Vibrational Energy Transport Research Articles

Coherent vibrational energy transfer along a peptide helix

To measure the transport of vibrational energy along a peptide helix, Hamm and co-workers [J. Phys. Chem. B 112, 9091 (2008)] performed time-resolved vibrational experiments, which showed that the energy transport rate increases by at least a factor of 4, when a localized C=O mode of the peptide instead of an attached chromophore is excited. This finding raises the question if coherent excitonic energy transfer between the C=O modes may be of importance for the overall energy transport in peptides. With this idea in mind, nonequilibrium molecular dynamics simulations as well as quantum-classical calculations are performed, which qualitatively reproduce the experimental findings. Moreover, the latter model (an exciton Hamiltonian whose matrix elements depend on the instantaneous positions of the peptide and solvent atoms) indeed exhibits the signatures of coherent quantum energy transport, at least within the first few picoseconds and at low temperatures. The origin of the observed decoherence, the absence of vibrational self-trapping, and the possibility of quantum interference between various transport paths are discussed in some detail.

Modeling the Vibrational Dynamics and Nonlinear Infrared Spectra of Coupled Amide I and II Modes in Peptides

The amide vibrational modes play an important role in energy transport and relaxation in polypeptides and proteins and provide us with spectral markers for structure and structural dynamics of these macromolecules. Here, we present a detailed model to describe the dynamic properties of the amide I and amide II modes and the resulting linear and nonlinear spectra. These two modes have large oscillator strengths, and their mutual coupling plays an important role in their relaxation. Using first-principles calculations of NMA-d(7) and a dipeptide in a fluctuating bath described by molecular dynamics simulations, we model the frequencies of the local vibrations as well as the coupling between them. Both the coherent couplings and the fluctuations induced by contact with their environment are taken into account. We apply the resulting model of interacting fluctuating oscillators to study the collective vibrations and the partially coherent transport of vibrational energy through a model α-helix. We find that the instantaneous vibrations are delocalized over a few (up to four) amide units, while the coherences in the helix survive for 0.5-1 ps, leading to coherent transport on a similar time scale.

Dynamics of Water Clusters Confined in Proteins: A Molecular Dynamics Simulation Study of Interfacial Waters in a Dimeric Hemoglobin

Water confined in proteins exhibits dynamics distinct from the dynamics of water in the bulk or near the surface of a biomolecule. We examine the water dynamics at the interface of the two globules of the homodimeric hemoglobin from Scapharca inaequivalvis (HbI) by molecular dynamics (MD) simulations, with focus on water-protein hydrogen bond lifetimes and rotational anisotropy of the interfacial waters. We find that relaxation of the waters at the interface of both deoxy- and oxy-HbI, which contain a cluster of 17 and 11 interfacial waters, respectively, is well described by stretched exponentials with exponents from 0.1 to 0.6 and relaxation times of tens to thousands of picoseconds. The interfacial water molecules of oxy-HbI exhibit slower rotational relaxation and hydrogen bond rearrangement than those of deoxy-HbI, consistent with an allosteric transition from unliganded to liganded conformers involving the expulsion of several water molecules from the interface. Though the interfacial waters are translationally and rotationally static on the picosecond time scale, they contribute to fast communication between the globules via vibrations. We find that the interfacial waters enhance vibrational energy transport across the interface by ≈10%.

Vibrational Energy Transport through a Capping Layer of Appropriately Designed Peptide Helices over Gold Nanoparticles

We design and characterize spherical gold nanoparticles, which are covalently linked to and completely covered by 3(10)-helical peptides. These helices provide a scaffold to place (13)C=O isotope labels at defined distances from the gold surface, which we employ as local thermometers. Probing these reporter groups with transient infrared spectroscopy, we monitor the vibrational energy flow across the peptide capping layer following excitation of the nanoparticle plasmon resonance.

The vibrational contribution to the thermal conductivity of a polyatomic fluid

A simple analytical expression is proposed in this article to calculate the vibrational contribution to the thermal conductivity of a polyatomic fluid. The analytic expression was obtained based on the assumption that the self-diffusion process is the major mechanism in the transport of vibrational energy. The proposed expression is validated by comparing the thermal conductivity of CO2 calculated by molecular dynamics (MD) simulations to experimental data over a wide range of temperature and pressure. It is also demonstrated that the proposed analytic expression greatly increases the accuracy of calculated thermal conductivity for CO2 at the supercritical state.

