Principles of Protein Structure - H. Schulz 1982

Statistical Mechanics of the Helix-Coil Transition
The Zimm-Bragg Model for the Helix-Coil Transition
Number and Length of Helical Segments

The maximum number of helical segments corresponds to the transition point. In equation (A.13), the variable v denotes the number of helical segments in a given chain conformation. The average number of helical segments (v).

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This function, illustrated in Fig. A.1, b, exhibits a maximum at s = 1. The number of segments decreases as σ decreases. The average length of a helical segment (l) is given by

Fig. A.1. The Zimm–Bragg model for the helix-coil transition in a polypeptide chain of length N. Values of σ are indicated next to the curves. a — average fraction of helices as a function of the relative statistical weight s. b — ratio of the average number of helical segments to N as a function of s. c — ratio of the average length of helical segments to N as a function of s.

As can be seen from Fig. A.1, c, the helix length increases monotonically with increasing s.

It should be noted that the division of the chain into multiple segments of helical and coil Conformations is consistent with the more general Treatment by Landau and Lifshitz [791]. The authors argue that in the one-dimensional case, Separation into two distinct phases is impossible unless the surface tension is infinite. Infinite surface tension corresponds to the state with σ = 0, under which the Zimm–Bragg model also leads to phase separation.