Vibrational energy transport in the presence of intrasite vibrational energy redistribution

Energy Transport and Its Function in Heptahelical Transmembrane Proteins

Photoproteins such as bacteriorhodopsin (bR) and rhodopsin (Rho) need to effectively dissipate photoinduced excess energy to prevent themselves from damage. Another well-studied seven transmembrane (TM) helices protein is the β₂ adrenergic receptor (β₂AR), a G protein-coupled receptor for which energy dissipation paths have been linked with allosteric communication. To study the vibrational energy transport in the active and inactive states of these proteins, a master equation approach [J. Chem. Phys.2020, 152, 045103] is employed, which uses scaling rules that allow us to calculate energy transport rates solely based on the protein structure. Despite their overall structural similarity, the three 7TM proteins reveal quite different strategies to redistribute excess energy. While bR quickly removes the energy using the TM7 helix as a "lightning rod", Rho exhibits a rather poor energy dissipation, which might eventually require the hydrolysis of the Schiff base between the protein and the retinal chromophore to prevent overheating. Heating the ligand adrenaline of β₂AR, the resulting energy transport network of the protein is found to change significantly upon switching from the active state to the inactive state. While the energy flow may highlight aspects of the inter-residue couplings of β₂AR, it seems not particularly suited to explain allosteric phenomena.

Through bonds or contacts? Mapping protein vibrational energy transfer using non-canonical amino acids

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.

Stochastic simulation of nonequilibrium heat conduction in extended molecular junctions

Understanding phononic heat transport processes in molecular junctions is a central issue in the developing field of nanoscale heat conduction. Here, we present a Langevin dynamics simulation framework to investigate heat transport processes in molecular junctions at and beyond the linear response regime and apply it to saturated and unsaturated linear hydrocarbon chains connecting two gold substrates. Thermal boundary conditions represented by Markovian noise and damping are filtered through several (up to four) gold layers to provide a realistic and controllable bath spectral density. Classical simulations using the full universal force field are compared with quantum calculations that use only the harmonic part of this field. The close agreement found at about room temperature between these very different calculations suggests that heat transport at such temperatures is dominated by lower frequency vibrations whose dynamics is described well by classical mechanics. The results obtained for alkanedithiol molecules connecting gold substrates agree with previous quantum calculations based on the Landauer formula and match recent experimental measurements [e.g., thermal conductance around 20 pW/K for alkanedithiols in single-molecule junctions (SMJs)]. Heat conductance simulations on polyynes of different lengths illuminate the effects of molecular conjugation on thermal transport. The difference between alkanes and polyynes is not large but correlates with the larger rigidity and stronger mode localization that characterize the polyyne structure. This computational approach has been recently used [R. Chen, I. Sharony, and A. Nitzan, J. Phys. Chem. Lett. 11, 4261-4268 (2020)] to unveil local atomic heat currents and phononic interference effect in aromatic-ring based SMJs.

Crucial effect of transverse vibrations on the transport through polymer chains

The low temperature transport of electron, or vibrational or electronic exciton toward polymer chains, turns out to be dramatically sensitive to its interaction with transverse acoustic vibrations. We show that this interaction leads to a substantial polaron effect and decoherence, which are generally stronger than those associated with longitudinal vibrations. For site-dependent interactions, transverse phonons form subohmic bath leading to the quantum phase transition accompanied by full suppression of the transport at zero temperature and fast decoherence characterized by temperature dependent rate k₂ ∝ T^3/4 at low temperature, while k₂ ∝ T² for site-independent interactions. The latter dependence was used to interpret recent measurements of temperature dependent vibrational energy transport in polyethylene glycol oligomers.

Topology, landscapes, and biomolecular energy transport

While ubiquitous, energy redistribution remains a poorly understood facet of the nonequilibrium thermodynamics of biomolecules. At the molecular level, finite-size effects, pronounced nonlinearities, and ballistic processes produce behavior that diverges from the macroscale. Here, we show that transient thermal transport reflects macromolecular energy landscape architecture through the topological characteristics of molecular contacts and the nonlinear processes that mediate dynamics. While the former determines transport pathways via pairwise interactions, the latter reflects frustration within the landscape for local conformational rearrangements. Unlike transport through small-molecule systems, such as alkanes, nonlinearity dominates over coherent processes at even quite short time- and length-scales. Our exhaustive all-atom simulations and novel local-in-time and space analysis, applicable to both theory and experiment, permit dissection of energy migration in biomolecules. The approach demonstrates that vibrational energy transport can probe otherwise inaccessible aspects of macromolecular dynamics and interactions that underly biological function.

Understanding vibrational energy transfer in macromolecules has been challenging to both theory and experiment. Here the authors use non-equilibrium molecular dynamics to reveal the relationship between heat transport in a model peptide, emergent nonlinearity, and the underlying free energy landscape.

Modelling vibrational relaxation in complex molecular systems

In this paper we show how it is possible to treat the quantum vibrational relaxation of a chromophore, embedded in a complex atomic-molecular environment, via the explicit solution of the time-dependent Schroedinger equation once using a proper separation between quantum and semiclassical degrees of freedom. The rigorous theoretical framework derived, based on first principles and making use of well defined approximations/assumptions, is utilized to construct a general model for the kinetics of the vibrational relaxation as obtained by the direct evaluation of the density matrix for all the relevant quantum state transitions. Application to (deuterated) N-methylacetamide (the typical benchmark used as a model for the amino acids) shows that the obtained theoretical-computational approach captures the essential features of the experimental process, unveiling the basic relaxation mechanism involving several vibrational state transitions.

