Comparison of Theories of the Helix—Coil Transition in Polypeptides

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Abstract
Using Lifson's recent formalism of sequence‐generating functions, several theories of the helix—coil transition in polypeptides are compared. The general helix—coil model, say as treated by Lifson and Roig, gives rise to a cubic secular equation. The largest root of this equation can be approximated closely by a quadratic equation, similar to the procedure of Zimm and Bragg, if isolated single helical states are assigned hydrogen bonds of positive (unfavorable) energy of formation. Equations are given to evaluate the effect of this artifice on the entropy of the random coil. It is pointed out that Peller's combinatorial theory, in its present form, significantly underestimates the combinatorial entropy due to the artifice of introducing a triplet of three amino acid residues (the span of a hydrogen bond) to define a unit. If the use of triplets as units is replaced by the use of amino acid residues, and if a positive energy of formation of a hydrogen bond is assigned to single helical states, then Peller's result is identical to the quadratic approximation.