Computational Study of Ion Conductance in the KcsA K⁺ Channel Using a Nernst-Planck Model with Explicit Resident Ions

In this dissertation, we describe the biophysical mechanisms underlying the relationship between the structure and function of the KcsA K+ channel. Because of the conciseness of electro-diffusion theory and the computational advantages of a continuum approach, Nernst-Planck (NP) type models such as the Goldman-Hodgkin-Katz (GHK) and Poisson-Nernst-Planck (PNP) models have been used to describe currents in ion channels. However, the standard PNP (SPNP) model is known to be inapplicable to narrow ion channels because it cannot handle discrete ion properties. To overcome this weakness, we formulated the explicit resident ions Nernst-Planck (ERINP) model, which applies a local explicit model where the continuum model fails. Then we tested the effects of the ERI Coulomb potential, the ERI induced potential, and the ERI dielectric constant for ion conductance were tested in the ERINP model. Using the current-voltage (I-V ) and current-concentration (I-C) relationships determined from the ERINP model, we discovered biologically significant information that is unobtainable from the traditional continuum model. The mathematical analysis of the K+ ion dynamics revealed a tight structure-function system with a shallow well, a deep well, and two K+ ions resident in the selectivity filter. We also demonstrated that the ERINP model not only reproduced the experimental results with a realistic set of parameters, it also reduced CPU costs.