Use of the boundary element method in electrostatic modeling of the interaction between two blockers in sodium ion channels

The presence of positively-charged DEA molecules in the solution bathing the intracellular side of a sodium channel in a lipid bilayer, blocks the current through the channel. This blocking is inhibited by adding the positively-charged μ-conotoxin GIIIA derivative, R13Q, to the extracellular solution. The hypothesis that this inhibitory effect can be explained by electrostatic repulsion between two molecules is tested in this thesis.; For this purpose, the potential inside the channel due to the toxin molecule was calculated. Calculations were performed using a cylindrical geometry for the channel and spherical model of the R13Q-molecule under the mean field approximation for ionic solution. The Boundary Element Method was chosen, as it is more efficient for this problem then the typical finite difference methods. To implement the method, a program was written and tested on a variety of simple geometries.; Experiment shows that the probability for the DEA to be unbound increases when R13Q is bound at the extracellular end of the channel. Based on the experimental data and our calculated potential, an estimate of the position DEA adsorption site in the channel was obtained. This estimate is in reasonable agreement with the present understanding of the sodium channel structure, demonstrating that the method produces plausible results.