We calculated MSD as a function of time lag for this sample and compared it to the MSD calculated using all other control samples, and found very good agreement (Appendix 1—figure 2). (Note that the error bars are 95% confidence intervals calculated on a bootstrap over trajectories; the larger error bars for the heldout sample reflect the smaller number of trajectories.) We thus concluded that barrier effects on the margins of the fin fold did not drive the transition we observed in the MSD.
Data availability
Sequencing data have been deposited in GEO under accession code GSE137770. All source data, including cell trajectories, and analysis code are available at: https://github.com/erjerison/TCellMigration (copy archived at https://github.com/elifesciencespublications/TCellMigration).

NCBI Gene Expression OmnibusID GSE137770. Characterization of T cells from the larval zebrafish tail via singlecell RNAseq.
References

Live imaging reveals distinct modes of neutrophil and macrophage migration within interstitial tissuesJournal of Cell Science 130:3801–3808.https://doi.org/10.1242/jcs.206128

Characterizing T cell movement within lymph nodes in the absence of antigenThe Journal of Immunology 178:5505–5512.https://doi.org/10.4049/jimmunol.178.9.5505

Lymph node topology dictates T cell migration behaviorJournal of Experimental Medicine 204:771–780.https://doi.org/10.1084/jem.20061278

Towards estimating the true duration of dendritic cell interactions with T cellsJournal of Immunological Methods 347:54–69.https://doi.org/10.1016/j.jim.2009.05.013

Analysing immune cell migrationNature Reviews Immunology 9:789–798.https://doi.org/10.1038/nri2638

STAR: ultrafast universal RNAseq alignerBioinformatics 29:15–21.https://doi.org/10.1093/bioinformatics/bts635

Persistence and adaptation in immunity: t cells balance the extent and thoroughness of searchPLOS Computational Biology 12:e1004818.https://doi.org/10.1371/journal.pcbi.1004818

Exact numerical simulation of the OrnsteinUhlenbeck process and its integralPhysical Review E 54:2084–2091.https://doi.org/10.1103/PhysRevE.54.2084

Dendritic cells regulate highspeed interstitial T cell migration in the lymph node via LFA1/ICAM1The Journal of Immunology 191:1188–1199.https://doi.org/10.4049/jimmunol.1300739

Live imaging of effector cell trafficking and autoantigen recognition within the unfolding autoimmune encephalomyelitis lesionJournal of Experimental Medicine 201:1805–1814.https://doi.org/10.1084/jem.20050011

T cell migration, search strategies and mechanismsNature Reviews Immunology 16:193–201.https://doi.org/10.1038/nri.2015.16

Random migration precedes stable target cell interactions of tumorinfiltrating T cellsJournal of Experimental Medicine 203:2749–2761.https://doi.org/10.1084/jem.20060710

Cellautonomous and environmental contributions to the interstitial migration of T cellsSeminars in Immunopathology 32:257–274.https://doi.org/10.1007/s0028101002121

OpenSPIM: an openaccess lightsheet microscopy platformNature Methods 10:598–599.https://doi.org/10.1038/nmeth.2507

Navigating in tissue mazes: chemoattractant interpretation in complex environmentsCurrent Opinion in Cell Biology 36:93–102.https://doi.org/10.1016/j.ceb.2015.08.001

ConferenceIlastik: interactive learning and segmentation toolkitBiomedical Imaging: From Nano to Macro, 2011 IEEE International Symposium on IEEE. pp. 230–233.https://doi.org/10.1109/ISBI.2011.5872394

The WASPWAVE protein network: connecting the membrane to the cytoskeletonNature Reviews Molecular Cell Biology 8:37–48.https://doi.org/10.1038/nrm2069

Dissecting hematopoietic and renal cell heterogeneity in adult zebrafish at singlecell resolution using RNA sequencingJournal of Experimental Medicine 214:2875–2887.https://doi.org/10.1084/jem.20170976

On the theory of the brownian motionPhysical Review 36:823–841.https://doi.org/10.1103/PhysRev.36.823

The leukocyte cytoskeleton in cell migration and immune interactionsInternational Review of Cytology 216:233–289.https://doi.org/10.1016/s00747696(02)160074

