Linear and nonlinear infrared signatures of local α- and 310-helical structures in alanine polypeptides

High pressure Raman study of type-I collagen

The high pressure response of type-I collagen from bovine Achilles tendon is investigated with micro-Raman spectroscopy. Fluorinert™ and methanol-ethanol mixtures were used as pressure transmitting media (PTM) in a diamond anvil cell. The Raman spectrum of collagen is dominated by three bands centred at approximately 1450, 1660 and 2930 cm^-1 , attributed to C-H deformation, C=O stretching of the peptide bond (amide-I band) and C-H stretching modes respectively. Upon pressure increase, using Fluorinert™ as PTM, a shift towards higher frequencies of the C-H stretching and deformation peaks is observed. Contrary, the amide-I band peaks are shifted to lower frequencies with moderate pressure slopes. On the other hand, when using the alcohol mixture as PTM, the amide-I band exhibits more pronounced C=O bond softening, deduced from the shift to lower frequencies, suggesting a strengthening of the hydrogen bonds between glycine and proline residues of different collagen chains due to the presence of the polar alcohol molecules. Furthermore, some of the peaks exhibit abrupt changes in their pressure slopes at approximately 2 GPa, implying a variation in the compressibility of the collagen fibres. This could be attributed to a pitch change from 10/3 to 7/2, sliding of the tropocollagen molecules, twisting variation at the molecular level and/or elimination of the D-gaps induced by kink compression. All spectral changes are reversible upon pressure release, which indicates that denaturation has not taken place. Finally, a minor lipid phase contamination was detected in some sample spots. Its pressure response is also monitored.

Dissecting amide-I vibration in β-peptide helices

The vibrational properties of the amide-I modes of β-peptides in five helical conformations (8-helix, 10-helix, 12-helix, 14-helix, and 10/12-helix) from tetramer to heptamer were examined by ab initio calculations. The normal modes have been first decoupled into local modes, whose transition energies are found to be intrinsically sensitive to peptide structure and intramolecular hydrogen bonding interactions. By further removing the intramolecular hydrogen bonding interactions, pure local modes are obtained, whose transition energies still exhibit some conformational dependence in 8-helix and 10/12 hybrid helix, but not much in homogeneous 10-, 12-, and 14-helical conformations. This suggests that a set of nearly degenerated pure local-mode transitions can be specified when excitonic modeling the amide-I vibration in latter cases. The work provides important benchmark measurements for understanding the complexity of the amide-I absorption spectra of β-polypeptides.

Monitoring the folding of Trp-cage peptide by two-dimensional infrared (2DIR) spectroscopy

Protein folding is one of the most fundamental problems in modern molecular biology. Uncovering the detailed folding mechanism requires methods that can monitor the structures at high temporal and spatial resolution. Two-dimensional infrared (2DIR) spectroscopy is a new tool for studying protein structures and dynamics with high time resolution. Using atomistic molecular dynamics simulations, we illustrate the folding process of Trp-cage along the dominant pathway on the free energy landscape by analyzing nonchiral and chiral coherent 2DIR spectra along the pathway. Isotope labeling is used to reveal residue-specific information. We show that the high resolution structural sensitivity of 2DIR can differentiate the ensemble evolution of protein and thus provides a microscopic picture of the folding process.

Spectroscopic studies of protein folding: linear and nonlinear methods

Although protein folding is a simple outcome of the underlying thermodynamics, arriving at a quantitative and predictive understanding of how proteins fold nevertheless poses huge challenges. Therefore, both advanced experimental and computational methods are continuously being developed and refined to probe and reveal the atomistic details of protein folding dynamics and mechanisms. Herein, we provide a concise review of recent developments in spectroscopic studies of protein folding, with a focus on new triggering and probing methods. In particular, we describe several laser-based techniques for triggering protein folding/unfolding on the picosecond and/or nanosecond timescales and various linear and nonlinear spectroscopic techniques for interrogating protein conformations, conformational transitions, and dynamics.

