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 ß2-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.

The origin and impact of bound water around intrinsically disordered proteins.

Proteins and water couple dynamically over a wide range of time scales. Motivated by their central role in protein function, protein-water dynamics and thermodynamics have been extensively studied for structured proteins, where correspondence to structural features has been made. However, properties controlling intrinsically disordered protein (IDP)-water dynamics are not yet known. We report results of megahertz-to-terahertz dielectric spectroscopy and molecular dynamics simulations of a group of IDPs with varying charge content along with structured proteins of similar size. Hydration water around IDPs is found to exhibit more heterogeneous rotational and translational dynamics compared with water around structured proteins of similar size, yielding on average more restricted dynamics around individual residues of IDPs, charged or neutral, compared with structured proteins. The on-average slower water dynamics is found to arise from excess tightly bound water in the first hydration layer, which is related to greater exposure to charged groups. The more tightly bound water to IDPs correlates with the smaller hydration shell found experimentally, and affects entropy associated with protein-water interactions, the contribution of which we estimate based on the dielectric measurements and simulations. Water-IDP dynamic coupling at terahertz frequencies is characterized by the dielectric measurements and simulations.

A Statistical Journey through the Topological Determinants of the ß2 Adrenergic Receptor Dynamics.

Activation of G-protein-coupled receptors (GPCRs) is mediated by molecular switches throughout the transmembrane region of the receptor. In this work, we continued along the path of a previous computational study wherein energy transport in the ß2 Adrenergic Receptor (ß2-AR) was examined and allosteric switches were identified in the molecular structure through the reorganization of energy transport networks during activation. In this work, we further investigated the allosteric properties of ß2-AR, using Protein Contact Networks (PCNs). In this paper, we report an extensive statistical analysis of the topological and structural properties of ß2-AR along its molecular dynamics trajectory to identify the activation pattern of this molecular system. The results show a distinct character to the activation that both helps to understand the allosteric switching previously identified and confirms the relevance of the network formalism to uncover relevant functional features of protein molecules.

Change in vibrational entropy with change in protein volume estimated with mode Grüneisen parameters.

For a small adjustment in average volume, due to a change in state of a protein or other macromolecule at constant temperature, the change in vibrational entropy is related to the mode Grüneisen parameters, which relate shifts in frequency to a small volume change. We report here values of mode Grüneisen parameters computed for two hydrated proteins, cytochrome c and myoglobin, which exhibit trends with mode frequency resembling those of glassy systems. We use the mode Grüneisen parameters to relate volumetric thermal expansion to previously computed values of the isothermal compressibility for several proteins. We also estimate changes in vibrational entropy resulting from the change in volume upon ligand bonding of myoglobin and the homodimeric hemoglobin from Scapharca inaequivalvis (HbI). We compare estimates of the change in entropy upon ligation obtained in terms of mode Grüneisen parameters with the results of normal mode analysis for myoglobin and earlier molecular dynamics simulations of HbI. The results illustrate how small changes in average volume can yield changes in entropy that contribute to ligand binding and allostery.

Water-mediated biomolecular dynamics and allostery.

Dynamic coupling with water contributes to regulating the functional dynamics of a biomolecule. We discuss protein-water dynamics, with emphasis on water that is partially confined, and the role of protein-confined water dynamics in allosteric regulation. These properties are illustrated with two systems, a homodimeric hemoglobin from Scapharca inaequivalvis (HbI) and an A2A adenosine receptor (A2AAR). For HbI, water-protein interactions, long known to contribute to the thermodynamics of cooperativity, are seen to influence the dynamics of the protein not only around the protein-water interface but also into the core of each globule, where dynamic and entropic changes upon ligand binding are coupled to protein-water contact dynamics. Similarly, hydration waters trapped deep inside the core region of A2AAR enable the formation of an allosteric network made of water-mediated inter-residue contacts. Extending from the ligand binding pocket to the G-protein binding site, this allosteric network plays key roles in regulating the activity of the receptor.

Tuning Molecular Vibrational Energy Flow within an Aromatic Scaffold via Anharmonic Coupling.

