Vibrational energy relaxation in proteins

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.

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 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.

Nonlinear quantum heat transfer in hybrid structures: sufficient conditions for thermal rectification

We present a unified description of heat flow in two-terminal hybrid quantum systems. Using simple models, we analytically study nonlinear aspects of heat transfer between various reservoirs--metals, solids, and spin baths--mediated by the excitation and the relaxation of a central (subsystem) mode. We demonstrate rich nonlinear current-temperature characteristics, originating from either the molecular anharmonicity or the reservoir (complex) energy spectra. In particular, we establish sufficient conditions for thermal rectification in two-terminal junctions. We identify two classes of rectifiers. In type- A rectifiers the energy-dependent density of states of the reservoirs are dissimilar. In type- B rectifiers the baths are identical, but include particles whose statistics differ from that of the subsystem, to which they asymmetrically couple. Nonlinear heat flow and specifically thermal rectification are thus ubiquitous effects that could be observed in a variety of systems--phononic, electronic, and photonic.

Relaxation-assisted two-dimensional infrared (RA 2DIR) method: accessing distances over 10 A 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.

Efforts toward developing probes of protein dynamics: vibrational dephasing and relaxation of carbon-deuterium stretching modes in deuterated leucine

The spectral position of C-D stretching absorptions in the so-called "transparent window" of protein absorption (1800-2300 cm(-1)) makes them well suited as probes of protein dynamics with high temporal and structural resolution. We have previously incorporated single deuterated amino acids into proteins to site-selectively follow protein folding and ligand binding by steady-state FT IR spectroscopy. Ultimately, our goal is to use C-D bonds as probes in time-resolved IR spectroscopy to study dynamics and intramolecular vibrational energy redistribution (IVR) in proteins. As a step toward this goal, we now present the first time-resolved experiments characterizing the population and dephasing dynamics of selectively excited C-D bonds in a deuterated amino acid. Three differently deuterated, Boc-protected leucines were selected to systematically alter the number of additional C-D bonds that may mediate IVR out of the initially populated bright C-D stretching mode. Three-pulse photon echo experiments show that the steady-state C-D absorption linewidths are broadened by both homogeneous and inhomogeneous effects, and transient grating experiments reveal that IVR occurs on a subpicosecond time scale and is nonstatistical. The results have important implications for the interpretation of steady-state C-D spectra and demonstrate the potential utility of C-D bonds as probes of dynamics and IVR within a protein.

Applications of 2D IR spectroscopy to peptides, proteins, and hydrogen-bond dynamics

Following a survey of 2D IR principles, this article describes recent experiments on the hydrogen-bond dynamics of small ions, amide-I modes, nitrile probes, peptides, reverse transcriptase inhibitors, and amyloid fibrils.

Vibrational Energy Relaxation of Isotopically Labeled Amide I Modes in Cytochrome c: Theoretical Investigation of Vibrational Energy Relaxation Rates and Pathways

With use of a time-dependent perturbation theory, vibrational energy relaxation (VER) of isotopically labeled amide I modes in cytochrome c solvated with water is investigated. Contributions to the VER are decomposed into two contributions from the protein and water. The VER pathways are visualized by using radial and angular excitation functions for resonant normal modes. Key differences of VER among different amide I modes are demonstrated, leading to a detailed picture of the spatial anisotropy of the VER. The results support the experimental observation that amide I modes in proteins relax with subpicosecond time scales, while the relaxation mechanism turns out to be sensitive to the environment of the amide I mode.

A relaxation-assisted 2D IR spectroscopy method

A method of two-dimensional infrared (2D IR) spectroscopy called relaxation-assisted 2D IR (RA 2DIR) is proposed that utilizes vibrational energy relaxation transport in molecules to enhance cross-peak amplitudes. This method substantially increases the range of distances accessible by 2D IR and is capable of identifying long-range connectivity patterns in molecules. RA 2DIR is illustrated in interactions among CN and CO modes in 3-cyanocoumarin and 4-acetylbenzonitrile, where the distances between the CN and CO groups are approximately 3.1 and approximately 6.5 A, respectively. A 6-fold increase in cross-peak amplitude was observed in 4-acetylbenzonitrile when the dual-frequency RA 2DIR method was used.