Amide vibrations and their conformational dependences in β-peptide

The characteristics of the amide-A and amide-I modes in a β-homoalanine dipeptide (β-HADP) have been examined as a function of backbone dihedral angles. The harmonic frequencies were obtained using the density functional theory. The anharmonic frequencies and diagonal anharmonicities were obtained by using the Morse potential. Local-mode frequencies and intermode couplings were obtained using the computed normal-mode frequencies and eigenvectors. It was found that the vibrational frequencies for the two types of amide modes are both conformational-dependent. The inter-amide-A and inter-amide-I couplings in the β-peptides were predicted to be generally weaker than those in the α-peptides. Structural bases of the amide-A and amide-I local modes in the β-peptides are discussed.

Vibrational dynamics of DNA. III. Molecular dynamics simulations of DNA in water and theoretical calculations of the two-dimensional vibrational spectra

A theoretical description of the vibrational excitons in DNA is presented by using the vibrational basis mode theory developed in Papers I and II. The parameters obtained from the density functional theory calculations, such as vibrational coupling constants and basis mode frequencies, are used to numerically simulate two-dimensional (2D) IR spectra of dG(n):dC(n) and dA(n):dT(n) double helices with n varying from 1 to 10. From the molecular dynamics simulations of dG(5)C(5) and dA(5)T(5) double helices in D(2)O solution, it is found that the thermally driven internal motions of these systems in an aqueous solution do not induce strong fluctuations of basis mode frequencies nor vibrational couplings. In order to construct the two-exciton Hamiltonian, the vibrational anharmonicities of eight basis modes are obtained by carrying out B3LYP6-31G(*) calculations for the nine basis modes. The simulated 2D IR spectra of dG(n):dC(n) double helix in D(2)O solution are directly compared with closely related experimental results. The 2D IR spectra of dG(n):dC(n) and dA(n):dT(n) are found to be weakly dependent on the number of base pairs. The present work demonstrates that the computational procedure combining quantum chemistry calculation and molecular dynamics simulation methods can be of use to predict 2D IR spectra of nucleic acids in solutions.

Vibron-polaron in alpha-helices. I. Single-vibron states

The vibron dynamics associated to amide-I vibrations in a three-dimensional alpha-helix is described according to a generalized Davydov model. The helix is modeled by three spines of hydrogen-bonded peptide units linked via covalent bonds. To remove the intramolecular anharmonicity of each amide-I mode and to renormalize the vibron-phonon coupling, two unitary transformations have been applied to reach the dressed anharmonic vibron point of view. It is shown that the vibron dynamics results from the competition between interspine and intraspine vibron hops and that the two kinds of hopping processes do not experience the same dressing mechanism. Therefore, at low temperature (or weak vibron-phonon coupling), the polaron behaves as an undressed vibron delocalized over all the spines whereas at biological temperature (or strong vibron-phonon coupling), the dressing effect strongly reduces the vibrational exchanges between different spines. As a result the polaron propagates along a single spine as in the one-dimensional Davydov model. Although the helix supports both acoustical and optical phonons, this feature originates in the coupling between the vibron and the acoustical phonons only. Finally, the lattice distortion which accompanies the polaron has been determined and it is shown that residues located on the excited spine are subjected to a stronger deformation than the other residues.

Chirality-induced signals in coherent multidimensional spectroscopy of excitons

The nonlocal second- and third-order susceptibilities of an isotropic ensemble of aggregates are calculated by solving the nonlinear exciton equations which map the system into coupled anharmonic oscillators. Both electric and magnetic contributions are included using the minimal-coupling Hamiltonian. The various tensor components are evaluated to first order in the optical wave vector k. Additional structural information about the interchromophore distances, which is not accessible through zeroth-order contributions (the dipole approximation), is contained to the first order in k. New resonant second- and third-order signals predicted for chiral molecules provide multidimensional extensions of circular dichroism spectroscopy. Numerical simulations demonstrate the sensitivity of third-order signals to the secondary structural motiffs of peptides.

