Partial molar rotatory powers and optical activity in proteins and polypeptides. I. The fully extended chain and the antiparallel beta-pleated sheet.

Partial Rotatory Powers.-Recent experimental data on the circular dichroism spectra of a planar, cyclic, model compound, L-5-methyl pyrrolid-2-one," 2 and on the vacuum ultraviolet-absorption spectra of poly-L-alanine,3 as well as recent theoretical work on the spectra of simple amides4 and polypeptides,5 indicate that there is much to be clarified before a truly satisfactory theory of optical rotation of polypeptides can be developed. Specifically, it has been found that L-5-methyl pyrrolid-2-one in hexane exhibits a circular dichroism pattern which markedly resembles that pattern previously assumed to be unique to the a-helix;" 2 the vacuum ultraviolet-absorption spectra of poly-L-alanine contain a relatively intense transition near 165 m1A which is not present at such intensity in the monomer' and which is predicted theoretically5' 6 but which has not yet been considered in theoretical calculations of optical activity of polypeptides; all electron calculations on the amide chromophore indicate the presence of a mystery band, possibly an n-o* transition, near 200 msA,4 which has not previously been considered; and, in general, the number and assignments of transitions at wavelengths less than 200 mgu, which are important in giving rise to the observed rotatory properties of the peptide groups, are far from being understood.7 Because of these difficulties with the peptide chromophore, as well as a realization of the multiplicity of terms8-"1 contributing to optical activity, an empirical approach has recently been proposed' that will be applied to polypeptides and proteins in this and subsequent communications. The approach finds its application primarily to transitions with large magnetic dipole moments and small electric dipole moments such as the n-7r* transition, though it can be shown to encompass a substantial part of the optical activity of strong electric transitions. In this approach the mean rotational strength of an n-7r* transition, for example, may be expressed as the sum of products of geometric factors, Gum, and quantities called partial molar rotatory powers, [Pnm], i.e.,