Unperturbed dimensions for homopolypeptides and sequential copolypeptides cross-linked via a disulfide bond

Rotational isomeric state theory, in the form appropriate for branched molecules, has been used to calculate the mean-square unperturbed radius of gyration, (s2)0, for cross-linked polyglycine, poly(L-alanine), poly(L-proline), poly(L-alanyl-D-alanine), poly(L-propyl-L-prolylglycine), poly(L-prolyl-L-alanylglycine, poly(glycyl-L-alanyl-L-proline), and poly(L-alanyl-L-alanylglycine). The central amino acid residue in each polypeptide chain is replaced by the L-cysteinyl residue involved in cross-link formation. Each cross-linked molecular is considered to contain two trifunctional branch points, the alpha-carbon atoms of the two L-cysteinyl residues. Random flight statistics provide a poor estimate for g, defined as the ratio of (s2)0 for branched and linear polypeptides containing the same number of amino acid residues, for molecules of moderate molecular weight. The values of g obtained by random flight statistics and rotational isomeric state theory merge as the molecular weight becomes infinite. Deviations of g from its random flight value correlate with the size of the characteristic ratio, (s2)0/nplp2, for the linear polypeptides. The number of peptide bonds is np, and lp denotes the distance between neighboring alpha carbon atoms. Random flight statistics perform better in estimating the change in (s2)0 accompanying the cross-linking of the two polypeptide chains than it does in the estimation of g.