The intramolecular formation of multiple clusters of interacting helices has been characterized in a homopolymer. The configuration partition function permits the formation of clusters in which the number of interacting helices may be as large as the greatest integer in n/2, where n denotes the number of amino acid residues in the chain.
The theoretical formulation has its origin in a recent [Mattice, W. L. & Scheraga, H.
A. (1984)
Biopolymers 23,1701-17241, tractable matrix expression for the configuration partition function for intramolecular antiparallel P-sheet formation. Reassignment of the expression for one of the n(n+3)/2 elements in the sparse statistical weight matrix, along with a simple change in notation, converts that treatment into a matrix formulation of the configuration partition function for a chain containing multiple clusters of interacting antiparallel helices. The five statistical weights used are 6, fi, w, and the Zimm-Bragg u and s. Each tight bend that connects two interacting helices contributes a factor of 6, fi is used in the weight for larger loops between interacting helices, and w arises from helix-helix interaction. The influence of the helix-helix interaction is well illustrated by two helix-coil transitions in a chain with n = 156 and u = 0.001. In the absence of helix-helix interaction, the transition occurs by the nucleation and subsequent elongation of a small number of helices. When helix-helix interaction is attractive, the transition can occur by a different mechanism. Formation of a single pair of interacting helices is followed by addition of new helices to the initial cluster. In the latter process, individual helices experience relatively little growth after they are formed.