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To facilitate the observation of biomolecular energy transport in real time and with single-residue resolution, recent experiments by Baumann et al. ( Angew. Chem. Int. Ed. 2019 , 58 , 2899 , DOI: 10.1002/anie.201812995 ) have used unnatural amino acids β-(1-azulenyl)alanine (Azu) and azidohomoalanine (Aha) to site-specifically inject and probe vibrational energy in proteins. To aid the interpretation of such experiments, non-equilibrium molecular dynamics simulations of the anisotropic energy flow in proteins TrpZip2 and PDZ3 domains are presented. On this account, an efficient simulation protocol is established that accurately mimics the excitation and probing steps of Azu and Aha. The simulations quantitatively reproduce the experimentally found cooling times of the solvated proteins at room temperature and predict that the cooling slows by a factor 2 below the glass temperature of water. In PDZ3, vibrational energy is shown to travel from the initially excited peptide ligand via a complex network of inter-residue contacts and backbone transport to distal regions of the protein. The supposed connection of these energy transport pathways with pathways of allosteric communication is discussed.

Computational studies of vibrational energy flow in biomolecules have to date mapped out transport pathways on a case-by-case basis. To provide a more general approach, we derive scaling rules for vibrational energy transport in a globular protein, which are identified from extensive nonequilibrium molecular dynamics simulations of vibrational energy flow in the villin headpiece subdomain HP36. We parametrize a master equation based on inter-residue, residue-solvent, and heater-residue energy-transfer rates, which closely reproduces the results of the all-atom simulations. From that fit, two scaling rules emerge, one for energy transport along the protein backbone which relies on a diffusion model and another for energy transport between tertiary contacts, which is based on a harmonic model. Requiring only the calculation of mean and variance of relatively few atomic distances, the approach holds the potential to predict the pathways and time scales of vibrational energy flow in large proteins.

A systematic molecular dynamics (MD) simulation study of the photoinduced heat transfer from the model peptide N-methylacetamide (NMA) to various solvents is presented, which considers four types of solvent (water, dimethyl sulfoxide, chloroform, and carbon tetrachloride), and in total 24 different force field models for these solvents. To initiate nonstationary energy flow, an initial temperature jump of NMA is assumed and nonequilibrium MD simulations are performed. As expected from simple theoretical models of heat transfer, the cooling process is proportional to the heat capacity C(V) and--to some extent--to the viscosity eta of the solvent. The complex interplay of Coulomb and Lennard-Jones interactions is studied by scaling these interaction energies. The study reveals that realistic changes (< or approximately 10%) of the Lennard-Jones and Coulomb parameters do not change the cooling time considerably. Including polarizibility, on the other hand, appears to enhance the energy dissipation. Moreover, the solvent's internal degrees of freedom may significantly participate in the heat transfer. This is less so for water, which possesses only three high-frequency vibrational modes, but certainly so for the larger solvent molecules dimethyl sulfoxide and chloroform, which possess several low-frequency vibrational modes. For water, the simulated cooling rate is in excellent agreement with experiment, while only qualitative agreement (up to a factor of 2) is found for the other considered solvents. The importance of the force field model and quantum-mechanical effects to correctly describe the cooling process is discussed in some detail.

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.

Energy transport in a short helical peptide in chloroform solution is studied by time-resolved femtosecond spectroscopy and accompanying nonequilibrium molecular dynamics (MD) simulations. In particular, the heat transport after excitation of an azobenzene chromophore attached to one terminus of the helix with 3 eV (UV) photons is compared to the excitation of a peptide C=O oscillator with 0.2 eV (IR) photons. The heat in the helix is detected at various distances from the heat source as a function of time by employing vibrational pump-probe spectroscopy. As a result, the carbonyl oscillators at different positions along the helix act as local thermometers. The experiments show that heat transport through the peptide after excitation with low-energy photons is at least 4 times faster than after UV excitation. On the other hand, the heat transport obtained by nonequilibrium MD simulations is largely insensitive to the kind of excitation. The calculations agree well with the experimental results for the low-frequency case; however, they give a factor of 5 too fast energy transport for the high-energy case. Employing instantaneous normal mode calculations of the MD trajectories, a simple harmonic model of heat transport is adopted, which shows that the heat diffusivity decreases significantly at temperatures initially reached by high-energy excitation. This finding suggests that the photoinduced energy gets trapped, if it is deposited in high amounts. The various competing mechanisms, such as vibrational T(1) relaxation, resonant transfer between excitonic states, cascading down relaxation, and low-frequency mode transfer, are discussed in detail.

We examine vibrational energy flow in dehydrated and hydrated villin headpiece subdomain HP36 by master equation simulations. Transition rates used in the simulations are obtained from communication maps calculated for HP36. In addition to energy flow along the main chain, we identify pathways for energy transport in HP36 via hydrogen bonding between residues quite far in sequence space. The results of the master equation simulations compare well with all-atom non-equilibrium simulations to about 1 ps following initial excitation of the protein, and quite well at long times, though for some residues we observe deviations between the master equation and all-atom simulations at intermediate times from about 1-10 ps. Those deviations are less noticeable for hydrated than dehydrated HP36 due to energy flow into the water. [ABSTRACT FROM AUTHOR]

