Design of an Electrostatic Frequency Map for the NH Stretch of the Protein Backbone and Application to Chiral Sum Frequency Generation Spectroscopy

Abstract

We develop an electrostatic map for the vibrational NH stretch (amide A) of the protein backbone with a focus on vibrational chiral sum frequency generation spectroscopy (chiral SFG). Chiral SFG has been used to characterize protein secondary structure at interfaces using the NH stretch and to investigate chiral water superstructures around proteins using the OH stretch. Interpretation of spectra has been complicated because the NH stretch and OH stretch overlap spectrally. Although an electrostatic map for water OH developed by Skinner and co-workers was used previously to calculate the chiral SFG response of water structures around proteins, a map for protein NH that is directly responsive to biological complexity has yet to be developed. Here, we develop such a map, linking the local electric field to vibrational frequencies and transition dipoles. We apply the map to two protein systems and achieve much better agreement with experiment than was possible in our previous studies. We show that couplings between NH and OH vibrations are crucial to the line shape, which informs the interpretation of chiral SFG spectra, and that the chiral NH stretch response is sensitive to small differences in structure. This work increases the utility of the NH stretch in biomolecular spectroscopy.

Characterizing Interfaces by Voronoi Tessellation

“…We argued that this shift is due to significantly fewer backbone hydrogen bonds in LE 7 β compared to LK 7 β, which indicates weaker interstrand hydrogen-bonding interactions in LE 7 β, but we did not analyze the OH stretch components of the spectrum. 37 Figures 4b and 4c show that the first hydration shell and backbone water responses of LE 7 β are very different from those of LK 7 β, even though the systems appear similar. The OH stretch response of LE 7 β is both much smaller and somewhat blue-shifted compared to that of LK 7 β.…”

“…In particular, our previous work showed that intermolecular coupling is critical to the modeling of the combined NH/OH stretch chiral SFG response of LK 7 β. 37 If intermolecular coupling is neglected, a downward-pointing peak (indicated by a dip) appears that is not found in the experimental spectrum (Figure 5a). Our previous work also showed that almost all of the OH stretch signal and the most relevant NH/OH couplings arise between the biomolecule and the first hydration shell.…”

“…27 Here we obtain the first hydration shell by Voronoi tessellation, as discussed above, and then only consider the protein and the first hydration shell in the exciton Hamiltonian to speed up the calculation. 37 Figure 5a shows the result of the first-hydration-shell approximation along with the full-system calculation for LK 7 β. All features found in the full-system spectrum are present in the first-hydration-shell spectrum.…”

“…The agreement with experiment is good whether or not the approximation is applied, except for the low-frequency negative peak at ∼3150 cm −1 , which is missing in all the calculated spectra and is a focus of ongoing efforts by our group. 37 Figure 5b shows the increasing speedup of including only the first hydration shell as a function of system size. Using Voronoi tessellation to unambiguously define the first hydration shell can significantly accelerate prohibitively expensive spectral calculations and will enable modeling of vibrational spectra of large biological systems in the future without a significant sacrifice in accuracy.…”

“…This analysis suggests that the key variable in determining the chiral OH stretch response and the integrity of the first hydration shell is the stability of the protein structure rather than the strength of the interaction between the protein and the surrounding water. LK 7 β forms a more stable antiparallel β-sheet structure, 37 and therefore its hydration shell maintains a more rigid chiral structure. The blue-shift and smaller response of LE 7 β compared to LK 7 β illustrate differential chiral induction�a different degree of imprinting of chirality on an achiral solvent.…”