Effect of Loop Entropy on the Helix-Coil Transition of a-Helical, Two-Chain, Coiled Coils

The theory of the a-helix to random coil transition in two-chain, coiled coils is extended to include the effect of loop entropy. To ascertain the conditions under which loop entropy is important, expressions are derived with the neglect of loop entropy for the ratio (R) of the number of residues that are part of randomly coiled runs at the chain ends to the total number of randomly coiled residues. R is derived for single chains (R,) and for two-chain, coiled coil dimers (Rd) with and without coarse graining. When Rd lies near unity, there are few interior random coils, and the effect of loop entropy (which is important only for interior random coil sequences) can be neglected. In cases where loop entropy is important, we have extended Poland's recursion relation method (Biopolymers 1974,13, 1859) to two-chain, coiled coils to incorporate loop entropy into the theory. For chains of moderate length, loop entropy is so severe as to eliminate loops entirely, producing a single interacting helical stretch in the dimer. Calculations with and without loop entropy are presented for the fraction of helix for dimers (fhd) as a function of the helix-helix interaction parameter w and for the helix probability profiles in homopolymeric, two-chain, coiled coils. Where loop entropy cannot be neglected, it makes the helix-coil transition more cooperative and concomitantly modifies the helix probability profile. As expected, the interior of the dimer becomes more helical and the ends become less helical than if loop entropy is ignored.