Vibrational energy transfer (VET) is essential for protein function. It is responsible for efficient energy dissipation in reaction sites, and has been linked to pathways of allosteric communication. While it is understood that VET occurs via backbone as well as via non-covalent contacts, little is known about the competition of these two transport channels, which determines the VET pathways. To tackle this problem, we equipped the β-hairpin fold of a tryptophan zipper with pairs of non-canonical amino acids, one serving as a VET injector and one as a VET sensor in a femtosecond pump probe experiment. Accompanying extensive non-equilibrium molecular dynamics simulations combined with a master equation analysis unravel the VET pathways. Our joint experimental/computational endeavor reveals the efficiency of backbone vs. contact transport, showing that even if cutting short backbone stretches of only 3 to 4 amino acids in a protein, hydrogen bonds are the dominant VET pathway. Vibrational energy transfer (VET) is essential for protein function as it is responsible for efficient energy dissipation in reaction sites and is linked to pathways of allosteric communication. Here authors equipped a tryptophan zipper with a VET injector and a VET sensor for femtosecond pump probe experiments to map the VET. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Recent progress in transient infrared spectroscopy has made it possible to monitor the transient flow of vibrational energy along a peptide helix [V. Botan et al., Proc. Natl. Acad. Sci. U.S.A. 104, 12749 (2007)]. To provide a theoretical description of these experiments, extensive nonequilibrium molecular dynamics simulations of the photoinduced energy transport in a photoswitchable Aib peptide are performed. By calculating the response of the molecule caused by its excitation via optical and infrared pulses as well as temperature jump and stationary heating, it is shown that these methods are equivalent in that they provide approximately the same molecular energy transfer times. The resulting thermal diffusivity of 10 Å2 ps-1 qualitatively agrees with the results of previous normal mode calculations for proteins and with experimental bulk values (e.g., 14 Å2 ps-1 for water). To compare to experiment, a new way of approximating the measured signals is suggested which leads to an improved agreement with the experimental results and explains previous discrepancies. To elucidate the mechanism of energy transfer, modifications to the molecular dynamics force field are introduced, which reveal that the energy transfer occurs mainly through the peptide backbone and depends surprisingly little on the force field parametrization. Employing a harmonic model, quantum-mechanical effects are estimated to moderately (about a factor of 2) speed up the energy transport along the peptide. [ABSTRACT FROM AUTHOR]

Allostery represents a fundamental mechanism of biological regulation that is mediated via long-range communication between distant protein sites. Although little is known about the underlying dynamical process, recent time-resolved infrared spectroscopy experiments on a photoswitchable PDZ domain (PDZ2S) have indicated that the allosteric transition occurs on multiple timescales. Here, using extensive nonequilibrium molecular dynamics simulations, a time-dependent picture of the allosteric communication in PDZ2S is developed. The simulations reveal that allostery amounts to the propagation of structural and dynamical changes that are genuinely nonlinear and can occur in a nonlocal fashion. A dynamic network model is constructed that illustrates the hierarchy and exceeding structural heterogeneity of the process. In compelling agreement with experiment, three physically distinct phases of the time evolution are identified, describing elastic response (≲0.1 ns), inelastic reorganization (∼100 ns), and structural relaxation (≳1μs). Issues such as the similarity to downhill folding as well as the interpretation of allosteric pathways are discussed. [ABSTRACT FROM AUTHOR]

A recent paper by Hamm and Stock [Phys. Rev. Lett.109, 173201 (2012)] has introduced the concept of vibrational conical intersections as a potential source of ultrafast vibrational relaxation, using the coupling between high-frequency OH modes and low-frequency intramolecular hydrogen bonding modes of malonaldehyde as an example. Here, the question is addressed whether such conical intersections may also appear for intermolecular hydrogen bonds. To that end, the water dimer [(H2O)2] is studied as a minimal model for the hydrogen bonding in liquid water. Although a significant separation of time scales between intramolecular and intermolecular degrees of freedom exists in (H2O)2, a standard normal-mode description is found to lead to a complete breakdown of the adiabatic ansatz. This is due to strong nonlinear couplings between high- and low-frequency normal modes, which in turn give rise to large overall non-adiabatic couplings. A valid adiabatic picture is obtained, on the other hand, when internal coordinates are employed. The resulting adiabatic potential energy surfaces indeed exhibit low-lying conical intersections, whose possible relevance for ultrafast relaxation and energy transfer in water is discussed. [ABSTRACT FROM AUTHOR]

Employing extensive quantum-chemical calculations at the DFT/B3LYP and MP2 level, quartic force fields of isolated N-methylacetamide are constructed. Taking into account 24 vibrational degrees of freedom, the model is employed to perform numerically exact vibrational configuration interaction calculations of the vibrational energy relaxation of the amide I mode. It is found that the energy transfer pathways may sensitively depend on details of the theoretical description. Moreover, the exact reference calculations were used to study the applicability and accuracy of (i) the quasiclassical trajectory method, (ii) time-dependent second-order perturbation theory, and (iii) the instantaneous normal mode description of frequency fluctuations. Based on the results, several strategies to describe vibrational energy relaxation in biomolecular systems are discussed. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [ABSTRACT FROM AUTHOR]

Performing comprehensive quantum-chemical calculations, a vibrational Hamiltonian of acetylbenzonitrile is constructed, on the basis of which a quantum-mechanical “tier model” is developed that describes the vibrational dynamics following excitation of the CN stretch mode. Taking into account 36 vibrational modes and cubic and quartic anharmonic couplings between up to three different modes, the tier model calculations are shown to qualitatively reproduce the main findings of the experiments of Rubtsov and coworkers (2011), including the energy relaxation of the initially excited CN mode and the structure-dependent vibrational transport. Moreover, the calculations suggest that the experimentally measured cross-peak among the CN and CO modes does not correspond to direct excitation of the CO normal mode but rather reflects excited low-frequency vibrations that anharmonically couple to the CO mode. Complementary quasiclassical trajectory calculations are found to be in good overall agreement with the quantum calculations. [ABSTRACT FROM AUTHOR]