From guiding chemical reactivity in synthesis or protein folding to the design of energy diodes, intramolecular vibrational energy redistribution harnesses the power to influence the underlying fundamental principles of chemistry. To evaluate the ability to steer these processes, the mechanism and time scales of intramolecular vibrational energy redistribution through aromatic molecular scaffolds have been assessed by utilizing two-dimensional infrared (2D IR) spectroscopy. 2D IR cross peaks reveal energy relaxation through an aromatic scaffold from the azido- to the cyano-vibrational reporters in para-azidobenzonitrile (PAB) and para-(azidomethyl)benzonitrile (PAMB) prior to energy relaxation into the solvent. The rates of energy transfer are modulated by Fermi resonances, which are apparent by the coupling cross peaks identified within the 2D IR spectrum. Theoretical vibrational mode analysis allowed the determination of the origins of the energy flow, the transfer pathway, and a direct comparison of the associated transfer rates, which were in good agreement with the experimental results. Large variations in energy-transfer rates, approximately 1.9 ps for PAB and 23 ps for PAMB, illustrate the importance of strong anharmonic coupling, i.e., Fermi resonance, on the transfer pathways. In particular, vibrational energy rectification is altered by Fermi resonances of the cyano- and azido-modes allowing control of the propensity for energy flow.

Hydrophobic Collapse of Ubiquitin Generates Rapid Protein-Water Motions.

We report time-resolved measurements of the coupled protein-water modes of solvated ubiquitin during protein folding. Kinetic terahertz absorption (KITA) spectroscopy serves as a label-free technique for monitoring large scale conformational changes and folding of proteins subsequent to a sudden T-jump. We report here KITA measurements at an unprecedented time resolution of 500 ns, a resolution 2 orders of magnitude better than those of any previous KITA measurements, which reveal the coupled ubiquitin-solvent dynamics even in the initial phase of hydrophobic collapse. Complementary equilibrium experiments and molecular simulations of ubiquitin solutions are performed to clarify non-equilibrium contributions and reveal the molecular picture upon a change in structure, respectively. On the basis of our results, we propose that in the case of ubiquitin a rapid (<500 ns) initial phase of the hydrophobic collapse from the elongated protein to a molten globule structure precedes secondary structure formation. We find that these very first steps, including large-amplitude changes within the unfolded manifold, are accompanied by a rapid (<500 ns) pronounced change of the coupled protein-solvent response. The KITA response upon secondary structure formation exhibits an opposite sign, which indicates a distinct effect on the solvent-exposed surface.

Vibrational States and Nitrile Lifetimes of Cyanophenylalanine Isotopomers in Solution.

Nitrile lifetimes and the structure of the vibrational state space of four isotopomers of cyanophenylalanine in solution are calculated. While the frequency of the nitrile of the four isotopomers decreases in the order 12C14N, 12C15N, 13C14N, and 13C15N, the lifetime varies nonmonotonically with the change in frequency. The vibrational properties of the molecules that control the lifetime are examined. The specific resonances that contribute to the lifetime are tuned by isotopic substitution, and the magnitudes of the anharmonic constants involved in the coupling of vibrations that mediate the lifetime of the nitrile vary with CN mass. The nature of the modes coupled to the nitrile varies, as the frequency of the nitrile changes with isotopic substitution. For some CN frequencies the modes coupled to the CN are rather localized to the ring, while at other frequencies the modes coupled to the CN are more delocalized. Comparison of the calculated frequencies and lifetimes with recent experimental measurements on these molecules is discussed.

Molecules and the Eigenstate Thermalization Hypothesis.

We review a theory that predicts the onset of thermalization in a quantum mechanical coupled non-linear oscillator system, which models the vibrational degrees of freedom of a molecule. A system of N non-linear oscillators perturbed by cubic anharmonic interactions exhibits a many-body localization (MBL) transition in the vibrational state space (VSS) of the molecule. This transition can occur at rather high energy in a sizable molecule because the density of states coupled by cubic anharmonic terms scales as N3, in marked contrast to the total density of states, which scales as exp(aN), where a is a constant. The emergence of a MBL transition in the VSS is seen by analysis of a random matrix ensemble that captures the locality of coupling in the VSS, referred to as local random matrix theory (LRMT). Upon introducing higher order anharmonicity, the location of the MBL transition of even a sizable molecule, such as an organic molecule with tens of atoms, still lies at an energy that may exceed the energy to surmount a barrier to reaction, such as a barrier to conformational change. Illustrative calculations are provided, and some recent work on the influence of thermalization on thermal conduction in molecular junctions is also discussed.

