Energetics of ion competition in the DEKA selectivity filter of neuronal sodium channels

The energetics of ionic selectivity in the neuronal sodium channels is studied. A simple model constructed for the selectivity filter of the channel is used. The selectivity filter of this channel type contains aspartate (D), glutamate (E), lysine (K), and alanine (A) residues (the DEKA locus). We use Grand Canonical Monte Carlo simulations to compute equilibrium binding selectivity in the selectivity filter and to obtain various terms of the excess chemical potential from a particle insertion procedure based on Widom's method. We show that K$^{+}$ ions in competition with Na$^{+}$ are efficiently excluded from the selectivity filter due to entropic hard sphere exclusion. The dielectric constant of protein has no effect on this selectivity. Ca$^{2+}$ ions, on the other hand, are excluded from the filter due to a free energetic penalty which is enhanced by the low dielectric constant of protein.Comment: 14 pages, 7 figure

Monte Carlo study of gating and selection in potassium channels

The study of selection and gating in potassium channels is a very important issue in modern biology. Indeed such structures are known in all types of cells in all organisms where they play many important functional roles. The mechanism of gating and selection of ionic species is not clearly understood. In this paper we study a model in which gating is obtained via an affinity-switching selectivity filter. We discuss the dependence of selectivity and efficiency on the cytosolic ionic concentration and on the typical pore open state duration. We demonstrate that a simple modification of the way in which the selectivity filter is modeled yields larger channel efficiency

Model Channel Ion Currents in NaCl - SPC/E Solution with Applied-Field Molecular Dynamics

Using periodic boundary conditions and a constant applied field, we have simulated current flow through an 8.125 Angstrom internal diameter, rigid, atomistic channel with polar walls in a rigid membrane using explicit ions and SPC/E water. Channel and bath currents were computed from ten 10-ns trajectories for each of 10 different conditions of concentration and applied voltage. An electric field was applied uniformly throughout the system to all mobile atoms. On average, the resultant net electric field falls primarily across the membrane channel, as expected for two conductive baths separated by a membrane capacitance. The channel is rarely occupied by more than one ion. Current-voltage relations are concentration-dependent and superlinear at high concentrations.Comment: Accepted for publication in Biophysical Journa

Controlling ion transport through nanopores: modeling transistor behavior

We present a modeling study of a nanopore-based transistor computed by a mean-field continuum theory (Poisson-Nernst-Planck, PNP) and a hybrid method including particle simulation (Local Equilibrium Monte Carlo, LEMC) that is able to take ionic correlations into account including finite size of ions. The model is composed of three regions along the pore axis with the left and right regions determining the ionic species that is the main charge carrier, and the central region tuning the concentration of that species and, thus, the current flowing through the nanopore. We consider a model of small dimensions with the pore radius comparable to the Debye-screening length ($R_{\mathrm{pore}}/\lambda_{\mathrm{D}}\approx 1$), which, together with large surface charges provides a mechanism for creating depletion zones and, thus, controlling ionic current through the device. We report scaling behavior of the device as a function the $R_{\mathrm{pore}}/\lambda_{\mathrm{D}}$ parameter. Qualitative agreement between PNP and LEMC results indicates that mean-field electrostatic effects determine device behavior to the first order

The Role of the Dielectric Barrier in Narrow Biological Channels: a Novel Composite Approach to Modeling Single-channel Currents

A composite continuum theory for calculating ion current through a protein channel of known structure is proposed, which incorporates information about the channel dynamics. The approach is utilized to predict current through the Gramicidin A ion channel, a narrow pore in which the applicability of conventional continuum theories is questionable. The proposed approach utilizes a modified version of Poisson-Nernst-Planck (PNP) theory, termed Potential-of-Mean-Force-Poisson-Nernst-Planck theory (PMFPNP), to compute ion currents. As in standard PNP, ion permeation is modeled as a continuum drift-diffusion process in a self-consistent electrostatic potential. In PMFPNP, however, information about the dynamic relaxation of the protein and the surrounding medium is incorporated into the model of ion permeation by including the free energy of inserting a single ion into the channel, i.e., the potential of mean force along the permeation pathway. In this way the dynamic flexibility of the channel environment is approximately accounted for. The PMF profile of the ion along the Gramicidin A channel is obtained by combining an equilibrium molecular dynamics (MD) simulation that samples dynamic protein configurations when an ion resides at a particular location in the channel with a continuum electrostatics calculation of the free energy. The diffusion coefficient of a potassium ion within the channel is also calculated using the MD trajectory. Therefore, except for a reasonable choice of dielectric constants, no direct fitting parameters enter into this model. The results of our study reveal that the channel response to the permeating ion produces significant electrostatic stabilization of the ion inside the channel. The dielectric self-energy of the ion remains essentially unchanged in the course of the MD simulation, indicating that no substantial changes in the protein geometry occur as the ion passes through it. Also, the model accounts for the experimentally observed saturation of ion current with increase of the electrolyte concentration, in contrast to the predictions of standard PNP theory

A model for enhanced and selective transport through biological membranes with alternating pores

We investigate the outflux of ions through the channels in a cell membrane. The channels undergo an open/close cycle according to a periodic schedule. Our study is based both on theoretical considerations relying on homogenization theory, and on Monte Carlo numerical simulations. We examine the onset of a limiting boundary behavior characterized by a constant ratio between the outflux and the local density, in the thermodynamics limit. The focus here is on the issue of selectivity, that is on the different behavior of the ion currents through the channel in the cases of the selected and non-selected species.Comment: arXiv admin note: text overlap with arXiv:1307.418