J-coupling constants for a trialanine peptide as a function of dihedral angles calculated by density functional theory over the full Ramachandran space

We present 13 (3)J, seven (2)J and four (1)J coupling constants (24 in all) calculated using B3LYP/D95** as a function of the φ and ψ Ramachandran dihedral angles of the acetyl(Ala)(3)NH(2) capped trialanine peptide over the entire Ramachandran space. With the exception of three of these J couplings, all show significant dependence upon both dihedral angles. For each J coupling considered, a two dimensional grid with respect to φ and ψ angles can be used to interpolate the values for any pair of φ and ψ values. Such simple interpolation is shown to be very accurate. Most of these calculated J couplings should prove useful for improving the accuracy of the determination of peptide and protein structures from NMR measurements in solution over that provided by the common procedure of treating the J couplings as functions of a single dihedral angle by means of Karplus-type fittings.     

Conformation and orientation of tetraalanine in a lyotropic liquid crystal studied by nuclear magnetic resonance

The (1)H NMR spectra of two isotopomers of tetraalanine deuterated on the two external methyl groups and on the two internal ones, respectively, were recorded in the lyotropic solvent cesium pentadecafluorooctanoate (CsPFO)/water. Eight dipolar couplings could be estimated from the spectra. The set of dipolar couplings was fitted assuming that one rigid conformer is present. Of the four major conformers considered, selected on the basis of theoretical calculations, the one characterized by the two couples of internal dihedral angles in the Ramachandran region of PPII resulted to be the only one to fit the set of couplings within experimental error. The data indicate that the molecule is oriented with the long molecular axis tilted with respect to the surface of the micelles formed by CsPFO.     

Bath-induced correlations and relaxation of vibronic dimers

We consider a vibronic dimer bilinearly coupled through its two vibrational monomer modes to two harmonic reservoirs and study, both analytically and numerically, how correlations of the reservoir-induced fluctuations affect dimer relaxation. For reservoirs with fully correlated fluctuations, we derive an exact quantum master equation for the density matrix of the symmetric vibronic dimer. We demonstrate that reservoirs with fully correlated or anticorrelated fluctuations do not allow for complete vibrational relaxation of the dimer due to the existence of decoherence-free subspaces. For reservoirs with partially correlated fluctuations, we establish the existence of three different mechanisms of vibrational relaxation. Weak inter-monomer couplings, as well as predominantly correlated or anticorrelated fluctuations, render two of these mechanisms relatively inefficient, leading to slow decays of the populations and coherences of the dimer density matrix. The analytical results are illustrated and substantiated by numerical studies of the relaxation behavior of photoexcited dimers.     

Vibrational relaxation in simulated two-dimensional infrared spectra of two amide modes in solution

Two-dimensional infrared spectroscopy is capable of following the transfer of vibrational energy between modes in real time. We develop a method to include vibrational relaxation in simulations of two-dimensional infrared spectra at finite temperature. The method takes into account the correlated fluctuations that occur in the frequencies of the vibrational states and in the coupling between them as a result of interaction with the environment. The fluctuations influence the two-dimensional infrared line shape and cause vibrational relaxation during the waiting time, which is included using second-order perturbation theory. The method is demonstrated by applying it to the amide-I and amide-II modes in N-methylacetamide in heavy water. Stochastic information on the fluctuations is obtained from a molecular dynamics trajectory, which is converted to time dependent frequencies and couplings with a map from a density functional calculation. Solvent dynamics with the same frequency as the energy gap between the two amide modes lead to efficient relaxation between amide-I and amide-II on a 560 fs time scale. We show that the cross peak intensity in the two-dimensional infrared spectrum provides a good measure for the vibrational relaxation.     

