Tanaka S, Scheraga H A
Macromolecules. 1976 Jan-Feb;9(1):159-67. doi: 10.1021/ma60049a027.
A one-dimensional three-state Ising model [involving alpha-helical (alpha), extended (epsilon), and coil (or other) (c) states] for specific-sequence copolymers of amino acids ahs been formulated in order to treat the conformational states of proteins. This model involves four parameters (wh,iota, vh, iota, v episilon, iota, and uc, iota), and requires a 4 X 4 matrix for generating statistical weights. Some problems in applying this model to a specific-sequence copolymer of amino acids are discussed. A nearest-neighbor approximation for treating this three-state model is also formulated; it requires a 3 X 3 matrix, in which the same four parameters appear, but (as with the 4 X 4 matrix treatment) only three parameters (wh, uh, and v epsilon) are required if relative statistical weights are used. The relationship between the present three-state model (3 X 3 matrix treatment) and models of the helix--coil transition is discussed. Then, the three-state model (3 X 3 matrix treatment) is incorporated into an earlier (Tanaka--Scheraga) model of the helix-coil transition, in which asymmetric nucleation of helical sequences is taken into account. A method for calculating molecular averages and conformational-sequence probabilities, P(iota/eta/(rho)), i.e., the probability of finding a sequence of eta residues in a specific conformational state (rho), starting at the iotath position of the chain, is described. Two alternative methods for calculating P(iota/eta/(rho)), that can be applied to a model involving any number of states, are proposed and presented; one is the direct matrix-multiplication method, and the other uses a first-order a priori probability and a conditional probability. In this paper, these calculations are performed with the nearest-neighbor model, and without the feature of asymmetric nucleation. Finally, it is indicated how the three-state model and the methods for computing P(iota/eta/(rho)) can be applied to predict protein conformation.
为了处理蛋白质的构象状态，已经构建了一种用于氨基酸特定序列共聚物的一维三态伊辛模型（涉及α-螺旋（α）、伸展（ε）和卷曲（或其他）（c）状态）。该模型包含四个参数（wh,iota, vh, iota, v episilon, iota, 和uc, iota），并且需要一个4×4矩阵来生成统计权重。讨论了将该模型应用于氨基酸特定序列共聚物时的一些问题。还构建了一种用于处理此三态模型的最近邻近似；它需要一个3×3矩阵，其中出现相同的四个参数，但是（与4×4矩阵处理一样）如果使用相对统计权重，则仅需要三个参数（wh, uh, 和v epsilon）。讨论了当前三态模型（3×3矩阵处理）与螺旋-卷曲转变模型之间的关系。然后，将三态模型（3×3矩阵处理）纳入早期（田中-谢拉加）螺旋-卷曲转变模型，其中考虑了螺旋序列的不对称成核。描述了一种计算分子平均值和构象-序列概率P(iota/eta/(rho))的方法，即从链上的iotath位置开始，在特定构象状态（rho）中找到eta个残基序列的概率。提出并给出了两种可用于涉及任意数量状态的模型的计算P(iota/eta/(rho))的替代方法；一种是直接矩阵乘法方法，另一种使用一阶先验概率和条件概率。在本文中，这些计算是使用最近邻模型进行的，并且没有不对称成核的特征。最后，指出了三态模型和计算P(iota/eta/(rho))的方法如何可用于预测蛋白质构象。
