Infrared dichroism from the X-ray structure of bacteriorhodopsin

A detailed comparison with the three-dimensional protein structure provides a stringent test of the models and parameters commonly used in determining the orientation of the alpha-helices from the linear dichroism of the infrared amide bands, particularly in membranes. The order parameters of the amide vibrational transition moments are calculated for the transmembrane alpha-helices of bacteriorhodopsin by using the crystal structure determined at a resolution of 1.55 A (PDB accession number 1C3W). The dependence on the angle delta(M) that the transition moment makes with the peptide carbonyl bond is fit by the expression ((3)/(2)S(alpha) cos(2) alpha)cos(2)(delta(M) + beta) - 1/2S(alpha), where S(alpha) (0.91) is the order parameter of the alpha-helices, alpha (13 degrees ) is the angle that the peptide plane makes with the helix axis, and beta (11 degrees ) is the angle that the peptide carbonyl bond makes with the projection of the helix axis on the peptide plane. This result is fully consistent with the model of nested axial distributions commonly used in interpreting infrared linear dichroism of proteins. Comparison with experimental infrared dichroic ratios for bacteriorhodopsin yields values of Theta(A) = 33 +/- 1 degree, Theta(I) = 39.5 +/- 1 degree, and Theta(II) = 70 +/- 2 degrees for the orientation of the transition moments of the amide A, amide I, and amide II bands, respectively, relative to the helix axis. These estimates are close to those found for model alpha-helical polypeptides, indicating that side-chain heterogeneity and slight helix imperfections are unlikely to affect the reliability of infrared measurements of helix orientations.