A Model of Electrodiffusion and Osmosis in Cells and Tissues
Yoichiro Mori, University of Minnesota

Control of cell volume and intracellular electrolyte content is a  fundamental problem in physiology and is central to the functioning of  epithelial systems.  These physiological processes are modeled using  pump-leak models, a system of differential algebraic equations that  describes the balance of ions and water flowing across the cell  membrane.  Despite their widespread use, very little is known about  their mathematical properties.  In this talk, we shall establish analytical results on the existence and stability of steady states for a general class of pump-leak models.  The key to these results is that pump-leak models possess a natural thermodynamic structure.  We shall then use this thermodynamic structure as a guiding principle to obtain a spatial generalization of pump leak models - a PDE system that describes three-dimensional electrodiffusion and osmosis in cellular systems.  If time permits, we shall also discuss analytical properties of the three dimensional cable model, which may be seen as capturing the short-time behavior of the above PDE model.