SynopsisA coupling constant-dihedral angle correlation for the H-C,-C@-H system of amino acid residues in peptides has been derived from a set of model compounds covering the full range of dihedral angles. The expression obtained, J = 11.0 cosz 0 -1.4 cos 0 + 1.6 sin%, is close to those already used in pmr studies of peptide conformation, and provides a firmer foundation for them. A factor limiting the precision of this and other "Karplus relations" is illustrated.Coupling constant-dihedral angle correlations for the vicinal protonproton coupling of the H-C,-N-H system of amino acid residues's2 have been important to the use of nuclear magnetic resonance data for estimation of peptide backbone conformation in solution, particularly for cyclic oligopeptides. (Examples are cited in Refs. 3-6.) A natural extension would be the use of similar relations for the H-C,-C@-H unit, to obtain information about the side-chain angle x1. However, it should be conceded at the outset that the rotational freedom of most peptide side chains may limit the information present and available.Suggested relations between dihedral angle and H,-H@ coupling constant already exist, of course. Pachler' combined observed average a-@ coupling constants of amino acids with the results of an earlier analysis of the spectra of hydroxyprolines,8 and suggested that J1S0o = 13.6 Hz and JW = 2.6 Hz. These values have been used for describing side-chain conformation in terms of a distribution among the XI = 60, 180, and 300" r o t a m e r~.~ While it may not be accurate to describe side-chain conformation in terms of a distribution restricted to these rotamers, a Karplus equation for the c.-@ system ought to be useful for the more rigid cyclic amino acid residues and also for peptides sufficiently complex that non-bonded interactions cause one value of x1 t o be dominant. The expressions J = 8.5 cos2 e + 1.4 J = 10.5 C O S~ e + 1.4 oo < e < 90" 90" < e < 1800(1) based on the general experience for H -G G H systems,'O has been used for cyclotriprolyl, and yields results in agreement with the X-ray crystal-
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