Inhomogeneous Fluid Solvation Theory Research Articles

Structural and thermodynamic properties of conserved water molecules in Mpro native: A combined approach by MD simulation and Grid Inhomogeneous Solvation Theory.

The new viral strains of severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) are continuously rising, becoming more virulent, and transmissible. Therefore, the development of new antiviral drugs is essential. Due to its significant role in the viral life cycle of SARS-CoV-2, the main protease (Mpro) enzyme is a leading target for antiviral drug design. The Mpro monomer consists of domain DI, DII, and DI-DII interface. Twenty-one conserved water molecules (W4-W24) are occupied at these domains according to multiple crystal structure analyses. The crystal and MD structures reveal the presence of eight conserved water sites in domain DI, DII and remaining in the DI-DII interface. Grid-based inhomogeneous fluid solvation theory (GIST) was employed on MD structures of Mpro native to predict structural and thermodynamic properties of each conserved water site for focusing to identify the specific conserved water molecules that can easily be displaced by proposed ligands. Finally, MD water W13 is emerged as a promising candidate for water mimic drug design due to its low mean interaction energy, loose binding character with the protein, and its involvement in a water-mediated H-bond with catalytic His41 via the interaction Thr25(OG)---W13---W---His41(NE2). In this context, water occupancy, relative interaction energy, entropy, and topologies of W13 are thermodynamically acceptable for the water displacement method. Therefore, the strategic use of W13's geometrical position in the DI domain may be implemented for drug discovery against COVID disease by designing new ligands with appropriately oriented chemical groups to mimic its structural, electronic, and thermodynamic properties.

Large-Scale Study of Hydration Environments through Hydration Sites.

Hydration sites are locations of interest to water and they can be used to classify the behavior of water around chemical motifs commonly found on the surface of proteins. Inhomogeneous fluid solvation theory (IFST) is a method for calculating hydration free-energy changes from molecular dynamics (MD) trajectories. In this paper, hydration sites are identified from MD simulations of 380 diverse protein structures. The hydration free energies of the hydration sites are calculated using IFST and distributions of these free-energy changes are analyzed. The results show that for some hydration sites near features conventionally regarded as attractive to water, such as hydrogen bond donors, the water molecules are actually relatively weakly bound and are easily displaced. We also construct plots of the spatial density of hydration sites with high, medium, and low hydration free-energy changes which represent weakly and strongly bound hydration sites. It is found that these plots show consistent features around common polar amino acids for all of the proteins studied.

Thermodynamic Insight into the Effects of Water Displacement and Rearrangement upon Ligand Modifications using Molecular Dynamics Simulations.

Computational methods, namely molecular dynamics (MD) simulations in combination with inhomogeneous fluid solvation theory (IFST) were used to retrospectively investigate various cases of ligand structure modifications that led to the displacement of binding site water molecules. Our findings are that water displacement per se is energetically unfavorable in the discussed examples, and that it is merely the fine balance between change in protein-ligand interaction energy, ligand solvation free energies, and binding site solvation free energies that determine if water displacement is favorable or not. We furthermore evaluated if we can reproduce experimental binding affinities by a computational approach combining changes in solvation free energies with changes in protein-ligand interaction energies and entropies. In two of the seven cases, this estimation led to large errors, implying that accurate predictions of relative binding free energies based on solvent thermodynamics is challenging. Nevertheless, MD simulations can provide insight regarding which water molecules can be targeted for displacement.

Solvation Structure and Thermodynamic Mapping (SSTMap): An Open-Source, Flexible Package for the Analysis of Water in Molecular Dynamics Trajectories.

We have developed SSTMap, a software package for mapping structural and thermodynamic water properties in molecular dynamics trajectories. The package introduces automated analysis and mapping of local measures of frustration and enhancement of water structure. The thermodynamic calculations are based on Inhomogeneous Fluid Solvation Theory (IST), which is implemented using both site-based and grid-based approaches. The package also extends the applicability of solvation analysis calculations to multiple molecular dynamics (MD) simulation programs by using existing cross-platform tools for parsing MD parameter and trajectory files. SSTMap is implemented in Python and contains both command-line tools and a Python module to facilitate flexibility in setting up calculations and for automated generation of large data sets involving analysis of multiple solutes. Output is generated in formats compatible with popular Python data science packages. This tool will be used by the molecular modeling community for computational analysis of water in problems of biophysical interest such as ligand binding and protein function.

On the accuracy of one- and two-particle solvation entropies.