BookThe Physics of Foraging: An Introduction to Random Searches and Biological EncountersCambridge University Press.https://doi.org/10.1017/CBO9780511902680

CCR7 ligands stimulate the intranodal motility of T lymphocytes in vivoJournal of Experimental Medicine 204:489–495.https://doi.org/10.1084/jem.20061706

Kinetics and extent of T cell activation as measured with the calcium signalJournal of Experimental Medicine 185:1815–1825.https://doi.org/10.1084/jem.185.10.1815
Decision letter

Armita NourmohammadReviewing Editor; University of Washington, United States

Aleksandra M WalczakSenior Editor; École Normale Supérieure, France

Judy CannonReviewer

Michael L DustinReviewer; University of Oxford, United Kingdom
In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.
Acceptance summary:
The paper by Jerison and Quake characterizes Tcell motility in tissues that span a broad range of length scales from microns, when contacting APCs, to millimeters, relevant for finding rare antigens. With sophisticated experiments the authors tracked populations of Tcells in live larval fish over several hours and built a theoretical model that relates persistence and speed of Tcells. This work is a significant contribution that will enable better understanding of immune responses in vivo.
Decision letter after peer review:
Thank you for submitting your article "Heterogeneous T cell motility behaviors emerge from a coupling between speed and turning in vivo" for consideration by eLife. Your article has been reviewed by three peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Aleksandra Walczak as the Senior Editor. The following individuals involved in review of your submission have agreed to reveal their identity: Judy Cannon (Reviewer #2); Michael L Dustin (Reviewer #3).
The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.
Summary:
The manuscript characterizes Tcell motility in tissues. Tcells explore tissues over a wide range of scales that span from microns (e.g., when contacting APCs) to millimeters (e.g. relevant for finding rare antigens). An important point is made that a simple diffusion process is not sufficient to explain this broad range of behaviors in Tcell motility. Two possible solutions are discussed in the manuscript: Anomalous diffusion via cells making Levy walks, or regular random walks sampled from a wide distribution. Extensive and sophisticated experiments are conducted on the native population of T cells in live larval fish over several hours, imaging millimeter fields of view. By analyzing many cell trajectories, the authors show that, at least in the stationary state, the motility of Tcells seem to be consistent with a regular random walk sampled from a wide distribution. Interestingly, the data spans over an effective 1D manifold in the space of Tcell speed and persistence. Moreover, the authors observe similar statistics for cell motility in mouse and in Dictyostelium (from previously published data), pointing towards a more generic pattern of motility that could be thought as a population strategy to span a broad range of scales  one is tempted to call this "motility bethedging".
Overall, the reviewers agree that the experiments present a significant improvement to the existing methods in recording cell motility and that the manuscript provides a sufficient theoretical novelty in characterizing Tcell motility strategies. However, there are some concerns with the presentation and the analyses that we would like to see addressed.
Essential revisions:
1) There is a possibility that the celltocell variation can be associated with distinct behaviors of different Tcell subtypes. We suggest that the authors use single cell gene expression levels (reported in Figure 5) to investigate whether the differential expression of certain surface markers is predictive of the mode of cell motility. Perhaps there can even be some memory cells in the pool. This would not require more experiments but some more analyses, which should be doable within a reasonable time frame. In principle, this analysis could strongly add to the mechanistic understanding of the reported bethedging strategy in cell motility.
2) For analysis of persistence, the authors state that pi/2 radians before turning was used as a definition for a persistent cell. This may be too broad as cells that turn 60o would likely not be classified as persistent. The authors should reanalyze persistence using 15o or 30o as a cutoff to ensure that motility analysis holds with a more stringent definition of persistent motility.
3) The experimental detail as written in the current version is insufficient. For example, are T cells vascular or in tissues? While the authors state that "tail fin" is imaged, there is no description of how specific areas are selected to image. Why was the tail fin selected? Was there an infection or was all motility in the absence of infection? Also, T cells at 1012 dpf were imaged. This is an extremely early time point. The authors should explain why this time point is used rather than imaging T cell motility in adult fish (transparent zebrafish for imaging are available).
4) Previous work by Mairui and colleagues (Cell 2015) has shown the coupling between cell speed and persistence across many cell types. The authors seem to be unaware of this study.
5) Authors should discuss some of the other models for persistent random walks that have been recently considered in the field of active matter. Given the Maiuri et al's finding (Cell:2015) that actin flow and actin regulatory proteins drive cell motility, the nonequilibrium models for random walk could provide a better description for this process.
