An interactive two-state model for cell membrane potassium and sodium ion channels in electric fields using the pair approximation

An interactive two-state model for cell membrane potassium and sodium ion channels in the presence of electric fields is proposed and studied using the pair approximation. In the model, ion channels which can either be in an open or closed states are regarded as residing on a two-dimensional surface with a regular array of sites and the interactions between the neighbouring channels and the external electric field are incorporated. The minimization of the free energy is performed with respect to the pair or bond variables and maximum fractions of open potassium and sodium channels are obtained. Using known parameters for the squid giant axon the model gives qualitative agreement with the mean-field results and experimental measurements for potassium and sodium trans-membrane conductance.