Influence of thermalization on thermal conduction through molecular junctions: Computational study of PEG oligomers.

Thermalization in molecular junctions and the extent to which it mediates thermal transport through the junction are explored and illustrated with computational modeling of polyethylene glycol (PEG) oligomer junctions. We calculate rates of thermalization in the PEG oligomers from 100 K to 600 K and thermal conduction through PEG oligomer interfaces between gold and other materials, including water, motivated in part by photothermal applications of gold nanoparticles capped by PEG oligomers in aqueous and cellular environments. Variation of thermalization rates over a range of oligomer lengths and temperatures reveals striking effects of thermalization on thermal conduction through the junction. The calculated thermalization rates help clarify the scope of applicability of approaches that can be used to predict thermal conduction, e.g., where Fourier's law breaks down and where a Landauer approach is suitable. The rates and nature of vibrational energy transport computed for PEG oligomers are compared with available experimental results.

Long-range protein-water dynamics in hyperactive insect antifreeze proteins.

Antifreeze proteins (AFPs) are specific proteins that are able to lower the freezing point of aqueous solutions relative to the melting point. Hyperactive AFPs, identified in insects, have an especially high ability to depress the freezing point by far exceeding the abilities of other AFPs. In previous studies, we postulated that the activity of AFPs can be attributed to two distinct molecular mechanisms: (i) short-range direct interaction of the protein surface with the growing ice face and (ii) long-range interaction by protein-induced water dynamics extending up to 20 Å from the protein surface. In the present paper, we combine terahertz spectroscopy and molecular simulations to prove that long-range protein-water interactions make essential contributions to the high antifreeze activity of insect AFPs from the beetle Dendroides canadensis. We also support our hypothesis by studying the effect of the addition of the osmolyte sodium citrate.

Asymmetric energy flow in liquid alkylbenzenes: A computational study.

Ultrafast IR-Raman experiments on substituted benzenes [B. C. Pein et al., J. Phys. Chem. B 117, 10898-10904 (2013)] reveal that energy can flow more efficiently in one direction along a molecule than in others. We carry out a computational study of energy flow in the three alkyl benzenes, toluene, isopropylbenzene, and t-butylbenzene, studied in these experiments, and find an asymmetry in the flow of vibrational energy between the two chemical groups of the molecule due to quantum mechanical vibrational relaxation bottlenecks, which give rise to a preferred direction of energy flow. We compare energy flow computed for all modes of the three alkylbenzenes over the relaxation time into the liquid with energy flow through the subset of modes monitored in the time-resolved Raman experiments and find qualitatively similar results when using the subset compared to all the modes.

Vibrational energy flow in the villin headpiece subdomain: master equation simulations.

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.

Communication maps of vibrational energy transport through Photoactive Yellow Protein.

We calculate communication maps for Photoactive Yellow Protein (PYP) from the purple phototropic eubacterium Halorhodospira halophile and use them to elucidate energy transfer pathways from the chromophore through the rest of the protein in the ground and excited state. The calculations reveal that in PYP excess energy from the chromophore flows mainly to regions of the surrounding residues that hydrogen bond to the chromophore. In addition, quantum mechanics/molecular mechanics and molecular dynamics (MD) simulations of the dielectric response of the protein and solvent environment due to charge rearrangement on the chromophore following photoexcitation are also presented, with both approaches yielding similar time constants for the response. Results of MD simulations indicate that the residues hydrogen bonding to the chromophore make the largest contribution to the response.

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 ß2AR, 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 ß2AR are found where structural and dynamic changes occur upon activation, contributing to allosteric regulation.

Dynamics of Hydrogen Bonds between Water and Intrinsically Disordered and Structured Regions of Proteins.