Simulation protocols for coherent femtosecond vibrational spectra of peptides

Two algorithms for simulating the response of peptides to sequences of IR pulses are developed and applied to N-methyl acetamide (NMA) and a 17 residue alpha-helical peptide (YKKKH17) in D(2)O. A fluctuating vibrational-exciton Hamiltonian for the amide I mode is constructed from molecular dynamics trajectories. Coupling with the environment is described using a density functional theory electrostatic map. The cumulant expansion of Gaussian fluctuation incorporates motional narrowing due to fast frequency fluctuations and is adequate for NMA and for isotopically labeled bands in large peptides. Real-space truncation of the scattering matrix of the nonlinear exciton equations significantly reduces the computational cost, making it particularly attractive for slow fluctuations in large globular proteins.

Two-Dimensional Infrared Spectral Signatures of 310- and α-Helical Peptides

Two-dimensional infrared (2D IR) spectra of Calpha-alkylated model octapeptides Z-(Aib)8-OtBu, Z-(Aib)5-L-Leu-(Aib)2-OMe, and Z-[L-(alphaMeVal)]8-OtBu have been measured in the amide I region to acquire 2D spectral signatures characteristic of 3(10)- and alpha-helical conformations. Phase-adjusted 2D absorptive spectra recorded with parallel polarizations are dominated by intense diagonal peaks, whereas 2D rephasing spectra obtained at the double-crossed polarization configuration reveal cross-peak patterns that are essential for structure determination. In CDCl3, all three peptides are of the 3(10)-helix conformation and exhibit a doublet cross-peak pattern. In 1,1,1,3,3,3-hexafluoroisopropanol, Z-[L-(alphaMeVal)]8-OtBu undergoes slow acidolysis and 3(10)-to-alpha-helix transition. In the course of this conformational change, its 2D rephasing spectrum evolves from an elongated doublet, characteristic of a distorted 3(10)-helix, to a multiple-peak pattern, after becoming an alpha-helix. The linear IR and 2D absorptive spectra are much less informative in discerning the structural changes. The experimental spectra are compared to simulations based on a vibrational exciton Hamiltonian model. The through-bond and through-space vibrational couplings are modeled by ab initio coupling maps and transition dipole interactions. The local amide I frequency is evaluated by a new approach that takes into account the effects of hydrogen-bond geometry and sites. The static diagonal and off-diagonal disorders are introduced into the Hamiltonian through statistical models to account for conformational fluctuations and inhomogeneous broadening. The sensitivity of cross-peak patterns to different helical conformations and the chain length dependence of the spectral features for short 3(10)- and alpha-helices 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.

Self-trapping of the N–H vibrational mode in α-helical polypeptides

Recent calculations on the formation of self-trapped amide group vibrational states in alpha-helical polypeptides [J. Chem. Phys. 124, 134907 (2006)] are extended to the amide N-H normal mode vibrations. First, the adiabatic N-H vibrational single- and two-exciton states are examined by treating the longitudinal chain coordinates as parameters. Then, in using the multiconfiguration time-dependent Hartree method coupled exciton-chain vibrational quantum dynamics are accounted for. Based on the respective exciton-chain vibrational wave function propagation the infrared transient absorption related to a sequential pump-probe experiment is calculated. The modulation of local amide vibrational energies by the longitudinal chain coordinates is found to have a pronounced effect on the broadening of absorption lines. Moreover, the ultrafast exciton transfer in the system is studied in order to characterize the dynamics of the self-trapped single-exciton states on a time scale below 10 ps.

Structural disorder of the CD3zeta transmembrane domain studied with 2D IR spectroscopy and molecular dynamics simulations

In a recently reported study [Mukherjee, et al. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 3528] we used 2D IR spectroscopy and 1-(13)C=(18)O isotope labeling to measure the vibrational dynamics of 11 amide I modes in the CD3zeta transmembrane domain. We found that the homogeneous line widths and population relaxation times were all nearly identical, but that the amount of inhomogeneous broadening correlated with the position of the amide group inside the membrane. In this study, we use molecular dynamics simulations to investigate the structural and dynamical origins of these experimental observations. We use two models to convert the simulations to frequency trajectories from which the mean frequencies, standard deviations, frequency correlation functions, and 2D IR spectra are calculated. Model 1 correlates the hydrogen-bond length to the amide I frequency, whereas model 2 uses an ab initio-based electrostatic model. We find that the structural distributions of the peptidic groups and their environment are reflected in the vibrational dynamics of the amide I modes. Environmental forces from the water and lipid headgroups partially denature the helices, shifting the infrared frequencies and creating larger inhomogeneous distributions for residues near the ends. The least inhomogeneously broadened residues are those located in the middle of the membrane where environmental electrostatic forces are weakest and the helices are most ordered. Comparison of the simulations to experiment confirms that the amide I modes near the C-terminal are larger than at the N-terminal because of the asymmetric structure of the peptide bundle in the membrane. The comparison also reveals that residues at a kink in the alpha-helices have broader line widths than more helical parts of the peptide because the peptide backbone at the kink exhibits a larger amount of structural disorder. Taken together, the simulations and experiments reveal that infrared line shapes are sensitive probes of membrane protein structural and environmental heterogeneity.