Evaluating solvation entropies directly and combining with direct energy calculations is one way of calculating free energies of solvation and is used by Inhomogeneous Fluid Solvation Theory (IFST). The configurational entropy of a fluid is a function of the interatomic correlations and can thus be expressed in terms of correlation functions. The entropies in this work are directly calculated from a truncated series of integrals over these correlation functions. Many studies truncate all terms higher than the solvent-solute correlations. This study includes an additional solvent-solvent correlation term and assesses the associated free energy when IFST is applied to a fixed Lennard-Jones particle solvated in neon. The strength of the central potential is varied to imitate larger solutes. Average free energy estimates with both levels of IFST are able to reproduce the estimate made using the Free energy Perturbation (FEP) to within 0.16 kcal/mol. We find that the signal from the solvent-solvent correlations is very weak. Our conclusion is that for monatomic fluids simulated by pairwise classical potentials the correction term is relatively small in magnitude. This study shows it is possible to reproduce the free energy from a path based method like FEP, by only considering the endpoints of the path. This method can be directly applied to more complex solutes which break the spherical symmetry of this study.

Exploring the role of water in molecular recognition: predicting protein ligandability using a combinatorial search of surface hydration sites

The interaction between any two biological molecules must compete with their interaction with water molecules. This makes water the most important molecule in medicine, as it controls the interactions of every therapeutic with its target. A small molecule binding to a protein is able to recognize a unique binding site on a protein by displacing bound water molecules from specific hydration sites. Quantifying the interactions of these water molecules allows us to estimate the potential of the protein to bind a small molecule. This is referred to as ligandability. In the study, we describe a method to predict ligandability by performing a search of all possible combinations of hydration sites on protein surfaces. We predict ligandability as the summed binding free energy for each of the constituent hydration sites, computed using inhomogeneous fluid solvation theory. We compared the predicted ligandability with the maximum observed binding affinity for 20 proteins in the human bromodomain family. Based on this comparison, it was determined that effective inhibitors have been developed for the majority of bromodomains, in the range from 10 to 100 nM. However, we predict that more potent inhibitors can be developed for the bromodomains BPTF and BRD7 with relative ease, but that further efforts to develop inhibitors for ATAD2 will be extremely challenging. We have also made predictions for the 14 bromodomains with no reported small molecule Kd values by isothermal titration calorimetry. The calculations predict that PBRM1(1) will be a challenging target, while others such as TAF1L(2), PBRM1(4) and TAF1(2), should be highly ligandable. As an outcome of this work, we assembled a database of experimental maximal Kd that can serve as a community resource assisting medicinal chemistry efforts focused on BRDs. Effective prediction of ligandability would be a very useful tool in the drug discovery process.

Solvation thermodynamic mapping of molecular surfaces in AmberTools: GIST.

The expulsion of water from surfaces upon molecular recognition and nonspecific association makes a major contribution to the free energy changes of these processes. In order to facilitate the characterization of water structure and thermodynamics on surfaces, we have incorporated Grid Inhomogeneous Solvation Theory (GIST) into the CPPTRAJ toolset of AmberTools. GIST is a grid-based implementation of Inhomogeneous Fluid Solvation Theory, which analyzes the output from molecular dynamics simulations to map out solvation thermodynamic and structural properties on a high-resolution, three-dimensional grid. The CPPTRAJ implementation, called GIST-cpptraj, has a simple, easy-to-use command line interface, and is open source and freely distributed. We have also developed a set of open-source tools, called GISTPP, which facilitate the analysis of GIST output grids. Tutorials for both GIST-cpptraj and GISTPP can be found at ambermd.org. © 2016 Wiley Periodicals, Inc.

Quantifying the Entropy of Binding for Water Molecules in Protein Cavities by Computing Correlations

Protein structural analysis demonstrates that water molecules are commonly found in the internal cavities of proteins. Analysis of experimental data on the entropies of inorganic crystals suggests that the entropic cost of transferring such a water molecule to a protein cavity will not typically be greater than 7.0 cal/mol/K per water molecule, corresponding to a contribution of approximately +2.0 kcal/mol to the free energy. In this study, we employ the statistical mechanical method of inhomogeneous fluid solvation theory to quantify the enthalpic and entropic contributions of individual water molecules in 19 protein cavities across five different proteins. We utilize information theory to develop a rigorous estimate of the total two-particle entropy, yielding a complete framework to calculate hydration free energies. We show that predictions from inhomogeneous fluid solvation theory are in excellent agreement with predictions from free energy perturbation (FEP) and that these predictions are consistent with experimental estimates. However, the results suggest that water molecules in protein cavities containing charged residues may be subject to entropy changes that contribute more than +2.0 kcal/mol to the free energy. In all cases, these unfavorable entropy changes are predicted to be dominated by highly favorable enthalpy changes. These findings are relevant to the study of bridging water molecules at protein-protein interfaces as well as in complexes with cognate ligands and small-molecule inhibitors.

