Abstract
Formal expressions are derived for the mean square of the end-to-end distance and the electric moment of polypeptide molecules in the helix-coil transition region. It is assumed that each amino acid residue of a polypeptide molecule in the transition region is involved either in a helical section or in a randomly coiled section. A partition function of a polypeptide molecule is constructed by means of the matrix method. First, the partition function is used in obtaining the average of some scalar quantities, e.g., the mean fraction of residues involved in helical sections. Next, we obtain the average of a product of martices, which is used in calculating the mean square of the end-to-end distance and the electric moment. Expressions for the α-helix are also derived. An improved partition function including various effects, e.g., the end effect, is given in the appendix.
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