Orientation of cholesterol in hybrid bilayer membranes calculated from the phases of methyl resonances in sum frequency generation spectra

The phases of Sum Frequency Generation (SFG) vibrational resonances recorded from thin films on metal surfaces provide information on the orientation and tilt angles of the functional groups of molecules in the film. SFG spectra have been simulated for monolayer films in which the adsorbed molecule has an unequal number of methyl groups oriented in two different directions. The phases, on resonance, of the methyl symmetric (r(+)) and asymmetric (r(-)) resonances are determined as a function of the two methyl group tilt angles and the fraction of groups pointing in that particular direction. The results are first presented as two-dimensional projection plots for the r(+) and r(-) resonances and then combined to show the tilt angles of the methyl groups, and fraction of methyl groups in that orientation, for which both resonances are in phase or out of phase with one another. Mathematical expressions have been calculated to identify the precise boundary conditions for when the phases of the r(+) and r(-) resonances change. The results of these simulations are compared to the phases of the methyl resonances in experimental SFG spectra of d7-cholesterol in a hybrid bilayer membrane.