A model of ion channel kinetics using deterministic chaotic rather than stochastic processes

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.