A pulse sequence for directly measuring the anharmonicities of coupled vibrations: Two-quantum two-dimensional infrared spectroscopy

We have experimentally demonstrated a pulse sequence for the acquisition of heterodyned two-dimensional infrared (2D IR) spectra that correlates the overtone and combination bands to the fundamental frequencies. The spectra are generated by Fourier transforming the time domain signal that is allowed to evolve during one- and two-quantum coherence times. In this manner, the overtone and combination bands appear along the two-quantum axis, resulting in a direct determination of the diagonal and off-diagonal anharmonicities. To demonstrate this pulse sequence, we have collected two-quantum 2D IR spectra of a ruthenium dicarbonyl complex, extracted the diagonal and off-diagonal anharmonicities, and simulated the spectra using an exciton model. Several polarization conditions are presented that suppress the diagonal or cross peaks and we have used them to improve the accuracy of the measurement.

Non-Gaussian statistics of amide I mode frequency fluctuation of N-methylacetamide in methanol solution: linear and nonlinear vibrational spectra

By carrying out molecular dynamics simulations of an N-methylacetamide (NMA) in methanol solution, the amide I mode frequency fluctuation and hydrogen bonding dynamics were theoretically investigated. Combining an extrapolation formula developed from systematic ab initio calculation studies of NMA-(CH3OH)n clusters with a classical molecular dynamics simulation method, we were able to quantitatively describe the solvatochromic vibrational frequency shift induced by the hydrogen-bonding interaction between NMA and solvent methanol. It was found that the fluctuating amide I mode frequency distribution is notably non-Gaussian and it can be decomposed into two Gaussian peaks that are associated with two distinctively different solvation structures. The ensemble-average-calculated linear response function associated with the IR absorption is found to be oscillating, which is in turn related to the doublet amide I band shape. Numerically calculated infrared absorption spectra are directly compared with experiment and the agreement was found to be excellent. By using the Onsager's regression hypothesis, the rate constants of the interconversion process between the two solvation structures were obtained. Then, the nonlinear response functions associated with two-dimensional infrared pump-probe spectroscopy were simulated. The physics behind the two-dimensional line shape and origin of the cross peaks in the time-resolved pump-probe spectra is explained and the result is compared with 2D spectra experimentally measured recently by Woutersen et al.

Vibrational excitons in α-helical polypeptides: Multiexciton self-trapping and related infrared transient absorption

Based on the multiexciton expansion of a model Hamiltonian, an accurate quantum-dynamical description of vibrational states formed by amide modes in alpha-helical polypeptides is presented. Using the multiconfiguration time-dependent Hartree method, linear and pump-probe infrared absorption spectra are calculated by numerical time propagation of the exciton-chain vibrational wave function. The formation of self-trapped exciton states is discussed within the approximation of adiabatic excitons and within the full quantum description.

