Liu Y, Dilger J P
Department of Anesthesiology, State University of New York, Stony Brook 11794-8480.
Biophys J. 1993 Jan;64(1):26-35. doi: 10.1016/S0006-3495(93)81337-7.
The Ising model of statistical physics provides a framework for studying systems of protomers in which nearest neighbors interact with each other. In this article, the Ising model is applied to the study of cooperative phenomena between ligand-gated ion channels. Expressions for the mean open channel probability, rho o, and the variance, sigma 2, are derived from the grand partition function. In the one-dimensional Ising model, interactions between neighboring open channels give rise to a sigmoidal rho o versus concentration curve and a nonquadratic relationship between sigma 2 and rho o. Positive cooperativity increases the slope at the midpoint of the rho o versus concentration curve, shifts the apparent binding affinity to lower concentrations, and increases the variance for a given rho o. Negative cooperativity has the opposite effects. Strong negative cooperativity results in a bimodal sigma 2 versus rho o curve. The slope of the rho o versus concentration curve increases linearly with the number of binding sites on a protomer, but the sigma 2 versus rho o relationship is independent of the number of ligand binding sites. Thus, the sigma 2 versus rho o curve provides unambiguous information about channel interactions. In the two-dimensional Ising model, rho o and sigma 2 are calculated numerically from a series expansion of the grand partition function appropriate for weak interactions. Virtually all of the features exhibited by the one-dimensional model are qualitatively present in the two-dimensional model. These models are also applicable to voltage-gated ion channels.
统计物理学中的伊辛模型提供了一个研究原体系统的框架，其中最近邻之间相互作用。在本文中，伊辛模型被应用于研究配体门控离子通道之间的协同现象。平均开放通道概率ρo和方差σ2的表达式是从巨配分函数推导出来的。在一维伊辛模型中，相邻开放通道之间的相互作用产生了一条S形的ρo与浓度曲线，以及σ2与ρo之间的非二次关系。正协同性增加了ρo与浓度曲线中点处的斜率，将表观结合亲和力转移到较低浓度，并在给定的ρo下增加方差。负协同性则产生相反的效果。强负协同性导致σ2与ρo曲线呈双峰状。ρo与浓度曲线的斜率随原体上结合位点的数量线性增加，但σ2与ρo的关系与配体结合位点的数量无关。因此，σ2与ρo曲线提供了关于通道相互作用的明确信息。在二维伊辛模型中，ρo和σ2是根据适用于弱相互作用的巨配分函数的级数展开式数值计算得到的。一维模型所展示的几乎所有特征在二维模型中都定性地存在。这些模型也适用于电压门控离子通道。
