| Abstract: |
| We study a quasi-one-dimensional Poisson-Nernst-Planck system 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 to account for finite ion size effects. Under the framework of a geometric singular perturbation theory, together with specific structures of this concrete model, the existence of solutions to the boundary value problem for small ion sizes is established. Furthermore, 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 selectivity between two cations due to finite ion sizes for 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. |
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