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.

作为实验工作的补充，数学模型被广泛用于研究离子通道的功能特性。尽管通常认为离子通道的门控是马尔可夫现象，但基于对实验记录的非传统分析的报告表明，也可能存在非马尔可夫过程。尽管到目前为止，随机马尔可夫模型是最常用的离子通道建模方法，但Liebovitch和Toth（Liebovitch，LS and Toth，TI，Libovitch and Toth）提出了一种基于确定性过程的离子通道门控基础的模型。 1991. Journal of Theoretical Biology，148（2），第243-267页。）在这里，通过使用电压依赖性K ⁺ 作为第一个近似通道，我们提出了Liebovitch和Toth确定性模型的修改版本，该模型除了可以再现由两态马尔可夫模型模拟的单通道电流外，还可以再现所产生的全细胞电流由K人口${}^{+}$ 渠道。