Drift-diffusion of a localized quantum state along a thermal gradient in a model α-helix

We consider here a model for the transport of a self-trapped exciton on a lattice under thermal bias in order to develop a quantum mechanical theory for vibrational energy transport along a molecular wire that is in contact with thermal reservoirs at either end of the molecule. For the specific case of the migration of a C O vibrational excitation along a poly-amide α-helix, we find that within our model a C O vibrational exciton can become self-trapped due to strong hydrogen bonding interactions with amide groups even at physiologically relevant temperatures. Furthermore, we find that under the non-equilibrium condition in which the temperature of the two baths are different, the self-trapped state will diffuse towards the cooler end with a diffusion constant proportional to the average temperature of the lattice D ∝ ( T hot + T cold ) / 2 and a drift proportional to the temperature gradient ( T hot - T cold ) / N .

Energy transport via coordination bonds

Vibrational energy transport in transition metal complexes involves stages where energy crosses relatively weak coordination bonds between a coordinated metal atom and the ligands. Understanding the energy transport rules on a molecular level is fundamentally important; it is also essential in relation to a recently proposed structural method, the relaxation-assisted two-dimensional infrared (RA 2DIR) technique, where the vibrational population transport time across the molecule of interest is linked to the transport distance. In this study we report on the energy transport across coordination bonds in tetraethylammonium bis(maleonitriledithiolate)iron(III)nitrosyl complex, studied using dual-frequency RA 2DIR spectroscopy. Three mode pairs, C[triple bond]N and N=O, N=O and C[triple bond]N, and N=O and C-C, were interrogated. All three cross-peaks show substantial amplification due to vibrational energy transport from the initially excited mode toward the "probed" mode, including a record amplification of 27-fold observed for the C[triple bond]N/N=O cross-peak. A ninefold amplification measured for the N=O/C[triple bond]N cross-peak, where the "probed" CN mode has higher frequency than the initially excited NO, proves unequivocally that the excitation of the "probed" mode via energy transport is not essential for observing stronger cross-peaks and that lower frequency modes serve as the energy accepting modes. A simple modeling of the energy transport is presented highlighting the role of a spatial overlap of the interacting modes. The observed strong cross-peak amplifications and a correlation between the energy transport time and the intermode distance, the distance between atom pairs on which vibrational excitations predominantly reside, demonstrate an applicability of the RA 2DIR method for structural interrogation of transition metal complexes.

Vibrational Energy Transport in Peptide Helices after Excitation of C−D Modes in Leu-d10

Vibrational energy transport in a short 3(10)-helical peptide is studied by time-resolved femtosecond infrared spectroscopy. The C-D vibrations of decadeuterated leucine incorporated in the helical chain are excited, and the subsequent flow of vibrational energy through the helix is monitored by employing C horizontal lineO probes at various distances from the heat source as local thermometers. The C-D modes are not resonant to the C horizontal lineO modes, neither directly nor through any Fermi resonance, thereby suppressing resonant energy transfer directly along the C horizontal lineO oscillators of the peptide backbone. In contrast to our previous work (J. Phys. Chem. B 2008, 112, 9091), we no longer find any substantial difference in the vibrational energy transport efficiency after high- or low-energy excitation. That is, the heat diffusion constant of (2.0 +/- 0.5) A(2) ps(-1) is the same as that after depositing vibrational energy through the ultrafast internal conversion of a covalently bound chromophore.

Dynamical Transition in a Small Helical Peptide and Its Implication for Vibrational Energy Transport

The two-dimensional infrared spectrum of an octameric helical peptide in chloroform was measured as a function of temperature. Isotope labeling of the carbonyl group of one of the amino acids was used to obtain information for an isolated vibration. The antidiagonal width of the 2D-IR signal, which is a measure of the homogeneous dephasing time T(2), is constant from 220 to 260 K (within experimental error), and increases steeply above. The homogeneous dephasing time of the carbonyl vibration is attributed to the flexibility of the system and/or its immediate surrounding. The system undergoes a dynamical transition at about 270 K, with similarities to the protein dynamical transition. Furthermore, the temperature dependence of the antidiagonal width strongly resembles that of the efficiency of vibrational energy transport along the helix, which has been studied in a recent paper (J. Phys. Chem. B 2008, 112, 15487). The connection between the two processes, structural flexibility and energy transport mechanism, is discussed.

