Investigation of Continuum Approaches to Modelling of Membrane Channels

 
                     

Principal Investigator

Serdar Kuyucak

Research School of Physical Sciences and Engineering

Co-Investigators

Shin-Ho Chung

Department of Chemistry

Faculty of Science

Ben Corry

Department of Chemistry

Faculty of Science

Projects

x15, r53 - VPP

     
Our aim in this project is to assess the suitability of continuum theories as models of ion channels. The central assumption of continuum theories is that individual ions can be replaced by a space-time averaged charge density and the properties of ion channels can be understood by solving the appropriate continuum equations such as Poisson-Boltzmann for static potential and Poisson-Nernst-Planck for diffusion. This assumption can be tested by comparing the predictions of the continuum theories with the microscopic Brownian dynamics simulations where the motion of individual ions are traced.      
                 

       
                 

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

As a first step, we tested the Poisson-Boltzmann (PB) equation for an electrolyte inside a sphere. The force acting on an ion due to the induced surface charges on the boundary is compared with the one obtained from Brownian dynamics (BD) simulations. Agreement is obtained only when the distance of the ion from the surface is larger than the Debye length. As the ion gets nearer the surface, the deviation between the PB and BD results increases, with PB always underestimating the force. This failure of the PB approach is due to the shielding effect being overestimated in the continuum theories. In subsequent work, we plan to generalize this finding to geometries that are more appropriate for channels, such as cylinders with and without vestibules at either end.
In a parallel development, we tested the Poisson-Nernst-Planck (PNP) equation by comparing the diffusion results for ions in a cylindrical channel with those obtained from the BD simulations. Again, the conductance results obtained in the two approaches agree only when the channel radius is larger than the Debye length. At 3-4 Angstrom radii, typically used in the applications of the PNP to ion channels, the conductance obtained in BD is an order of magnitude smaller than PNP. The failure of PNP approach is again due to overestimation of the shielding, which cancels the barrier due to the image forces. In future, these results will be generalized to more realistic channel geometries, and this will also require solving PNP equations in such geometries which is currently not available.

 
                     
- Appendix A
 

   
 

       

 

 

 

 

 

 

 

 

 

 

 

 

What computational techniques are used?

The Brownian dynamics program uses the Verlet algorithm in solving the Langevin equation for ions moving in water enclosed by a dielectric boundary. The electric forces are initially calculated by solving Posisson's equation on a grid and stored in a lookup table. The forces acting on ions at each time step are extrapolated from the table entries. The program is about 90% vectorized and ideally suited to run on VPP.

       
Appendix A -