A hybrid computational model for collective cell durotaxis

Abstract

Collective cell migration is regulated by a complex set of mechanical interactions and cellular mechanisms. Collective migration emerges from mechanisms occurring at single cell level, involving processes like contraction, polymerization and depolymerization, of cell–cell interactions and of cell–substrate adhesion. Here, we present a computational framework which simulates the dynamics of this emergent behavior conditioned by substrates with stiffness gradients. The computational model reproduces the cell’s ability to move toward the stiffer part of the substrate, process known as durotaxis. It combines the continuous formulation of truss elements and a particle-based approach to simulate the dynamics of cell–matrix adhesions and cell–cell interactions. Using this hybrid approach, researchers can quickly create a quantitative model to understand the regulatory role of different mechanical conditions on the dynamics of collective cell migration. Our model shows that durotaxis occurs due to the ability of cells to deform the substrate more in the part of lower stiffness than in the stiffer part. This effect explains why cell collective movement is more effective than single cell movement in stiffness gradient conditions. In addition, we numerically evaluate how gradient stiffness properties, cell monolayer size and force transmission between cells and extracellular matrix are crucial in regulating durotaxis.