Vibrational energy transport in the presence of intrasite vibrational energy redistribution

The mechanism of vibrational energy flow is studied in a regime where a diffusion equation is likely to break down, i.e., on length scales of a few chemical bonds and time scales of a few picoseconds. This situation occurs, for example, during photochemical reactions in protein environment. To that end, a toy model is introduced that on the one hand mimics the vibrational normal mode distribution of proteins, and on the other hand is small enough to numerically time propagate the system fully quantum mechanically. Comparing classical and quantum-mechanical results, the question is addressed to what extent the classical nature of the molecular dynamics simulations (which would be the only choice for the modeling of a real molecular system) affects the vibrational energy flow mechanism. Small differences are found which are due to the different ways classical and quantum mechanics distribute thermal energy over vibrational modes. In either case, a ballistic and a diffusive phase can be identified. For these small length and time scales, the latter is governed by intrasite vibrational energy redistribution, since vibrational energy does not necessarily thermalize completely within individual peptide units. Overall, the model suggests a picture that unifies many of the observations made recently in experiments.

Relaxation-Assisted Two-Dimensional Infrared (RA 2DIR) Method: Accessing Distances over 10 Å and Measuring Bond Connectivity Patterns

Development of new approaches for measuring three-dimensional structures and dynamics of structural changes is important for a number of natural sciences, including structural biology, where it can lead to understanding the physical bases of molecular recognition and catalysis. A two-dimensional infrared (2DIR) spectroscopy method permits measuring pairwise interactions among vibrational modes in molecules providing a molecular scale ruler for delivering structural constraints, such as the distances between the vibrational modes, angles between their transition dipoles, and the energy-transfer rates between them. While there is a large variety of systems that have recently been interrogated using 2DIR, questions remain of how to measure structural features of larger molecules. The challenges of working with larger molecules, such as proteins, include very congested vibrational spectra, a small range of distances accessible by the 2DIR method, and sensitivity issues. This Account describes the efforts of our laboratory to overcome some of these challenges. First, we discuss the dual-frequency 2DIR approach, which provides the highest selectivity to a particular pair of vibrational reporters and highest sensitivity. Second, we describe our steps in developing vibrational labels, novel for 2DIR, such as C identical withN and C-D stretching modes that have frequencies in the water transparency region, as well as the modes in the fingerprint region. The schemes suitable for labeling amino acids are discussed. Next, we describe the novel relaxation-assisted 2DIR (RA 2DIR) method, developed in our laboratory. The method uses vibrational relaxation and vibrational energy transport in molecules and the thermalization process on a molecular scale, to generate stronger cross-peaks. An 18-fold cross-peak amplification was observed for the modes separated by about 11 A using the RA 2DIR method, and larger amplifications are expected for larger distances between the modes. Large amplification provided by the RA 2DIR method enhances the sensitivity of 2DIR spectroscopy and permits longer range structural measurements. In addition to generating stronger cross-peaks, a correlation of the energy transport time with the intermode distance is demonstrated. This correlation permits measurements of mode-connectivity patterns in molecules much similar to those available in total correlation spectroscopy (TOCSY) and heteronuclear multiple-bond correlation (HMBC) methods of 2D nuclear magnetic resonance (NMR) spectroscopy. It is our hope that, with a proper calibration, the RA 2DIR method will permit speedy assessments of distances and the bond connectivity patterns in molecules and reach the level of an analytical method.

Frequency-resolved communication maps for proteins and other nanoscale materials

Proteins exhibit highly anisotropic flow of energy. There is presently much interest in locating channels that enable signaling between distant sites, possibly playing a role in protein function such as allostery. We present an approach for computing frequency-resolved local energy diffusivities, which provide a map of communication between protein residues as a function of the vibrational frequencies of the modes that carry energy between them. A network of vibrational energy transport channels can then be identified at select frequencies. Over most frequency ranges the communication maps vary widely with vibrational frequency, as we illustrate for the protein myoglobin. We expect the approach presented here to be useful in mapping frequency-sensitive signaling in a variety of materials on the nanoscale.

Structural Flexibility of a Helical Peptide Regulates Vibrational Energy Transport Properties

Applying ultrafast vibrational spectroscopy, we find that vibrational energy transport along a helical peptide changes from inefficient but mostly ballistic below approximately 270 K into diffusive and significantly more efficient above. On the basis of molecular dynamics simulations, we attribute this change to the increasing flexibility of the helix above this temperature, similar to the glass transition in proteins. Structural flexibility enhances intramolecular vibrational energy redistribution, thereby refeeding energy into the few vibrational modes that delocalize over large parts of the structure and therefore transport energy efficiently. The paper outlines concepts how one might regulate vibrational energy transport properties in ultrafast photobiological processes, as well as in molecular electronic devices, by engineering the flexibility of their components.

