Mechanically-driven growth and competition in a Voronoi model of tissues

TL;DR

This study couples tissue mechanics and evolutionary dynamics using a Self-Propelled Voronoi model to understand how mechanical properties influence cell competition and invasion in tissues, with implications for cancer development and therapy.

Contribution

It introduces a novel coupling of mechanical variables with stochastic growth rates in a Voronoi tissue model, analyzing invasion dynamics and predicting outcomes with a mean-field approach.

Findings

Liquid-like tissue states resist invasion more effectively.

Preferred cell area and perimeter are key factors in fitness advantage.

Mean-field approximation accurately predicts mutation outcomes.

Abstract

The mechanisms leading cells to acquire a fitness advantage and establish themselves in a population are paramount to understanding the development and growth of cancer. Although there are many works that study separately either the evolutionary dynamics or the mechanics of cancer, little has been done to couple evolutionary dynamics to mechanics. To address this question, we study a confluent model of tissue using a Self-Propelled Voronoi (SPV) model with stochastic growth rates that depend on the mechanical variables of the system. The SPV model is an out-of-equilibrium model of tissue derived from an energy functional that has a jamming/unjamming transition between solid-like and liquid-like states. By considering several scenarios of mutants invading a resident population in both phases, we determine the range of parameters that confer a fitness advantage and show that the preferred area and perimeter are the most relevant ones. We find that the liquid-like state is more resistant to invasion and show that the outcome of the competition can be determined from the simulation of a non-growing mixture. Moreover, a mean-field approximation can accurately predict the fate of a mutation affecting mechanical properties of a cell. Our results can be used to infer evolutionary dynamics from tissue images, understand cancer-suppressing effects of tissue mechanics, and even search for mechanics-based therapies.