Dimensional Properties of Polypeptides in the Helix–Coil Transition Region I. Molecular Dimension

Abstract

An expression was derived to correlate the unperturbed mean-square radius of gyration of an intermediate polypeptide chain ‹S2›oI with helical content fH (see eq 10). An unperturbed state corresponding to the α-helix was obtained by converting the helix to a tortuous random-coil with a bond-rotation angle of +100° or −100° (in cis-convention) per residue, or per “virtual bond,” and a bond angle satisfying the experimental value of 8.8 for the characteristic ratio of the random-coil of PBLG. The “quasi” linear expansion factor αh of a helical sequence in an intermediate chain was evaluated (see eq 18) using the Zimm–Bragg–Nagai theory in collaboration with our expression for ‹S2›o. The intermediate chain may be a kind of swollen random-coil owing to the existence of helical sequences in the chain, and thus, the linear expansion factor αsI of the entire intermediate chain was approximately formulated as αsI=αsCαh where αsC is the linear expansion factor for the radius of gyration of a random-coil. With αsI and ‹S2›oI, the mean-square radius of gyration ‹S2›I of polypeptides in the transition region was calculated (eq 12) and compared with that obtained experiment (see Figure 4). Our theoretical results were found to agree well with experiment.