Phase transitions in biological tissue mechanics

Biological systems exhibit states analogous to physical states of matter such as solid, liquid, and gas, resulting from cellular interactions that manifest in macroscopic properties such as fluidity, rigidity, and resistance to shape and volume changes. These transitions, where tissues change their structural and functional states, are key to phenomena like embryogenesis, wound healing, and tumor development. In this dissertation, we employ numerical frameworks to probe the phase transition and mechanical responses of dense biological tissues under varying conditions. First, we employ a Voronoi-based vertex model to investigate the nonlinear mechanical behavior of dense biological tissue subjected to shear deformations. We show that solid-like tissues exhibit pronounced nonlinear tendencies and stress-stiffening behaviors, aligning with empirical observations, and fluid-like tissues could undergo strain-induced solidification upon surpassing a critical strain threshold. A mean-field theory is proposed to explain these phenomena. In addition, we introduce an Active Finite Voronoi (AFV) model, which exhibits an additional non-confluent phase than traditional vertex models, enabled by the potential for intercellular gaps. This uncouples the confluency transition from tissue aggregation and glassy transitions. This rich phase diagram has been systematically studied. The study employs a combination of theoretical modeling and computational simulations, leveraging tools from non-equilibrium statistical mechanics, soft matter physics, and topological mechanics. This comprehensive approach allows us to span a diverse range of topics within the realm of biophysics.--Author's abstract