Signatures of β-sheet secondary structures in linear and two-dimensional infrared spectroscopy

Using idealized models for parallel and antiparallel β sheets, we calculate the linear and two-dimensional infrared spectra of the amide I vibration as a function of size and secondary structure. The model assumes transition–dipole coupling between the amide I oscillators in the sheet and accounts for the anharmonic nature of these oscillators. Using analytical and numerical methods, we show that the nature of the one-quantum vibrational eigenstates, which govern the linear spectrum, is, to a large extent, determined by the symmetry of the system and the relative magnitude of interstrand interactions. We also find that the eigenstates, in particular their trends with system size, depend sensitively on the secondary structure of the sheet. While in practice these differences may be difficult to distinguish in congested linear spectra, we demonstrate that they give rise to promising markers for secondary structure in the two-dimensional spectra. In particular, distinct differences occur between the spectra of parallel and antiparallel β sheets and between β hairpins and extended β sheets.