Nonadiabatic effects on peptide vibrational dynamics induced by conformational changes

Quantum dynamical simulations of vibrational spectroscopy have been carried out for glycine dipeptide (CH(3)-CO-NH-CH(2)-CO-NH-CH(3)). Conformational structure and dynamics are modeled in terms of the two Ramachandran dihedral angles of the molecular backbone. Potential energy surfaces and harmonic frequencies are obtained from electronic structure calculations at the density functional theory (DFT) [B3LYP/6-31+G(d)] level. The ordering of the energetically most stable isomers (C(7) and C(5)) is reversed upon inclusion of the quantum mechanical zero point vibrational energy. Vibrational spectra of various isomers show distinct differences, mainly in the region of the amide modes, thereby relating conformational structures and vibrational spectra. Conformational dynamics is modeled by propagation of quantum mechanical wave packets. Assuming a directed energy transfer to the torsional degrees of freedom, transitions between the C(7) and C(5) minimum energy structures occur on a sub-picosecond time scale (700...800 fs). Vibrationally nonadiabatic effects are investigated for the case of the coupled, fundamentally excited amide I states. Using a two state-two mode model, the resulting wave packet dynamics is found to be strongly nonadiabatic due to the presence of a seam of the two potential energy surfaces. Initially prepared adiabatic vibrational states decay upon conformational change on a time scale of 200...500 fs with population transfer of more than 50% between the coupled amide I states. Also the vibrational energy transport between localized (excitonic) amide I vibrational states is strongly influenced by torsional dynamics of the molecular backbone where both enhanced and reduced decay rates are found. All these observations should allow the detection of conformational changes by means of time-dependent vibrational spectroscopy.     

Multivariate analysis of a data matrix containing A-DNA and B-DNA dinucleoside monophosphate steps: Multidimensional Ramachandran plots for nucleic acids

A method to construct the equivalent of multidimensional Ramachandran plots for nucleic acids on the basis of singular value decomposition (SVD) is presented. For this purpose, a data matrix containing 244 DNA dinucleoside monophosphate steps, represented by nine torsion angles, was decomposed into a score and loading matrix. It is shown that biplots, containing both score points and loading vectors, provide a simple tool to interpret the principles of DNA class separation. Scores separate the data matrix into one A-DNA class, two different B-DNA classes, and one so-called crankshaft class. Loading vectors correlate torsion angles. The projections of scores on loading vectors indicate which torsion angles play a dominant role in DNA class separation. The results of the biplots are supported by (simple) physical interpretations. From a three-dimensional score space the nine original torsion angles can be reconstructed. Hence, the potential to create the multidimensional equivalent of a Ramachandran plot is available; that is, forbidden and accessible regions in the reduced space reflect these same regions in the nine-dimensional original space. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 695–715, 1998     

Design of UV laser pulses for the preparation of matrix isolated homonuclear diatomic molecules in selective vibrational superposition states

The preparation of matrix isolated homonuclear diatomic molecules in a vibrational superposition state c0Phie=1,v=0+cjPhie=1,v=j, with large (|c0|2 approximately 1) plus small contributions (|cj|2<1) of the ground v=0 and specific v=j low excited vibrational eigenstates, respectively, in the electronic ground (e=1) state, and without any net population transfer to electronic excited (e>1) states, is an important challenge; it serves as a prerequisite for coherent spin control. For this purpose, the authors investigate two scenarios of laser pulse control, involving sequential or intrapulse pump- and dump-type transitions via excited vibronic states Phiex,k with a dominant singlet or triplet character. The mechanisms are demonstrated by means of quantum simulations for representative nuclear wave packets on coupled potential energy surfaces, using as an example a one-dimensional model for Cl2 in an Ar matrix. A simple three-state model (including Phi1,0, Phi1,j and Phiex,k) allows illuminating analyses and efficient determinations of the parameters of the laser pulses based on the values of the transition energies and dipole couplings of the transient state which are derived from the absorption spectra.     

Is styrene planar in liquid phases?

The proton NMR spectra of two (13)C-labeled isotopomers of styrene dissolved in two liquid crystalline solvents have been obtained and analyzed to yield four sets each of 24 dipolar couplings. These couplings were then used to investigate the structure of the ring and the ene fragments of the molecule, and the position of the maximum, phi(0), in the ring-ene bond rotational probability distribution. To do this, the effect on the dipolar couplings of small-amplitude vibrational motion was taken into account using vibrational wave functions calculated by molecular orbital and density functional methods. It is concluded that the NMR data are consistent with the ring fragment, averaged over the ring-ene rotation, planar, while the ene fragment is not. The value of phi(0) is found to be 18.0 degrees +/-0.2 degrees for the two solutions, compared with a value of 27 degrees calculated by the molecular method MP2/6-31G(*).     

