Workshop on Ion Channels, Wed, 10 Oct, 2007
Speaker: Dmitry Karpeev
Abstract
Singular perturbation theory of a coupled ion channel-baths system based on the continuum Poisson-Nernst-Planck (PNP) equations predicts ion concentration layers near the openings of the channel. These layers effectively match the channel to the nearly homogeneous concentrations in the baths controlled by the boundary conditions. How essential are these spatial structures to the correct response of the channel to the macroscopic boundary conditions? In particular, how are the predicted current-voltage (I-V) characteristics of the channel affected by varying the models of the channel with different spatial resolution capabilities?
We study these questions in the context of particle-based stochastic models of the permeation of the channel by ions. These models, Brownian Dynamics (BD) and Transport Monte-Carlo (TMC) treat ions at the atomic level and are frequently considered necessary to capture the important structural details of the channel. They are coupled to the baths described by BD/TMC or by reduced continuum models such as PNP, or even cruder circuit models such as a resistor with a battery. In what essentially amounts to a sensitivity study, we consider the simultaneous effects of the bath model on the I-V characteristics of the channel and the spatial structure of ion concentrations near its openings.
Channels often operate within a few Debye lengths of other channels densely packed into a cell membrane and are bounded by highly heterogeneous ionic environments. Therefore it has been suggested that channels evolved to desensitize themselves to variations in the bath ionic concentration profiles. We study this hypothesis under different physiological conditions.
The immediate question is whether it is possible to replace a full (in atomistic fidelity and spatial extent) bath model with a coarse-grained homogeneous representation coupled to the channel through appropriate boundary conditions. In particular, we address the questions of spurious numerical boundary layers that are well-known to exist in coupling uncharged particle simulations to controls implementing macroscopic boundary conditions.
The study is largely numerical, but it relies on existing theoretical results and suggests further theoretical studies of stochastic-continuum model coupling and model reduction for charged systems charged particles in confined geometries.
URL: www.ricam.oeaw.ac.at/specsem/ssqbm/participants/abstracts/index.php
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