Different Spectral Signatures of Octapeptide 310- and α-Helices Revealed by Two-Dimensional Infrared Spectroscopy

Femtosecond two-dimensional infrared (2D IR) spectroscopy is applied to the amide I modes of the terminally protected homo-octapeptide Z-[L-(alphaMe)Val](8)-OtBu in CDCl(3), 2,2,2-trifluoroethanol (TFE), and 1,1,1,3,3,3-hexafluoro-2-propanol (HFIP) solutions to acquire 2D spectral signatures that distinguish between 3(10)- and alpha-helix structures. Suppression of diagonal peaks by controlling polarizations of IR pulses clearly reveals cross-peak patterns that are crucial for structural determination. A doublet feature is observed when the peptide ester forms a 3(10)-helix in CDCl(3) and TFE and when it is at the initial stage of 3(10)- to alpha-helix transition in HFIP. In contrast, the 2D IR spectrum shows a multiple peak pattern after the peptide ester has acidolyzed and become an alpha-helix in HFIP. Electronic circular dichroism spectra accompanying the acidolysis-driven conformational change are also reported. This is the first report on the experimental 2D IR signature of a 3(10)-helical peptide. These results, using a model octapeptide, demonstrate the powerful capability of 2D IR spectroscopy to discriminate between different helical structures.

Vibrational spectroscopic characteristics of secondary structure polypeptides in liquid water: Constrained MD simulation studies

Using the constrained MD simulation method in combination with quantum chemistry calculation, Hessian matrix reconstruction, and fragmentation approximation methods, we established a computational scheme for numerical simulations of amide I IR absorption, vibrational circular dichroism (VCD), and 2D IR photon echo spectra of peptides in solution. Six different secondary structure peptides, i.e., alpha-helix, 3(10)-helix, pi-helix, antiparallel and parallel beta-sheets, and polyproline II (P(II)), are considered, and the vibrational characteristic features in their linear and nonlinear spectra in the amide I band region are discussed. Isotope-labeling effects on IR and VCD spectra are notable only for alpha- and pi-helical peptides due to the strong vibrational couplings between two nearest neighboring amide I local oscillators. The amplitudes of difference 2D IR spectra are shown to be strongly dependent on both the extent of mode delocalization and the relative orientation of local mode transition dipoles determined by secondary structure.

Multidimensional infrared spectroscopy for molecular vibrational modes with dipolar interactions, anharmonicity, and nonlinearity of dipole moments and polarizability

We present an analytical expression for the linear and nonlinear infrared spectra of interacting molecular vibrational motions. Each of the molecular modes is explicitly represented by a classical damped oscillator on an anharmonic multidimensional potential-energy surface. The two essential interactions, the dipole-dipole (DD) and the dipole-induced-dipole (DID) interactions, are taken into account, and each dipole moment and polarizability are expanded to nonlinear order with respect to the nuclear vibrational coordinate. Our analytical treatment leads to expressions for the contributions of anharmonicity, DD and DID interactions, and the nonlinearity of dipole moments and polarizability elements to the one-, two-, and three-dimensional spectra as separated terms, which allows us to discuss the relative importance of these respective contributions. We can calculate multidimensional signals for various configurations of molecules interacting through DD and DID interactions for different material parameters over the whole range of frequencies. We demonstrate that contributions from the DD and DID interactions and anharmonicity are separately detectable through the third-order three-dimensional IR spectroscopy, whereas they cannot be distinguished from each other in either the linear or the second-order IR spectroscopies. The possibility of obtaining the intra- or intermolecular structural information from multidimensional spectra is also discussed.

Vibron-polaron in α-helices. II. Two-vibron bound states

The two-vibron dynamics associated to amide-I vibrations in a three-dimensional (3D) alpha-helix is described according to a generalized Davydov model. The helix is modeled by three spines of hydrogen-bonded peptide units linked via covalent bonds. It is shown that the two-vibron energy spectrum supports both a two-vibron free states continuum and two kinds of bound states, called two-vibron bound states (TVBS)-I and TVBS-II, connected to the trapping of two vibrons onto the same amide-I mode and onto two nearest-neighbor amide-I modes belonging to the same spine, respectively. At low temperature, nonvanishing interspine hopping constants yield a three-dimensional nature of both TVBS-I and TVBS-II which the wave functions extend over the three spines of the helix. At biological temperature, the pairs are confined in a given spine and exhibit the same features as the bound states described within a one-dimensional model. The interplay between the temperature and the 3D nature of the helix is also responsible for the occurrence of a third bound state called TVBS-III which refers to the trapping of two vibrons onto two different spines. The experimental signature of the existence of bound states is discussed through the simulation of their infrared pump-probe spectroscopic response. Finally, the fundamental question of the breather-like behavior of two-vibron bound states is addressed.

