Rapid estimation of hydration thermodynamics of macromolecular regions

WaterKit: Thermodynamic Profiling of Protein Hydration Sites

Water desolvation is one of the key components of the free energy of binding of small molecules to their receptors. Thus, understanding the energetic balance of solvation and desolvation resulting from individual water molecules can be crucial when estimating ligand binding, especially when evaluating different molecules and poses as done in High-Throughput Virtual Screening (HTVS). Over the most recent decades, several methods were developed to tackle this problem, ranging from fast approximate methods (usually empirical functions using either discrete atom-atom pairwise interactions or continuum solvent models) to more computationally expensive and accurate ones, mostly based on Molecular Dynamics (MD) simulations, such as Grid Inhomogeneous Solvation Theory (GIST) or Double Decoupling. On one hand, MD-based methods are prohibitive to use in HTVS to estimate the role of waters on the fly for each ligand. On the other hand, fast and approximate methods show an unsatisfactory level of accuracy, with low agreement with results obtained with the more expensive methods. Here we introduce WaterKit, a new grid-based sampling method with explicit water molecules to calculate thermodynamic properties using the GIST method. Our results show that the discrete placement of water molecules is successful in reproducing the position of crystallographic waters with very high accuracy, as well as providing thermodynamic estimates with accuracy comparable to more expensive MD simulations. Unlike these methods, WaterKit can be used to analyze specific regions on the protein surface, (such as the binding site of a receptor), without having to hydrate and simulate the whole receptor structure. The results show the feasibility of a general and fast method to compute thermodynamic properties of water molecules, making it well-suited to be integrated in high-throughput pipelines such as molecular docking.

Thermodynamic Decomposition of Solvation Free Energies with Particle Mesh Ewald and Long-Range Lennard-Jones Interactions in Grid Inhomogeneous Solvation Theory

Grid Inhomogeneous Solvation Theory (GIST) maps out solvation thermodynamic properties on a fine meshed grid and provides a statistical mechanical formalism for thermodynamic end-state calculations. However, differences in how long-range nonbonded interactions are calculated in molecular dynamics engines and in the current implementation of GIST have prevented precise comparisons between free energies estimated using GIST and those from other free energy methods such as thermodynamic integration (TI). Here, we address this by presenting PME-GIST, a formalism by which particle mesh Ewald (PME)-based electrostatic energies and long-range Lennard-Jones (LJ) energies are decomposed and assigned to individual atoms and the corresponding voxels they occupy in a manner consistent with the GIST approach. PME-GIST yields potential energy calculations that are precisely consistent with modern simulation engines and performs these calculations at a dramatically faster speed than prior implementations. Here, we apply PME-GIST end-state analyses to 32 small molecules whose solvation free energies are close to evenly distributed from 2 kcal/mol to -17 kcal/mol and obtain solvation energies consistent with TI calculations (R² = 0.99, mean unsigned difference 0.8 kcal/mol). We also estimate the entropy contribution from the second and higher order entropy terms that are truncated in GIST by the differences between entropies calculated in TI and GIST. With a simple correction for the high order entropy terms, PME-GIST obtains solvation free energies that are highly consistent with TI calculations (R² = 0.99, mean unsigned difference = 0.4 kcal/mol) and experimental results (R² = 0.88, mean unsigned difference = 1.4 kcal/mol). The precision of PME-GIST also enables us to show that the solvation free energy of small hydrophobic and hydrophilic molecules can be largely understood based on perturbations of the solvent in a region extending a few solvation shells from the solute. We have integrated PME-GIST into the open-source molecular dynamics analysis software CPPTRAJ.

Hydration thermodynamics of cytosolic phospholipase A2 GIVA predict its membrane-associated parts and its highly hydrated binding site

During biological events, the water molecules associated with the protein are re-oriented to adapt to the new conditions, inducing changes in the system's free energy. The characterization of water structure and thermodynamics may facilitate the prediction of certain biological events, such as the binding of a ligand and the membrane-associated parts of a protein. In this computational study, we calculated the hydration thermodynamics of cytosolic phospholipase A₂ group IV (GIVA cPLA₂) to study the hydration properties of the protein's surface and binding pocket. Hydrophobicity scales and the Grid Inhomogeneous Solvation Theory (GIST) tool were employed for the calculations. The hydrophobic areas of the protein's surface were predicted more accurately with the GIST method rather than with the hydrophobicity scales. Based on this, a model of the protein-membrane complex was constructed. In addition, the calculation revealed the highly hydrated binding pocket that further contribute to our understanding of the ligands' binding. Communicated by Ramaswamy H. Sarma.

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.