Energy transport in peptide helices

We investigate energy transport through an alpha-aminoisobutyric acid-based 3(10)-helix dissolved in chloroform in a combined experimental-theoretical approach. Vibrational energy is locally deposited at the N terminus of the helix by ultrafast internal conversion of a covalently attached, electronically excited, azobenzene moiety. Heat flow through the helix is detected with subpicosecond time resolution by employing vibrational probes as local thermo meters at various distances from the heat source. The experiment is supplemented by detailed nonequilibrium molecular dynamics (MD) simulations of the process, revealing good qualitative agreement with experiment: Both theory and experiment exhibit an almost instantaneous temperature jump of the reporter units next to the heater which is attributed to the direct impact of the isomerizing azobenzene moiety. After this impact event, helix and azobenzene moiety appear to be thermally decoupled. The energy deposited in the helix thermalizes on a subpicosecond timescale and propagates along the helix in a diffusive-like process, accompanied by a significant loss into the solvent. However, in terms of quantitative numbers, theory and experiment differ. In particular, the MD simulation seems to overestimate the heat diffusion constant (2 A(2) ps(-1) from the experiment) by a factor of five.

Ultrafast heme dynamics in ferrous versus ferric cytochrome c studied by time-resolved resonance Raman and transient absorption spectroscopy

Cytochrome c (Cyt c) is a heme protein involved in electron transfer and also in apoptosis. Its heme iron is bisaxially ligated to histidine and methionine side chains and both ferric and ferrous redox states are physiologically relevant, as well as a ligand exchange between internal residue and external diatomic molecule. The photodissociation of internal axial ligand was observed for several ferrous heme proteins including Cyt c, but no time-resolved studies have been reported on ferric Cyt c. To investigate how the oxidation state of the heme influences the primary photoprocesses, we performed a comprehensive comparative study on horse heart Cyt c by subpicosecond time-resolved resonance Raman and femtosecond transient absorption spectroscopy. We found that in ferric Cyt c, in contrast to ferrous Cyt c, the photodissociation of an internal ligand does not take place, and relaxation dynamics is dominated by vibrational cooling in the ground electronic state of the heme. The intermolecular vibrational energy transfer was found to proceed in a single phase with a temperature decay of approximately 7 ps in both ferric and ferrous Cyt c. For ferrous Cyt c, the instantaneous photodissociation of the methionine side chain from the heme iron is the dominant event, and its rebinding proceeds in two phases, with time constants of approximately 5 and approximately 16 ps. A mechanism of this process is discussed, and the difference in photoinduced coordination behavior between ferric and ferrous Cyt c is explained by an involvement of the excited electronic state coupled with conformational relaxation of the heme.

Vibrational energy relaxation of azide in water

Vibrational lifetimes of the asymmetric stretch fundamental of azide anion in normal and heavy water have been measured experimentally, with results in the range of a few picoseconds. This is an interesting problem for theoretical study because of the competition between intramolecular (relaxation to the other excited vibrational states of azide) and purely intermolecular (relaxation to azide's ground vibrational state) pathways. In addition it is important to understand the origin of the solvent isotope effect. Building on the seminal work of Morita and Kato [J. Chem. Phys. 109, 5511 (1998)], the authors develop a simple model based on a two-dimensional description of the azide stretching vibrations. A novel aspect of their theory is the use of an "on-the-fly" optimized quantum mechanical/molecular mechanical approach to calculate the system-bath coupling. Their theoretical lifetimes are in good agreement with experiment for azide in both normal and heavy water. They find that the predominant relaxation pathway is intramolecular. The solvent isotope effect arises from the different librational frequencies in normal and heavy water.

Vibrational relaxation of the CH stretch fundamental in liquid CHBr3

In continuation of our work on haloforms, the decay of CH stretch excitation in bromoform is modeled using molecular dynamics simulations. An intermolecular force field is obtained by fitting ab initio energies at select CHBr3 dimer geometries to a potential function. The solvent forces on vibrational modes obtained in the simulation are used to compute relaxation rates. The Landau-Teller approach points to a single acceptor state in the initial step of CH stretch relaxation. The time scale for this process is found to be 50-90 ps, which agrees well with the experimental value of 50 ps. The reason for the selectivity of the acceptor is elaborated. Results from a time-dependent approach to the decay rates are also discussed.

The Mechanism of TC230′s Thermostability: A Molecular Dynamics Simulation Study

The quasielastic neutron scattering index beta and the modulus of a protein's quasi-electric dipole moment were utilized to quantitate the thermostability of wildtype TC23O and its mutants. Charged residues Arg314, Glu246, Glu291, and some prolines near the C-terminus of the sequence (Pro228, Pro296, and Pro308) were identified to be critical for the thermostability of wildtype TC23O according to these two criteria. By analyzing the molecular conformation changes during the simulation, it was demonstrated how the mutant P228S was destabilized by disrupting two salt-bridges Asp116OD1-Lys215N and Glu210OE1-Lys217N at an adjacent beta-turn. The destabilization of P296S also shown to be intimate correlated with the break down of ion pair Lys188N-Glu291OE1. The sensitivity of its electrostatic network to the local structure is an important feature. It reveals that the 'proline effect' and electrostatic interactions together influences the thermostability of TC23O a lot.

