Scaling Rules for Vibrational Energy Transport in Globular Proteins

Vibrational Energy Landscapes and Energy Flow in GPCRs

We construct and analyze disconnectivity graphs to provide the first graphical representation of the vibrational energy landscape of a protein, in this study β2AR, a G-protein coupled receptor (GPCR), in active and inactive states. The graphs, which indicate the relative free energy of each residue and the minimum free energy barriers for energy transfer between them, reveal important composition, structural and dynamic properties that mediate the flow of energy. Prolines and glycines, which contribute to GPCR plasticity and function, are identified as bottlenecks to energy transport along the backbone from which alternative pathways for energy transport via nearby noncovalent contacts emerge, seen also in the analysis of first passage time (FPT) distributions presented here. Striking differences between the disconnectivity graphs and FPT distributions for the inactive and active states of β2AR are found where structural and dynamic changes occur upon activation, contributing to allosteric regulation.

Intermolecular Protein-Water Coupling Impedes the Coupling Between the Amide A and Amide I Mode in Interfacial Proteins

The coupling between different vibrational modes in proteins is essential for chemical dynamics and biological functions and is linked to the propagation of conformational changes and pathways of allosteric communication. However, little is known about the influence of intermolecular protein-H2O coupling on the vibrational coupling between amide A (NH) and amide I (C═O) bands. Here, we investigate the NH/CO coupling strength in various peptides with different secondary structures at the lipid cell membrane/H2O interface using femtosecond time-resolved sum frequency generation vibrational spectroscopy (SFG-VS) in which a femtosecond infrared pump is used to excite the amide A band, and SFG-VS is used to probe transient spectral evolution in the amide A and amide I bands. Our results reveal that the NH/CO coupling strength strongly depends on the bandwidth of the amide I mode and the coupling of proteins with water molecules. A large extent of protein-water coupling significantly reduces the delocalization of the amide I mode along the peptide chain and impedes the NH/CO coupling strength. A large NH/CO coupling strength is found to show a strong correlation with the high energy transfer rate found in the light-harvesting proteins of green sulfur bacteria, which may understand the mechanism of energy transfer through a molecular system and assist in controlling vibrational energy transfer by engineering the molecular structures to achieve high energy transfer efficiency.

Locating dynamic contributions to allostery via determining rates of vibrational energy transfer

Determining rates of energy transfer across non-covalent contacts for different states of a protein can provide information about dynamic and associated entropy changes during transitions between states. We investigate the relationship between rates of energy transfer across polar and nonpolar contacts and contact dynamics for the β₂-adrenergic receptor, a rhodopsin-like G-protein coupled receptor, in an antagonist-bound inactive state and agonist-bound active state. From structures sampled during molecular dynamics (MD) simulations, we find the active state to have, on average, a lower packing density, corresponding to generally more flexibility and greater entropy than the inactive state. Energy exchange networks (EENs) are computed for the inactive and active states from the results of the MD simulations. From the EENs, changes in the rates of energy transfer across polar and nonpolar contacts are found for contacts that remain largely intact during activation. Change in dynamics of the contact, and entropy associated with the dynamics, can be estimated from the change in rates of energy transfer across the contacts. Measurement of change in the rates of energy transfer before and after the transition between states thereby provides information about dynamic contributions to activation and allostery.

Time-resolved spectroscopic mapping of vibrational energy flow in proteins: Understanding thermal diffusion at the nanoscale

Vibrational energy exchange between various degrees of freedom is critical to barrier-crossing processes in proteins. Hemeproteins are well suited for studying vibrational energy exchange in proteins because the heme group is an efficient photothermal converter. The released energy by heme following photoexcitation shows migration in a protein moiety on a picosecond timescale, which is observed using time-resolved ultraviolet resonance Raman spectroscopy. The anti-Stokes ultraviolet resonance Raman intensity of a tryptophan residue is an excellent probe for the vibrational energy in proteins, allowing the mapping of energy flow with the spatial resolution of a single amino acid residue. This Perspective provides an overview of studies on vibrational energy flow in proteins, including future perspectives for both methodologies and applications.

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.

