Torsion angle analysis of glycolipid order at membrane surfaces

A method is presented for determining the average glycosidic torsion angles and motion about those angles for a glycolipid headgroup at a model membrane surface. Dipolar and quadrupolar coupling constants were previously collected on the headgroup of beta-dodecyl glucoside embedded in phospholipid/detergent bilayers which orient in a magnetic field (Sanders, C.R., and J.H. Prestegard. 1991. J. Am. Chem. Soc. 113:1987-1996). These observables are expressed as averages of second order spherical harmonics, and Wigner rotation matrices are used here to transform the spherical harmonics from the laboratory frame to a set of frames which allow motional averaging to be described as the result of simple bond rotations. Euler angles corresponding to rotations about glycosidic torsion angles phi and psi are chosen to best reproduce experimental coupling constants, using models which have varying degrees of motional averaging. These models include a rigid headgroup, axially symmetric headgroup motion, and independent motion about each torsion angle in a square well potential. The square well model proves to be significantly better than the rigid model in reproducing experimental observations and it offers a more physically meaningful description of motion than the axially symmetric model. The structures obtained, assuming a square well potential, are compared to potential energy maps for the glycolipid torsional angles to illustrate the need for inclusion of the membrane interface in energetic modeling of glycolipid conformations.