Tanaka S, Scheraga H A
Macromolecules. 1975 Jul-Aug;8(4):494-503. doi: 10.1021/ma60046a023.
The states of three residues are correlated in a nearest-neighbor Ising model matrix treatment of a one-dimensional phase transition, in which nucleation is assumed to differ at each end of a regular sequence (asymmetric nucleation). The correlation of the states of three residues requires a 4 X 4 matrix, which cannot be reduced in size because of the asymmetric nature of the nucleation. Also, because of the asymmetry, at least four independent parameters for a homopolymer (rather than the two usually encountered in the helix-coil transition), ant at least five for a specific-sequence copolymer, are required to describe the transition behavior. The most important current interest in such a treatment (for a homopolymer) is its applicability to the poly(L-proline) form I in equilibrium form II interconversion. The earlier treatment of Schwarz, using the nearest-neighbor Ising model (with correlation of only two residues), is identical with the above treatment, and requires only a 2 X 2 matrix which greatly simplifies numerical computations, which are presented in the next two papers of this series. However, the 4 X 4 matrix treatment is required in order to make the asymmetric nature of the nucleation explicit and physically understandable, for a homopolymer; for a specific-sequence copolymer, such as a protein, it is essential in order to show how the asymmetric nature of helix nucleation differs from one amino acid to another.
在一维相变的最近邻伊辛模型矩阵处理中，三个残基的状态是相关的，其中假定在规则序列的两端成核情况不同（不对称成核）。三个残基状态的相关性需要一个4×4矩阵，由于成核的不对称性，其大小无法缩减。此外，由于不对称性，描述均聚物的转变行为需要至少四个独立参数（而非螺旋 - 线团转变中通常遇到的两个），对于特定序列共聚物则至少需要五个。目前对此类处理（针对均聚物）最重要的关注点在于其对聚（L - 脯氨酸）I型与平衡态II型相互转化的适用性。施瓦茨早期使用最近邻伊辛模型（仅两个残基相关）的处理方法与上述处理相同，且仅需要一个2×2矩阵，这极大地简化了数值计算，该计算将在本系列的接下来两篇论文中给出。然而，对于均聚物，为了使成核的不对称性明确且易于理解，需要采用4×4矩阵处理；对于特定序列共聚物，如蛋白质，为了展示螺旋成核的不对称性如何因氨基酸不同而不同，这种处理至关重要。
