We show that a non-Markovian behavior can appear in a type of Markovian multimeric channels. Such a channel consists of $N_{\thinspace }$independent subunits, and each subunit has at least one open state and more than one closed state. Suppose the open state of the channel is defined as $M$ out of $N$ subunits in the open state with $N $> $M $> 0. We show that, although the gating dynamics for each subunit between open and closed states is Markovian, the channel can appear a memory behavior of weak anti-cross-correlation between the adjacent open and closed durations. Our study indicates that a non-Markovian binary time series can be obtained from a linear superposition of some independent channel subunits with Markovian gating dynamics.

中文翻译：

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马尔可夫通道的相邻打开和关闭持续时间之间的反互相关

我们表明，非马尔可夫行为可以出现在一种马尔可夫多聚体通道中。这样的通道由$ N _ {\ thinspace} $个独立的子单元组成，每个子单元至少具有一个打开状态和一个以上闭合状态。假设通道的打开状态定义为$\mathrm{中号}$ 在......之外 $ñ$$ N $> $ M $> 0时处于打开状态的子单元。我们显示，尽管打开和关闭状态之间每个子单元的门控动力学是马尔可夫关系，但通道之间可能会出现弱反相关的记忆行为。相邻的开放时间和封闭时间。我们的研究表明，可以从一些具有马尔可夫门控动力学的独立通道亚基的线性叠加中获得非马尔可夫二进制时间序列。