Atomic-level thermodynamics analysis of the binding free energy of SARS-CoV-2 neutralizing antibodies.

Understanding how protein-protein binding affinity is determined from molecular interactions at the interface is essential in developing protein therapeutics such as antibodies, but this has not yet been fully achieved. Among the major difficulties are the facts that it is generally difficult to decompose thermodynamic quantities into contributions from individual molecular interactions and that the solvent effect-dehydration penalty-must also be taken into consideration for every contact formation at the binding interface. Here, we present an atomic-level thermodynamics analysis that overcomes these difficulties and illustrate its utility through application to SARS-CoV-2 neutralizing antibodies. Our analysis is based on the direct interaction energy computed from simulated antibody-protein complex structures and on the decomposition of solvation free energy change upon complex formation. We find that the formation of a single contact such as a hydrogen bond at the interface barely contributes to binding free energy due to the dehydration penalty. On the other hand, the simultaneous formation of multiple contacts between two interface residues favorably contributes to binding affinity. This is because the dehydration penalty is significantly alleviated: the total penalty for multiple contacts is smaller than a sum of what would be expected for individual dehydrations of those contacts. Our results thus provide a new perspective for designing protein therapeutics of improved binding affinity.

Evolutionary conservation of amino acids contributing to the protein folding transition state.

The question of whether amino acids critical to protein folding kinetics are evolutionarily conserved has been investigated intensively in the past, but no consensus has yet been reached. Recently, we have demonstrated that the transition state, dictating folding kinetics, is characterized as the state of maximum dynamic cooperativity, i.e., the state of maximum correlations between amino acid contact formations. Here, we investigate the evolutionary conservation of those amino acids contributing significantly to the dynamic cooperativity. We find a strong indication of a new kind of relationship-necessary but not sufficient causality-between the evolutionary conservation and the dynamic cooperativity: larger contributions to the dynamic cooperativity arise from more conserved residues, but not vice versa. This holds for all the protein systems for which long folding simulation trajectories are available. To our knowledge, this is the first systematic demonstration of any kind of evolutionary conservation of amino acids relevant to folding kinetics.

Comparing the influence of explicit and implicit solvation models on site-specific thermodynamic stability of proteins.

Understanding the molecular basis for protein stability requires a thermodynamic analysis of protein folding. Thermodynamic analysis is often performed by sampling many atomistic conformations using molecular simulations that employ either explicit or implicit water models. However, it remains unclear to what extent thermodynamic results from different solvation models are reliable at the molecular level. In this study, we quantify the influence of both solvation models on folding stability at the individual backbone and side chain resolutions. We assess the residue-specific folding free energy components of a ß-sheet protein and a helical protein using trajectories resulting from TIP3P explicit and generalized Born/surface area implicit solvent simulations of model proteins. We found that the thermodynamic discrepancy due to the implicit solvent mostly originates from charged side chains, followed by the under-stabilized hydrophobic ones. In contrast, the contributions of backbone residue in both proteins were comparable for explicit and implicit water models. Our study lays out the foundation for detailed thermodynamic assessment of solvation models in the context of protein simulation.

Effects of intramolecular chain conformation on the hydration and miscibility of polyethylene glycol in water studied by means of polymer reference interaction site model theory.

To examine the conventional idea that the gauche conformation of the OCCO dihedral angle promotes the dissolution of polyethylene glycol (PEG) in water through strong hydration, the thermodynamic properties of liquid mixtures of PEG and water were studied by means of polymer reference interaction site model (PRISM) theory. The intramolecular correlation functions required as input for PRISM theory were calculated by the generator matrix method, accompanied by changes in the distribution of dihedral angles. In the infinite dilution limit, the increased probability of gauche conformation of the OCCO dihedral angles stabilizes the hydration of PEG through enhanced hydrogen bonding between the ether oxygen of PEG and water. The mixing Gibbs energies of the liquid mixtures were also calculated in the whole concentration range based on the Gibbs-Duhem equation, as per our recent proposal. A liquid-liquid phase separation was observed when all the dihedral angles of PEG were in the trans conformation; for the liquid mixture to be miscible in the whole concentration range, the introduction of the OCCO gauche conformation was found to be indispensable. The above theoretical results support the conventional idea that the OCCO gauche conformation is important for the high miscibility of PEG and water.

Phase equilibrium of three-component liquid systems composed of water, alcohol, and sodium chloride studied by the reference interaction-site model integral equation theory.

