Principles of Protein Structure - H. Schultz 1982

Statistical Mechanics of the Helix-Coil Transition
The Zimm-Bragg Model for the Helix-Coil Transition

A nearest-neighbor interaction term is introduced into the simplified formula. Zimm and Bragg [789] applied The Ising Model to the helix-coil transition in homopolypeptide chains. To this end, they divided the conformational space into two regions, a_R or "a" rather than a_R or "coil". In addition, they used the approximate equation (A.4), which disregards residue-residue interactions, and subsequently incorporated a nearest-neighbor interaction term. For a chain consisting of N residues of a given type, equation (A.4) takes the form:

Class="center">

After multiplication, we obtain a sum of 2^N terms

For each possible helix-coil and coil-helix junction, an additional multiplier is introduced

This can be expressed in the form

by pairing the factors and applying them exclusively to helix-coil junctions. This is permissible because the number of helical segments equals that of coil segments; in cases where one structural type outnumbers the other, the difference is neglected.

The factor a leads to unfavorable results if there are too many junctions, while favoring extended segments of identical conformation. This provides an alternative description of "cooperativity of residues with identical conformation," or in this case, "cooperativity of helical residues." One can also speak of the energetic favorability of "coil or helix nucleation." Therefore, the parameter a is referred to as the "cooperativity or nucleation parameter."