Ionic solutions and ion channels: An energetic variational approach

Mathematics  

Penn State University

The interactions of ions flowing through biological systems has been a central topic in biology for more than 100 years. Flows of ions produce signaling in the nervous system, initiation of contraction in muscle, coordinating the pumping of the heart and regulating the flow of water through kidney and intestine. Ion concentrations inside cells are controlled by ion channel proteins through the lipid membranes. In this talk, a continuum model is derived from the energetic variational approach which include the coupling between the electrostatic forces, the hydrodynamics, diffusion and crowding (due to the finite size effects). The model provides some basic understanding of one of the most important properties of proteins, the ion selectivity. Transport of charged particles and ions in biological environments is by nature a multiscale and multiphysics problem. I will also discuss the roles of other important ingredients such as those of nonlocal diffusion and also the connection between kinetic description and continuum approaches. This is a joint work with Yunkyong Hyon (NIMS, Korea), Taichia Lin (National Taiwan University), Hao Wu (Fudan University) and Robert Eisenberg (Rush Medical School).