6) The authors reject that cell motility is a levy walk, which was previously proposed by Harris et al., 2012, for CD8^{+} Tcells. The conditions of the two experiments are not comparable as as Harris et al. studied CD8^{+} cells chasing antigens, whereas the analyses in this manuscript are based on cell trajectories in the stationary state. This should more clearly be pointed out.
7) Authors should include a discussion on prior related work:
i) Negulescu PA, et al. Polarity of T cell shape, motility, and sensitivity to antigen. Immunity. 1996;4(5):42130.
ii) Dong TX, et al. Intermittent Ca(2+) signals mediated by Orai1 regulate basal T cell motility. eLife. 2017;6. doi: 10.7554/eLife.27827.
iii) Harris TH, et al. Generalized Levy walks and the role of chemokines in migration of effector CD8^{+} T cells. Nature. 2012;486(7404):5458.
iv) Maiuri P , et al. Actin flows mediate a universal coupling between cell speed and cell persistence. Cell 2015:161(2):37486
8) A more detailed discussion is necessary on how the proposed search strategy in the manuscript compare with Levy or intermittent migration (Maiuri et al., 2015; Harris et al., 2012).
https://doi.org/10.7554/eLife.53933.sa1Author response
Essential revisions:
1) There is a possibility that the celltocell variation can be associated with distinct behaviors of different Tcell subtypes. We suggest that the authors use single cell gene expression levels (reported in Figure 5) to investigate whether the differential expression of certain surface markers is predictive of the mode of cell motility. Perhaps there can even be some memory cells in the pool. This would not require more experiments but some more analyses, which should be doable within a reasonable time frame. In principle, this analysis could strongly add to the mechanistic understanding of the reported bethedging strategy in cell motility.
This is a great suggestion. While it is not technologically feasible at this time to associate an individual cell (and its trajectory) with a singlecell RNA expression profile, we can nonetheless use the singlecell RNA sequencing data to ask whether there is covariation in motility genes amongst the T cells. We performed additional analysis of the singlecell RNA sequencing data, and found that there are two main subgroups of cells (Figure 6AB). Additionally, we found statistically significant covariation of actin remodeling genes from cell to cell (Figure 6CD). Interestingly, although distinct in other dimensions of gene expression space, the two cell subtypes have overlapping, continuous distributions of the actinremodeling related genes. This analysis suggests that there is real celltocell variation in actin nucleation at the transcriptional level, which may induce longlived heterogeneous motility states. It is also consistent with a continuous motility axis. We note that speed and other motility characteristics may well also be regulated posttranscriptionally. We have included the results of this analysis as the final subsection of the Results.
Regarding the presence of memory cells: unfortunately the incomplete homology between zebrafish and mammalian systems makes it difficult to draw firm conclusions regarding T cell subtypes. For example, memory T cells are often classified with respect to their expression of CD45 isotypes. While the zebrafish homologue of CD45 (ptprc) is highly expressed, the exon structure of the zebrafish gene is not readily mappable to its mammalian counterpart. Additionally, even for the much better studied mammalian systems, there is currently significant controversy regarding the relationship between the traditional cellsurface markers and singlecell transcriptional profiles and how to use the latter to classify T cell subtypes. We expect that the rapidlyincreasing volume and discussions around scRNAseq from immune cells will clarify this significantly over the next few years, but for the present we believe there is not enough information to confidently annotate T cell subtypes.
2) For analysis of persistence, the authors state that pi/2 radians before turning was used as a definition for a persistent cell. This may be too broad as cells that turn 60o would likely not be classified as persistent. The authors should reanalyze persistence using 15o or 30o as a cutoff to ensure that motility analysis holds with a more stringent definition of persistent motility.
Thanks for the suggestion. We have repeated the analysis of persistence times as a function of cell speed with 30 degrees as a cutoff for persistence (Figure 4—figure supplement 2). We find a similar linear relationship between speed and persistence, with, as expected, shorter times over which cells are persistent under this definition.
3) The experimental detail as written in the current version is insufficient. For example, are T cells vascular or in tissues? While the authors state that "tail fin" is imaged, there is no description of how specific areas are selected to image. Why was the tail fin selected? Was there an infection or was all motility in the absence of infection? Also, T cells at 1012 dpf were imaged. This is an extremely early time point. The authors should explain why this time point is used rather than imaging T cell motility in adult fish (transparent zebrafish for imaging are available).
