Permeation of Ions Through Membrane Channels

Principal Investigator

Shin-Ho Chung

Department of Chemistry

The Faculties

Ion channels are protein complexes found in the membranes of living cells. While they are large proteins, they are still sub-microscopic in size, being around one millionth of a centimetre across. Their function is well understood: ion channels create, amplify and modify electrical signals in living tissue the signals that make nerves and muscles work. They do this by selectively allowing large numbers of inorganic ions(small charged particles) to flow across the cell membrane, which otherwise would be impermeable to ions.

What is not well understood is how ion channels work. The mechanisms of ion channels that need to be explained are those of conductance, selectivity, and gating: their ability to rapidly pass large numbers of ions, their ability to pass only some types of ions while blocking others, and their ability to open in response to electrical or chemical signals, and close a short time later. These are the basic questions our research addresses, and our approach is to use the techniques of computer simulation to build a working model of an ion channel and the water, ions and electric field that surround it.


Matthew Hoyles

Serdar Kuyucak

Department of Theoretical Physics

Research School of Physical Sciences and Engineering


r06 - VPP

What are the results to date and the future of the work?

This year we have made considerable progress towards our goal. We derived analytical solutions of Poisson's equation for the electric field around a dielectric torus; a torus can function as a model of an ion channel since it has a funnel shaped hole in its centre. We developed a computer program to implement these solutions, and later a vectorized version of the program that could run efficiently on the VPP. We also developed a Brownian dynamics program to simulate multiple ions moving in the changing electrical fields around a channel. We used the two programs to investigate the properties of ion channels, producing interesting results and developing new insights in consequence. We are currently preparing three papers based on our work in 1996: one on the analytical solutions, one on the results of the Brownian dynamics simulations, and one on the vectorized algorithm.

The future of the work lies along two paths. The first is continued improvement of the Brownian dynamics simulations, and use of these to investigate channel properties and model possible mechanisms: we have only begun exploring the possibilities created by the use of Brownian dynamics. The second is the use of molecular dynamics. Although simulation of the whole channel via molecular dynamics is impractical due to the small time steps and large number of

particles it involves, there are some questions which Brownian dynamics cannot answer. Molecular dynamics simulations will be needed to investigate the effects of the constricted environment of the channel on dielectric constants and diffusion coefficients. They will also be needed to investigate the mechanisms of selection between ions of different species but the same polarity.

What computational techniques are used?

Our Brownian dynamics program uses the algorithm devised by Gunsteren and Berendsen (Molecular Physics, 1982, 45:637-647). We use reflective boundaries to prevent ions from penetrating the walls of the channel or escaping from the reservoirs at either end. The analytical solutions involve nested infinite series and continued fractions. Our vectorized algorithm evaluates these from the bottom up, truncating after a fixed number of terms. This approach simplifies the algorithm and allows it to be vectorized. The time lost in calculating extra terms is more than compensated for by the increased speed due to vectorization. The new algorithm is around 100 times faster than the numerical method (described in last years report), although the numerical method is more flexible, as it can simulate channels of arbitrary shape, not just toruses.


Hoyles, M., Kuyucak, S., Chung, S.H., Energy Barrier Presented to Ions by the Vestibule of the Biological Membrane Channel, Biophysical Journal, 70, 1996, 1628-1642

- Appendix A