Cells contain a large number of organic molecules that do not leak out through the cell membrane. The presence of organic molecules and their attendant counterions results in excess intracellular osmotic pressure. The plasma membrane is not mechanically strong enough to withstand significant differences in osmotic pressure, and thus the cell will tend to swell and burst. Animal cells maintain their cell volume with ionic pumps and ionic channels that together regulate the ionic content and volume of a cell. This process is modeled using the pump-leak model, a widely used model in mathematical physiology. We are studying the theoretical aspects of this pump-leak model. More generally, there are many processes in the body in which ionic electrodiffusion and osmosis play a prominent role. We are developing PDE models that can describe electrodiffusion and osmosis in biological tissue in a physically consistent fashion.
Mathematical problems in physiology