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

Abstract

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 frequen cies 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 linewidths 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 linewidth. Narrower linewidths 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.

Electrostatic frequency shifts in amide I vibrational spectra: Direct parameterization against experiment

“…In the past, direct comparison between simulated and experimental spectra has been generally limited to analysis of peak widths 41,66 (rather than frequencies) or is accompanied by arbitrary peak shifts of up to 30 cm −1 in order to improve agreement between simulation and experiment. 11,26,39,40 A particular difficulty appears to be the assignment of 13 44,45,67 or assumed 12,41,42 in various applications in the literature. In the absence of a well-defined shift, the absolute frequencies of isotope labeled units do not appear to us to be a meaningful metric for map performance, although relative frequency shifts between different isotope labels within the same peptide can, of course, provide a qualitative comparison.…”

“…For this purpose, label pairs should be intentionally chosen both to have stable structures (e.g., larger peptides than in some previous studies 68,69 ) and to have significant coupling constants since experimental validation of a coupling constant less than a few wavenumbers in the presence of tens of wavenumbers of disorder is not practically feasible (see, e.g., Ref. 42). …”

“…Although useful for qualitative interpretation, comparison with experimental data is generally limited (at best) to peak shapes and must be assisted by the application of arbitrary frequency shifts to simulated spectra. 11,12,26,[39][40][41][42] The development of accurate spectral maps faces several formidable challenges. At the outset, spectral calculations are limited by the practical requirement to make simplifying assumptions that neglect certain physical features.…”

Vibrational coherence and energy transfer in two-dimensional spectra with the optimized mean-trajectory approximation

“…(14). The canonical transformations between these sets of variables must be determined, as must transformations between the phase space variables used in the OMT diagrams and the action-angle variables in which the quantization conditions are imposed.…”

“…To reveal a maximally detailed picture of both structure and dynamics, these response function calculations should treat atomistic models. [7][8][9][10][11][12][13][14][15] Numerically exact quantum dynamical calculations of response functions are generally impractical while purely classical calculations may be qualitatively incorrect except at the shortest time scales. [16][17][18][19][20][21][22][23] These challenges motivate the development of approximate methods for computing response functions.…”