Deterministic model of ion channel flipping with fractal scaling of kinetic rates.

Abstract

The flipping of ion channels in biological membranes has usually been modeled in terms of Markov transitions between open and closed states. The basic assumption of this approach is that channel flipping between open and closed states is an inherent stochastic process, due to random thermal fluctuations of units forming the channel protein. In this paper, we propose a different view of channel flipping, one not involving external stochastic causes. We consider the channel as a physical dynamic system, the unpredictable flipping of which is due to a deterministic mechanism which sustains a chaotic dynamics. In particular, we presume the changes in the channel conformation are due to delayed interaction between the ionic flow through the channel and the protein forming the channel. The model proposed here describes the channel by means of macroscopic physical quantities such as conductance, current, membrane, and reversal potentials and predicts open and closed dwell time distributions consisting of multiple exponential components and exhibiting power-law scaling over a wide range of time scales. The effective kinetic rate computed through use of simulation data shows fractal properties in good agreement with those seen experimentally. This mathematical model of the ion channel is physically consistent in terms of a plausible real system and may provide a novel key to understanding the complex behavior of the flipping process.