Effect of Loop Entropy on the Helix-Coil Transition of a-Helical, Two-Chain, Coiled Coils. 2. Supermatrix Formulation of the Perfect-Matching Model

The loops-excluded model of the a-helix to random coil transition of a-helical, two-chain, coiled coils (dimers) in which loop entropy acts to produce a single interacting helical stretch in the dimer has been reformulated in terms of the supermatrix method of Jernigan and Flory. It is demonstrated that the loops-excluded model is a member of the class of nearest-neighbor models. Serial matrix product expressions for the internal partition function of the dimer, Zd, the overall helix content, f h d , the helix probability profiles, and the ratio, Rd, of the number of residues that are part of randomly coiled runs at the chain ends to the total number of random coils are derived. The supermatrix method is demonstrated to possess none of the numerical instabilities of our previously developed extension of the Poland recursion relation method to two-chain, coiled coils. Application of the supermatrix formalism to homopolymers demonstrates that all the conclusions of the loops-excluded model based on the recursion relation method remain unchanged. In the limit that Rd lies near unity, the neglect-loop-entropy theory (in which loop entropy is entirely ignored) and the loops-excluded model are identical. When Rd is significantly less than one, loop entropy makes the helix-coil transition more cooperative; thus values of the helix-helix interaction parameter w extracted from experiment and employing the neglect-loop-entropy theory may be significantly in error, overestimating the helix-helix interaction at high helix content and underestimating it at low helix content.