Extension of Poisson-Nernst Planck Theory of Ion Conductivity with Soft-Repulsion Potential between Ions and Protein. Sensitivity of I-V Properties of α-Hemolysin Channel on its Penetration Depth into Membrane

Abstract

A soft repulsion (SR) potential between mobile ions and protein atoms is introduced to Poisson-Nernst-Plank (PNP) theory of ion transport as an alternative to commonly used hard sphere repulsion (HR). Two sets of SR were tested: one is parameterized for all atoms of 20 essential amino-acid residues using full atomic molecular dynamic simulation (SR-MD); and another is a truncated Lennard-Jones potential (SR-LJ). The effect of different models of short-range interaction between protein atoms and mobile ions (HR, SR-MD and SR-LJ) were studied using α-hemolysin channel protein. In addition, four different methods of setting the diffusion coefficients were analyzed in order to evaluate the effect of diffusion distribution on predicted currents. Our calculations show that the diffusion distribution has a strong influence on the size of total currents whereas has significantly less effect on rectifications, reverse potentials and selectivity. Therefore, for proper modeling of these properties, the potential of mean force (PMF) may play a more important role than the diffusion distribution. SR-MD has a better approximation of PMF near the protein surface than HR and significantly improves selectivity predictions. Additionally, we have studied the dependency of α-hemolysin I-V properties on the penetration depth of the channel into the membrane. The results show that rectification and reverse potentials are very sensitive to the penetration depth. The depth, predicted by matching calculated rectification with the experimentally determined one, is in a very good agreement with the neutron reflection experimental result. Our free energy estimation also indicates that there is a minima near the predicted depth.