Absolute and relative entropies from computer simulation with applications to ligand binding

A comparison between two related methods, Schlitter's formula and quasiharmonic analysis, for calculating absolute entropies from the covariance matrix of atomic fluctuations using molecular dynamics (MD) simulations is presented. Calculations for a set of organic compounds in the gas phase are compared to the corresponding statistical thermodynamics results for translational and rotational entropies and to experimental data for vibrational entropies. Encouraging agreement is obtained for translational entropies, but for the rotational contribution, both methods fail to reproduce the theoretically calculated values. Absolute and relative vibrational entropies are found to be better reproduced using quasiharmonic analysis compared to Schlitter's formula. For rotational entropies, we propose a method based on the variances in Euler angles, which gives good agreement with theory. Alternative methods for estimating translational entropies based on principal root mean-square (rms) fluctuations of the center of mass are also presented, and these reproduce theoretically calculated values well. These methodologies are applied to the binding of benzene to T4-lysozyme, where close agreement with the literature is obtained for translational and rotational entropies.     

Two-dimensional near-ultraviolet spectroscopy of aromatic residues in amyloid fibrils: a first principles study

We report a first principles study of two dimensional electronic spectroscopy of aromatic side chain transitions in the 32-residue β-amyloid (Aβ(9-40)) fibrils in the near ultraviolet (250-300 nm). An efficient exciton Hamiltonian with electrostatic fluctuations (EHEF) algorithm is used to compute the electronic excitations in the presence of environmental fluctuations. The through-space inter- and intra-molecular interactions are calculated with high level quantum mechanics (QM) approaches, and interfaced with molecular mechanics (MM) simulations. Distinct two dimensional near ultraviolet (2DNUV) spectroscopic signatures are identified for different aromatic transitions, and the couplings between them. 2DNUV signals associated with the transition couplings are shown to be very sensitive to the change of residue-residue interactions induced by residue mutations. Our simulations suggest that 2DNUV spectra could provide a useful local probe for the structure and kinetics of fibrils.     

The conformation of tetraalanine in water determined by polarized Raman, FT-IR, and VCD spectroscopy

The present article reports the conformation of cationic tetraalanine in aqueous solution. The determination of the dihedral angles of the two central amino acid residues was achieved by analyzing the amide I' band profile in the respective polarized visible Raman, Fourier transform-IR, and vibrational circular dichroism (VCD) spectra by means of a novel algorithm which utilizes the excitonic coupling between the amide I modes of nearest neighbor and second nearest peptide groups. It is an extension of a recently developed theory (Schweitzer-Stenner, R. Biophys. J., 2002, 83, 523-532). UV electronic circular dichroism (ECD) spectra of the peptides were used to validate the results of the structure analysis. The analyses yielded the dihedral angles (phi(12), psi(12)) = (-70 degrees, 155 degrees ) and (phi(23), psi(23)) = (-80 degrees, 145 degrees ). The obtained values are very close to the Ramachandran coordinates of the polyproline II helix (PPII). The data suggest that this is the conformation predominantly adopted by the peptide at room temperature. This notion was corroborated by the corresponding electronic circular dichroism spectrum. Tetraalanine exhibits a higher propensity for PPII than trialanine for which a 50:50 mixture of polyproline II and an extended beta-strand-like conformation was obtained from recent spectroscopic studies (Eker et al., J. Am. Chem. Soc. 2002, 124, 14330-14341). The temperature dependence of the CD spectra rule out that any cooperativity is involved in the strand if PPII transition. This led to the conclusion that solvent-peptide interactions give rise to the observed PPII stability. Our result can be utilized to understand why the denaturation of helix-forming peptides generally yields a PPII rather than a heterogeneous random conformation.     

