Modeling Dynamics of Contact Inhibition of Proliferation and Structural Order in a Confluent Epithelium

Contact inhibition of proliferation (CIP) enables epithelial tissues to self-regulate growth and maintain tissue homeostasis. However, how cell-level mechanical contact, tissue-scale structural order, and proliferation kinetics interplay remains a fundamental open question in living matter physics. Here, we present a particle-based model of a confluent epithelial monolayer governed by overdamped dynamics, where individual cells interact via a two-dimensional hard core- soft shoulder potential. By comparing structural evolution during quasistatic densification with previously reported experimental division kinetics, we find that the dynamics of proliferation arrest mimics the onset of direct steric contacts between the hard cores of the shell. Identifying hard core contacts as the physical driver of CIP, we couple our mechanical model with a stochastic Monte Carlo division scheme in which the instantaneous division rate decreases to zero from an intrinsic value as the number of hard core contact increases to six from zero. We demonstrate that for high intrinsic division rates, the cellular densification outpaces mechanical relaxation. This kinetic mismatch drives premature hard-core contact formation, shifts the onset of jamming and contact inhibition to lower packing fractions, and induces increasingly disordered transient configurations before the tissue universally converges to a hexagonal close-packed limit. Our model's predicted division kinetics and structural order evolution are consistent with epithelial monolayer experiments, both reported and our own. This minimal physical framework links single-cell steric contact mechanics directly to tissue-scale growth regulation and structural evolution.