Theoretical determination of helix-coil parameter sigma from a model of partly helical polypeptide chain

The Zimm and Bragg parameter sigma is calculated numerically for poly(L-alanine), polyglycine, and the copolymers of L-alanine and glycine using the molecular theory of s and sigma as developed by Go, Go, and Scheraga in a modified formulation. In this formulation, sigma is obtained from the partition function of the whole chain in the helix-coil transition region and represents therefore the contributions from the ends of helical and coil sequences and from the interactions between atoms in a coil sequence with those in the neighboring helical sequence. When the parameter sigma is calculated numerically from a hard-sphere potential, it appears that steric intractions between atoms in the coil sequence with atoms in the neighboring helical sequence, which have been neglected in previous calculations, contribute significantly to the value of sigma. Owing to these interactions the entropy of the coil sequence as well as sigma decrease, but the decrease of sigma is larger in poly(L-alanine) than in polyglycine, because of the higher flexibility of the monomer in polyglycine. The numerical value of sigma for polyglycine compared with that of poly(L-alanine) might be overestimated however by the model presented here due to approximations inherent in the hard-sphere treatment and because only regular helical sequences are considered.