報告人： Mingji Zhang (張明吉)
We study a quasi-one-dimensional steady-state Poisson-Nernst-Planck type model for ionic flows through a membrane channel. We consider three ion species, two positively charged with the same valence and one negatively charged, and assume zero permanent charge. Bikerman's local hard-sphere potential is included in the model to account for finite ion size effects. Treating the ion sizes as small parameters, we derive an approximation of individual fluxes, from which one can further study the qualitative properties of ionic flows and extract concrete information directly related to biological measurements. Of particular interest is the competition between two cations (positively charged ion species) due to finite ion sizes, which is closely related to selectivity phenomena of open ion channels with given protein structures. Furthermore, we are able to characterize the distinct effects of the nonlinear interplays between physical parameters, such as ion sizes, diffusion coefficients, boundary concentrations and boundary potentials. This is the novelty of our work. We believe this work will be useful for future numerical studies and stimulate further analytical studies of ionic flows concerning the selectivity of cations.