Anisotropic Structural Relaxation and Its Correlation with the Excess Energy Diffusion in the Incipient Process of Photodissociated MbCO: High-Resolution Analysis via Ensemble Perturbation Method

Capturing ultrafast energy flow of a heme protein in crowded milieu

Energy flow in biomolecules is a dynamic process vital for understanding health, disease, and applications in biotechnology and medicine. In crowded environments, where biomolecular functions are modulated, comprehending energy flow becomes crucial for accurately understanding cellular processes like signaling and subsequent functions. This study employs ultrafast transient absorption spectroscopy to demonstrate energy funneling from the photoexcited heme of bovine heart cytochrome c to the protein exterior, in the presence of common synthetic (Dextran 40, Ficoll 70, PEG 8 and Dextran 70) and protein-based (BSA and β-LG) crowders. The through-space energy transfer mode for ferric and the methionine rebinding mode for ferrous cytochrome c show the strongest solvent coupling. The heterogeneous behaviour of crowders, influenced by crowder-protein interactions and caging effects at certain higher concentrations, reveal diverse trends. Notably, protein crowders perturb all transport routes of vibrational energy transfer, causing delays in energy transfer processes. These findings provide significant insights into the basic tenets of energy flow, one of the most fundamental processes, in crowded cellular environments.

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.

Simulation toolkits at the molecular scale for trans-scale thermal signaling

Thermogenesis is a physiological activity of releasing heat that originates from intracellular biochemical reactions. Recent experimental studies discovered that externally applied heat changes intracellular signaling locally, resulting in global changes in cell morphology and signaling. Therefore, we hypothesize an inevitable contribution of thermogenesis in modulating biological system functions throughout the spatial scales from molecules to individual organisms. One key issue examining the hypothesis, namely, the "trans-scale thermal signaling," resides at the molecular scale on the amount of heat released via individual reactions and by which mechanism the heat is employed for cellular function operations. This review introduces atomistic simulation tool kits for studying the mechanisms of thermal signaling processes at the molecular scale that even state-of-the-art experimental methodologies of today are hardly accessible. We consider biological processes and biomolecules as potential heat sources in cells, such as ATP/GTP hydrolysis and multiple biopolymer complex formation and disassembly. Microscopic heat release could be related to mesoscopic processes via thermal conductivity and thermal conductance. Additionally, theoretical simulations to estimate these thermal properties in biological membranes and proteins are introduced. Finally, we envisage the future direction of this research field.

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 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.

Elucidating microscopic events driven by GTP hydrolysis reaction in the Ras-GAP system with semi-reactive molecular dynamics simulations: the alternative role of a phosphate binding loop for mechanical energy storage

ATPase and GTPase have been widely found as chemical energy-mechanical work transducers, whereas the physicochemical mechanisms are not satisfactorily understood. We addressed the problem by examining John Ross' conjecture that repulsive Coulomb interaction between ADP/GDP and inorganic phosphate (P_i) does the mechanical work upon the system. We effectively simulated the consequence of a GTP hydrolysis reaction in a complex system of Rat sarcoma (Ras) and GTPase activation protein (GAP) in the framework of classical molecular dynamics by switching force field parameters between the reactant and product systems. We then observed a ca. 5 kcal mol^-1 increase of potential energy about the phosphate-binding loop (P-loop) in the Ras protein, indicating that the mechanical work generated via the GTP hydrolysis is converted into the local interaction energy and stored in the P-loop. Interestingly, this local energy storage in the P-loop depends on neither impulsive nor consecutive collisions of GDP and P_i with the P-loop. Instead, GTP-GDP conversion itself does work on the Ras system, elevating the potential energy. These observations encourage us to challenge a conjecture previously given by Ross. We assert that triphosphate nucleotide hydrolyses do mechanical work by producing emergent steric interaction accompanied by relaxation, namely, a shift of the biomolecular system to the non-equilibrium state on the reshaped potential energy landscape. Recalling the universality of the P-loop motif among GTPases and ATPases, the observations that we obtained through this study would progress the physicochemical understanding of the operating principles of GTP/ATP hydrolysis-driven biological nano-machines.

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.

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.