Molecular simulations with solvent competition quantify water displaceability and provide accurate interaction maps of protein binding sites.

Binding sites present well-defined interaction patterns that putative ligands must meet. Knowing them is essential to guide structure-based drug discovery projects. However, complex aspects of molecular recognition-such as protein flexibility or the effect of aqueous solvation-hinder accurate predictions. This is particularly true for polar contacts, which are heavily influenced by the local environment and the behavior of discrete water molecules. Here we present and validate MDmix (Molecular Dynamics simulations with mixed solvents) as a method that provides much more accurate interaction maps than ordinary potentials (e.g., GRID). Additionally, MDmix also affords water displaceability predictions, with advantages over methods that use pure water as solvent (e.g., inhomogeneous fluid solvation theory). With current MD software and hardware solutions, predictions can be obtained in a matter of hours and visualized in a very intuitive manner. Thus, MDmix is an ideal complement in everyday structure-based drug discovery projects.

Estimating Translational and Orientational Entropies Using the k-Nearest Neighbors Algorithm.

Inhomogeneous fluid solvation theory (IFST) and free energy perturbation (FEP) calculations were performed for a set of 20 solutes to compute the hydration free energies. We identify the weakness of histogram methods in computing the IFST hydration entropy by showing that previously employed histogram methods overestimate the translational and orientational entropies and thus underestimate their contribution to the free energy by a significant amount. Conversely, we demonstrate the accuracy of the k-nearest neighbors (KNN) algorithm in computing these translational and orientational entropies. Implementing the KNN algorithm within the IFST framework produces a powerful method that can be used to calculate free-energy changes for large perturbations. We introduce a new KNN approach to compute the total solute-water entropy with six degrees of freedom, as well as the translational and orientational contributions. However, results suggest that both the solute-water and water-water entropy terms are significant and must be included. When they are combined, the IFST and FEP hydration free energies are highly correlated, with an R(2) of 0.999 and a mean unsigned difference of 0.9 kcal/mol. IFST predictions are also highly correlated with experimental hydration free energies, with an R(2) of 0.997 and a mean unsigned error of 1.2 kcal/mol. In summary, the KNN algorithm is shown to yield accurate estimates of the combined translational-orientational entropy and the novel approach of combining distance metrics that is developed here could be extended to provide a powerful method for entropy estimation in numerous contexts.

Combining Solvent Thermodynamic Profiles with Functionality Maps of the Hsp90 Binding Site to Predict the Displacement of Water Molecules

Intermolecular interactions in the aqueous phase must compete with the interactions between the two binding partners and their solvating water molecules. In biological systems, water molecules in protein binding sites cluster at well-defined hydration sites and can form strong hydrogen-bonding interactions with backbone and side-chain atoms. Displacement of such water molecules is only favorable when the ligand can form strong compensating hydrogen bonds. Conversely, water molecules in hydrophobic regions of protein binding sites make only weak interactions, and the requirements for favorable displacement are less stringent. The propensity of water molecules for displacement can be identified using inhomogeneous fluid solvation theory (IFST), a statistical mechanical method that decomposes the solvation free energy of a solute into the contributions from different spatial regions and identifies potential binding hotspots. In this study, we employed IFST to study the displacement of water molecules from the ATP binding site of Hsp90, using a test set of 103 ligands. The predicted contribution of a hydration site to the hydration free energy was found to correlate well with the observed displacement. Additionally, we investigated if this correlation could be improved by using the energetic scores of favorable probe groups binding at the location of hydration sites, derived from a multiple copy simultaneous search (MCSS) method. The probe binding scores were not highly predictive of the observed displacement and did not improve the predictivity when used in combination with IFST-based hydration free energies. The results show that IFST alone can be used to reliably predict the observed displacement of water molecules in Hsp90. However, MCSS can augment IFST calculations by suggesting which functional groups should be used to replace highly displaceable water molecules. Such an approach could be very useful in improving the hit-to-lead process for new drug targets.