Conformations of N-acetyl-L-prolinamide by two-dimensional infrared spectroscopy

Femtosecond two-dimensional infrared (2D IR) spectroscopy has been applied to study the conformations of a model dipeptide, N-acetyl-L-prolinamide (AcProNH2) in deuterated chloroform (CDCl3). Spectral features in the amide-I and -II regions are obtained by rephasing (R), nonrephasing (NR), and reverse photon echo (RPE) pulse sequences with two polarization conditions. The 2D spectra obtained by the RPE and NR sequences with (0, 0, 0, 0) polarization reveal new spectral features associated with the multiple conformers of AcProNH2 that are difficult to discern using R sequence and linear-IR spectroscopy. The high resolving power of the RPE sequence comes from destructive interference between the positive and negative peaks of nearby vibrators, similar to the NR sequence. The RPE response functions that are useful for 2D spectral simulations are evaluated, including the effects of vibrational frequency correlations. The 2D spectra obtained with (45, -45, 90, 0) polarization exhibit clear cross-peak patterns in the off-diagonal region for the R and RPE sequences but in the diagonal region for the NR sequence. These patterns, free from strong diagonal contributions, are crucial for structure determination. DFT calculations, normal-mode analysis, Hessian matrix reconstruction, and vibrational exciton Hamiltonian diagonalization yield molecular parameters needed for quantitative simulations of 2D spectra: angles between transition dipoles, coupling constants, and off-diagonal anharmonicities of the amide-I and -II modes are obtained for solvated trans-C7 and cis structures and for gas-phase trans conformers in the region of phi = -120 degrees to 0 degrees and psi = -100 degrees to 180 degrees in the Ramachandran space. Systematic simulations based on a 4:1 population ratio of the solvated trans-C7 and cis structures reproduce well the 2D spectral features obtained at both polarization conditions. However, better agreement between the experimental and simulated cross-peak patterns can be reached if the dihedral angles of the major trans conformer are close to (phi, psi) = (-80 degrees , 100 degrees ). Our results suggest that the major conformer of AcProNH2 in CDCl3 deviates from the gas-phase global minimum, the trans-C7 form, to an extended intermediate between the C7 and polyproline-II structure. These results are discussed in relationship with earlier findings obtained by NMR, transient IR studies, and MD simulations.     

Experimental and theoretical investigation of the 13C and 15N chemical shift tensors in melanostatin-exploring the chemical shift tensor as a structural probe

The determination of backbone conformations in powdered peptides using 13C and 15N shift tensor information is explored. The 13C and 15N principal shift values in natural abundance 13C and 15N melanostatin (L-Pro-L-Leu-Gly amide) are measured using the FIREMAT technique. Furthermore, the orientation of the C-N bond in the 13C shift principal axis system for the backbone carbons is obtained from the presence of the 13C-14N dipolar coupling. The Ramachandran angles for the title compound are obtained from solid-state NMR data by comparing the experimentally determined shift tensor information to systematic theoretical shielding calculations on N-formyl-L-amino acid-amide models. The effects of geometry optimization and neglect of intermolecular interactions on the theoretical shielding values in the model compounds are investigated. The sets of NMR derived Ramachandran angles are assembled in a set of test structures that are compared to the available single-crystal X-ray structure. Shift tensor calculations on the test structures and the X-ray structure are used to further assess the importance of intermolecular interactions when the shift tensor is used as a structural probe in powdered peptides.     

Ultrafast Structural Dynamics of Biomolecules Examined by Multiple‐Mode 2D IR Spectroscopy: Anharmonically Coupled Motions are in Harmony

Quantum chemical computations, molecular dynamics simulations, and linear and nonlinear infrared spectral simulations are carried out for four representative biomolecules: cellobiose, alanine tripeptide, L ‐α‐glycerylphosphorylethanolamine, and the DNA base monomer guanine. Anharmonic transition frequencies and anharmonicities for the molecules in vacuum are evaluated. Instantaneous normal‐mode analysis is performed and the vibrational frequency distribution correlations are examined for the molecules solvated in TIP3P water. Many local and regional motions of the biomolecules are predicted to be anharmonically coupled and their vibrational frequencies are predicted to be largely correlated. These coupled and correlated vibrational motions can be easily visualized by pairwise cross peaks in the femtosecond broadband two‐dimensional infrared (2D IR) spectra, which are simulated using time‐domain third‐order nonlinear response functions. A network of distinctive spectral profiles of the 2D IR cross peaks, including peak orientations and positive and negative signal patterns, are shown to be intimately connected with the couplings and correlations. The results show that the vibrational couplings and correlations, driven by solvent interactions and also by intrinsic vibrational interactions, are vibrational mode dependent and thus chemical group dependent, and form the structural and dynamical basis of the anharmonic vibrators that are ubiquitous in biomolecules.     

