Parallel β‑Sheet Vibrational Couplings Revealed by 2D IR Spectroscopy of an Isotopically Labeled Macrocycle: Quantitative Benchmark for the Interpretation of Amyloid and Protein Infrared Spectra

Infrared spectroscopy is playing an important role in the elucidation of amyloid fiber formation, but the coupling models that link spectra to structure are not well tested for parallel β-sheets. Using a synthetic macrocycle that enforces a two stranded parallel β-sheet conformation, we measured the lifetimes and frequency for six combinations of doubly ¹³C¹⁸O labeled amide I modes using 2D IR spectroscopy. The average vibrational lifetime of the isotope labeled residues was 550 fs. The frequencies of the labels ranged from 1585 to 1595 cm^–1, with the largest frequency shift occurring for in-register amino acids. The 2D IR spectra of the coupled isotope labels were calculated from molecular dynamics simulations of a series of macrocycle structures generated from replica exchange dynamics to fully sample the conformational distribution. The models used to simulate the spectra include through-space coupling, through-bond coupling, and local frequency shifts caused by environment electrostatics and hydrogen bonding. The calculated spectra predict the line widths and frequencies nearly quantitatively. Historically, the characteristic features of β-sheet infrared spectra have been attributed to through-space couplings such as transition dipole coupling. We find that frequency shifts of the local carbonyl groups due to nearest neighbor couplings and environmental factors are more important, while the through-space couplings dictate the spectral intensities. As a result, the characteristic absorption spectra empirically used for decades to assign parallel β-sheet secondary structure arises because of a redistribution of oscillator strength, but the through-space couplings do not themselves dramatically alter the frequency distribution of eigenstates much more than already exists in random coil structures. Moreover, solvent exposed residues have amide I bands with >20 cm^–1 line width. Narrower line widths indicate that the amide I backbone is solvent protected inside the macrocycle. This work provides calculated and experimentally verified couplings for parallel β-sheets that can be used in structure-based models to simulate and interpret the infrared spectra of β-sheet containing proteins and protein assemblies, such as amyloid fibers