Energy Transport in Class B GPCRs: Role of Protein-Water Dynamics and Activation

We compute energy exchange networks (EENs) through glucagon-like peptide-1 receptor (GLP-1R), a class B G-protein-coupled receptor (GPCR), in inactive and two active states, one activated by a peptide ligand and the other by a small molecule agonist, from results of molecular dynamics simulations. The reorganized network upon activation contains contributions from structural as well as from dynamic changes and corresponding entropic contributions to the free energy of activation, which are estimated in terms of the change in rates of energy transfer across non-covalent contacts. The role of water in the EENs and in activation of GLP-1R is also investigated. The dynamics of water in contact with the central polar network of the transmembrane region is found to be significantly slower for both activated states compared to the inactive state. This result is consistent with the contribution of water molecules to activation of GLP-1R previously suggested and resembles water dynamics in parts of the transmembrane region found in earlier studies of rhodopsin-like GPCRs.

Computational Study on the Thermal Conductivity of a Protein

Protein molecules are thermally fluctuating and tightly packed amino acid residues strongly interact with each other. Such interactions are characterized in terms of heat current at the atomic level. We calculated the thermal conductivity of a small globular protein, villin headpiece subdomain, based on the linear response theory using equilibrium molecular dynamics simulation. The value of its thermal conductivity was 0.3 ± 0.01 [W m^-1 K^-1], which is in good agreement with experimental and computational studies on the other proteins in the literature. Heat current along the main chain was dominated by local vibrations in the polypeptide bonds, with amide I, II, III, and A bands on the Fourier transform of the heat current autocorrelation function.

Mechanism for the rare fluctuation that powers protein conformational change

Most functional processes of biomolecules are rare events. Key to a rare event is the rare fluctuation that enables the energy activation process that precedes and powers crossing of the activation barrier. However, the physical nature of this rare fluctuation and how it enables energy activation and subsequently barrier crossing are unknown. We developed a novel metric, the reaction capacity pC, that rigorously defines the beginning and parameterizes the progress of energy activation. This enabled us to identify the rare fluctuation as a special phase-space condition that is necessary and sufficient for initiating systematic energy flow from the non-reaction coordinates into the reaction coordinates. The energy activation of a prototype biomolecular isomerization reaction is dominated by kinetic energy transferring into and accumulating in the reaction coordinates, administered by inertial forces alone. This mechanism for energy activation is fundamentally different from the mechanism suggested by Kramers theory.

Emergence of quasiequilibrium state and energy distribution for the beads-spring molecule interacting with a solvent

We study the energy distribution during the emergence of a quasiequilibrium (QE) state in the course of relaxation to equipartition in slow-fast Hamiltonian systems. A bead-spring model where beads (masses) are connected by springs is considered. The QE lasts for a long time because the energy exchange between the high-frequency vibrational and other motions is prevented when springs in the molecule become stiff. We numerically calculated the time-averaged kinetic energy and found that the kinetic energy of the solvent particles was always higher than that of the bead in a molecule. This is explained by adopting the equipartition theorem in QE, and it agrees well with the numerical results. The energy difference can help determine how far the system is from achieving equilibrium, and it can be used as an indicator of the number of frozen or inactive degrees existing in the molecule.

Activation-Induced Reorganization of Energy Transport Networks in the β2 Adrenergic Receptor

We compute energy exchange networks (EENs) through the β₂ adrenergic receptor (β₂AR), a G-protein coupled receptor (GPCR), in inactive and active states, based on the results of molecular dynamics simulations of this membrane bound protein. We introduce a new definition for the reorganization of EENs upon activation that depends on the relative change in rates of energy transfer across noncovalent contacts throughout the protein. On the basis of the reorganized network that we obtain for β₂AR upon activation, we identify a branched pathway between the agonist binding site and the cytoplasmic region, where a G-protein binds to the receptor when activated. The pathway includes all of the motifs containing molecular switches previously identified as contributing to the allosteric transition of β₂AR upon agonist binding. EENs and their reorganization upon activation are compared with structure-based contact networks computed for the inactive and active states of β₂AR.

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.

Energy Transfer across Nonpolar and Polar Contacts in Proteins: Role of Contact Fluctuations

Molecular dynamics simulations of the villin headpiece subdomain HP36 have been carried out to examine relations between rates of vibrational energy transfer across non-covalently bonded contacts and equilibrium structural fluctuations, with focus on van der Waals contacts. Rates of energy transfer across van der Waals contacts vary inversely with the variance of the contact length, with the same constant of proportionality for all nonpolar contacts of HP36. A similar relation is observed for hydrogen bonds, but the proportionality depends on contact pairs, with hydrogen bonds stabilizing the α-helices all exhibiting the same constant of proportionality, one that is distinct from those computed for other polar contacts. Rates of energy transfer across van der Waals contacts are found to be up to 2 orders of magnitude smaller than rates of energy transfer across polar contacts.

