A one-dimensional diffusion-reaction equation for the probability of finding of a random walker (ion) in a space-time domain (protein channel) is proposed to model the process of ionic wave propagation through membranes. The diffusion process stands here for a kind of kinetic hindrance or perturbation because it is assumed to be very slow. The chemical reaction, in turn, proceeds in an usual way rather, but is presumed to be considered in the fractal-like chemical reaction kinetics regime. The damped pendulum theory is effectively applied to get the solution to the problem studied. This solution has been found to reflect the Kohlrausch-Williams-Watts behaviour characteristic of the slow relaxation kinetics, e g. in spin glasses or fragile liquids. As a quite specific result, the Weibull function stated in the work of L.S. Liebovitch and J.M. Sullivan, Biophys.J. 52 (1987) 979- 988, and describing the channel kinetics in cultured mouse hippocampal neurons has been gained.
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