Hierarchical modeling of mechano-chemical dynamics of epithelial sheets across cells and tissue

Abstract

Collective cell migration is a macroscopic population-level phenomenon that has emerged across hierarchy from mi-croscopic interactions between cells; however, the underlying mechanism remains unclear. Here, we targeted epithe-lial collective cell migration, driven by the mechanical force regulated by chemical signals of traveling ERK activation waves, observed in wound healing. We propose a hierarchical mathematical framework for understanding how cells are orchestrated through mechanochemical cell-cell interaction. We mathematically transformed a particle-based model at the cellular level into a continuum model at the tissue level. The continuum model described relationships between cell migration and mechanochemical variables, namely, ERK activity gradients, cell density, and velocity field, which could be compared with live-cell imaging data. The continuum model recapitulated the ERK wave-induced collective cell migration in wound healing. We also numerically confirmed a consistency between the two models. This framework allows us to connect hierarchical causality from the single-cell level to the tissue level.