Random Walks of a Cell With Correlated Speed and Persistence Influenced by the Extracellular Topography

Kejie Chen,Kai-Rong Qin

doi:10.3389/fphy.2021.719293

Kejie Chen, Kai-Rong Qin

Open Access

https://doi.org/10.3389/fphy.2021.719293

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Abstract

Cell migration through extracellular matrices is critical to many physiological processes, such as tissue development, immunological response and cancer metastasis. Previous models including persistent random walk (PRW) and Lévy walk only explain the migratory dynamics of some cell types in a homogeneous environment. Recently, it was discovered that the intracellular actin flow can robustly ensure a universal coupling between cell migratory speed and persistence for a variety of cell types migrating in the in vitro assays and live tissues. However, effects of the correlation between speed and persistence on the macroscopic cell migration dynamics and patterns in complex environments are largely unknown. In this study, we developed a Monte Carlo random walk simulation to investigate the motility, the search ability and the search efficiency of a cell moving in both homogeneous and porous environments. The cell is simplified as a dimensionless particle, moving according to PRW, Lévy walk, random walk with linear speed-persistence correlation (linear RWSP) and random walk with nonlinear speed-persistence correlation (nonlinear RWSP). The coarse-grained analysis showed that the nonlinear RWSP achieved the largest motility in both homogeneous and porous environments. When a particle searches for targets, the nonlinear coupling of speed and persistence improves the search ability (i.e. find more targets in a fixed time period), but sacrifices the search efficiency (i.e. find less targets per unit distance). Moreover, both the convex and concave pores restrict particle motion, especially for the nonlinear RWSP and Lévy walk. Overall, our results demonstrate that the nonlinear correlation of speed and persistence has the potential to enhance the motility and searching properties in complex environments, and could serve as a starting point for more detailed studies of active particles in biological, engineering and social science fields.

Highlights

Eukaryotic cell migration is a crucial process for the normal development and maintenance of organs and tissues
The divergence of the particle distribution from a Gaussian distribution is quantitatively characterized using the relative entropy (Figure 4E). These results show that persistent random walk (PRW) and linear RWSP become more Brownian-like at long times, while Lévy walk and nonlinear RWSP are anomalous
We developed a coarse-grained random walk model to study the dynamics of a cell, which is represented by a dimensionless particle, moving in the homogeneous and porous media with correlated speed and persistence

Summary

Introduction

Eukaryotic cell migration is a crucial process for the normal development and maintenance of organs and tissues. Works extracted cell speed v and persistence τ (i.e. the time duration of a straight motion between two switches of directions) from fits of the mean squared displacements (MSDs, x(t)2) using a persistent random walk (PRW) model [6,7,8,9,10]. Metastasizing tumor cells moving along linear fibers or in vitro channels acquire superdiffusive motion at long times ( < x(t)2 > ∼ tα, α > 1) [12]. These types of cell migratory motions are better explained by the Lévy walk dynamics rather than the PRW, where the persistence follows a heavy-tailed and power-law distribution (p(tp) ∼ tp−μ), and μ is the Lévy exponent (1 < μ < 3)

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