Two-dimensional circularly polarized IR photon echo spectroscopy of polypeptides: four-wave-mixing optical activity measurement

A coherent two-dimensional (2D) optical spectroscopy utilizing circularly polarized (CP) beams, which was shown to be useful in studying molecular chirality in condensed phases, was theoretically proposed recently [Cho et al. J. Chem. Phys. 2003, 119, 7003]. A photon echo (PE) version of 2D optical activity spectroscopy is discussed in this paper. Considering various dipeptide and polypeptide systems, where the amide I local modes constitute the set of basis modes used to describe exciton and biexciton states as linear combinations of those basis modes, we present numerically simulated 2D circularly polarized IR PE spectra. It is shown that this novel spectroscopic method can provide additional information on the angles between the transition magnetic dipole and the transition electric dipole of two different vibrationally excited states, which are highly sensitive to the 3D structure and chirality of a given polypeptide. Also, a hierarchical relation of IR absorption, vibrational circular dichroism, 2D IR PE, and 2D CP-IR PE is discussed to show advantages of 2D optical activity spectroscopy in general.     

Polarization-angle-scanning two-dimensional spectroscopy: application to dipeptide structure determination

Coherent two-dimensional optical spectroscopy based on a heterodyne-detected stimulated photon echo measurement technique requires four ultrashort pulses whose pulse-to-pulse delay times, wavevectors, and frequencies are experimentally controllable variables. In addition, the polarization directions of the four radiations can also be arbitrarily adjusted. We show that the polarization-angle-scanning two-dimensional spectroscopy can be of effective use to selectively suppress either all the diagonal peaks or a cross-peak in a given two-dimensional spectrum. Theoretical relationships between the transition dipole vectors of a given pair of coupled modes or quantum transitions and the polarization angle configuration making the corresponding cross-peak vanish are established. Here, to shed light into the underlying principles of the polarization-angle-scanning two-dimensional spectroscopy, we considered the amide I vibrations of various isotope-labeled dipeptide conformers and show that one can selectively suppress a cross-peak by properly controlling the polarization angle of a chosen beam among them. Once the relative directions of the amide I transition dipole vectors are determined using the polarization-angle-scanning technique theoretically proposed here, they can serve as a set of constraints for determining structures of model peptides. The present work demonstrates that the polarization-controlled two-dimensional vibrational or electronic spectroscopy can provide invaluable information on intricate details of molecular structures.     

Characteristic two-dimensional IR spectroscopic features of antiparallel and parallel beta-sheet polypeptides: simulation studies

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.     

Site-specific vibrational dynamics of the CD3zeta membrane peptide using heterodyned two-dimensional infrared photon echo spectroscopy

Heterodyned two-dimensional infrared (2D IR) spectroscopy has been used to study the amide I vibrational dynamics of a 27-residue peptide in lipid vesicles that encompasses the transmembrane domain of the T-cell receptor CD3zeta. Using 1-(13)C[Double Bond](18)O isotope labeling, the amide I mode of the 49-Leucine residue was spectroscopically isolated and the homogeneous and inhomogeneous linewidths of this mode were measured by fitting the 2D IR spectrum collected with a photon echo pulse sequence. The pure dephasing and inhomogeneous linewidths are 2 and 32 cm(-1), respectively. The population relaxation time of the amide I band was measured with a transient grating, and it contributes 9 cm(-1) to the linewidth. Comparison of the 49-Leucine amide I mode and the amide I band of the entire CD3zeta peptide reveals that the vibrational dynamics are not uniform along the length of the peptide. Possible origins for the large amount of inhomogeneity present at the 49-Leucine site are discussed.     

Computational spectroscopy of ubiquitin: comparison between theory and experiments

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.     

Residual native structure in a thermally denatured beta-hairpin

We investigate the thermal denaturation of trpzip2 between 15 and 82 degrees C using two-dimensional infrared (2D IR) vibrational spectroscopy, dispersed vibrational echo (DVE) spectroscopy, and Fourier transform infrared (FTIR) spectroscopy. The FTIR and DVE spectra of trpzip2 show in the amide I region of the spectrum two resonances, which arise primarily from the interstrand coupling between local amide I oscillators along the peptide backbone. The coupling is seen directly in the 2D IR spectra as the formation of cross-peak ridges. Although small shifts of these frequencies occur on heating the sample, the existence of cross-peak ridges at all temperatures indicates that stable hydrogen bond interactions persist between the two beta-strands. These observations indicate a significant amount of native structure in the thermally denatured state of trpzip2.     

