Extension of the tryptophan chi2,1 dihedral angle-W3 band frequency relationship to a full rotation: correlations and caveats.

The correlation of the UVRR nuW3 mode with the tryptophan chi(2,1) dihedral angle [Maruyama and Takeuchi (1995) J. Raman Spectrosc. 26, 319; Miura et al. (1989) J. Raman Spectrosc. 20, 667; Takeuchi (2003) Biopolymers 72, 305] has been extended to a full, 360 degrees rotation. The 3-fold periodicity of the relationship (cos 3chi(2,1)) over 360 degrees results in up to six dihedral angles for a given nuW3. Consideration of a Newman plot of dihedral angles for proteinaceous tryptophans taken from the Protein Data Bank shows that sterically hindered ranges of dihedral angle reduce the possible chi(2,1) to one or two. However, not all proteinaceous tryptophans follow the nuW3-chi(2,1) relationship. Hydrogen bonding at the indole amine, weaker, electrostatic cation-pi and anion-quadrapole interactions, and environmental hydrophobicity are examined as possible contributing factors to noncompliance with the relationship. This evaluation suggests that cumulative weak electrostatic and nonpolar interactions, contributing to steric hindrance, characterize the environment of tryptophans that obey the nuW3-chi(2,1) relationship, matching that of the crystalline tryptophan derivatives used to formulate the relationship. In the absence of methods to quantify these weak interactions, measurement of the full width half-maximum bandwidth (fwhm) of the W3 band is suggested as a primary screen for evaluating the applicability of the nuW3-chi(2,1) relationship.