Correlation between speed and turning naturally arises for sparsely sampled cell movements

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 (TA) between two sequential displacements and can be characterized by an average TA or persistence time. Recent studies documenting T cell movement in zebrafish found that a cell's average speed and average TA are negatively correlated, suggesting a fundamental cell-intrinsic program whereby cells with a lower TA (and larger persistence time) are intrinsically faster (or faster cells turn less). In this paper we confirm the existence of the correlation between turning and speed for six different datasets on 3D movement of CD8 T cells in murine lymph nodes or liver. Interestingly, the negative correlation between TA and speed was observed in experiments in which liver-localized CD8 T cells rapidly displace due to floating with the blood flow, suggesting that other mechanisms besides cell-intrinsic program may be at play. By simulating correlated random walks using two different frameworks (one based on the von Mises-Fisher (vMF) distribution and another based on the 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 typically make movements. This effect is strongest when the sampling frequency is of the order of magnitude of the inverse of persistence time of cells and when cells vary in persistence time. The effect arises in part due to the sensitivity of estimated cell speeds to the frequency of imaging whereby less frequent imaging results in slower speeds. Interestingly, by using estimated persistence times for cells in two of our datasets and simulating cell movements using the OU process, we could partially reproduce the experimentally observed correlation between TA and speed without a cell-intrinsic program linking the two processes. 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 the inference of critical cellular parameters of cell motility such as speeds.