Probing the communication of deoxythymidine triphosphate in HIV-1 reverse transcriptase by communication maps and interaction energy studies

We calculate communication maps for HIV-1 Reverse Transcriptase (RT) to elucidate energy transfer pathways between deoxythymidine triphosphate (dTTP) and other parts of the protein.

Scaling Rules for Vibrational Energy Transport in Globular Proteins

Computational studies of vibrational energy flow in biomolecules have to date mapped out transport pathways on a case-by-case basis. To provide a more general approach, we derive scaling rules for vibrational energy transport in a globular protein, which are identified from extensive nonequilibrium molecular dynamics simulations of vibrational energy flow in the villin headpiece subdomain HP36. We parametrize a master equation based on inter-residue, residue-solvent, and heater-residue energy-transfer rates, which closely reproduces the results of the all-atom simulations. From that fit, two scaling rules emerge, one for energy transport along the protein backbone which relies on a diffusion model and another for energy transport between tertiary contacts, which is based on a harmonic model. Requiring only the calculation of mean and variance of relatively few atomic distances, the approach holds the potential to predict the pathways and time scales of vibrational energy flow in large proteins.

Anisotropic energy flow and allosteric ligand binding in albumin

Allosteric interactions in proteins generally involve propagation of local structural changes through the protein to a remote site. Anisotropic energy transport is thought to couple the remote sites, but the nature of this process is poorly understood. Here, we report the relationship between energy flow through the structure of bovine serum albumin and allosteric interactions between remote ligand binding sites of the protein. Ultrafast infrared spectroscopy is used to probe the flow of energy through the protein backbone following excitation of a heater dye, a metalloporphyrin or malachite green, bound to different binding sites in the protein. We observe ballistic and anisotropic energy flow through the protein structure following input of thermal energy into the flexible ligand binding sites, without local heating of the rigid helix bundles that connect these sites. This efficient energy transport mechanism enables the allosteric propagation of binding energy through the connecting helix structures.

Energy exchange network of inter-residue interactions within a thermally fluctuating protein molecule: A computational study

Protein function is regulated not only by the structure but also by physical dynamics and thermal fluctuations. We have developed the computer program, CURrent calculation for proteins (CURP), for the flow analysis of physical quantities within thermally fluctuating protein media. The CURP program was used to calculate the energy flow within the third PDZ domain of the neuronal protein PSD-95, and the results were used to illustrate the energy exchange network of inter-residue interactions based on atomistic molecular dynamics simulations. The removal of the α3 helix is known to decrease ligand affinity by 21-fold without changing the overall protein structure; nevertheless, we demonstrated that the helix constitutes an essential part of the network graph.

Non-site-specific allosteric effect of oxygen on human hemoglobin under high oxygen partial pressure

Protein allostery is essential for vital activities. Allosteric regulation of human hemoglobin (HbA) with two quaternary states T and R has been a paradigm of allosteric structural regulation of proteins. It is widely accepted that oxygen molecules (O₂) act as a “site-specific” homotropic effector, or the successive O₂ binding to the heme brings about the quaternary regulation. However, here we show that the site-specific allosteric effect is not necessarily only a unique mechanism of O₂ allostery. Our simulation results revealed that the solution environment of high O₂ partial pressure enhances the quaternary change from T to R without binding to the heme, suggesting an additional “non-site-specific” allosteric effect of O₂. The latter effect should play a complementary role in the quaternary change by affecting the intersubunit contacts. This analysis must become a milestone in comprehensive understanding of the allosteric regulation of HbA from the molecular point of view.

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.

Ligand migration in myoglobin: a combined study of computer simulation and x-ray crystallography

A ligand-migration mechanism of myoglobin was studied by a multidisciplinary approach that used x-ray crystallography and molecular dynamics simulation. The former revealed the structural changes of the protein along with the ligand migration, and the latter provided the statistical ensemble of protein conformations around the thermal average. We developed a novel computational method, homogeneous ensemble displacement, and generated the conformational ensemble of ligand-detached species from that of ligand-bound species. The thermally averaged ligand-protein interaction was illustrated in terms of the potential of mean force. Although the structural changes were small, the presence of the ligand molecule in the protein matrix significantly affected the 3D scalar field of the potential of mean force, in accordance with the self-opening model proposed in the previous x-ray study.

