The antiparallel and parallel beta sheets are two of the most abundant secondary structures found in proteins. Although various spectroscopic methods have been used to distinguish these two different structures, the linear spectroscopic measurements could not provide incisive information for distinguishing an antiparallel beta sheet from a parallel beta sheet. After carrying out quantum-chemistry calculations and model simulations, we show that the polarization-controlled two-dimensional (2D) IR photon echo spectroscopy can be of critical use in distinguishing these two different beta sheets. Particularly, the ratio between the diagonal peak and the cross peak is found to be strongly dependent on the quasi-2D array of the amide I local-mode transition dipole vectors. The relative intensities of the cross peaks in the 2D difference spectrum of an antiparallel beta sheet are significantly larger than those of the diagonal peaks, whereas the cross-peak amplitudes in the 2D difference spectrum of a parallel beta sheet are much weaker than the main diagonal-peak amplitudes. A detailed discussion on the origin of the diagonal- and cross-peak intensity distributions of both the antiparallel and parallel beta sheets is presented by examining vibrational exciton delocalization, relative angles between two different normal-mode transition dipoles, and natures of the cross peaks in the 2D difference spectrum.
Amide I IR absorption and two-dimensional (2D) IR photon echo spectra of a model β hairpin in aqueous solution are theoretically studied and simulated by combining semiempirical quantum chemistry calculations and molecular dynamics simulation methods. The instantaneous normal-mode analysis of the β hairpin in solution is performed to obtain the density of states and the inverse participation ratios of the one-exciton states. The motional and exchange narrowing processes are taken into account by employing the time-correlation function theory for the linear and nonlinear response functions. Numerically simulated IR absorption and 2D spectra are then found to be determined largely by the amide I normal modes delocalized on the peptides in the two strands. The site-specific isotope-labeling effects on the IR and 2D IR spectra are discussed. The simulation results for the ideal (A 17 ) β hairpin are directly compared with those of the realistic 16-residue (GB1) β hairpin from an immunoglobulin G-binding protein. It was found that the characteristic features in IR and 2D spectra of both the ideal (A 17 ) β hairpin and the GB1 β hairpin are the same. The simulated IR spectrum of the GB1 β hairpin is found to be in good agreement with experiment, which demonstrates that the present computational method is quantitatively reliable.
Chain length and site dependencies of amide I local mode frequencies of R-helical polyalanines are theoretically studied by carrying out semiempirical quantum chemistry calculations. A theoretical model that can be used to quantitatively predict both the local amide I mode frequencies and coupling constants between two different local amide I modes is developed. Using this theoretical model and performing molecular dynamics simulation of an R-helical polyalanine in liquid water, we investigate conformational fluctuation and hydrogen-bonding dynamics by monitoring amide I frequency fluctuations. The instantaneous normal-mode analysis method is used to obtain densities of states of the one-and two-exciton bands and to quantitatively investigate the extent of delocalization of the instantaneous amide I normal modes. Also, by introducing a novel concept of the so-called weighted phase-correlation factor, the symmetric natures of the delocalized amide I normal modes are elucidated, and it is also shown that there is no unique way to classify any given amide I normal mode of the R-helical polyalanine in liquid water to be either A-mode-like or E 1 -mode-like. From the ensembleaveraged dipole strength spectrum and density of one-exciton states, the amide I infrared absorption spectrum is numerically calculated and its asymmetric line shape is theoretically described. Considering both transitions from the ground state to one-exciton states and those from one-exciton states to two-exciton states, we calculate the two-dimensional IR pump-probe spectra and directly compare them with recent experimental results. A brief discussion on the cross-peaks previously observed in the two-dimensional difference spectrum is presented.
Using the constrained molecular dynamics simulation method in combination with quantum chemistry calculation, Hessian matrix reconstruction, and fragmentation approximation methods, the authors have established computational schemes for numerical simulations of amide I IR absorption, vibrational circular dichroism (VCD), and two-dimensional (2D) IR photon echo spectra of the protein ubiquitin in water. Vibrational characteristic features of these spectra in the amide I vibration region are discussed. From the semiempirical quantum chemistry calculation results on an isolated ubiquitin, amide I local mode frequencies and vibrational coupling constants were fully determined. It turns out that the amide I local mode frequencies of ubiquitin in both gas phase and aqueous solution are highly heterogeneous and site dependent. To directly test the quantitative validity of thus obtained spectroscopic properties, they compared the experimentally measured amide I IR, 2D IR, and electronic circular dichroism spectra with experiments, and found good agreements between theory and experiments. However, the simulated VCD spectrum is just qualitatively similar to the experimentally measured one. This indicates that, due to delicate cancellations between the positive and negative VCD contributions, the prediction of protein VCD spectrum is critically relied on quantitative accuracy of the theoretical model for predicting amide I local mode frequencies. On the basis of the present comparative investigations, they found that the site dependency of amide I local mode frequency, i.e., diagonal heterogeneity of the vibrational Hamiltonian matrix in the amide I local mode basis, is important. It is believed that the present computational methods for simulating various vibrational and electronic spectra of proteins will be of use in further refining classical force fields and in addressing the structure-spectra relationships of proteins in solution.
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