Energy flow and intersubunit signalling in GSAM: A non-equilibrium molecular dynamics study

Non-equilibrium molecular dynamics simulations of vibrational energy flow induced by the imposition of a thermal gradient have been performed on the μ2-dimeric enzyme glutamate-1-semialdehyde aminomutase (GSAM), the key enzyme in the biosynthesis of chlorophyll, in order to identify energy transport pathways and to elucidate their role as potential allosteric communication networks for coordinating functional dynamics, specifically the negative cooperativity observed in the motion of the two active site gating loops. Fully atomistic MD simulations of thermal diffusion were executed with a GROMACS simulation package on a fully solvated GSAM enzyme by heating various active site target ligands (initially, catalytic intermediates and cofactors) to 300K while holding the remainder of the protein and the solvent bath at 10K and monitoring the temperature T(t) of all the enzyme residues as a function of time over a 1ns observation window. Energy is observed to be deposited in a relatively small number of discrete chains of residues most of which contribute to specific structural or biochemical functionality. Thermal linkages between all thermally active chains were established by isolating a specific pair of chains and performing a thermal diffusion simulation on the pair, one held at 300K and the other at 10K, with the rest of the protein frozen in its initial atomic configuration and thus thermally unresponsive. Proceeding in this way, it was possible to map out multiple pathways of vibrational energy flow leading from one of the active sites through a network of contiguous residues, many of which were evolutionarily conserved and linked by hydrogen bonds, into the other active site and ultimately to the other gating loop.

Role of atomic contacts in vibrational energy transfer in myoglobin

Heme proteins are ideal systems to investigate vibrational energy flow at the atomic level. Upon photoexcitation, a large amount of excess vibrational energy is selectively deposited on heme due to extremely fast internal conversion. This excess energy is redistributed to the surrounding protein moiety and then to water. Vibrational energy flow in myoglobin (Mb) was examined using picosecond time-resolved anti-Stokes ultraviolet resonance Raman (UVRR) spectroscopy. We used the Trp residue directly contacting the heme group as a selective probe for vibrationally excited populations. Trp residues were placed at different position close to the heme by site-directed mutagenesis. This technique allows us to monitor the excess energy on residue-to-residue basis. Anti-Stokes UVRR measurements for Mb mutants suggest that the dominant channel for energy transfer in Mb is the pathway through atomic contacts between heme and nearby amino acid residues as well as that between the protein and solvent water. It is found that energy flow through proteins is analogous to collisional exchange processes in solutions.

Recent developments in the computational study of protein structural and vibrational energy dynamics

Recent developments in the computational study of energy transport in proteins are reviewed, including advances in both methodology and applications. The concept of energy exchange network (EEN) is discussed, and a recent calculation of EENs for the allosteric protein FixL is reviewed, which illustrates how residues and protein regions involved in the allosteric transition can be identified. Recent work has examined relations between EENs and protein dynamics as well as structure. We review some of the computational studies carried out on several proteins that explore connections between energy conductivity across polar contacts in proteins and between proteins and water and equilibrium dynamics of the contacts, and we discuss some of the recent experimental work that addresses this topic.

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.

Energy Transport Pathways in Proteins: A Non-equilibrium Molecular Dynamics Simulation Study

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.

Vibrational Energy in Proteins Correlates with Topology

The exchange of vibrational energy in proteins is crucial for their function. Here, we establish a connection between quantities related to it with geometry-based properties such as the proteins' residues coordination number. This relation is proven by molecular simulation in a neuro-pharmacologically relevant transmembrane receptor. The connection demonstrated here paves the way to studies of protein allostery and conformational changes based solely on protein structure.

Energy transport pathway in proteins: Insights from non-equilibrium molecular dynamics with elastic network model

Intra-molecular energy transport between distant functional sites plays important roles in allosterically regulating the biochemical activity of proteins. How to identify the specific intra-molecular signaling pathway from protein tertiary structure remains a challenging problem. In the present work, a non-equilibrium dynamics method based on the elastic network model (ENM) was proposed to simulate the energy propagation process and identify the specific signaling pathways within proteins. In this method, a given residue was perturbed and the propagation of energy was simulated by non-equilibrium dynamics in the normal modes space of ENM. After that, the simulation results were transformed from the normal modes space to the Cartesian coordinate space to identify the intra-protein energy transduction pathways. The proposed method was applied to myosin and the third PDZ domain (PDZ3) of PSD-95 as case studies. For myosin, two signaling pathways were identified, which mediate the energy transductions form the nucleotide binding site to the 50 kDa cleft and the converter subdomain, respectively. For PDZ3, one specific signaling pathway was identified, through which the intra-protein energy was transduced from ligand binding site to the distant opposite side of the protein. It is also found that comparing with the commonly used cross-correlation analysis method, the proposed method can identify the anisotropic energy transduction pathways more effectively.