Thanks for the comments. We have clarified these points in the manuscript. The T cells are in tissue; there are also T cells in circulation, but they move orders of magnitude faster and are therefore not captured in our analysis. (Occasionally one is caught in a frame; see e.g. Figure 2—video 1, at 0:19:00 on the timestamp in the upper left.) All motility was measured in the absence of infection. We imaged as much as possible of the region of the fish posterior to the anus; this region of the fish is composed primarily of the tail fin and larval fin fold (annotated in Figure 1—figure supplement 1). We chose this region because it enabled us to image cell behavior within a millimeterscale tissue, while also avoiding the highly autofluorescent gut, which overwhelmed signal from the cells. We note that we have also added a short section (subsection “Model predicts wide variation in length scales of exploration across the population” penultimate paragraph and Appendix 1 final subsection and figure) addressing any potential effects of the fin fold boundary. Finally, it is currently infeasible to image older fish for long timespans because once the gills fully develop, the fish must pump their gills to remain oxygenated, which is incompatible with immobilization for light sheet microscopy. (At earlier timepoints, the fish acquire oxygen through passive diffusion via the skin.) Some intubation platforms for adult zebrafish have been developed, but no such technology exists yet for light sheet microscopy.
4) Previous work by Mairui and colleagues (Cell 2015) has shown the coupling between cell speed and persistence across many cell types. The authors seem to be unaware of this study.
Thanks very much for pointing out this highly relevant paper! We were indeed unaware. We have modified our main text and discussion to include this paper.
5) Authors should discuss some of the other models for persistent random walks that have been recently considered in the field of active matter. Given the Maiuri et al's finding (Cell:2015) that actin flow and actin regulatory proteins drive cell motility, the nonequilibrium models for random walk could provide a better description for this process.
Related to this point and comments 7 and 8 below, we have added discussion of the role of intermittency and alternative models of the random walk process to the Discussion.
6) The authors reject that cell motility is a levy walk, which was previously proposed by Harris et al., 2012, for CD8^{+} Tcells. The conditions of the two experiments are not comparable as as Harris et al. studied CD8^{+} cells chasing antigens, whereas the analyses in this manuscript are based on cell trajectories in the stationary state. This should more clearly be pointed out.
We have added this clarification to the manuscript. (Discussion section).
7) Authors should include a discussion on prior related work:
i) Negulescu PA, et al. Polarity of T cell shape, motility, and sensitivity to antigen. Immunity. 1996;4(5):42130.
ii) Dong TX, et al. Intermittent Ca(2+) signals mediated by Orai1 regulate basal T cell motility. eLife. 2017;6. doi: 10.7554/eLife.27827.
iii) Harris TH, et al. Generalized Levy walks and the role of chemokines in migration of effector CD8^{+} T cells. Nature. 2012;486(7404):5458.
iv) Maiuri P , et al. Actin flows mediate a universal coupling between cell speed and cell persistence. Cell 2015:161(2):37486
Thanks for the references. In response to this comment as well as points 3 and 7, we have added to the Discussion to comment on how intermittency manifests in our model and its relationship with prior work.
8) A more detailed discussion is necessary on how the proposed search strategy in the manuscript compare with Levy or intermittent migration (Maiuri et al., 2015; Harris et al., 2012).
Thanks for the suggestion. The question of optimality of different search strategies depends sensitively on the distribution (sometimes called patchiness) of targets, which is generally unknown in in vivo contexts. Exploring this question in depth would thus require extensive simulations of different possible target distributions, which is beyond the scope of our present study. However, we have added comments on this to the manuscript. (Discussion section).
https://doi.org/10.7554/eLife.53933.sa2Article and author information
Author details
Funding
Chan Zuckerberg Biohub
 Elizabeth R Jerison
 Stephen R Quake
The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.
Acknowledgements
We acknowledge Aya LudinTal and Leonard Zon for the generous gift of the Tg(lck:GFP) zebrafish line. We acknowledge Kiran Kocherlakota and the Stanford VSC for assistance with zebrafish management and husbandry. We acknowledge Saroja Korullu for assistance with library preparation. We also acknowledge Stanford Research Computing and the Sherlock2 computer cluster for computational support and resources. Finally, we acknowledge Louis Leung and Karen Mruk for invaluable advice regarding microscopy and zebrafish; Edward Marti for helpful discussions on imaging, analysis, and the manuscript, and Felix Hornes and Michael Swift for comments on the manuscript. Funding: This project was supported by the Chan Zuckerberg Biohub Competing interests: Authors declare no competing interests. Data and materials availability: Sequencing data and the gene expression count table have been deposited on GEO (accession: GSE137770). Analysis code and trajectory data are available at https://github.com/erjerison/TCellMigration.
Ethics
Animal experimentation: This study was performed in strict accordance with the recommendations in the Guide for the Care and Use of Laboratory Animals of the National Institutes of Health. All of the animals were handled according to approved institutional animal care and use committee (IACUC) protocols (#32107) of Stanford University.
Senior Editor
 Aleksandra M Walczak, École Normale Supérieure, France
Reviewing Editor
 Armita Nourmohammad, University of Washington, United States
Reviewers
 Judy Cannon
 Michael L Dustin, University of Oxford, United Kingdom
Publication history
 Received: November 25, 2019
 Accepted: April 30, 2020
 Version of Record published: May 19, 2020 (version 1)
Copyright
© 2020, Jerison and Quake
This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.
Metrics

