title: A model of ion channel kinetics using deterministic chaotic rather than stochastic processes.
abstract: Models of ion channel kinetics have previously assumed that the switching between the open and closed states is an intrinsically random process. Here, we present an alternative model based on a deterministic process. This model is a piecewise linear iterated map. We calculate the dwell time distributions, autocorrelation function, and power spectrum of this map. We also explore non-linear generalizations of this map. The chaotic nature of our model implies that its long-term behavior mimics the stochastic properties of a random process. In particular, the linear map produces an exponential probability distribution of dwell times in the open and closed states, the same as that produced by the two-state, closed in equilibrium open, Markov model. We show how deterministic and random models can be distinguished by their different phase space portraits. A test of some experimental data seems to favor the deterministic model, but further experimental evidence is needed for an unequivocal decision.
authors.affiliation: Department of Ophthalmology, Columbia University, College of Physicians and Surgeons, New York 10032.
authors.forename: L S
authors.initials: LS
authors.lastname: Liebovitch
authors.forename: T I
authors.initials: TI
authors.lastname: Toth
mesh_terms: D000818:Animals; D003198:Computer Simulation; D015640:Ion Channel Gating / Q000502:physiology*; D007473:Ion Channels / Q000502:physiology*; D007700:Kinetics; D008433:Mathematics; D008954:Models, Biological; D012964:Sodium / Q000378:metabolism*
chemical_list: D007473:Ion Channels; D012964:Sodium