Photoinduced conformational dynamics of a photoswitchable peptide: a nonequilibrium molecular dynamics simulation study

Employing nonequilibrium molecular dynamics simulations, a comprehensive computational study of the photoinduced conformational dynamics of a photoswitchable bicyclic azobenzene octapeptide is presented. The calculation of time-dependent probability distributions along various global and local reaction coordinates reveals that the conformational rearrangement of the peptide is rather complex and occurs on at least four timescales: 1) After photoexcitation, the azobenzene unit of the molecule undergoes nonadiabatic photoisomerization within 0.2 ps. 2) On the picosecond timescale, the cooling (13 ps) and the stretching (14 ps) of the photoexcited peptide is observed. 3) Most reaction coordinates exhibit a 50-100 ps component reflecting a fast conformational rearrangement. 4) The 500-1000 ps component observed in the simulation accounts for the slow diffusion-controlled conformational equilibration of the system. The simulation of the photoinduced molecular processes is in remarkable agreement with time-resolved optical and infrared experiments, although the calculated cooling as well as the initial conformational rearrangements of the peptide appear to be somewhat too slow. Based on an ab initio parameterized vibrational Hamiltonian, the time-dependent amide I frequency shift is calculated. Both intramolecular and solvent-induced contributions to the frequency shift were found to change by < or = 2 cm(-1), in reasonable agreement with experiment. The potential of transient infrared spectra to characterize the conformational dynamics of peptides is discussed in some detail.

Time-dependent perturbation theory for vibrational energy relaxation and dephasing in peptides and proteins

Without invoking the Markov approximation, we derive formulas for vibrational energy relaxation (VER) and dephasing for an anharmonic system oscillator using a time-dependent perturbation theory. The system-bath Hamiltonian contains more than the third order coupling terms since we take a normal mode picture as a zeroth order approximation. When we invoke the Markov approximation, our theory reduces to the Maradudin-Fein formula which is used to describe the VER properties of glass and proteins. When the system anharmonicity and the renormalization effect due to the environment vanishes, our formulas reduce to those derived by and Mikami and Okazaki [J. Chem. Phys. 121, 10052 (2004)] invoking the path-integral influence functional method with the second order cumulant expansion. We apply our formulas to VER of the amide I mode of a small amino-acid like molecule, N-methylacetamide, in heavy water.

Highly accurate potential-energy and dipole moment surfaces for vibrational state calculations of methane

Full-dimensional ab initio potential-energy surface (PES) and dipole moment surface are constructed for a methane molecule at the CCSD(T)/cc-pVTZ and MP2/cc-pVTZ levels of theory, respectively, by the modified Shepard interpolation method based on the fourth-order Taylor expansion [MSI(4th)]. The reference points for the interpolation have been set in the coupling region of CH symmetric and antisymmetric stretching modes so as to reproduce the vibrational energy levels related to CH stretching vibrations. The vibrational configuration-interaction calculations have been performed to obtain the energy levels and the absorption intensities up to 9000 cm(-1) with the use of MSI(4th)-PES. The calculated fundamental frequencies and low-lying vibrational energy levels show that MSI(4th) is superior to the widely employed quartic force field, giving a better agreement with the experimental values. The absorption bands of overtones as well as combination bands, which are caused by purely anharmonic effects, have been obtained up to 9000 cm(-1). Strongly coupled states with visible intensity have been found in the 6500-9000 cm(-1) region where the experimental data are still lacking.

Conformational Properties of and a Reorientation Triggered by Sugar−Water Vibrational Resonance in the Hydroxymethyl Group in Hydrated β-Glucopyranose

In this paper, we discuss the conformational properties of the hydroxymethyl group of beta-glucopyranose in aqueous solution and its reorientation mechanism. First, using the values for the hydroxymethyl torsion (O5-C5-C6-O6) angle obtained by our ab initio simulations, we reestimate the experimental ratio of the hydroxymethyl rotamer populations. The reestimated ratio is found to be in agreement with those previously reported in several computational studies, which probably partly explains the discrepancies between theoretical and experimental studies that have been discussed in the literature. Second, our time-frequency analysis on a reorientation in the hydroxymethyl group in an ab initio molecular dynamics trajectory suggests that, before the reorientation, the O6-H6 stretching mode is vibrationally coupled with a proton-accepting first-hydration-shell water molecule, whereas the C6-O6 stretching mode is vibrationally coupled with a proton-donating one. The amount of the total vibrational energy induced by these vibrational couplings is estimated to be comparable to typical values for the potential barriers between hydroxymethyl rotamers. To elucidate the vibrational couplings, we investigate the hydrogen-bonding properties around the hydroxymethyl group during the pretransition period. The implications, validity, and limitation of a possible reorientation mechanism based on these findings are also discussed.