A new approach unifies mechanical rigidity in cell-based tissue models and biopolymer networks
Matthias Merkel (Turing Center for Living Systems, Marseille)
Understanding how mechanical properties of biological tissues arise from collective cellular behavior is vital for understanding the mechanisms that guide embryonic development, cancer growth, and wound healing. With my group, I am studying several questions of collective effects and self-organization in biological tissue. Recently, a new type of rigidity transition was discovered in a family of cell-based models for 2D and 3D tissues. Here I discuss these transitions and show that they are an instance of a much more general class of transitions, which appear when introducing geometric incompatibility into so-called under-constrained systems. This kind of transition also provides an important limiting case to understand stiffening in fiber network models, which are used to describe biopolymer networks like collagen. We show that all of these models exhibit generic elastic behavior close to the transition, which is largely independent of the microscopic structure and the disorder in the system. We obtain analytic expressions for the relevant elastic properties and numerically verify our findings by simulations of under-constrained spring networks as well as 2D and 3D vertex models for dense biological tissues. Several of our predictions are parameter-free, and we thus expect them to be general hallmarks for geometric-incompatibility-induced stiffening in under-constrained materials. Hence, they provide quantitative experimental tests for whether stiffening in a given material is due to this effect or not. Finally, I will briefly discuss another project of current interest in my group, where we will explore conditions for robust self-organized oriented deformation of biological tissue.