# Nonaxiality in infrared dichroic ratios of polytopic transmembrane proteins.

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## Abstract

In polytopic alpha-helical transmembrane proteins, the distribution of amide vibrational transition moments can be nonaxial, if the helix axes are tilted relative to the symmetry axis of the helix bundle. The infrared dichroic ratios from oriented samples then contain nonaxial terms and, in the most general case, require a second-order parameter for the axis of the helix bundle. The extent of nonaxiality depends on the summation over the individual amide transition moments along the helix. Because this is strongly oscillatory, with a 3.6-residue periodicity, complete axial symmetry is not achieved rapidly on progressive summation. Expressions for the contributions of residual nonaxiality to the dichroic ratios are derived. A similar situation arises for oligomers of transmembrane beta-barrel proteins, e.g., the porin trimer. In this case, the extent of nonaxiality depends not only on the number of residues in the beta-barrel, but also on the tilt of the beta-strands relative to the barrel axis and the characteristic dimensions of a beta-sheet, which together determine the axial periodicity. The nonaxial contributions to the dichroic ratios of beta-barrel oligomers are also derived. Estimates are given of the likely size of the nonaxial contributions for the different alpha-helical and beta-sheet systems.