Liebovitch L S, Todorov A T
Center for Complex Systems, Florida Atlantic University, Boca Raton 33431-0991, USA.
Crit Rev Neurobiol. 1996;10(2):169-87.
Three examples are given of how concepts from fractals and nonlinear dynamics have been used to analyze the voltages and currents recorded through ion channels in an attempt to determine the physical properties of ion channel proteins. (1) Early models had assumed that the switching of the ion channel protein from one conformational state to another can be represented by a Markov process that has no long-term correlations. However, one support for the existence of long-term correlations in channel function is that the currents recorded through individual ion channels have self-similar properties. These fractal properties can be characterized by a scaling function determined from the distribution of open and closed time intervals, which provides information on the distribution of activation energy barriers between the open and closed conformational substates of the ion channel protein and/or on how those energy barriers change in time. (2) Another support for such long-term correlations is that the whole-cell membrane voltage recorded across many channels at once may also have a fractal form. The Hurst rescaled range analysis of these fluctuations provides information on the type and degree of correlation in time of the functioning of ion channels. (3) The early models had also assumed that the switching from one state to another is an inherently random process driven by the energy from thermal fluctuations. More recently developed models have shown that deterministic dynamics may also produce the same distributions of open and closed times as those previously attributed to random events. This raises the possibility that the deterministic atomic and electrostatic forces play a role in switching the channel protein from one conformational shape to another. Debate exists about whether random, fractal, or deterministic models best represent the functioning of ion channels. However, fractal and deterministic dynamics provide a new approach to the study of ion channels that should be seriously considered by neuroscientists.
文中给出了三个例子，说明分形和非线性动力学中的概念是如何用于分析通过离子通道记录的电压和电流，以试图确定离子通道蛋白的物理性质。（1）早期模型假设离子通道蛋白从一种构象状态转变为另一种构象状态可以用一个没有长期相关性的马尔可夫过程来表示。然而，通道功能中存在长期相关性的一个证据是，通过单个离子通道记录的电流具有自相似特性。这些分形特性可以通过一个由开放和关闭时间间隔的分布确定的标度函数来表征，该函数提供了关于离子通道蛋白开放和关闭构象亚状态之间活化能垒分布的信息，和/或关于这些能垒如何随时间变化的信息。（2）这种长期相关性的另一个证据是，同时在许多通道上记录的全细胞膜电压也可能具有分形形式。对这些波动的赫斯特重标极差分析提供了关于离子通道功能随时间的相关类型和程度的信息。（3）早期模型还假设从一种状态到另一种状态的转变是由热涨落能量驱动的固有随机过程。最近发展的模型表明，确定性动力学也可能产生与先前归因于随机事件的开放和关闭时间相同的分布。这就增加了确定性原子力和静电力在将通道蛋白从一种构象形状转变为另一种构象形状中起作用的可能性。关于随机、分形或确定性模型是否最能代表离子通道的功能存在争议。然而，分形和确定性动力学为离子通道的研究提供了一种新方法，神经科学家应予以认真考虑。