The Role of Interfacial Water in Protein-Ligand Binding: Insights from the Indirect Solvent Mediated Potential of Mean Force

Classical density functional theory (DFT) can be used to relate the thermodynamic properties of solutions to the indirect solvent mediated part of the solute-solvent potential of mean force (PMF). Standard, but powerful numerical methods can be used to estimate the solute-solvent PMF from which the indirect part can be extracted. In this work we show how knowledge of the direct and indirect parts of the solute-solvent PMF for water at the interface of a protein receptor can be used to gain insights about how to design tighter binding ligands. As we show, the indirect part of the solute-solvent PMF is equal to the sum of the 1-body (energy + entropy) terms in the inhomogeneous solvation theory (IST) expansion of the solvation free energy. To illustrate the effect of displacing interfacial water molecules with particular direct/indirect PMF signatures on the binding of ligands, we carry out simulations of protein binding with several pairs of congeneric ligands. We show that interfacial water locations that contribute favorably or unfavorably at the 1-body level (energy + entropy) to the solvation free energy of the solute can be targeted as part of the ligand design process. Water locations where the indirect PMF is larger in magnitude provide better targets for displacement when adding a functional group to a ligand core.

Waterdock 2.0: Water placement prediction for Holo-structures with a pymol plugin

Water is often found to mediate interactions between a ligand and a protein. It can play a significant role in orientating the ligand within a binding pocket and contribute to the free energy of binding. It would thus be extremely useful to be able to accurately predict the position and orientation of water molecules within a binding pocket. Recently, we developed the WaterDock protocol that was able to predict 97% of the water molecules in a test set. However, this approach generated false positives at a rate of over 20% in most cases and whilst this might be acceptable for some applications, in high throughput scenarios this is not desirable. Here we tackle this problem via the inclusion of knowledge regarding the solvation structure of ligand functional groups. We call this new protocol WaterDock2 and demonstrate that this protocol maintains a similar true positive rate to the original implementation but is capable of reducing the false-positive rate by over 50%. To improve the usability of the method, we have also developed a plugin for the popular graphics program PyMOL. The plugin also contains an implementation of the original WaterDock.

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 K d 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 K d 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.

The solvation structure of alprazolam

Alprazolam is a benzodiazepine that is commonly prescribed for the treatment of anxiety and other related disorders.

Spatial Decomposition of Translational Water-Water Correlation Entropy in Binding Pockets

A number of computational tools available today compute the thermodynamic properties of water at surfaces and in binding pockets by using inhomogeneous solvation theory (IST) to analyze explicit-solvent simulations. Such methods enable qualitative spatial mappings of both energy and entropy around a solute of interest and can also be applied quantitatively. However, the entropy estimates of existing methods have, to date, been almost entirely limited to the first-order terms in the IST’s entropy expansion. These first-order terms account for localization and orientation of water molecules in the field of the solute but not for the modification of water–water correlations by the solute. Here, we present an extension of the Grid Inhomogeneous Solvation Theory (GIST) approach which accounts for water–water translational correlations. The method involves rewriting the two-point density of water in terms of a conditional density and utilizes the efficient nearest-neighbor entropy estimation approach. Spatial maps of this second order term, for water in and around the synthetic host cucurbit[7]uril and in the binding pocket of the enzyme Factor Xa, reveal mainly negative contributions, indicating solute-induced water–water correlations relative to bulk water; particularly strong signals are obtained for sites at the entrances of cavities or pockets. This second-order term thus enters with the same, negative, sign as the first order translational and orientational terms. Numerical and convergence properties of the methodology are examined.

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.

Spatial analysis and quantification of the thermodynamic driving forces in protein-ligand binding: binding site variability

The thermodynamic driving forces behind small molecule-protein binding are still not well-understood, including the variability of those forces associated with different types of ligands in different binding pockets. To better understand these phenomena we calculate spatially resolved thermodynamic contributions of the different molecular degrees of freedom for the binding of propane and methanol to multiple pockets on the proteins Factor Xa and p38 MAP kinase. Binding thermodynamics are computed using a statistical thermodynamics based end-point method applied on a canonical ensemble comprising the protein-ligand complexes and the corresponding free states in an explicit solvent environment. Energetic and entropic contributions of water and ligand degrees of freedom computed from the configurational ensemble provide an unprecedented level of detail into the mechanisms of binding. Direct protein-ligand interaction energies play a significant role in both nonpolar and polar binding, which is comparable to water reorganization energy. Loss of interactions with water upon binding strongly compensates these contributions leading to relatively small binding enthalpies. For both solutes, the entropy of water reorganization is found to favor binding in agreement with the classical view of the "hydrophobic effect". Depending on the specifics of the binding pocket, both energy-entropy compensation and reinforcement mechanisms are observed. It is notable to have the ability to visualize the spatial distribution of the thermodynamic contributions to binding at atomic resolution showing significant differences in the thermodynamic contributions of water to the binding of propane versus methanol.

