A model for the emergence of epithelial-mesenchymal transition in collective cell migration

Abstract

Collective cell migration (CCM) is a fundamental biological process involved in development, wound healing, and cancer metastasis. In this study, we present a simplified two-dimensional dynamical model that captures the key features of CCM using self-propelled particles governed by ordinary differential equations for velocity and polarity. A diffusion-like term is introduced to model migration towards unoccupied space, while cell shapes are estimated using Voronoi tessellations based on cell centers of mass. Parameter tuning reveals the individual effects of five key parameters — αv, αp, β, κ, and D on cell dynamics, particularly on the progression speed of the leading edge. Simulations with the diffusion term showed enhanced border advancement and increased digitisation at the front. While a clear epithelial–mesenchymal transition (EMT) was not identified via shape function plots, increasing trends in both polarity–velocity correlation and nematic order shape function |γ2| suggest signs of such a transition. The model qualitatively reproduces experimentally observed features of CCM, and future work could extend this framework to more spatially detailed models and incorporate experimentally derived physical parameters to enhance predictive accuracy.