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

Inclusion of Water Multipoles into the Implicit Solvation Framework Leads to Accuracy Gains

The current practical "workhorses" of the atomistic implicit solvation─the Poisson-Boltzmann (PB) and generalized Born (GB) models─face fundamental accuracy limitations. Here, we propose a computationally efficient implicit solvation framework, the Implicit Water Multipole GB (IWM-GB) model, that systematically incorporates the effects of multipole moments of water molecules in the first hydration shell of a solute, beyond the dipole water polarization already present at the PB/GB level. The framework explicitly accounts for coupling between polar and nonpolar contributions to the total solvation energy, which is missing from many implicit solvation models. An implementation of the framework, utilizing the GAFF force field and AM1-BCC atomic partial charges model, is parametrized and tested against the experimental hydration free energies of small molecules from the FreeSolv database. The resulting accuracy on the test set (RMSE ∼ 0.9 kcal/mol) is 12% better than that of the explicit solvation (TIP3P) treatment, which is orders of magnitude slower. We also find that the coupling between polar and nonpolar parts of the solvation free energy is essential to ensuring that several features of the IWM-GB model are physically meaningful, including the sign of the nonpolar contributions.

Improving the Accuracy of Physics-Based Hydration-Free Energy Predictions by Machine Learning the Remaining Error Relative to the Experiment

The accuracy of computational models of water is key to atomistic simulations of biomolecules. We propose a computationally efficient way to improve the accuracy of the prediction of hydration-free energies (HFEs) of small molecules: the remaining errors of the physics-based models relative to the experiment are predicted and mitigated by machine learning (ML) as a postprocessing step. Specifically, the trained graph convolutional neural network attempts to identify the "blind spots" in the physics-based model predictions, where the complex physics of aqueous solvation is poorly accounted for, and partially corrects for them. The strategy is explored for five classical solvent models representing various accuracy/speed trade-offs, from the fast analytical generalized Born (GB) to the popular TIP3P explicit solvent model; experimental HFEs of small neutral molecules from the FreeSolv set are used for the training and testing. For all of the models, the ML correction reduces the resulting root-mean-square error relative to the experiment for HFEs of small molecules, without significant overfitting and with negligible computational overhead. For example, on the test set, the relative accuracy improvement is 47% for the fast analytical GB, making it, after the ML correction, almost as accurate as uncorrected TIP3P. For the TIP3P model, the accuracy improvement is about 39%, bringing the ML-corrected model's accuracy below the 1 kcal/mol threshold. In general, the relative benefit of the ML corrections is smaller for more accurate physics-based models, reaching the lower limit of about 20% relative accuracy gain compared with that of the physics-based treatment alone. The proposed strategy of using ML to learn the remaining error of physics-based models offers a distinct advantage over training ML alone directly on reference HFEs: it preserves the correct overall trend, even well outside of the training set.

A Closed-Form, Analytical Approximation for Apparent Surface Charge and Electric Field of Molecules

Closed-form, analytical approximations for electrostatic properties of molecules are of unique value as these can provide computational speed, versatility, and physical insight. Here, we have derived a simple, closed-form formula for the apparent surface charge (ASC) as well as for the electric field generated by a molecular charge distribution in aqueous solution. The approximation, with no fitted parameters, was tested against numerical solutions of the Poisson equation, where it has produced a significant speed-up. For neutral small molecules, the hydration free energies estimated from the closed-form ASC formula are within 0.8 kcal/mol RMSD from the numerical Poisson reference; the electric field at the surface is in quantitative agreement with the reference. Performance of the approximation was also tested on larger structures, including a protein, a DNA fragment, and a viral receptor-target complex. For all structures tested, a near-quantitative agreement with the numerical Poisson reference was achieved, except in regions of high negative curvature, where the new approximation is still qualitatively correct. A unique efficiency feature of the proposed "source-based″ closed-form approximation is that the ASC and electric field can be estimated individually at any point or surface patch, without the need to obtain the full global solution. An open-source software implementation of the method is available: https://people.cs.vt.edu/~onufriev/CODES/aasc.zip.