Assessing the Accuracy of Inhomogeneous Fluid Solvation Theory in Predicting Hydration Free Energies of Simple Solutes

Accurate prediction of hydration free energies is a key objective of any free energy method that is applied to modeling and understanding interactions in the aqueous phase. Inhomogeneous fluid solvation theory (IFST) is a statistical mechanical method for calculating solvation free energies by quantifying the effect of a solute acting as a perturbation to bulk water. IFST has found wide application in understanding hydration phenomena in biological systems, but quantitative applications have not been comprehensively assessed. In this study, we report the hydration free energies of six simple solutes calculated using IFST and independently using free energy perturbation (FEP). This facilitates a validation of IFST that is independent of the accuracy of the force field. The results demonstrate that IFST shows good agreement with FEP, with an R2 coefficient of determination of 0.99 and a mean unsigned difference of 0.7 kcal/mol. However, sampling is a major issue that plagues IFST calculations and the results suggest that a histogram method may require prohibitively long simulations to achieve convergence of the entropies, for bin sizes which effectively capture the underlying probability distributions. Results also highlight the sensitivity of IFST to the reference interaction energy of a water molecule in bulk, with a difference of 0.01 kcal/mol changing the predicted hydration free energies by approximately 2.4 kcal/mol for the systems studied here. One of the major advantages of IFST over perturbation methods such as FEP is that the systems are spatially decomposed to consider the contribution of specific regions to the total solvation free energies. Visualizing these contributions can yield detailed insights into solvation thermodynamics. An insight from this work is the identification and explanation of regions with unfavorable free energy density relative to bulk water. These regions contribute unfavorably to the hydration free energy. Further work is necessary before IFST can be extended to yield accurate predictions of binding free energies, but the work presented here demonstrates its potential.

Benchmarking the thermodynamic analysis of water molecules around a model beta sheet.

Water molecules play a vital role in biological and engineered systems by controlling intermolecular interactions in the aqueous phase. Inhomogeneous fluid solvation theory provides a method to quantify solvent thermodynamics from molecular dynamics or Monte Carlo simulations and provides an insight into intermolecular interactions. In this study, simulations of TIP4P-2005 and TIP5P-Ewald water molecules around a model beta sheet are used to investigate the orientational correlations and predicted thermodynamic properties of water molecules at a protein surface. This allows the method to be benchmarked and provides information about the effect of a protein on the thermodynamics of nearby water molecules. The results show that the enthalpy converges with relatively little sampling, but the entropy and thus the free energy require considerably more sampling to converge. The two water models yield a very similar pattern of hydration sites, and these hydration sites have very similar thermodynamic properties, despite notable differences in their orientational preferences. The results also predict that a protein surface affects the free energy of water molecules to a distance of approximately 4.0 Å, which is in line with previous work. In addition, all hydration sites have a favorable free energy with respect to bulk water, but only when the water-water entropy term is included. A new technique for calculating this term is presented and its use is expected to be very important in accurately calculating solvent thermodynamics for quantitative application.

Application of inhomogeneous fluid solvation theory to model the distribution and thermodynamics of water molecules around biomolecules

The structures of biomolecules and the strengths of association between them depend critically on interactions with water molecules. Thus, understanding these interactions is a prerequisite for understanding the structure and function of all biomolecules. Inhomogeneous fluid solvation theory provides a framework to derive thermodynamic properties of individual water molecules from a statistical mechanical analysis. In this work, two biomolecules are analysed to probe the distribution and thermodynamics of surrounding water molecules. The great majority of hydration sites are predicted to contribute favourably to the total free energy with respect to bulk water, though hydration sites close to non-polar regions of the solute do not contribute significantly. Analysis of a biomolecule with a positively and negatively charged functional group predicts that a charged species perturbs the free energy of water molecules to a distance of approximately 6.0 Å. Interestingly, short simulations are found to provide converged predictions if samples are taken with sufficient frequency, a finding that has the potential to significantly reduce the required computational cost of such analysis. In addition, the predicted thermodynamic properties of hydration sites with the potential for direct hydrogen bonding interactions are found to disagree significantly for two different water models. This study provides important information on how inhomogeneous fluid solvation theory can be employed to understand the structures and intermolecular interactions of biomolecules.

Thermodynamic Properties of Water Molecules at a Protein–Protein Interaction Surface

