Ball F G, Yeo G F, Milne R K, Edeson R O, Madsen B W, Sansom M S
Department of Mathematics, University of Nottingham, United Kingdom.
Biophys J. 1993 Feb;64(2):357-74. doi: 10.1016/S0006-3495(93)81375-4.
We present a general theoretical framework, incorporating both aggregation of states into classes and time interval omission, for stochastic modeling of the dynamic aspects of single channel behavior. Our semi-Markov models subsume the standard continuous-time Markov models, diffusion models and fractal models. In particular our models allow for quite general distributions of state sojourn times and arbitrary correlations between successive sojourn times. Another key feature is the invariance of our framework with respect to time interval omission: that is, properties of the aggregated process incorporating time interval omission can be derived directly from corresponding properties of the process without it. Even in the special case when the underlying process is Markov, this leads to considerable clarification of the effects of time interval omission. Among the properties considered are equilibrium behavior, sojourn time distributions and their moments, and auto-correlation and cross-correlation functions. The theory is motivated by ion channel mechanisms drawn from the literature, and illustrated by numerical examples based on these.
我们提出了一个通用的理论框架，该框架将状态聚合到类别以及时间间隔省略相结合，用于单通道行为动态方面的随机建模。我们的半马尔可夫模型包含标准的连续时间马尔可夫模型、扩散模型和分形模型。特别地，我们的模型允许状态停留时间有相当一般的分布以及连续停留时间之间有任意相关性。另一个关键特性是我们的框架相对于时间间隔省略的不变性：也就是说，包含时间间隔省略的聚合过程的性质可以直接从没有时间间隔省略的过程的相应性质推导出来。即使在基础过程是马尔可夫的特殊情况下，这也能极大地阐明时间间隔省略的影响。所考虑的性质包括平衡行为、停留时间分布及其矩，以及自相关和互相关函数。该理论的动机来自文献中的离子通道机制，并通过基于这些机制的数值示例进行说明。