Energy-entropy method using multiscale cell correlation to calculate binding free energies in the SAMPL8 host-guest challenge

Free energy drives a wide range of molecular processes such as solvation, binding, chemical reactions and conformational change. Given the central importance of binding, a wide range of methods exist to calculate it, whether based on scoring functions, machine-learning, classical or electronic structure methods, alchemy, or explicit evaluation of energy and entropy. Here we present a new energy-entropy (EE) method to calculate the host-guest binding free energy directly from molecular dynamics (MD) simulation. Entropy is evaluated using Multiscale Cell Correlation (MCC) which uses force and torque covariance and contacts at two different length scales. The method is tested on a series of seven host-guest complexes in the SAMPL8 (Statistical Assessment of the Modeling of Proteins and Ligands) "Drugs of Abuse" Blind Challenge. The EE-MCC binding free energies are found to agree with experiment with an average error of 0.9 kcal mol-1. MCC makes clear the origin of the entropy changes, showing that the large loss of positional, orientational, and to a lesser extent conformational entropy of each binding guest is compensated for by a gain in orientational entropy of water released to bulk, combined with smaller decreases in vibrational entropy of the host, guest and contacting water.

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.

Effects of Metal Ions on Aβ42 Peptide Conformations from Molecular Simulation Studies

In this study, we investigate the conformational characteristics of full-length Aβ₄₂ peptide monomers in the presence of Na⁺ and Zn²⁺ metal ions using atomistic molecular dynamics (MD) simulations with an aim to explore the possible driving forces behind enhanced aggregation rates of the peptides in the presence of salts. The calculations reveal that the presence of metal ions shifts the conformational equilibrium more toward the compact ordered Aβ structures. Such compact ordered structures stabilized by distant nonlocal contacts between two crucial hydrophobic segments, hp1 and hp2, primarily through two important hydrophobic aromatic residues, Phe-19 and Phe-20, are expected to trigger the aggregation process at a faster rate by populating and stabilizing the aggregation prone structures. Formation of a significant number of such distant contacts in the presence of Na⁺ ions has also been found to result in breaking of the N-terminal helix. On the contrary, binding of Zn²⁺ ion to Aβ peptide is highly specific, which stabilizes the N-terminal helix instead of breaking it. This explains why the aggregation rate of Aβ peptides is higher in the presence of divalent Zn²⁺ ions than monovalent Na⁺ ions. Relatively higher overall stability of the most populated Aβ peptide monomers in the presence of Zn²⁺ ions has been found to be associated with specific Zn²⁺-Aβ binding and significant free energy gain.

Free Energies and Entropies of Binding Sites Identified by MixMD Cosolvent Simulations

In our recent efforts to map protein surfaces using mixed-solvent molecular dynamics (MixMD) (Ghanakota, P.; Carlson, H. A. Moving Beyond Active-Site Detection: MixMD Applied to Allosteric Systems. J. Phys. Chem. B 2016, 120, 8685-8695), we were able to successfully capture active sites and allosteric sites within the top-four most occupied hotspots. In this study, we describe our approach for estimating the thermodynamic profile of the binding sites identified by MixMD. First, we establish a framework for calculating free energies from MixMD simulations, and we compare our approach to alternative methods. Second, we present a means to obtain a relative ranking of the binding sites by their configurational entropy. The theoretical maximum and minimum free energy and entropy values achievable under such a framework along with the limitations of the techniques are discussed. Using this approach, the free energy and relative entropy ranking of the top-four MixMD binding sites were computed and analyzed across our allosteric protein targets: Abl Kinase, Androgen Receptor, Pdk1 Kinase, Farnesyl Pyrophosphate Synthase, Chk1 Kinase, Glucokinase, and Protein Tyrosine Phosphatase 1B.

