Helix–Coil Transition in Heterogeneous Chains. I. Protein Model

Abstract

Helix–coil transition curves are calculated for heterogeneous chains with random and correlated sequences of residue types by an approximate method. The distinction is made between the a priori probability of a residue sequence, and an effective probability which must be used when the sequence is treated as if it were in open chemical equilibrium with a reservoir. It is assumed that the effective probability does not correlate residue types in different sections of unbroken helix or coil. The required cumulants of the effective probability can then be determined from those of the a priori probability. Agreement with recent exact calculations is tested and found to be especially good when the cumulant expansion of the effective probability is terminated with three cumulants. The method is applicable to models of DNA which include entropy of ring formation. In this approximation the partition function for the heterogeneous chain has the same form as for the homogeneous chain, but an effective energy parameter is determined by the scheme just outlined. In the next approximation, which allows correlations between adjacent sections of helix and coil in the effective probability, the partition function still has the same form but an effective cooperative parameter would be required. The next approximation has not been studied in detail since no tractable scheme to evaluate the effective cooperative parameter has come to light.