A theoretical method for calculating the thermodynamic properties and phase equilibria of a binary liquid mixture using the reference interaction-site model (RISM) integral equation theory, which we had proposed recently, was extended to ternary liquid systems containing salt. A novel dielectric correction of the RISM theory for a mixture of solvents was also proposed. The theory was applied to mixtures composed of water, alcohol, and NaCl, where the alcohol was either methanol or ethanol. The decrease in NaCl solubility with increasing alcohol molar fractions in the solvent was calculated. In the ethanol system, the theory yielded salt-induced liquid-liquid phase separation, which was observed experimentally in a ternary mixture of water, 1-propanol, and NaCl. The phase diagram of the ternary system was determined theoretically.

Coexistence of two coacervate phases of polyglycine in water suggested by polymer reference interaction site model theory.

Mixing Gibbs energy and phase equilibria of aqueous solutions of polyglycine were studied theoretically by means of polymer reference interaction site model integral equation theory combined with the Gibbs-Duhem method. In addition to the ordinary liquid-liquid phase separation between dilute and concentrated solutions, the theoretical calculation predicted the coexistence of two coacervate phases, namely, the lower- and higher-density coacervates. The relative thermodynamic stabilities of these two phases change with the polymerization degree of polyglycine. The higher-density coacervate phase was rapidly stabilized by increasing the polymer length, and the lower-density phase became metastable at large polymers. The hydrogen bonds between the peptide chains were strengthened, and water was thermodynamically destabilized in the higher-density coacervate. A possible relation with the formation of amyloid fibril within a liquid droplet is also discussed.

Study of phase equilibria and thermodynamic properties of liquid mixtures using the integral equation theory: Application to water and alcohol mixtures.

A theoretical method for calculating the thermodynamic properties and phase equilibria of liquid-liquid mixtures using the integral equation theory is proposed. The solvation chemical potentials of the two components are evaluated by the integral equation theory and the isothermal-isobaric variation of the total density with composition is determined to satisfy the Gibbs-Duhem relation. Given the density of a pure component, the method can calculate the densities of the mixture at any composition. Furthermore, it can treat the phase equilibrium without thermodynamic inconsistency with respect to the Gibbs-Duhem relation. This method was combined with the reference interaction-site model integral equation theory and applied to mixtures of water + 1-alcohol by changing the alcohol from methanol to 1-butanol. The destabilization of the mixing Gibbs energy by increasing the hydrophobicity of the alcohol and demixing of the water-butanol mixture were reproduced. However, quantitative agreement with experiments is not satisfactory, and further improvements of the integral equation theory and the molecular models are required.

Computer Simulations of Intrinsically Disordered Proteins.

The investigation of intrinsically disordered proteins (IDPs) is a new frontier in structural and molecular biology that requires a new paradigm to connect structural disorder to function. Molecular dynamics simulations and statistical thermodynamics potentially offer ideal tools for atomic-level characterizations and thermodynamic descriptions of this fascinating class of proteins that will complement experimental studies. However, IDPs display sensitivity to inaccuracies in the underlying molecular mechanics force fields. Thus, achieving an accurate structural characterization of IDPs via simulations is a challenge. It is also daunting to perform a configuration-space integration over heterogeneous structural ensembles sampled by IDPs to extract, in particular, protein configurational entropy. In this review, we summarize recent efforts devoted to the development of force fields and the critical evaluations of their performance when applied to IDPs. We also survey recent advances in computational methods for protein configurational entropy that aim to provide a thermodynamic link between structural disorder and protein activity.

Distinct role of hydration water in protein misfolding and aggregation revealed by fluctuating thermodynamics analysis.

