Investigation of Continuum Approaches to Modelling of Membrane Channels |
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Principal InvestigatorSerdar KuyucakResearch School of Physical Sciences and Engineering Co-InvestigatorsShin-Ho ChungDepartment of Chemistry Faculty of Science Ben CorryDepartment of Chemistry Faculty of Science Projectsx15, r53 - VPP |
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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. |
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- Appendix A |
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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. |
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Appendix A - |
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