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%.

Ligand diffusion in globins: simulations versus experiment

Computer simulations in molecular biophysics describe in atomic detail the structure, dynamics, and function of biological macromolecules. To assess the quality of these models and to pick up new mechanisms, comparisons with experimental measurements are made. Most comparisons examine thermodynamic and average structural properties. Here we discuss studies of dynamics and fluctuations in a protein. The diffusion of a small ligand between internal cavities in myoglobin, and its escape to solvent are considered. Qualitative and semi-quantitative agreements between experiment and simulation are obtained for the identities of the cavities that physically trap the ligand and for the connections between them. However, experimental and computational 'doors' are at significant variance. Simulations suggest multiple gates while kinetic experiments point to one dominant exit.

Heat transfer in protein-water interfaces

We investigate using transient non-equilibrum molecular dynamics simulation the temperature relaxation process of three structurally different proteins in water, namely; myoglobin, green fluorescence protein (GFP) and two conformations of the Ca(2+)-ATPase protein. By modeling the temperature relaxation process using the solution of the heat diffusion equation we compute the thermal conductivity and thermal diffusivity of the proteins, as well as the thermal conductance of the protein-water interface. Our results indicate that the temperature relaxation of the protein can be described using a macroscopic approach. The protein-water interface has a thermal conductance of the order of 100-270 MW K(-1) m(-2), characteristic of water-hydrophilic interfaces. The thermal conductivity of the proteins is of the order of 0.1-0.2 W K(-1) m(-1) as compared with approximately 0.6 W K(-1) m(-1) for water, suggesting that these proteins can develop temperature gradients within the biomolecular structures that are larger than those of aqueous solutions. We find that the thermal diffusivity of the transmembrane protein, Ca(2+)-ATPase is about three times larger than that of myoglobin or GFP. Our simulation shows that the Kapitza length of these structurally different proteins is of the order of 1 nm, showing that the protein-water interface should play a major role in defining the thermal relaxation of biomolecules.

Diversity of solvent dependent energy transfer pathways in heme proteins

The time scales and pathways of heme cooling in both reduced cytochrome c and oxidized cytochrome c following heme photoexcitation were studied using molecular dynamics simulation. Five different solvent models, including normal water, heavy water, normal glycerol, deuterated glycerol, and a nonpolar solvent, were used in the simulation. Single exponential decay of the excess kinetic energy of the heme following photoexcitation was observed in all systems studied. The simulated time scale for heme cooling in normal water agrees with recent experimental results. In contrast to heme cooling in myoglobin, no solvent dependence was observed for the time scale for heme cooling in cytochrome c. The diversity of solvent dependence results from the different local heme environments in the two proteins. In myoglobin, it has been established that the dominant mechanism for heme cooling is direct energy transfer from the heme to the solvent. In cytochrome c, direct interaction between heme and protein residues forms the dominant energy transfer pathway. This distinction is dictated by protein topology and linked to function.

Toward quantitative simulations of carbon monoxide escape pathways in myoglobin

Straightforward molecular dynamics trajectories have been computed to explore the diffusion of carbon monoxide through myoglobin. The classical equations of motion were integrated for 2 ns and the resulting pathways analyzed. Two types of runs were examined. Type i: Myoglobin and a ligand embedded in a periodic box with 9996 water molecules; the water molecules are rigid but the bonds of the protein are flexible. Type ii: Myoglobin with a solvation shell (153 water molecules) in which all bond lengths are fixed. In trajectories of type i, the diffusing ligand visits a significant part of the protein matrix and was not constrained to the proximity of the heme pocket before escaping. The maximum time of the trajectories was 2 ns. It was shorter if the ligand escaped earlier. Two ligands (from a total of 88) escape to the solvent from nonclassical gates (non-E-helix gates). In trajectories of type ii, the overall fluctuations of the protein are smaller and the ligand explores significantly smaller internal space. The escape rate from type ii trajectories (11 of 400) is comparable to type i and is not dramatically different from experiment (1 of 100). Interestingly, the two simulations with comparable rates sampled different pathways. In trajectories of type ii, we observe escapes from the classical gate (His 64) and from the Xe4 cavity. Further studies (that are underway) are required to define the escape pathways and the overall rate.