First-Principles-Based Calculations of Vibrational Normal Modes in Polyatomic Materials with Translational Symmetry: Application to PETN Molecular Crystal

Numerical studies of vibrational energy transport and associated (non)linear infrared and Raman response in polyatomic materials require knowledge of the multidimensional vibrational potential-energy surface and the ability to perform normal-mode analysis on that potential. The presence of translational symmetry, as in crystals, leads to the observed dispersion of the unit cell normal modes and has to be accounted for in calculations of energy transfer rates and other spectroscopic quantities. Here we report on the implementation of a computational approach that combines the generalized supercell method and density functional theory electronic structure calculations to investigate the vibrational structure in translationally symmetric materials containing relatively large numbers of atoms in the unit cell (58 atoms in the present study). The method is applied to calculate the phonon and vibron dispersion relations and the vibrational density of states in pentaerythritol tetranitrate (PETN) molecular crystal which is an important energetic material. The results set the stage for future investigations of vibrational energy transport and associated nonlinear spectroscopic signatures in this class of materials.

Heat Conduction in a One-Dimensional Harmonic Chain with Three-Dimensional Vibrations

We study vibrational energy transport in a quasi one-dimensional (1D) harmonic chain with both longitudinal and transverse vibrations. We demonstrate via both numerical simulation and theoretic analysis that for 1D atomic chain connected by three-dimensional (3D) harmonic springs, the coefficient of heat conduction changes continuously with its lattice constant, indicating the qualitative difference from the corresponding 1D case where the coefficient is independent of the lattice constant.

Bond connectivity measured via relaxation-assisted two-dimensional infrared spectroscopy

The relaxation-assisted two-dimensional infrared (RA 2DIR) method is a novel technique for probing structures of molecules, which relies on vibrational energy transport in molecules. In this article we demonstrate the ability of RA 2DIR to detect the bond connectivity patterns in molecules using two parameters, a characteristic intermode energy transport time (arrival time) and a cross-peak amplification coefficient. A correlation of the arrival time with the distance between the modes is demonstrated. An 18-fold amplification of the cross-peak amplitude for the modes separated by approximately 11 A is shown using RA 2DIR; larger cross-peak amplifications are expected for the modes separated by larger distances. The RA 2DIR method enhances the applicability of 2DIR spectroscopy by making practical the long-range measurements using a variety of structural reporters, including weak IR modes. The data presented demonstrate the analytical power of RA 2DIR which permits the speedy structural assessments of the bond connectivity patterns.

1SD05 Vibrational dynamics and energy transport in proteins

1SD05 Vibrational dynamics and energy transport in proteins

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.

Energy transport in α-helical protein models: One-strand versus three-strand systems

We study the transport of vibrational energy in α-helix forms of proteins within the frame of a steric Davydov model. Our main objective is the comparison of the localization and transport properties of the widely used one-strand approximation of the a helix associated with a linear chain of hydrogen bonded peptide groups and the complete three-dimensional helical system consisting of three such strands being connected via covalent bonds. We construct polaron solutions of the set of discrete equations utilizing a nonlinear map method for finding the ground state. With respect to the polaron wave pattern, we found that while the excitonic wave function of the one-strand system is localized at a site and monotonically decaying apart from it on the three-strand system a multihump structure arises whose envelope exhibits monotonic decay. For the polaronic states the static deformations of the H bonds are stronger for an isolated strand than for a strand embedded in the three-dimensional protein cage. In the excited region the radius of the helix slightly decreases. The participation numbers show that the exciton localization is more strongly pronounced on the one-strand system than on its three-strand counterpart. In our dynamical studies we pay special attention to the mobility of the polarons when their internal pinning modes are initiated. The latter are identified as certain isolated Floquet eigenvalues obtained from the Floquet map, which is derived from the linearized equations in tangent space. It is shown that the polarons on the one-strand system move with higher velocity than on the three-strand system. In the latter case the preferred transport path proceeds across the hydrogen bonds and polaron motion along the covalent channel is suppressed.

Complex behavior in biosystems: an information-theoretic approach

The particular question of transport of vibrational energy in biosystems is considered within the scope of Fröhlich–Davydov's model. It is shown that Davydov's solitary waves, strongly damped in near equilibrium conditions, can display long-range propagation when travelling in Fröhlich's condensate. The latter consists in the emergence of a self-organized dissipative structure (in Prigogine's sense), resembling a nonequilibrium Bose–Einstein-like condensation in the low-lying in frequency modes of vibration, once a critical level of pumping of metabolic energy is achieved.