Amide I vibrational dynamics of N-methylacetamide in polar solvents: the role of electrostatic interactions

The vibrational frequency of the amide I transition of peptides is known to be sensitive to the strength of its hydrogen bonding interactions. In an effort to account for interactions with hydrogen bonding solvents in terms of electrostatics, we study the vibrational dynamics of the amide I coordinate of N-methylacetamide in prototypical polar solvents: D2O, CDCl3, and DMSO-d6. These three solvents have varying hydrogen bonding strengths, and provide three distinct solvent environments for the amide group. The frequency-frequency correlation function, the orientational correlation function, and the vibrational relaxation rate of the amide I vibration in each solvent are retrieved by using three-pulse vibrational photon echoes, two-dimensional infrared spectroscopy, and pump-probe spectroscopy. Direct comparisons are made to molecular dynamics simulations. We find good quantitative agreement between the experimentally retrieved and simulated correlation functions over all time scales when the solute-solvent interactions are determined from the electrostatic potential between the solvent and the atomic sites of the amide group.     

Two-dimensional infrared spectroscopy of antiparallel beta-sheet secondary structure

We investigate the sensitivity of femtosecond Fourier transform two-dimensional infrared spectroscopy to protein secondary structure with a study of antiparallel beta-sheets. The results show that 2D IR spectroscopy is more sensitive to structural differences between proteins than traditional infrared spectroscopy, providing an observable that allows comparison to quantitative models of protein vibrational spectroscopy. 2D IR correlation spectra of the amide I region of poly-l-lysine, concanavalin A, ribonuclease A, and lysozyme show cross-peaks between the IR-active transitions that are characteristic of amide I couplings for polypeptides in antiparallel hydrogen-bonding registry. For poly-l-lysine, the 2D IR spectrum contains the eight-peak structure expected for two dominant vibrations of an extended, ordered antiparallel beta-sheet. In the proteins with antiparallel beta-sheets, interference effects between the diagonal and cross-peaks arising from the sheets, combined with diagonally elongated resonances from additional amide transitions, lead to a characteristic "Z"-shaped pattern for the amide I region in the 2D IR spectrum. We discuss in detail how the number of strands in the sheet, the local configurational disorder in the sheet, the delocalization of the vibrational excitation, and the angle between transition dipole moments affect the position, splitting, amplitude, and line shape of the cross-peaks and diagonal peaks.     

Theoretical calculations of infrared absorption, vibrational circular dichroism, and two-dimensional vibrational spectra of acetylproline in liquids water and chloroform

Infrared absorption, vibrational circular dichroism, and two-dimensional infrared pump-probe and photon echo spectra of acetylproline solutions are theoretically calculated and directly compared with experiments. In order to quantitatively determine interpeptide interaction-induced amide I mode frequency shifts, high-level quantum chemistry calculations were performed. The solvatochromic amide I mode frequency shift and fluctuation were taken into account by carrying out molecular dynamics simulations of acetylproline dissolved in liquids water and chloroform and by using the extrapolation method developed recently. We first studied correlation time scales of the two amide I vibrational frequency fluctuations, cross correlation between the two fluctuating local mode frequencies, ensemble averaged conformations of the acetylproline molecule in liquids water and chloroform. The corresponding conformations of the acetylproline in liquids water and chloroform are close to the ideal 3(10) helix and the C(7) structure, respectively. A few methods proposed to determine the angle between the two transition dipoles associated with the amide I vibrations were tested and their limitations are discussed.     

