Ion channels are transport proteins present in the lipid bilayers of biological membranes. They are involved in many physiological processes, such as the generation of nerve impulses, hormonal secretion, and heartbeat. Conformational changes in the ion channel-forming protein allow the opening or closing of pores to control the ionic flux through the cell membranes. The opening and closing of the ion channel have been classically treated as a random kinetic process, known as a Markov process. Here the time the channel remains in a given state is assumed to be independent of the condition it had in the previous state. More recently, however, several studies have shown that this process is not random but a deterministic one, where both the open and closed dwell-times and the ionic current flowing through the channel are history-dependent. This property is called long memory or long-range correlation. However, there is still much controversy regarding how this memory originates, which region of the channel is responsible for this property, and which models could best reproduce the memory effect. In this article, we provide a review of what is, where it is, its possible origin, and the mathematical methods used to analyze the long-term memory present in the kinetic process of ion channels.

离子通道是存在于生物膜脂双层中的转运蛋白。它们参与许多生理过程，如神经冲动的产生、激素分泌和心跳。离子通道形成蛋白的构象变化允许孔的打开或关闭以控制通过细胞膜的离子通量。离子通道的打开和关闭经典地被视为随机动力学过程，称为马尔可夫过程。这里假设信道保持在给定状态的时间与其在先前状态中的条件无关。然而，最近的一些研究表明，这个过程不是随机的，而是一个确定性的过程，其中打开和关闭的停留时间以及流经通道的离子电流都与历史相关。此属性称为长记忆或长程相关性。然而，关于这种记忆是如何起源的，通道的哪个区域负责这种特性，以及哪种模型最能再现记忆效应，仍然存在很多争议。在本文中，我们回顾了什么是、它在哪里、它的可能起源，以及用于分析离子通道动力学过程中存在的长期记忆的数学方法。