Math Biology Seminar: A Numerical Model of Cellular Blebbing

In animal cells, a "bleb" is a balloon-like protrusion of the plasma membrane that forms when the membrane separates from the underlying cytoskeletal network and is pushed outward by pressure-driven cytosol. The protrusion later retracts due to the formation and subsequent myosin-II driven contraction of a new actin cortex within the bleb. Blebs are one of a number of cell motility mechanisms and they also play a key role in apoptosis and mitosis.

We have developed a computational model of this phenomenon. This two-dimensional fluid-structure interaction model includes the motion of the actin filaments, the actin and myosin monomer concentrations, the plasma membrane, and the cytosol. The membrane is modeled by a damped wave equation with a strain-dependent elasticity modulus. The cytosol is modeled by Stokes flow and the protein concentrations are modeled via advection-diffusion equations. The cytoskeleton is represented by a set of filaments each governed by Hooke?s law. This discrete representation is a departure from the commonly utilized notion of treating the cytoskeleton as a continuum. A volume constraint is also included in the model to maintain the overall cell volume at a constant value. The simulation is carried out via an operator splitting procedure where the components of the model interact through external forces and boundary conditions.

However, the cytoskeleton is a dynamic structure whose overall mechanical properties change due to underlying biochemical reactions and thus exhibits non-equilibrium behavior. In particular, the stiffness of the filaments in the above model are coarse-grained representations of the microscopic actin network. I will present preliminary results on coupling the time evolution of coarse-grained and microscopic descriptions by statistical sampling of the dynamics of the cytoskeletal network.