Pronounced non-Condon effects in the ultrafast infrared spectroscopy of water

In the context of vibrational spectroscopy in liquids, non-Condon effects refer to the dependence of the vibrational transition dipole moment of a particular molecule on the rotational and translational coordinates of all the molecules in the liquid. For strongly hydrogen-bonded systems, such as liquid water, non-Condon effects are large. That is, the bond dipole derivative of an OH stretch depends strongly on its hydrogen-bonding environment. Previous calculations of nonlinear vibrational spectroscopy in liquids have not included these non-Condon effects. We find that for water, inclusion of these effects is important for an accurate calculation of, for example, homodyned and heterodyned three-pulse echoes. Such echo experiments have been "inverted" to obtain the OH stretch frequency time-correlation function, but by necessity the Condon and other approximations are made in this inversion procedure. Our conclusion is that for water, primarily because of strong non-Condon effects, this inversion may not lead to the correct frequency time-correlation function. Nevertheless, one can still make comparison between theory and experiment by calculating the experimental echo observables themselves.     

Comment on a sum rule for vibrational raman optical activity

The expressions for the sum of vibrational Raman optical activity (ROA) intensities indicate that the ROA intensity sum for chiral molecules is non-zero for those with an anisotropic electric dipole polarizability. The non-zero sum depends upon the electric dipole, magnetic dipole and electric quadrupole polarizability components and moments of inertia at equilibrium geometry.     

Ultrafast exciton-exciton coherent transfer in molecular aggregates and its application to light-harvesting systems

Effects of the exciton-exciton coherence transfer (EECT) in strongly coupled molecular aggregates are investigated from the reduced time-evolution equation which we have developed to describe EECT. Starting with the nonlinear response function, we obtained explicit contributions from EECT to four-wave-mixing spectrum such as photon echo, taking into account double exciton states, static disorder, and heat-bath coupling represented by arbitrary spectral densities. By using the doorway-window picture and the projection operator technique, the transfer rates between two different electronic coherent states are obtained within a framework of cumulant expansion at high temperature. Applications of the present theory to strongly coupled B850 chlorophylls in the photosynthetic light harvesting system II (LH2) are discussed. It is shown that EECT is indispensable in properly describing ultrafast phenomena of strongly coupled molecular aggregates such as LH2 and that the EECT contribution to the two-dimensional optical spectroscopy is not negligible.     

Excitonic effects in two-dimensional vibrational spectra of liquid formamide

The linear and two-dimensional infrared (2DIR) responses of the amide I vibrational mode in liquid formamide are investigated experimentally and theoretically using molecular dynamics simulations. The recent method based on the numerical integration of the Schr?dinger equation is employed to calculate the 2DIR spectra. Special attention is devoted to the interplay of the structural dynamics and the excitonic nature of the amide I modes in determining the optical response of the studied system. In particular, combining experimental data, simulated spectra and analysis of the simulated atomic trajectory in terms of a transition dipole coupling model, we provide a convincing explanation of the peculiar features of the 2DIR spectra, which show a substantial increase of the antidiagonal bandwidth with increasing frequency. We point out that, at variance with liquid water, the 2DIR spectral profile of formamide is determined more by the excitonic nature of the vibrational states than by the fast structural dynamics responsible for the frequency fluctuations.     

Spectrally resolved femtosecond two-color three-pulse photon echoes: study of ground and excited state dynamics in molecules

We report the use of spectrally resolved femtosecond two-color three-pulse photon echoes as a potentially powerful multidimensional technique for studying vibrational and electronic dynamics in complex molecules. The wavelengths of the pump and probe laser pulses are found to have a dramatic effect on the spectrum of the photon echo signal and can be chosen to select different sets of energy levels in the vibrational manifold, allowing a study of the dynamics and vibrational splitting in either the ground or the excited state. The technique is applied to studies of the dynamics of vibrational electronic states in the dye molecule Rhodamine 101 in methanol.     

Detection of electronic and vibrational coherences in molecular systems by 2D electronic photon echo spectroscopy

Two-dimensional optical photon echo spectra are simulated for model systems which exhibit vibrational, electronic and a combination of electronic and vibrational coherent dynamics. The coherent motion manifests itself as periodic beatings of the spectrum cross-peak intensity with the population time. The intensity modulations are compared to evolution of the excited-state population and coordinate expectation value. The advantageous capabilities of the technique as well as possible difficulties in spectra interpretations are outlined. Possibilities for distinguishing electronic and vibrational coherences are discussed.