Deterministic modeling of single-channel and whole-cell currents

•A chaotic deterministic model was validated as an alternative to Markov models of ionic channels.•The proposed model reproduces key features of experimental recordings.•Deterministic whole-cell currents reproduced the experimental responses.•Overall, a methodology for developing deterministic models of single-channels was proposed. As a complement to the experimental work, mathematical models are extensively used to study the functional properties of ionic channels. Even though it is generally assumed that the gating of ionic channels is a Markovian phenomenon, reports based on non-traditional analyses of experimental recordings suggest that non-Markovian processes might be also present. While the stochastic Markov models are by far the most adopted approach for the modeling of ionic channels, a model based on the idea of a deterministic process underlying the gating of ionic channels was proposed by Liebovitch and Toth (Liebovitch, L.S. and Toth, T.I., 1991. Journal of Theoretical Biology, 148(2), pp.243–267.) Here, by using a voltage-dependent K+ channel as a first approximation, we propose a modified version of the deterministic model of Liebovitch and Toth that, in addition to reproducing the single-channel currents simulated by a two-states Markov model, it is capable of reproducing the whole-cell currents produced by a population of K+ channels.