Nonlinear Dynamics Of Cell Migration In Anisotropic Microenvironment*

Cell migration in anisotropic microenvironment plays an important role in the development of normal tissues and organs as well as neoplasm progression, e.g., osteogenic differentiation of embryonic stem cells was facilitated on stiffer substrates, indicating that the mechanical signals greatly affect both early and terminal differentiation of embryonic stem cells. However, the effect of anisotropy on cell migration dynamics, in particular, in terms of acceleration profiles which is important for recognizing dynamics modes of cell migration and analyzing the regulation mechanisms of microenvironment in mechanical signal transmission, has not been systematically investigated. In this work, we firstly rigorously investigate and quantify the differences between persistent random walk and anisotropic persistent random walk models based on the analysis of cell migration trajectories and velocity auto-covariance function, both qualitatively and quantitatively. Secondly, we introduce the concepts of positive and negative anisotropy based on the motility parameters to study the effect of anisotropy on acceleration profiles, especially the nonlinear decrease and non-monotonic behaviors. We particularly elaborate and discuss the mechanisms, and physical insights of non-monotonic behaviors in the case of positive anisotropy, focusing on the force exerted on migrating cells. Finally, we analyze two types of in vitro cell migration experiments and verify the universality of nonlinear decrease and the consistence of non-monotonic behaviors with numerical results. We conclude that the anisotropy of microenvironment is the cause of the non-monotonic and nonlinear dynamics, and the anisotropic persistent random walk can be as a suitable tool to analyze in vitro cell migration with different combinations of motility parameters. Our analysis provides new insights into the dynamics of cell migration in complex microenvironment, which also has implications in tissue engineering and cancer research.