Stability and Bifurcations in a Free Boundary PDE Models of Cell Motility
Leonid Berlyand discusses mathematical models for the onset of cell motion driven by myosin contraction. A two-dimensional free-boundary PDE model links cell-shape evolution to diffusion and Keller–Segel-type transport. The talk examines linear stability, a stability-determining eigenvalue and the way nonlinear diffusion changes the bifurcation from supercritical to subcritical. It also considers the curvature of the bifurcation curve, connections to bistability, and the role of non-self-adjoint operators. An example illustrates why a spectral gap alone need not guarantee stability. This is an in-person Analysis of Fluids and Related Topics seminar at Princeton.
“Rigidity and Fluidity in Biological Tissue”
The coordinated migration of groups of cells underlies many biological processes, including embryo development, wound healing and cancer metastasis. In many of these situations, tissues are able to tune themselves between liquid-like states, where cells flow collectively as in a liquid, and solid-like states that can support shear stresses. In this talk I will describe mesoscopic models of cell assemblies inspired by active matter physics to examine the roles of cell motility, cell crowding and the interplay of contractility and adhesion in controlling the rheological state of biological tissue.