Thermodynamic model of epithelial-substrate coupling in monolayers: Effects on traction forces and colony size

Abstract

Epithelial cells form cohesive colonies that interact with substrates by generating extracellular forces through focal adhesions. This study develops a thermodynamic model integrating monolayer elasticity and force-mediated focal adhesion formation to understand how epithelial-substrate-coupling strength affects traction forces, cellular displacements, and focal adhesion distributions in cohesive monolayers. We derive and solve the steady-state equations of the system both semi-analytically and numerically. Our findings show that epithelial-substrate-coupling strength significantly influences traction force landscapes and focal adhesion distributions. Strong coupling increases average traction force as colony size decreases, while weak coupling shows the opposite trend. This model reconciles previously observed differences in scaling laws relating average traction force to colony size.