Scaling of Rates of Vibrational Energy Transfer in Proteins with Equilibrium Dynamics and Entropy

Thermal Energy Transport through Nonbonded Native Contacts in Protein

Within the protein interior, where we observe various types of interactions, nonuniform flow of thermal energy occurs along the polypeptide chain and through nonbonded native contacts, leading to inhomogeneous transport efficiencies from one site to another. The folded native protein serves not merely as thermal transfer medium but, more importantly, as sophisticated molecular nanomachines in cells. Therefore, we are particularly interested in what sort of "communication" is mediated through native contacts in the folded proteins and how such features are quantitatively depicted in terms of local transport coefficients of heat currents. To address the issue, we introduced a concept of inter-residue thermal conductivity and characterized the nonuniform thermal transport properties of a small globular protein, HP36, using equilibrium molecular dynamics simulation and the Green-Kubo formula. We observed that the thermal transport of the protein was dominated by that along the polypeptide chain, while the local thermal conductivity of nonbonded native contacts decreased in the order of H-bonding > π-stacking > electrostatic > hydrophobic contacts. Furthermore, we applied machine learning techniques to analyze the molecular mechanism of protein thermal transport. As a result, the contact distance, variance in contact distance, and H-bonding occurrence probability during MD simulations are found to be the top three important determinants for predicting local thermal transport coefficients.

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.

Noncovalent π Interactions in Mutated Aquomet-Myoglobin Proteins: A QM/MM and Local Vibrational Mode Study

Protein dynamics and function is strongly connected to the energy flow taking place. Myoglobin (Mb) and its mutations are ideal systems to study the process of vibrational energy transfer (VET) at the molecular level. Anti-Stokes ultraviolet resonance Raman studies using a tryptophan (Trp) probe, introduced at different Mb positions by amino acid replacement, have suggested that the amount of VET depends on the position of the Trp probe relative to the heme group. Inspired by this experimental work, we explored the strength of noncovalent π interactions, as well as covalent interactions for both the axial and distal ligands bound to iron in aquomet-Mb with the local vibrational mode analysis (LMA), originally developed by Konkoli and Cremer. Two sets of noncovalent interactions were investigated: (1) the interaction between the water ligand and Trp rings and (2) the interaction between the Trp and the porphyrin rings of the heme group. We assessed the strength of these noncovalent interactions via a special local mode force constant. Various Trp-modified water-bound ferric Mb proteins in the ground state were studied (6 in total) using gas-phase and QM/MM calculations followed by LMA. Our results disclose that VET is indeed dependent on the position of the Trp probe relative to the heme group but also on the tautomeric nature of distal histidine. They provide new guidelines on how to assess noncovalent π interactions in proteins utilizing LMA and how to use these data to explore VET, and more generally protein dynamics and function.

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.

Information Flow and Allosteric Communication in Proteins

Based on Schreiber's work on transfer entropy, a molecular theory of nonlinear information transfer in proteins is developed. The joint distribution function for residue fluctuations is expressed in terms of tensor Hermite polynomials which conveniently separate harmonic and nonlinear contributions to information transfer. The harmonic part of information transfer is expressed as the difference between time dependent and independent mutual information. Third order nonlinearities are discussed in detail. Amount and speed of information transfer between residues, important for understanding allosteric activity in proteins, are discussed. While mutual information shows the maximum amount of information that may be transferred between two residues, it does not explain the actual amount of transfer nor the transfer rate of information. For this, dynamic equations of the system are needed. The solution of the Langevin equation and molecular dynamics trajectories are used in the present work for this purpose. Allosteric communication in Human NAD-dependent isocitrate dehydrogenase is studied as an example. Calculations show that several paths contribute collectively to information transfer. Important residues on these paths are identified. Time resolved information transfer between these residues, their amplitudes and transfer rates, which are in agreement with time resolved ultraviolet resonance Raman measurements in general, are estimated. Estimated transfer rates are in the order of 1-20 megabits per second. Information transfer from third order contributions are one to two orders of magnitude smaller than the harmonic terms, showing that harmonic analysis is a good approximation to information transfer.

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.

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.

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.

Normal mode analysis and beyond

Normal mode analysis provides a powerful tool in biophysical computations. Particularly, we shed light on its application to protein properties because they directly lead to biological functions. As a result of normal mode analysis, the protein motion is represented as a linear combination of mutually independent normal mode vectors. It has been widely accepted that the large amplitude motions throughout the entire protein molecule can be well described with a few low-frequency normal modes. Furthermore, it is possible to represent the effect of external perturbations, e.g., ligand binding, hydrostatic pressure, as the shifts of normal mode variables. Making use of this advantage, we are able to explore mechanical properties of proteins such as Young's modulus and compressibility. Within thermally fluctuating protein molecules under physiological conditions, tightly packed amino acid residues interact with each other through heat and energy exchanges. Since the structure and dynamics of protein molecules are highly anisotropic, the flow of energy and heat should also be anisotropic. Based on the harmonic approximation of the heat current operator, it is possible to analyze the communication map of a protein molecule. By using this method, the energy transfer pathways of photoactive yellow protein were calculated. It turned out that these pathways are similar to those obtained via the Green-Kubo formalism with equilibrium molecular dynamics simulations, indicating that normal mode analysis captures the intrinsic nature of the transport properties of proteins.

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.