Ballistic and diffusive vibrational energy transport in molecules

Energy transport in molecules is essential for many areas of science and technology. Strong covalent bonds of a molecular backbone can facilitate the involvement of the molecule's high-frequency modes in energy transport, which, under certain conditions, makes the transport fast and efficient. We discuss such conditions and describe various transport regimes in molecules, including ballistic, diffusive, directed diffusion, and intermediate regime cases, in light of recently developed experimental and theoretical approaches.

Temperature dependence of the ballistic energy transport in perfluoroalkanes

Temperature dependence of intramolecular energy transport in perfluoroalkane oligomers with a chain length of 3-11 carbon atoms terminated by a carboxylic acid moiety on one end and a -CF2H group on another end was studied in solution experimentally and theoretically. Experiments were performed using a dual-frequency relaxation-assisted two-dimensional infrared spectroscopy method. The energy transport was initiated by exciting the C═O stretching mode of the acid and recorded by measuring a cross-peak amplitude between the C═O stretching and the C-H bending modes as a function of the waiting time between the excitation and probing. An efficient transport regime with a mean free path of 16.4 ± 2 Å is observed at 35 °C. The energy transport speed decreases at elevated temperatures, indicating a switch from the ballistic transport regime to diffusive. The modeling of the energy transport involving both ballistic and diffusive mechanisms is performed. It explains the temperature dependence of the energy transport speed and confirms a switch of the transport regime from ballistic at lower temperatures to diffusive at higher temperatures.

Ballistic energy transport along PEG chains: distance dependence of the transport efficiency

Dual-frequency relaxation-assisted two-dimensional infrared (RA 2DIR) spectroscopy was used to investigate energy transport in polyethylene glycol (PEG) oligomers of different length, having 0, 4, 8, and 12 repeating units and end-labeled with azido and succinimide ester moieties (azPEGn). The energy transport initiated by excitation of the N≡N stretching mode of the azido group in azPEGn in CCl(4) at ca. 2100 cm(-1) was recorded by probing the C=O stretching modes (reporters) of the succinimide ester moiety. Sensitive to the excess energy delivered to the reporter modes, RA 2DIR permits observation of both the through-bond and through-solvent energy transport contributions. The cross-peak data involving the reporter modes with different thermal sensitivity and the data for mixtures of compounds permitted concluding that through-bond energy transport is the dominant mechanism for most cross peaks in all four azPEGn compounds. The through-bond energy transport time, evaluated as the waiting time at which the cross peak maximum is reached, was found to be linearly dependent on the chain length of up to 60 Å, suggesting a ballistic energy transport regime. The through-bond energy transport speed determined from the chain-length dependence of T(max) in CCl(4) is found to be ca. 450 m s(-1). The cross-peak amplitude at the maximum decays exponentially with the chain length; a characteristic decay distance is found to be 15.7 ± 1 Å. The cross-peak amplitude at zero waiting time, determined by the end-to-end distance distribution, is found to decay with the chain length (L) as ∼L(-1.4), which is close to predictions of the free flight chain model. The match indicates that the end-group interaction does not strongly perturb the end-to-end distribution, which is close to the ideal random coil distribution with the Gaussian probability density.

Temperature dependence of the heat diffusivity of proteins

In a combined experimental-theoretical study, we investigated the transport of vibrational energy from the surrounding solvent into the interior of a heme protein, the sperm whale myoglobin double mutant L29W-S108L, and its dependence on temperature from 20 to 70 K. The hindered libration of a CO molecule that is not covalently bound to any part of the protein but is trapped in one of its binding pockets (the Xe4 pocket) was used as the local thermometer. Energy was deposited into the solvent by IR excitation. Experimentally, the energy transfer rate increased from (30 ps)(-1) at 20 K to (8 ps)(-1) at 70 K. This temperature trend is opposite to what is expected, assuming that the mechanism of heat transport is similar to that in glasses. In order to elucidate the mechanism and its temperature dependence, nonequilibrium molecular dynamics (MD) simulations were performed, which, however, predicted an essentially temperature-independent rate of vibrational energy flow. We tentatively conclude that the MD potentials overestimate the coupling between the protein and the CO molecule, which appears to be the rate-limiting step in the real system at low temperatures. Assuming that this coupling is anharmonic in nature, the observed temperature trend can readily be explained.

Structure dependent energy transport: relaxation-assisted 2DIR measurements and theoretical studies

Vibrational energy relaxation and transport in a molecule that is far from thermal equilibrium can affect its chemical reactivity. Understanding the energy transport dynamics in such molecules is also important for measuring molecular structural constraints via relaxation-assisted two-dimensional infrared (RA 2DIR) spectroscopy. In this paper we investigated vibrational relaxation and energy transport in the ortho, meta, and para isomers of acetylbenzonitrile (AcPhCN) originated from excitation of the CN stretching mode. The amplitude of the cross-peak among the CN and CO stretching modes served as an indicator for the energy transport from the CN group toward the CO group. A surprisingly large difference is observed in both the lifetimes of the CN mode and in the energy transport rates for the three isomers. The anharmonic DFT calculations and energy transport modeling performed to understand the origin of the differences and to identify the main cross-peak contributors in these isomers described well the majority of the experimental results including mode excited-state lifetimes and the energy transport dynamics. The strong dependence of the energy transport on molecular structure found in this work could be useful for recognizing different isomers of various compounds via RA 2DIR spectroscopy.

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.