Mathematical model of electrogenic transport through biomembranes via oligomeric channels capable of conformational transitions

A mathematical model of electrogenic ion transport across biomembranes by oligomeric channels liable to conformational transformations has been derived. The model describes changes with time of the membrane potential and near--membrane ion concentrations. Different types of the channel conductance regulation such as activation or inhibition by the permeating ions and membrane potential have been considered. It appears that in the presence of such regulations 1) the channel voltage-current curves have negative resistance regions; 2) the dependence of the quasisteady state (or resting) potential on the ion concentrations in the solution is of hysteresis nature; 3) the model may have multiple steady-state and oscillating solutions.