Ionic Currents in a Flat Membrane

The ionic currents passing through the membranes forming the surface of a cell play an important role in the behavior of biological objects. The behavior of a flat membrane in an electrolyte is considered in terms of the electrodiffusion model. It is shown that an instability leading to the development of ionic currents in a cell can emerge under the action of membrane protein density fluctuations, an external potential, or electrolyte ion concentrations. A long-wavelength mode describing the change in electrolyte ion concentrations along the membrane has been found. The instability thresholds have been determined. The influence of membrane surface charges on the instability thresholds has been studied.