Strategies to calculate water binding free energies in protein-ligand complexes

Water molecules are commonplace in protein binding pockets, where they can typically form a complex between the protein and a ligand or become displaced upon ligand binding. As a result, it is often of great interest to establish both the binding free energy and location of such molecules. Several approaches to predicting the location and affinity of water molecules to proteins have been proposed and utilized in the literature, although it is often unclear which method should be used under what circumstances. We report here a comparison between three such methodologies, Just Add Water Molecules (JAWS), Grand Canonical Monte Carlo (GCMC), and double-decoupling, in the hope of understanding the advantages and limitations of each method when applied to enclosed binding sites. As a result, we have adapted the JAWS scoring procedure, allowing the binding free energies of strongly bound water molecules to be calculated to a high degree of accuracy, requiring significantly less computational effort than more rigorous approaches. The combination of JAWS and GCMC offers a route to a rapid scheme capable of both locating and scoring water molecules for rational drug design.

Sampling of Organic Solutes in Aqueous and Heterogeneous Environments Using Oscillating Excess Chemical Potentials in Grand Canonical-like Monte Carlo-Molecular Dynamics Simulations

Solute sampling of explicit bulk-phase aqueous environments in grand canonical (GC) ensemble simulations suffer from poor convergence due to low insertion probabilities of the solutes. To address this, we developed an iterative procedure involving Grand Canonical-like Monte Carlo (GCMC) and molecular dynamics (MD) simulations. Each iteration involves GCMC of both the solutes and water followed by MD, with the excess chemical potential (μ_ex) of both the solute and the water oscillated to attain their target concentrations in the simulation system. By periodically varying the μ_ex of the water and solutes over the GCMC-MD iterations, solute exchange probabilities and the spatial distributions of the solutes improved. The utility of the oscillating-μ_ex GCMC-MD method is indicated by its ability to approximate the hydration free energy (HFE) of the individual solutes in aqueous solution as well as in dilute aqueous mixtures of multiple solutes. For seven organic solutes: benzene, propane, acetaldehyde, methanol, formamide, acetate, and methylammonium, the average μ_ex of the solutes and the water converged close to their respective HFEs in both 1 M standard state and dilute aqueous mixture systems. The oscillating-μ_ex GCMC methodology is also able to drive solute sampling in proteins in aqueous environments as shown using the occluded binding pocket of the T4 lysozyme L99A mutant as a model system. The approach was shown to satisfactorily reproduce the free energy of binding of benzene as well as sample the functional group requirements of the occluded pocket consistent with the crystal structures of known ligands bound to the L99A mutant as well as their relative binding affinities.

Thermodynamics of Water in an Enzyme Active Site: Grid-Based Hydration Analysis of Coagulation Factor Xa

Water molecules in the active site of an enzyme occupy a complex, heterogeneous environment, and the thermodynamic properties of active-site water are functions of position. As a consequence, it is thought that an enzyme inhibitor can gain affinity by extending into a region occupied by unfavorable water or lose affinity by displacing water from a region where it was relatively stable. Recent advances in the characterization of binding-site water, based on the analysis of molecular simulations with explicit water molecules, have focused largely on simplified representations of water as occupying well-defined hydration sites. Our grid-based treatment of hydration, GIST, offers a more complete picture of the complex distributions of water properties, but it has not yet been applied to proteins. This first application of GIST to protein-ligand modeling, for the case of Coagulation Factor Xa, shows that ligand scoring functions based on GIST perform at least as well as scoring functions based on a hydration-site approach (HSA), when applied to exactly the same simulation data. Interestingly, the displacement of energetically unfavorable water emerges as the dominant factor in the fitted scoring functions, for both GIST and HSA methods, while water entropy plays a secondary role, at least in the present context.

Comparing distance metrics for rotation using the k-nearest neighbors algorithm for entropy estimation

Distance metrics facilitate a number of methods for statistical analysis. For statistical mechanical applications, it is useful to be able to compute the distance between two different orientations of a molecule. However, a number of distance metrics for rotation have been employed, and in this study, we consider different distance metrics and their utility in entropy estimation using the k-nearest neighbors (KNN) algorithm. This approach shows a number of advantages over entropy estimation using a histogram method, and the different approaches are assessed using uniform randomly generated data, biased randomly generated data, and data from a molecular dynamics (MD) simulation of bulk water. The results identify quaternion metrics as superior to a metric based on the Euler angles. However, it is demonstrated that samples from MD simulation must be independent for effective use of the KNN algorithm and this finding impacts any application to time series data.

Prediction of Small Molecule Hydration Thermodynamics with Grid Cell Theory

An efficient methodology has been developed to quantify water energetics by analysis of explicit solvent molecular simulations of organic and biomolecular systems. The approach, grid cell theory (GCT), relies on a discretization of the cell theory methodology on a three-dimensional grid to spatially resolve the density, enthalpy, and entropy of water molecules in the vicinity of solute(s) of interest. Entropies of hydration are found to converge more efficiently than enthalpies of hydration. GCT predictions of free energies of hydration on a data set of small molecules are strongly correlated with thermodynamic integration predictions. Agreement with the experiment is comparable for both approaches. A key advantage of GCT is its ability to provide from a single simulation insightful graphical analyses of spatially resolved components of the enthalpies and entropies of hydration.