Shelley Christopher, Magleby Karl L
Department of Physiology and Biophysics and the Neuroscience Program, University of Miami, Miller School of Medicine, Miami, FL 33136, USA.
J Gen Physiol. 2008 Aug;132(2):295-312. doi: 10.1085/jgp.200810008. Epub 2008 Jul 14.
Discrete state Markov models have proven useful for describing the gating of single ion channels. Such models predict that the dwell-time distributions of open and closed interval durations are described by mixtures of exponential components, with the number of exponential components equal to the number of states in the kinetic gating mechanism. Although the exponential components are readily calculated (Colquhoun and Hawkes, 1982, Phil. Trans. R. Soc. Lond. B. 300:1-59), there is little practical understanding of the relationship between components and states, as every rate constant in the gating mechanism contributes to each exponential component. We now resolve this problem for simple models. As a tutorial we first illustrate how the dwell-time distribution of all closed intervals arises from the sum of constituent distributions, each arising from a specific gating sequence. The contribution of constituent distributions to the exponential components is then determined, giving the relationship between components and states. Finally, the relationship between components and states is quantified by defining and calculating the linkage of components to states. The relationship between components and states is found to be both intuitive and paradoxical, depending on the ratios of the state lifetimes. Nevertheless, both the intuitive and paradoxical observations can be described within a consistent framework. The approach used here allows the exponential components to be interpreted in terms of underlying states for all possible values of the rate constants, something not previously possible.
离散状态马尔可夫模型已被证明在描述单离子通道的门控方面很有用。这类模型预测，开放和关闭间隔持续时间的驻留时间分布由指数成分的混合来描述，指数成分的数量等于动力学门控机制中的状态数量。尽管指数成分很容易计算（科尔库洪和霍克斯，1982年，《英国皇家学会哲学学报》B辑300:1 - 59），但对于成分与状态之间的关系却缺乏实际的理解，因为门控机制中的每个速率常数都会对每个指数成分产生影响。我们现在为简单模型解决了这个问题。作为一个教程，我们首先说明所有关闭间隔的驻留时间分布是如何由组成分布的总和产生的，每个组成分布都来自特定的门控序列。然后确定组成分布对指数成分的贡献，从而得出成分与状态之间的关系。最后通过定义和计算成分与状态的联系来量化成分与状态之间的关系。发现成分与状态之间的关系既直观又自相矛盾，这取决于状态寿命的比率。然而，直观和自相矛盾的观察结果都可以在一个一致的框架内进行描述。这里使用的方法允许根据速率常数的所有可能值，从潜在状态的角度来解释指数成分，这是以前无法做到的。
