Differences in solute concentration across a semipermeable membrane of cells generates transmembrane osmotic water flow. The interaction of such flows with membrane and flow mechanics is an important area in many biological applications, including the study of cell migrations. Another driving force people observed in cell migration is the polymerization/depolymerization cycle of actin network inside the cell. In this presentation, we will discuss a mathematical model of cell migration that allows us studying the interplay between diffusive, osmotic and mechanical effects from all force factors, and the numerical simulations in 2D. In the model, an osmotically active solute obeys an advection-diffusion equation in a region demarcated by a deformable membrane. The interfacial membrane allows transmembrane water flow which is determined by osmotic and mechanical pressure differences across the membrane. Actin network is constantly in polymerization cycle and interact with the elastic membrane. The numerical method is based on an immersed boundary method for fluid-structure interaction and a Cartesian grid embedded boundary method for the solute and actin network. We demonstrate our numerical algorithm with the test case of an osmotic engine, a recently proposed mechanism for cell propulsion in confinements.

Dr. Lingxing Yao got his Ph.D. at the University of North Carolina at Chapel Hill and is currently working at the University of Akron. His research focus on mathematical model and numerical simulations for the applications in biological system and material sciences. His current research projects involves detailed mechanism of cell motley and active liquid crystal polymers. He will talk about a mathematical model that is capable to describe two different driving forces in cell migrations.