Predicting Displaceable Water Sites Using Mixed-Solvent Molecular Dynamics

Water molecules are an important factor in protein-ligand binding. Upon binding of a ligand with a protein's surface, waters can either be displaced by the ligand or may be conserved and possibly bridge interactions between the protein and ligand. Depending on the specific interactions made by the ligand, displacing waters can yield a gain in binding affinity. The extent to which binding affinity may increase is difficult to predict, as the favorable displacement of a water molecule is dependent on the site-specific interactions made by the water and the potential ligand. Several methods have been developed to predict the location of water sites on a protein's surface, but the majority of methods are not able to take into account both protein dynamics and the interactions made by specific functional groups. Mixed-solvent molecular dynamics (MixMD) is a cosolvent simulation technique that explicitly accounts for the interaction of both water and small molecule probes with a protein's surface, allowing for their direct competition. This method has previously been shown to identify both active and allosteric sites on a protein's surface. Using a test set of eight systems, we have developed a method using MixMD to identify conserved and displaceable water sites. Conserved sites can be determined by an occupancy-based metric to identify sites which are consistently occupied by water even in the presence of probe molecules. Conversely, displaceable water sites can be found by considering the sites which preferentially bind probe molecules. Furthermore, the inclusion of six probe types allows the MixMD method to predict which functional groups are capable of displacing which water sites. The MixMD method consistently identifies sites which are likely to be nondisplaceable and predicts the favorable displacement of water sites that are known to be displaced upon ligand binding.

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.

Hot-spot identification on a broad class of proteins and RNA suggest unifying principles of molecular recognition

Chemically diverse fragments tend to collectively bind at localized sites on proteins, which is a cornerstone of fragment-based techniques. A central question is how general are these strategies for predicting a wide variety of molecular interactions such as small molecule-protein, protein-protein and protein-nucleic acid for both experimental and computational methods. To address this issue, we recently proposed three governing principles, (1) accurate prediction of fragment-macromolecule binding free energy, (2) accurate prediction of water-macromolecule binding free energy, and (3) locating sites on a macromolecule that have high affinity for a diversity of fragments and low affinity for water. To test the generality of these concepts we used the computational technique of Simulated Annealing of Chemical Potential to design one small fragment to break the RecA-RecA protein-protein interaction and three fragments that inhibit peptide-deformylase via water-mediated multi-body interactions. Experiments confirm the predictions that 6-hydroxydopamine potently inhibits RecA and that PDF inhibition quantitatively tracks the water-mediated binding predictions. Additionally, the principles correctly predict the essential bound waters in HIV Protease, the surprisingly extensive binding site of elastase, the pinpoint location of electron transfer in dihydrofolate reductase, the HIV TAT-TAR protein-RNA interactions, and the MDM2-MDM4 differential binding to p53. The experimental confirmations of highly non-obvious predictions combined with the precise characterization of a broad range of known phenomena lend strong support to the generality of fragment-based methods for characterizing molecular recognition.

Solvent effects on ligand binding to a serine protease

ITC experiments and MD simulations reveal the mechanism behind enthalpy/entropy compensation upon trypsin-benzamidine binding at different solvation conditions.

AutoDock-GIST: Incorporating Thermodynamics of Active-Site Water into Scoring Function for Accurate Protein-Ligand Docking

Water plays a significant role in the binding process between protein and ligand. However, the thermodynamics of water molecules are often underestimated, or even ignored, in protein-ligand docking. Usually, the free energies of active-site water molecules are substantially different from those of waters in the bulk region. The binding of a ligand to a protein causes a displacement of these waters from an active site to bulk, and this displacement process substantially contributes to the free energy change of protein-ligand binding. The free energy of active-site water molecules can be calculated by grid inhomogeneous solvation theory (GIST), using molecular dynamics (MD) and the trajectory of a target protein and water molecules. Here, we show a case study of the combination of GIST and a docking program and discuss the effectiveness of the displacing gain of unfavorable water in protein-ligand docking. We combined the GIST-based desolvation function with the scoring function of AutoDock4, which is called AutoDock-GIST. The proposed scoring function was assessed employing 51 ligands of coagulation factor Xa (FXa), and results showed that both scoring accuracy and docking success rate were improved. We also evaluated virtual screening performance of AutoDock-GIST using FXa ligands in the directory of useful decoys-enhanced (DUD-E), thus finding that the displacing gain of unfavorable water is effective for a successful docking campaign.