Protein aggregation in aqueous cellular environments is linked to diverse human diseases. Protein aggregation proceeds through a multistep process initiated by conformational transitions, called protein misfolding, of monomer species toward aggregation-prone structures. Various forms of aggregate species are generated through the association of misfolded monomers including soluble oligomers and amyloid fibrils. Elucidating the molecular mechanisms and driving forces involved in the misfolding and subsequent association has been a central issue for understanding and preventing protein aggregation diseases such as Alzheimer's, Parkinson's, and type II diabetes. In this Account, we provide a thermodynamic perspective of the misfolding and aggregation of the amyloid-beta (Aß) protein implicated in Alzheimer's disease through the application of fluctuating thermodynamics. This approach "dissects" the conventional thermodynamic characterization of the end states into the one of the fluctuating processes connecting them, and enables one to analyze variations in the thermodynamic functions that occur during the course of protein conformational changes. The central quantity in this approach is the solvent-averaged effective energy, f = Eu + Gsolv, comprising the protein potential energy (Eu) and the solvation free energy (Gsolv), whose time variation reflects the protein dynamics on the free energy landscape. Protein configurational entropy is quantified by the magnitude of fluctuations in f. We find that misfolding of the Aß monomer when released from a membrane environment to an aqueous phase is driven by favorable changes in protein potential energy and configurational entropy, but it is also accompanied by an unfavorable increase in solvation free energy. The subsequent dimerization of the misfolded Aß monomers occurs in two steps. The first step, where two widely separated monomers come into contact distance, is driven by water-mediated attraction, that is, by a decrease in solvation free energy, harnessing the monomer solvation free energy earned during the misfolding. The second step, where a compact dimer structure is formed, is driven by direct protein-protein interactions, but again it is accompanied by an increase in solvation free energy. The increased solvation free energy of the dimer will function as the driving force to recruit another Aß protein in the approach stage of subsequent oligomerizations. The fluctuating thermodynamics analysis of the misfolding and dimerization of the Aß protein indicates that the interaction of the protein with surrounding water plays a critical role in protein aggregation. Such a water-centric perspective is further corroborated by demonstrating that, for a large number of Aß mutants and mutants of other protein systems, the change in the experimental aggregation propensity upon mutation has a significant correlation with the protein solvation free energy change. We also find striking discrimination between the positively and negatively charged residues on the protein surface by surrounding water molecules, which is shown to play a crucial role in determining the protein aggregation propensity. We argue that the protein total charge dictates such striking behavior of the surrounding water molecules. Our results provide new insights for understanding and predicting the protein aggregation propensity, thereby offering novel design principles for producing aggregation-resistant proteins for biotherapeutics.

Impact of chemical heterogeneity on protein self-assembly in water.

Hydrophobicity is thought to underlie self-assembly in biological systems. However, the protein surface comprises hydrophobic and hydrophilic patches, and understanding the impact of such a chemical heterogeneity on protein self-assembly in water is of fundamental interest. Here, we report structural and thermodynamic investigations on the dimer formation of full-length amyloid-ß proteins in water associated with Alzheimer's disease. Spontaneous dimerization process--from the individual diffusive regime at large separations, through the approach stage in which two proteins come close to each other, to the structural adjustment stage toward compact dimer formation--was captured in full atomic detail via unguided, explicit-water molecular dynamics simulations. The integral-equation theory of liquids was then applied to simulated protein structures to analyze hydration thermodynamic properties and the water-mediated interaction between proteins. We demonstrate that hydrophilic residues play a key role in initiating the dimerization process. A long-range hydration force of enthalpic origin acting on the hydrophilic residues provides the major thermodynamic force that drives two proteins to approach from a large separation to a contact distance. After two proteins make atomic contacts, the nature of the water-mediated interaction switches from a long-range enthalpic attraction to a short-range entropic one. The latter acts both on the hydrophobic and hydrophilic residues. Along with the direct protein-protein interactions that lead to the formation of intermonomer hydrogen bonds and van der Waals contacts, the water-mediated attraction of entropic origin brings about structural adjustment of constituent monomer proteins toward the formation of a compact dimer structure.

Site-directed analysis on protein hydrophobicity.

Hydrophobicity of a protein is considered to be one of the major intrinsic factors dictating the protein aggregation propensity. Understanding how protein hydrophobicity is determined is, therefore, of central importance in preventing protein aggregation diseases and in the biotechnological production of human therapeutics. Traditionally, protein hydrophobicity is estimated based on hydrophobicity scales determined for individual free amino acids, assuming that those scales are unaltered when amino acids are embedded in a protein. Here, we investigate how the hydrophobicity of constituent amino acid residues depends on the protein context. To this end, we analyze the hydration free energy-free energy change on hydration quantifying the hydrophobicity-of the wild-type and 21 mutants of amyloid-beta protein associated with Alzheimer's disease by performing molecular dynamics simulations and integral-equation calculations. From detailed analysis of mutation effects on the protein hydrophobicity, we elucidate how the protein global factor such as the total charge as well as underlying protein conformations influence the hydrophobicity of amino acid residues. Our results provide a unique insight into the protein hydrophobicity for rationalizing and predicting the protein aggregation propensity on mutation, and open a new avenue to design aggregation-resistant proteins as biotherapeutics.

Interaction with the surrounding water plays a key role in determining the aggregation propensity of proteins.

