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, the convex pores restrict particle motion more stringently than the concave pores, 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.

中文翻译：

---

受细胞外地形影响的具有相关速度和持久性的细胞随机游走

通过细胞外基质的细胞迁移对许多生理过程至关重要，例如组织发育、免疫反应和癌症转移。以前的模型包括持久随机游走 (PRW) 和 Lévy 游走，仅解释了同质环境中某些细胞类型的迁移动态。最近，发现细胞内肌动蛋白流动可以有力地确保细胞迁移速度和持久性之间的普遍耦合，用于在体外测定和活组织中迁移的各种细胞类型。然而，速度和持久性之间的相关性对复杂环境中宏观细胞迁移动力学和模式的影响在很大程度上是未知的。在这项研究中，我们开发了蒙特卡罗随机游走模拟来研究运动，在均质和多孔环境中移动的细胞的搜索能力和搜索效率。细胞被简化为一个无量纲粒子，按照 PRW、Lévy 游走、线性速度-持久性相关的随机游走（线性 RWSP）和非线性速度-持久性相关的随机游动（非线性 RWSP）移动。粗粒度分析表明，非线性 RWSP 在均质和多孔环境中均实现了最大的运动性。当粒子搜索目标时，速度和持久性的非线性耦合提高了搜索能力（即在固定时间段内找到更多的目标），但牺牲了搜索效率（即单位距离找到的目标更少）。此外，凸孔比凹孔更严格地限制粒子运动，特别是对于非线性 RWSP 和 Lévy 游走。总体而言，我们的结果表明，速度和持久性的非线性相关性具有增强复杂环境中的运动性和搜索特性的潜力，并可作为在生物、工程和社会科学领域对活性粒子进行更详细研究的起点。