A MATHEMATICAL MODEL FOR CHARGE DISTRIBUTIONS IN EXTERNAL MICRO-ENVIRONMENT OF ION CHANNELS

Abstract

Background: Current in ion channels has been modelled using Hodgkin-Huxley approach for past half century. There are models that are modified versions of Hodgkin-Huxley model but they only take macroscopic properties of current into consideration, thus termed large-scale models. In this paper another approach is used for modelling the immediate environment of ion channels in general and voltage-gated sodium channels in particular. Methods: Model of voltage-gated sodium channels is obtained using molecular dynamic analysis. Geometry of model that is obtained by molecular dynamic analysis is then mathematically approximated for electrical potential. Mathematical model of electric potential is built right from the first principle (i.e., Coulomb’s law). Results: Results show the computational graphing of such model in 3D. R-Minimal<R1<R2<R3<R-Maximal values of radii are plotted. This gives a progressive pattern to ion distribution in the outside environment of the ion channel. The distribution breaks at R-maximal and the ion channel behaves as a point charge at R-minimal. Conclusion: This type of models gives in-depth insight of physiology of the ion channels. This model directly implies and explains the clustering of preferred ions just outside the ion channel.