Understanding the molecular determinants of the relative propensities of proteins to aggregate in a cellular environment is a central issue for treating protein-aggregation diseases and developing peptide-based therapeutics. Despite the expectation that protein aggregation can largely be attributed to direct protein-protein interactions, a crucial role the surrounding water in determining the aggregation propensity of proteins both in vitro and in vivo was identified. The overall protein hydrophobicity, defined solely by the hydration free energy of a protein in its monomeric state sampling its equilibrium structures, was shown to be the predominant determinant of protein aggregation propensity in aqueous solution. Striking discrimination of positively and negatively charged residues by the surrounding water was also found. This effect depends on the protein net charge and plays a crucial role in regulating the solubility of the protein. These results pave the way for the design of aggregation-resistant proteins as biotherapeutics.

Atomic-level investigations on the amyloid-ß dimerization process and its driving forces in water.

We report the spontaneous dimerization process of the full-length Aß42 proteins in water by using unguided, fully atomistic, explicit-water molecular dynamics simulations. Based on the thermodynamic analysis, we demonstrate that Aß42 dimerization in water occurs via a two-step nucleation-accommodation mechanism driven by water-induced force and by protein internal force, respectively.

Aqueous interaction site integral-equation theory that exactly takes into account intramolecular correlations.

We report the development of a formally exact integral equation for the three-dimensional hydration structure around molecular solutes of arbitrary complexity. A distinctive feature of our theory--termed aqueous interaction site (AXIS) integral-equation theory--is that it fully takes into account the intramolecular structural correlations of solvent water, which has been missing in the previous integral-equation theories such as the three-dimensional reference interaction site model (3D-RISM) theory. With a simplifying approximation in which the intermolecular bridge function is neglected, an illustrative application of the AXIS theory is made on the equilibrium oxygen and hydrogen distributions of solvent water surrounding a solute water molecule at ambient and supercritical conditions. We demonstrate through a comparison with molecular dynamics simulation results that the inclusion of the exact intramolecular correlations improves upon the 3D-RISM theory in describing the water distribution around molecular solute, in particular near the surface region of the solute molecule, though there still remain quantitative differences from the simulation results. To further improve the quantitative accuracy of the theory, one needs to incorporate the intermolecular bridge function, and a possible formulation for the approximate bridge function is suggested based on the angular decomposition.

Mutation effects on FAS1 domain 4 based on structure and solubility.

Mutations in the fasciclin 1 domain 4 (FAS1-4) of transforming growth factor ß-induced protein (TGFBIp) are associated with insoluble extracellular deposits and corneal dystrophies (CDs). The decrease in solubility upon mutation has been implicated in CD; however, the exact molecular mechanisms are not well understood. Here, we performed molecular dynamics simulations followed by solvation thermodynamic analyses of the FAS1-4 domain and its three mutants-R555W, R555Q, and A546T-linked to granular corneal dystrophy type 1, Thiel-Behnke corneal dystrophy and lattice corneal dystrophy, respectively. We found that both R555W and R555Q mutants have less affinity toward solvent water relative to the wild-type protein. In the R555W mutant, a remarkable increase in solvation free energy was observed because of the structural changes near the mutation site. The mutation site W555 is buried in other hydrophobic residues, and R557 simultaneously forms salt bridges with E554 and D561. In the R555Q mutant, the increase in solvation free energy is caused by structural rearrangements far from the mutation site. R558 separately forms salt bridges with D575, E576, and E598. Thus, we thus identified the relationship between the decrease in solubility and conformational changes caused by mutations, which may be useful in designing potential therapeutics and in blocking FAS1 aggregation related to CD.

Structural and thermodynamic investigations on the aggregation and folding of acylphosphatase by molecular dynamics simulations and solvation free energy analysis.

Protein engineering method to study the mutation effects on muscle acylphosphatase (AcP) has been actively applied to describe kinetics and thermodynamics associated with AcP aggregation as well as folding processes. Despite the extensive mutation experiments, the molecular origin and the structural motifs for aggregation and folding kinetics as well as thermodynamics of AcP have not been rationalized at the atomic resolution. To this end, we have investigated the mutation effects on the structures and thermodynamics for the aggregation and folding of AcP by using the combination of fully atomistic, explicit-water molecular dynamics simulations, and three-dimensional reference interaction site model theory. The results indicate that the A30G mutant with the fastest experimental aggregation rate displays considerably decreased α1-helical contents as well as disrupted hydrophobic core compared to the wild-type AcP. Increased solvation free energy as well as hydrophobicity upon A30G mutation is achieved due to the dehydration of hydrophilic side chains in the disrupted α1-helix region of A30G. In contrast, the Y91Q mutant with the slowest aggregation rate shows a non-native H-bonding network spanning the mutation site to hydrophobic core and α1-helix region, which rigidifies the native state protein conformation with the enhanced α1-helicity. Furthermore, Y91Q exhibits decreased solvation free energy and hydrophobicity compared to wild type due to more exposed and solvated hydrophilic side chains in the α1-region. On the other hand, the experimentally observed slower folding rates in both mutants are accompanied by decreased helicity in α2-helix upon mutation. We here provide the atomic-level structures and thermodynamic quantities of AcP mutants and rationalize the structural origin for the changes that occur upon introduction of those mutations along the AcP aggregation and folding processes.