Ab initio-based exciton model of amide I vibrations in peptides: Definition, conformational dependence, and transferability

Various aspects of the ab initio-based parametrization of an exciton model of amide I vibrations in peptides are discussed. Adopting "glycine dipeptide" (Ac-Gly-NHCH3) as a simple building-block model that describes the vibrational interaction between two peptide units, we perform comprehensive quantum-chemical calculations to investigate the effect and importance of the level of theory, the choice of local coordinates, and the localization method. A solvent continuum model description turns out important to obtain planar CONH peptide units when a full geometry optimization (which is necessary to obtain the correct frequencies) is performed. To study the conformational dependence of the amide I vibrations, we calculate (phi,psi) maps of the local-mode frequencies and couplings. Performing conformational averages of the (phi,psi) maps with respect to the most important peptide conformational states in solution (alpha, beta, P(II), and C5), we discuss the relation between these measurable quantities and the corresponding conformation of the peptide. Finally, the transferability of these maps to dipeptides with hydrophilic and hydrophobic side chains as well as to tripeptides with charged end groups is investigated.

Collective Oscillations and the Linear and Two-Dimensional Infrared Spectra of Inhomogeneous β-Sheets

We numerically calculate the collective amide I oscillations and the associated linear and two-dimensional infrared (2DIR) spectra for model antiparallel beta-sheets and study the effect of inhomogeneity. To visualize the collective vibrational exciton states, a new method is introduced, which proves very useful in classifying the optically dominant states with respect to their symmetry properties and phase relations, even in the absence of exact symmetries. We find that energy (diagonal) and interaction (off-diagonal) disorder may have profoundly different effects on the main peaks in the linear spectrum. We also show that in the 2DIR spectra energy disorder leads to diagonal stretching of the diagonal peaks, while the cross-peaks are typically stretched more horizontally. This offers an explanation for the recently observed overall Z-shape in experimental spectra. Finally, we find that the anharmonic splitting between associated positive and negative features in the 2DIR spectra scales inversely proportionally with the exciton delocalization size imposed by the disorder, thus offering a spectroscopic ruler for this size.

Coherent third-order spectroscopic probes of molecular chirality

The third-order optical response of a system of coupled localized anharmonic vibrations is studied using a Green's function solution of the nonlinear exciton equations for bosonized excitons, which are treated as interacting quasiparticles. The explicit calculation of two-exciton states is avoided and the scattering of quasiparticles provides the mechanism of optical nonlinearities. To first-order in the optical wave vector we find several rotationally invariant tensor components for isotropic ensembles which are induced by chirality. The nonlocal nonlinear susceptibility tensor is calculated for infinitely large periodic structures in momentum space, where the problem size reduces to the exciton interaction radius. Applications are made to alpha and 3(10) helical infinite peptides.

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.

Stochastic Liouville equation simulation of multidimensional vibrational line shapes of trialanine

The line shapes detected in coherent femtosecond vibrational spectroscopies contain direct signatures of peptide conformational fluctuations through their effect on vibrational frequencies and intermode couplings. These effects are simulated in trialanine using a Green's function solution of a stochastic Liouville equation constructed for four collective bath coordinates (two Ramachandran angles affecting the mode couplings and two diagonal energies). We find that fluctuations of the Ramachandran angles which hardly affect the linear absorption can be effectively probed by two-dimensional spectra. The signal generated at k(1)+k(2)-k(3) is particularly sensitive to such fluctuations.

The origin of vibrational mode couplings in various secondary structural motifs of polypeptides

Electrostatic (through-space) and covalent (through-bond) contributions to couplings involving the C[double bond]O and C[bond]N vibrational stretching modes of the amide group in the alpha-helix and the parallel and antiparallel beta-sheet structures of alanine polypeptides are analyzed. Coupling constants computed at the density functional theory level are compared with the transition dipole coupling model and the complete electrostatic interaction between transition densities. We find that the transition densities of C[double bond]O modes are localized, and the electrostatic mechanism then holds. In contrast, the C[bond]N mode transition densities are delocalized, and covalent contributions to the coupling are significant.