Investigation of Continuum Approaches to Modelling of Membrane Channels

Understanding stucture and function of ion channels in membranes is one of the major problems in contemporary biophysics. During the last two decades, advances in experimental techniques have enabled accurate measurement of small channel currents, which are of the order of picoAmpere. Most recently, the crystal structure of a potassium channel has been determined from x-ray analysis for the first time. It is expected that similar techniques will be employed to reveal the structure of other channels. Thus the time is ripe for sophisticated modeling of channels so as to provide rigorous answers to some basic questions about ion channels such as their level of conductivity and its saturation with increasing concentration, and their selectivity towards a particular ion species. The simplest permeation models one can use for this purpose are the continuum theories based on the Nernst-Planck electro-diffusion equation. The project aims to address the validity of continuum theories in narrow pores and whether they can be used in studies of ion channels.

Principal Investigator

Serdar Kuyucak
Theoretical Physics


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Facilities Used



Shin-Ho Chung
Ben Corry
Scott Edwards
Faculty of Science

RFCD Codes


Significant Achievements, Anticipated Outcomes and Future Work

So far, most of the theoretical work on modeling of ion channels is based on methods borrowed from physical chemistry. For studies of ion conductivity, these range from the phenomenological reaction rate theories to solutions of the Poisson-Nernst-Planck equations. Similarly, the Poisson-Boltzman equation is routinely used to determine the electrostatic potential in channel studies. The radius of ion channels varies from a few angstroms in the narrow part to 10-15 A in the mouth region. In a similar vein, the number of ions inside the channel volume at a given time is at most a few. Intuitively, one would expect the continuum approaches to break down under these conditions, and one should ideally use microscopic approaches such as Brownian dynamics and molecular dynamics. While the use of continuum techniques could have been justified a decade ago (because there was no computationally feasible alternative), with the current speed of computers this is no longer a valid excuse.

This project provides a systematic comparison of the continuum and microscopic approaches to ion channels, establishing the region of validity for the former. Typical channel shapes are parametrised with a radius, and the predictions of the Poisson-Nernst-Planck and Brownian dynamics approaches for the conductivity are compared as a function of this radius. It is found that the continuum model results deviate significantly from those of the Brownian dynamics at small radii (2-5 A), and an agreement is recovered only when the radius is greater than two Debye lengths (16 A for a 150 mM solution). The detailed comparisons of the two theories show that macroscopic concepts such as shielding in fact play a much smaller role in a realistic channel environment than assumed in continuum models.


Computational Techniques Used

Two algorithms used in the project involve solutions of the Poisson and Langevin equations. The first is achieved using a boundary element method and the second involves numerical integration of a second order stochastic differential equation. Both programs are about 90% vectorized and have been succesfully implemented on the VPP. We have already used these codes in several Brownian dynamics investigations of membrane channels, to which we refer for details on the computation of the electric fields and the implemetation of the Brownian dynamics algorithm (see the contributions by S.H. Chung). Computation of the electrostatic forces in arbitrary channel geometries and running of the Brownian dynamics code are CPU intensive jobs and require the use of a supercomputer.


Publications, Awards and External Funding

B. Corry, S. Kuyucak, S. H. Chung, Test of Poisson-Nernst-Planck theory in ion channels, J. Gen. Physiol. 114, 1999, 597-599.

B. Corry, S. Kuyucak, S. H. Chung, Invalidity of continuum theories of electrolytes in nanopores, Chem. Phys. Lett. 320, 2000, 35-41.

G. Moy, B. Corry, S. Kuyucak, S. H. Chung, Tests of continuum theories as models of ion channels: I. Poisson-Boltzmann theory versus Brownian dynamics, Biophys. J. 78, 2000, 2349-2363.

B. Corry, S. Kuyucak, S. H. Chung, Tests of continuum theories as models of ion channels: II. Poisson-Nernst-Planck theory versus Brownian dynamics, Biophys. J. 78, 2000, 2364-2381.