Atomic decomposition of the protein solvation free energy and its application to amyloid-beta protein in water.

We report the development of an atomic decomposition method of the protein solvation free energy in water, which ascribes global change in the solvation free energy to local changes in protein conformation as well as in hydration structure. So far, empirical decomposition analyses based on simple continuum solvation models have prevailed in the study of protein-protein interactions, protein-ligand interactions, as well as in developing scoring functions for computer-aided drug design. However, the use of continuum solvation model suffers serious drawbacks since it yields the protein free energy landscape which is quite different from that of the explicit solvent model and since it does not properly account for the non-polar hydrophobic effects which play a crucial role in biological processes in water. Herein, we develop an exact and general decomposition method of the solvation free energy that overcomes these hindrances. We then apply this method to elucidate the molecular origin for the solvation free energy change upon the conformational transitions of 42-residue amyloid-beta protein (Aß42) in water, whose aggregation has been implicated as a primary cause of Alzheimer's disease. We address why Aß42 protein exhibits a great propensity to aggregate when transferred from organic phase to aqueous phase.

Communication: Propagator for diffusive dynamics of an interacting molecular pair.

We introduce a new method of solution for the Fredholm integral equations of the second kind. The method would be useful when the direct iterative approach leads to a divergent perturbation series solution. By using the method, we obtain an accurate expression of the propagator for diffusive dynamics of a pair of particles interacting via an arbitrary central potential and hydrodynamic interaction. We test the accuracy of the propagator expression by calculating the diffusion-controlled geminate and bimolecular reaction rates. It is shown that our propagator expression provides very accurate results for the whole time region.

Time-dependent communication between multiple amino acids during protein folding.

Cooperativity is considered to be a key organizing principle behind biomolecular assembly, recognition and folding. However, it has remained very challenging to quantitatively characterize how cooperative processes occur on a concerted, multiple-interaction basis. Here, we address how and when the folding process is cooperative on a molecular scale. To this end, we analyze multipoint time-correlation functions probing time-dependent communication between multiple amino acids, which were computed from long folding simulation trajectories. We find that the simultaneous multiple amino-acid contact formation, which is absent in the unfolded state, starts to develop only upon entering the folding transition path. Interestingly, the transition state, whose presence is connected to the macrostate cooperative behavior known as the two-state folding, can be identified as the state in which the amino-acid cooperativity is maximal. Thus, our work not only provides a new mechanistic view on how protein folding proceeds on a multiple-interaction basis, but also offers a conceptually novel characterization of the folding transition state and the molecular origin of the phenomenological cooperative folding behavior. Moreover, the multipoint correlation function approach adopted here is general and can be used to expand the understanding of cooperative processes in complex chemical and biomolecular systems.

Site-Specific Backbone and Side-Chain Contributions to Thermodynamic Stabilizing Forces of the WW Domain.

The native structure of a protein is stabilized by a number of interactions such as main-chain hydrogen bonds and side-chain hydrophobic contacts. However, it has been challenging to determine how these interactions contribute to protein stability at single amino acid resolution. Here, we quantified site-specific thermodynamic stability at the molecular level to extend our understanding of the stabilizing forces in protein folding. We derived the free energy components of individual amino acid residues separately for the folding of the human Pin WW domain based on simulated structures. A further decomposition of the thermodynamic properties into contributions from backbone and side-chain groups enabled us to identify the critical residues in the secondary structure and hydrophobic core formation, without introducing physical modifications to the system as in site-directed mutagenesis methods. By relating the structural and thermodynamic changes upon folding for each residue, we find that the simultaneous formation of the backbone hydrogen bonds and side-chain contacts cooperatively stabilizes the folded structure. The identification of stabilizing interactions in a folding protein at atomic resolution will provide molecular insights into understanding the origin of the protein structure and into engineering a more stable protein.