Charge-state Resolved Infrared Multiple Photon Dissociation (IRMPD) Spectroscopy of Ubiquitin Ions in the Gas Phase

In this study, we obtained for the first time the direct infrared multiple photon dissociation (IRMPD) spectra of ubiquitin ions in the range 2700-3750 cm-1. Ubiquitin ions with different charge states showed absorption in the two regions of 2940-3000 cm-1 and 3280-3400 cm-1. The increase of the charge state of ubiquitin ions broadened the absorption peak on the high-frequency side in the second region, indicating some hydrogen bonds were weakened due to Coulomb interaction. It is also found that the relative intensity of the absorption peak in the first region compared to the absorption peak in the second region increased with increasing charge state, making the IRMPD spectra charge-state resolved. Although it is usually reasonable to suggest the origin of the absorption in the range 2940-3000 cm-1 as the C-H bond stretching modes, the results show significantly reduced absorption after the deuteration of all labile hydrogen atoms. A possible explanation for this is that the coupling coefficients between the C-H vibrational mode and other selective modes decreased greatly after the deuteration, reducing the rate of energy redistribution and probability of consecutive IR absorption.

Computational study to understand the energy transfer pathways within amicyanin

Vibrational energy diffusivities between the residues present in Amicyanin copper protein are calculated and presented in form of communication map. From those results energy flow pathways from the copper metal ion to the inter protein residue Glu31 are identified. Our finding suggests many different pathways are possible and copper metal ion in oxidized and reduced state switches the pathways. Our finding also suggests the cooperative nature of surrounding residues and water molecules towards selecting the pathways. The major transport channels in the oxidised state are, Cu²⁺---> MET28---> LYS29---> TYR30---> GLU31 and Cu²⁺---> MET98---> TYR30--- > GLU31. And in the reduced state Cu⁺---> CYS9---> TYR30---> GLU31 and Cu⁺---> MET28---> LYS2---> TYR30---> GLU31. We studied further the interaction energies between the copper ion and neighbouring residues using B3LYP/QZVP method. Both the methods complement each other in predicting the energy flow pathways and the cooperative nature of residues.

Time-resolved observation of protein allosteric communication

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 ([Formula: see text] ns), inelastic reorganization ([Formula: see text] ns), and structural relaxation ([Formula: see text]s). Issues such as the similarity to downhill folding as well as the interpretation of allosteric pathways are discussed.

Importance of Atomic Contacts in Vibrational Energy Flow in Proteins

Vibrational energy flow in proteins was studied by monitoring the time-resolved anti-Stokes ultraviolet resonance Raman scattering of three myoglobin mutants in which a Trp residue substitutes a different amino acid residue near heme. The anti-Stokes Raman intensities of the Trp residue in the three mutants increased with similar rates after depositing excess vibrational energy at heme, despite the difference in distance between heme and each substituted Trp residue along the main chain of the protein. This indicates that vibrational energy is not transferred through the main chain of the protein but rather through atomic contacts between heme and the Trp residue. Distinct differences were observed in the amplitude of the band intensity change between the Trp residues at different positions, and the amplitude of the band intensity change exhibits a correlation with the extent of exposure of the Trp residue to solvent water. This correlation indicates that atomic contacts between an amino acid residue and solvent water play an important role in vibrational energy flow in a protein.

Water-Mediated Energy Dynamics in a Homodimeric Hemoglobin

We examine energy dynamics in the unliganded and liganded states of the homodimeric hemoglobin from Scapharca inaequivalvis (HbI), which exhibits cooperativity mediated by the cluster of water molecules at the interface upon ligand binding and dissociation. We construct and analyze a dynamic network in which nodes representing the residues, hemes, and water cluster are connected by edges that represent energy transport times, as well as a nonbonded network (NBN) indicating regions that respond rapidly to local strain within the protein via nonbonded interactions. One of the two largest NBNs includes the Lys30-Asp89 salt bridge critical for stabilizing the dimer. The other includes the hemes and surrounding residues, as well as, in the unliganded state, the cluster of water molecules between the globules. Energy transport in the protein appears to be controlled by the Lys30-Asp89 salt bridge critical for stabilizing the dimer, as well as the interface water cluster in the unliganded state. Possible connections between energy transport dynamics in response to local strain identified here and allosteric transitions in HbI are discussed.