Electrokinetic membrane processes in relation to properties excitable tissues. II. Some theoretical considerations

A quantitative theory is presented for the behavior of a membrane-electrolyte system subject to an electric current flow (the "membrane oscillator"). If the membrane is porous, carries "fixed charges," and separates electrolyte solutions of different conductances, it can be the site of repetitive oscillatory changes in the membrane potential, the membrane resistance, and the hydrostatic pressure difference across the membrane. These events are accompanied by a pulsating transport of bulk solutions. The theory assumes the superposition of electrochemical and hydrostatic gradients and centers round the kinetics of resistance changes within the membrane, as caused by effects from diffusion and electro-osmotic fluid streaming. The results are laid down in a set of five simple, basic expressions, which can be transformed into a pair of non-linear differential equations yielding oscillatory solutions. A graphical integration method is also outlined (Appendix II). The agreement between the theory and previous experimental observations is satisfactory. The applied electrokinetic concepts may have importance in relation to analyses of the behavior of living excitable cells or tissues.