Statistical mechanics of noncovalent bonds in polyamino acids. II. Combinatorial formulation for short chains, including hydrophobic bonding in random coil

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Abstract
A combinatorial formulation of the partition function is developed for short polypeptide chains, where summations can be evaluated. From the complete combinatorial expression it is possible to assess the validity of any approximations which are made in evaluating the partition function. It is shown that it is an excellent approximation to consider the hydrogen‐bonded portion of a short (20 residues) chain as consisting of a single helical sequence of any size, with all sizes of helical sequences being about equally probable at the transition temperature. Another approximation, involving a linear dependence of the energy and entropy on the number of hydrogen bonds, helps to clarify the nature of the intermediate states in the denaturation process. Expressions are developed which incorporate the effect of hydrophobic bonds on the stability of the α‐helix, and the binding of water to the random coil. It is concluded that hydrophobic bonds in helical sequences can greatly stabilize the helix, but that similar bonds in the random coil can largely offset this stabilization.

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