Correlation between speed and turning naturally arises for sparsely sampled cell movements
Authors: Ganusov Vitaly V. , Zenkov Viktor S. , Majumder Barun 
Published: January 2021

Mechanisms regulating cell movement are not fully understood. One feature of cell movement that determines how far cells displace from an initial position is persistence, the ability to perform movements in a direction similar to the previous movement direction. Persistence is thus determined by turning angles between two sequential displacements and be characterized by an average turning angle or persistence time. Recent studies found that a cell’s average speed and turning are negatively correlated, suggesting a fundamental cell-intrinsic program whereby cells with a lower turning ability (i.e., larger persistence time) are intrinsically faster (or faster cells turn less). By simulating correlated or persistent random walks (PRWs) using two different frameworks (one based on von Mises-Fisher (vMF) distribution and another based on Ornstein-Uhlenbeck (OU) process) we show that the negative correlation between speed and turning naturally arises when cell trajectories are sub-sampled, i.e., when the frequency of sampling is lower than frequency at which cells make movements. This effect is strongest when the sampling frequency is on the order of magnitude with the typical cell persistence time and when cells vary in persistence time. Both conditions are observed for datasets of T cell movements in vivo that we have analyzed. In simulations the correlation arises due to randomness of cell movements resulting in highly variable persistence times for individual cells that with sub-sampling leads to large variability of average cell speeds. Interestingly, previously suggested methodology of calculating displacement of cell cohorts with different speeds resulted in similar results whether or not there is a cell-intrinsic correlation between cell speed and persistence. For both vMF- and OU-based simulations of PRWs we could find parameter values (distribution of persistence times, speeds, and sampling frequency) that matched experimentally measured correlations between speed and turning for two datasets of T cell movement in vivo suggesting that such simple correlations are not fully informative on the intrinsic link between speed and persistence. Our results thus suggest that sub-sampling may contribute to (and perhaps fully explains) the observed correlation between speed and turning at least for some cell trajectory data and emphasize the role of sampling frequency in inference of critical cellular parameters of cell motility such as speeds.

Secondary Abstract

Measurement of cell movements often results in a negative correlation between average speed and average turning angle suggesting an existence of a universal, cell-intrinsic movement program. We show that such a negative correlation may arise if cells in the population differ in their ability for persistent movement when the movement data are sub-sampled. We show that sub-sampling of cell trajectories generated using two different frameworks of persistent random walk can match the experimentally observed correlation between speed and turning for T cell movements in vivo.