Ferroelectric diffused electrical bilayer model for membrane excitation

The gating mechanism of localized ion-conducting pores or channels in excitable membranes is discussed based on the ferroelectric model hypothesized by Leuchtag, and excitation is analyzed by a diffused electrical bilayer model. By the application of a self-organized chemical model to such membranes, which have ferroelectric transmembrane units, the membrane potential in ionic circumstances of aqueous electrolytic media is described by a nonlinear equation derived from a phenomenological function for a parameter that characterizes a phase transition of the membranes. The excitation appears with a jump in the potential at one of the points on the bifurcation sets at which the discriminant of the equation equals zero; the point represents the reaction threshold. Because the membrane potential is controlled by two variables (control parameters) in the nonlinear state equation, the jump is cusp catastrophic. The potential of a few types of membranes has been calculated by assuming suitable functions for these parameters semiempirically.

Keywords:

• membrane excitation
• Na+ channel
• ferroelectricity
• phase transition
• catastrophe