Vibrational sum-frequency generation (VSFG) spectra of the amide-I band of proteins can give detailed insight into biomolecular processes near membranes. However, interpreting these spectra in terms of the conformation and orientation of a protein can be difficult, especially in the case of complex proteins. Here we present a formalism to calculate the amide-I infrared (IR), Raman, and VSFG spectra based on the protein conformation and orientation distribution. Based on the protein conformation, we set up the amide-I exciton Hamiltonian for the backbone amide modes that generate the linear and nonlinear spectroscopic responses. In this Hamiltonian, we distinguish between nearest-neighbor and non-nearest-neighbor vibrational couplings. To determine nearest-neighbor couplings we use an ab initio 6-31G+(d) B3LYP-calculated map of the coupling as a function of the dihedral angles. The other couplings are estimated using the transition-dipole coupling model. The local-mode frequencies of hydrogen-bonded peptide bonds and of peptide bonds to proline residues are red-shifted. To obtain realistic hydrogen-bond shifts we perform a molecular dynamics simulation in which the protein is solvated by water. As a first application, we measure and calculate the amide-I IR, Raman, and VSFG spectra of cholera toxin B subunit docked to a model cell membrane. To deduce the orientation of the protein with respect to the membrane from the VSFG spectra, we compare the experimental and calculated spectral shapes of single-polarization results, rather than comparing the relative amplitudes of VSFG spectra recorded for different polarization conditions for infrared, visible, and sum-frequency light. We find that the intrinsic uncertainty in the interfacial refractive index essential to determine the overall amplitude of the VSFG spectra prohibits a meaningful comparison of the intensities of the different polarization combinations. In contrast, the spectral shape of most of the VSFG spectra is independent of the details of the interfacial refractive index and provides a reliable way of determining molecular interfacial orientation. Specifically, we find that the symmetry axis of the cholera toxin B subunit is oriented at an angle of 6 degrees +/- 17 degrees relative to the surface normal of the lipid monolayer, in agreement with 5-fold binding between the toxin's five subunits and the receptor lipids in the membrane.
