Using fractals and nonlinear dynamics to determine the physical properties of ion channel proteins

Three examples are given of how concepts from fractals and nonlinear dynamics have been used to analyze the voltages and currents recorded through ion channels in an attempt to determine the physical properties of ion channel proteins. (1) Early models had assumed that the switching of the ion channel protein from one conformational state to another can be represented by a Markov process that has no long-term correlations. However, one support for the existence of long-term correlations in channel function is that the currents recorded through individual ion channels have self-similar properties. These fractal properties can be characterized by a scaling function determined from the distribution of open and closed time intervals, which provides information on the distribution of activation energy barriers between the open and closed conformational substates of the ion channel protein and/or on how those energy barriers change in time. (2) Another support for such long-term correlations is that the whole-cell membrane voltage recorded across many channels at once may also have a fractal form. The Hurst rescaled range analysis of these fluctuations provides information on the type and degree of correlation in time of the functioning of ion channels. (3) The early models had also assumed that the switching from one state to another is an inherently random process driven by the energy from thermal fluctuations. More recently developed models have shown that deterministic dynamics may also produce the same distributions of open and closed times as those previously attributed to random events. This raises the possibility that the deterministic atomic and electrostatic forces play a role in switching the channel protein from one conformational shape to another. Debate exists about whether random, fractal, or deterministic models best represent the functioning of ion channels. However, fractal and deterministic dynamics provide a new approach to the study of ion channels that should be seriously considered by neuroscientists.