 1,673
 Page views

 194
 Downloads

 18
 Citations
Article citation count generated by polling the highest count across the following sources: Crossref, PubMed Central, Scopus.
Download links
Downloads (link to download the article as PDF)
Open citations (links to open the citations from this article in various online reference manager services)
Cite this article (links to download the citations from this article in formats compatible with various reference manager tools)
Further reading

 Physics of Living Systems
The actomyosin cytoskeleton is a crucial driver of morphogenesis. Yet how the behavior of largescale cytoskeletal patterns in deforming tissues emerges from the interplay of geometry, genetics, and mechanics remains incompletely understood. Convergent extension in D. melanogaster embryos provides the opportunity to establish a quantitative understanding of the dynamics of anisotropic nonmuscle myosin II. Cellscale analysis of protein localization in fixed embryos suggests that gene expression patterns govern myosin anisotropy via complex rules. However, technical limitations have impeded quantitative and dynamic studies of this process at the whole embryo level, leaving the role of geometry open. Here we combine in toto live imaging with quantitative analysis of molecular dynamics to characterize the distribution of myosin anisotropy and the corresponding genetic patterning. We found pair rule gene expression continuously deformed, flowing with the tissue frame. In contrast, myosin anisotropy orientation remained approximately static, and was only weakly deflected from the stationary dorsalventral axis of the embryo. We propose that myosin is recruited by a geometrically defined static source, potentially related to the embryoscale epithelial tension, and account for transient deflections by cytoskeletal turnover and junction reorientation by flow. With only one parameter, this model quantitatively accounts for the time course of myosin anisotropy orientation in wildtype, twist, and evenskipped embryos as well as embryos with perturbed egg geometry. Geometric patterning of the cytoskeleton suggests a simple physical strategy to ensure a robust flow and formation of shape.

 Neuroscience
 Physics of Living Systems
Naturally occurring body movements and collective neural activity both exhibit complex dynamics, often with scalefree, fractal spatiotemporal structure. Scalefree dynamics of both brain and behavior are important because each is associated with functional benefits to the organism. Despite their similarities, scalefree brain activity and scalefree behavior have been studied separately, without a unified explanation. Here we show that scalefree dynamics of mouse behavior and neurons in visual cortex are strongly related. Surprisingly, the scalefree neural activity is limited to specific subsets of neurons, and these scalefree subsets exhibit stochastic winnertakeall competition with other neural subsets. This observation is inconsistent with prevailing theories of scalefree dynamics in neural systems, which stem from the criticality hypothesis. We develop a computational model which incorporates known celltypespecific circuit structure, explaining our findings with a new type of critical dynamics. Our results establish neural underpinnings of scalefree behavior and clear behavioral relevance of scalefree neural activity.