Vibrational cooling in a cold ion trap: vibrationally resolved photoelectron spectroscopy of cold C60(-) anions

We demonstrate vibrational cooling of anions via collisions with a background gas in an ion trap attached to a cryogenically controlled cold head (10-400 K). Photoelectron spectra of vibrationally cold C60(-) anions, produced by electrospray ionization and cooled in the cold ion trap, have been obtained. Relative to spectra taken at room temperature, vibrational hot bands are completely eliminated, yielding well-resolved vibrational structures and a more accurate electron affinity for neutral C60. The electron affinity of C60 is measured to be 2.683+/-0.008 eV. The cold spectra reveal complicated vibrational structures for the transition to the C60 ground state due to the Jahn-Teller effect in the ground state of C60(-). Vibrational excitations in the two A(g) modes and eight H(g) modes are observed, providing ideal data to assess the vibronic couplings in C60(-).     

Two-dimensional Raman and infrared vibrational spectroscopy for a harmonic oscillator system nonlinearly coupled with a colored noise bath

Multidimensional vibrational response functions of a harmonic oscillator are reconsidered by assuming nonlinear system-bath couplings. In addition to a standard linear-linear (LL) system-bath interaction, we consider a square-linear (SL) interaction. The LL interaction causes the vibrational energy relaxation, while the SL interaction is mainly responsible for the vibrational phase relaxation. The dynamics of the relevant system are investigated by the numerical integration of the Gaussian-Markovian Fokker-Planck equation under the condition of strong couplings with a colored noise bath, where the conventional perturbative approach cannot be applied. The response functions for the fifth-order nonresonant Raman and the third-order infrared (or equivalently the second-order infrared and the seventh-order nonresonant Raman) spectra are calculated under the various combinations of the LL and the SL coupling strengths. Calculated two-dimensional response functions demonstrate that those spectroscopic techniques are very sensitive to the mechanism of the system-bath couplings and the correlation time of the bath fluctuation. We discuss the primary optical transition pathways involved to elucidate the corresponding spectroscopic features and to relate them to the microscopic sources of the vibrational nonlinearity induced by the system-bath interactions. Optical pathways for the fifth-order Raman spectroscopies from an "anisotropic" medium were newly found in this study, which were not predicted by the weak system-bath coupling theory or the standard Brownian harmonic oscillator model.     

Carbonyl vibrational wave packet circulation in Mn2(CO)10 driven by ultrashort polarized laser pulses

The excitation of the degenerate E(1) carbonyl stretching vibrations in dimanganese decacarbonyl is shown to trigger wave packet circulation in the subspace of these two modes. On the time scale of about 5 ps, intramolecular anharmonic couplings do not cause appreciable disturbance, even under conditions where the two E(1) modes are excited by up to about two vibrational quanta each. The compactness of the circulating wave packet is shown to depend strongly on the excitation conditions, such as pulse duration and field strength. Numerical results for the solution of the seven-dimensional vibrational Schro?dinger equation are obtained for a density functional theory based potential energy surface and using the multi-configuration time-dependent Hartree method.     

Approximate inclusion of four-mode couplings in vibrational coupled-cluster theory

The vibrational coupled cluster (VCC) equations are analyzed in terms of vibrational Mo?ller-Plesset perturbation theory aiming specifically at the importance of four-mode couplings. Based on this analysis, new VCC methods are derived for the calculation of anharmonic vibrational energies and vibrational spectra using vibrational coupled cluster response theory. It is shown how the effect of four-mode coupling and excitations can be efficiently and accurately described using approximations for their inclusion. Two closely related approaches are suggested. The computational scaling of the so-called VCC[3pt4F] method is not higher than the fifth power in the number of vibrational degrees of freedom when up to four-mode coupling terms are present in the Hamiltonian and only fourth order when only up to three-mode couplings are present. With a further approximation, one obtains the VCC[3pt4] model which is shown to scale with at most the fourth power in the number of vibrational degrees of freedom for Hamiltonians with both three- and four-mode coupling levels, while sharing the most important characteristics with VCC[3pt4F]. Sample calculations reported for selected tetra-atomic molecules as well as the larger dioxirane and ethylene oxide molecules support that the new models are accurate and useful.