Protein–protein interactions (PPIs) have been identified as a vital regulator of cellular pathways and networks. However, the determinants that control binding affinity and specificity at protein surfaces are incompletely characterized and thus unable to be exploited for the purpose of developing PPI inhibitors to control cellular pathways in disease states. One of the key factors in intermolecular interactions that remains poorly understood is the role of water molecules and in particular the importance of solvent entropy. This factor is expected to be particularly important at protein surfaces, and the release of water molecules from hydrophobic regions is one of the most important drivers of PPIs. In this work, we have studied the protein surface of a mutant of the protein RadA to quantify the thermodynamics of surface water molecules. RadA and its human homologue RAD51 function as recombinases in the process of homologous recombination. RadA binds to itself to form oligomeric structures and thus contains a well-characterized protein–protein binding surface. Similarly, RAD51 binds either to itself to form oligomers or to the protein BRCA2 to form filaments. X-ray crystallography has determined that the same interface functions in both interactions. Work in our group has generated a partially humanized mutant of RadA, termed MAYM, which has been crystallized in the apo form. We studied this apo form of MAYM using a combination of molecular dynamics (MD) simulations and inhomogeneous fluid solvation theory (IFST). The method locates a number of the hydration sites observed in the crystal structure and locates hydrophobic sites where hydrophobic species are known to bind experimentally. The simulations also highlight the importance of the restraints placed on the protein in determining the results. Finally, the results identify a correlation between the predicted entropy of water molecules at a given site and the solvent-accessible surface area and suggest that correlations between water molecules only need to be considered for water molecules separated by less than 3.2 Å. The combination of MD and IFST has been used previously to study PPIs and represents one of the few existing methods to quantify solvent thermodynamics. This is a vital aspect of molecular recognition and one which we believe must be developed.

Computational Analysis of Phosphopeptide Binding to the Polo-Box Domain of the Mitotic Kinase PLK1 Using Molecular Dynamics Simulation

The Polo-Like Kinase 1 (PLK1) acts as a central regulator of mitosis and is over-expressed in a wide range of human tumours where high levels of expression correlate with a poor prognosis. PLK1 comprises two structural elements, a kinase domain and a polo-box domain (PBD). The PBD binds phosphorylated substrates to control substrate phosphorylation by the kinase domain. Although the PBD preferentially binds to phosphopeptides, it has a relatively broad sequence specificity in comparison with other phosphopeptide binding domains. We analysed the molecular determinants of recognition by performing molecular dynamics simulations of the PBD with one of its natural substrates, CDC25c. Predicted binding free energies were calculated using a molecular mechanics, Poisson-Boltzmann surface area approach. We calculated the per-residue contributions to the binding free energy change, showing that the phosphothreonine residue and the mainchain account for the vast majority of the interaction energy. This explains the very broad sequence specificity with respect to other sidechain residues. Finally, we considered the key role of bridging water molecules at the binding interface. We employed inhomogeneous fluid solvation theory to consider the free energy of water molecules on the protein surface with respect to bulk water molecules. Such an analysis highlights binding hotspots created by elimination of water molecules from hydrophobic surfaces. It also predicts that a number of water molecules are stabilized by the presence of the charged phosphate group, and that this will have a significant effect on the binding affinity. Our findings suggest a molecular rationale for the promiscuous binding of the PBD and highlight a role for bridging water molecules at the interface. We expect that this method of analysis will be very useful for probing other protein surfaces to identify binding hotspots for natural binding partners and small molecule inhibitors.

Water at biomolecular binding interfaces

Water molecules are often found at the binding interface of biomolecular complexes mediating the interaction between polar groups via hydrogen bonds, or simply filling space providing van der Waals interactions. Recent studies have demonstrated the importance of taking such water molecules into account in docking and binding affinity prediction. Here, we review the recent experimental and theoretical work aimed at quantifying the influence of interfacial water on the thermodynamic properties of binding. We highlight especially our recent results obtained by inhomogeneous fluid solvation theory in several systems and the prediction of the thermodynamic consequences of displacement of the bound water molecule by ligand modification. Finally, we discuss possible directions for further progress in this field.

Thermodynamics of Buried Water Clusters at a Protein−Ligand Binding Interface

The structure of the complex of cyclophilin A (CypA) with cyclosporin A (CsA, 1) shows a cluster of four water molecules buried at the binding interface, which is rearranged when CsA is replaced by (5-hydroxynorvaline)-2-cyclosporin (2). The thermodynamic contributions of each bound water molecule in the two complexes are explored with the inhomogeneous fluid solvation theory and molecular dynamics simulations. Water (WTR) 133 in complex 1 contributes little to the binding affinity, while WTR6 and 7 in complex 2 play an essential role in mediating protein-ligand binding with a hydrogen bond network. The calculations reveal that the rearrangement of the water molecules contributes favorably to the binding affinity, even though one of them is displaced going from ligand 1 to 2. Another favorable contribution comes from the larger protein-ligand interactions of ligand 2. However, these favorable contributions are not sufficient to overcome the unfavorable desolvation free energy change and the conformational entropy of the hydroxylpropyl group of ligand 2 in the complex, leading to a lower binding affinity of ligand 2. These physical insights may be useful in the development of improved scoring functions for binding affinity prediction.