Electrochemical potential is the driving force for ionic flow (or more precisely ionic flux). An extremely counterintuitive phenomenon has been observed from experiments long ago; that is, as the electrochemical potential of an ion species increases to infinity in a special way, the flux decreases to zero. The cause of the declining phenomenon was unclear.
Based on the abstract invariant manifold theory of nonlinear dynamical systems (the geometric singular perturbation theory) together with the revealing of concrete intrinsic structures of ion channel problems, a geometric singular perturbation framework was developed for the Poisson-Nernst-Planck systems as models for ionic flow through ion channels. In a recent work, we investigate effects of large permanent charges on ionic flows and obtained several unintended results; in particular, we found that the large permanent charge is responsible for the above mentioned declining phenomenon.
The talk is based joint works with B. Eisenberg, a physiologist from Rush Medical Center at Chicago, and L. Zhang, a Ph. D. student from Shanghai Jiao Tong University.