Na+ permeation through its protein channels, from molecular dynamics to continuum modeling

Researchers can reach important information about cell cycles such as migration, growth and muscle contraction, by studying the change of ion concentrations in animal cells. In the current work we have proposed three dierent techniques to study the passive ions motion in protein channels on dierent time scales. Molecular dynamics, Langevin dynamics and continuum models of mass transport are used to investigate ion transport from small to large time scales. We have used molecular dynamics to compute diusivity and potential of mean force prole of NA+transport across its protein channel. The diusivity and potential of mean force of NA+ in this condition was 1.06 A2/ns and 18 kcal/mol, respectively. Then diusivity and potential of mean force prole of NA+ calculated from molecular dynamics simulation is incorporated in Langevin dynamics equation of motion to study NA+ transport across a group of channels working in parallel. Our results show that ion concentration distribution in the membrane protein channel is close to the phase-lagging model prediction. The achieved shock propagation speed in NA+ channel is v = 1:2 nm/ns and indicates that an inherent lag exists in the biological systems. The proposed method can be used in multiscale modeling of NA+ diusion across cell membranes.