Recent studies indicate more restricted dynamics of water around intrinsically disordered proteins (IDPs) than structured proteins. We examine here the dynamics of hydrogen bonds between water molecules and two proteins, small ubiquitin-related modifier-1 (SUMO-1) and ubiquitin-conjugating enzyme E2I (UBC9), which we compare around intrinsically disordered regions (IDRs) and structured regions of these proteins. It has been recognized since some time that excluded volume effects, which influence access of water molecules to hydrogen-bonding sites, and the strength of hydrogen bonds between water and protein affect hydrogen bond lifetimes. While we find those two properties to mediate lifetimes of hydrogen bonds between water and protein residues in this study, we also find that the lifetimes are affected by the concentration of charged groups on other nearby residues. These factors are more important in determining the hydrogen bond lifetimes than whether a residue hydrogen bonding with water belongs to an IDR or to a structured region.

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.

Enhanced Mobility during Diels-Alder Reaction: Results of Molecular Simulations.

Recent measurements indicate enhanced mobility of solvent molecules during Diels-Alder (DA) and other common chemical reactions. We present results of molecular dynamics simulations of the last stages of the DA cycloaddition reaction, from the transition state configuration to product, of furfurylamine and maleimide in acetonitrile at reactant concentrations studied experimentally. We find enhanced mobility of solvent and reactant molecules up to at least a nanometer from the DA product over hundreds of picoseconds. Local heating is ruled out as a factor in the enhanced mobility observed in the simulations, which is instead found to be due to solvent relaxation following the formation of the DA product.

Biophysical Insight into the SARS-CoV2 Spike-ACE2 Interaction and Its Modulation by Hepcidin through a Multifaceted Computational Approach.

At the center of the SARS-CoV2 infection, the spike protein and its interaction with the human receptor ACE2 play a central role in the molecular machinery of SARS-CoV2 infection of human cells. Vaccine therapies are a valuable barrier to the worst effects of the virus and to its diffusion, but the need of purposed drugs is emerging as a core target of the fight against COVID19. In this respect, the repurposing of drugs has already led to discovery of drugs thought to reduce the effects of the cytokine storm, but still a drug targeting the spike protein, in the infection stage, is missing. In this work, we present a multifaceted computational approach strongly grounded on a biophysical modeling of biological systems, so to disclose the interaction of the SARS-CoV2 spike protein with ACE2 with a special focus to an allosteric regulation of the spike-ACE2 interaction. Our approach includes the following methodologies: Protein Contact Networks and Network Clustering, Targeted Molecular Dynamics, Elastic Network Modeling, Perturbation Response Scanning, and a computational analysis of energy flow and SEPAS as a protein-softness and monomer-based affinity predictor. We applied this approach to free (closed and open) states of spike protein and spike-ACE2 complexes. Eventually, we analyzed the interactions of free and bound forms of spike with hepcidin (HPC), the major hormone in iron regulation, recently addressed as a central player in the COVID19 pathogenesis, with a special emphasis to the most severe outcomes. Our results demonstrate that, compared with closed and open states, the spike protein in the ACE2-bound state shows higher allosteric potential. The correspondence between hinge sites and the Allosteric Modulation Region (AMR) in the S-ACE complex suggests a molecular basis for hepcidin involvement in COVID19 pathogenesis. We verify the importance of AMR in different states of spike and then study its interactions with HPC and the consequence of the HPC-AMR interaction on spike dynamics and its affinity for ACE2. We propose two complementary mechanisms for HPC effects on spike of SARS-CoV-2; (a) HPC acts as a competitive inhibitor when spike is in a preinfection state (open and with no ACE2), (b) the HPC-AMR interaction pushes the spike structure into the safer closed state. These findings need clear molecular in vivo verification beside clinical observations.

Communication maps computed for homodimeric hemoglobin: computational study of water-mediated energy transport in proteins.

Frequency-resolved communication maps provide a coarse-grained picture of energy transport in nanoscale systems. We calculate communication maps for homodimeric hemoglobin from Scapharca inaequivalvis and sample them to elucidate energy transfer pathways between the binding sites and other parts of the protein with focus on the role of the cluster of water molecules at the interface between the globules. We complement analysis of communication maps with molecular simulations of energy flow. Both approaches reveal that excess energy in one heme flows mainly to regions of the interface where early hydrogen bond rearrangements occur in the allosteric transition. In particular, energy is carried disproportionately by the water molecules, consistent with the larger thermal conductivity of water compared to proteins.