Driving Structure-Based Drug Discovery through Cosolvent Molecular Dynamics

Identifying binding hotspots on protein surfaces is of prime interest in structure-based drug discovery, either to assess the tractability of pursuing a protein target or to drive improved potency of lead compounds. Computational approaches to detect such regions have traditionally relied on energy minimization of probe molecules onto static protein conformations in the absence of the natural aqueous environment. Advances in high performance computing now allow us to assess hotspots using molecular dynamics (MD) simulations. MD simulations integrate protein flexibility and the complicated role of water, thereby providing a more realistic assessment of the complex kinetics and thermodynamics at play. In this review, we describe the evolution of various cosolvent-based MD techniques and highlight a myriad of potential applications for such technologies in computational drug development.

Enthalpic and Entropic Contributions to Hydrophobicity

Hydrophobic hydration plays a key role in a vast variety of biological processes, ranging from the formation of cells to protein folding and ligand binding. Hydrophobicity scales simplify the complex process of hydration by assigning a value describing the averaged hydrophobic character to each amino acid. Previously published scales were not able to calculate the enthalpic and entropic contributions to the hydrophobicity directly. We present a new method, based on Molecular Dynamics simulations and Grid Inhomogeneous Solvation Theory, that calculates hydrophobicity from enthalpic and entropic contributions. Instead of deriving these quantities from the temperature dependence of the free energy of hydration or as residual of the free energy and the enthalpy, we directly obtain these values from the phase space occupied by water molecules. Additionally, our method is able to identify regions with specific enthalpic and entropic properties, allowing to identify so-called "unhappy water" molecules, which are characterized by weak enthalpic interactions and unfavorable entropic constraints.

Exploring ion induced folding of a single-stranded DNA oligomer from molecular simulation studies

One crucial issue in DNA hydration is the effect of salts on its conformational features. This has relevance in biology as cations present in the cellular environment shield the negative charges on the DNA backbone, thereby reducing the repulsive force between them. By screening the negative charges along the backbone, cations stabilize the folded structure of DNA. To study the effect of the added salt on single-stranded DNA (ss-DNA) conformations, we have performed room temperature molecular dynamics simulations of an aqueous solution containing the ss-DNA dodecamer with the 5'-CGCGAATTCGCG-3' sequence in the presence of 0.2, 0.5, and 0.8 M NaCl. Our calculations reveal that in the presence of the salt, the DNA molecule forms more collapsed coil-like conformations due to the screening of negative charges along the backbone. Additionally, we demonstrated that the formation of an octahedral inner-sphere complex by the strongly bound ion plays an important role in the stabilization of such folded conformation of DNA. Importantly, it is found that ion-DNA interactions can also explain the formation of non-sequential base stackings with longer lifetimes. Such non-sequential base stackings further stabilize the collapsed coil-like folded form of the DNA oligomer.

Quantitative Correlation of Conformational Binding Enthalpy with Substrate Specificity of Serine Proteases

Members of the same protease family show different substrate specificity, even if they share identical folds, depending on the physiological processes they are part of. Here, we investigate the key factors for subpocket and global specificity of factor Xa, elastase, and granzyme B which despite all being serine proteases and sharing the chymotrypsin-fold show distinct substrate specificity profiles. We determined subpocket interaction potentials with GRID for static X-ray structures and an in silico generated ensemble of conformations. Subpocket interaction potentials determined for static X-ray structures turned out to be insufficient to explain serine protease specificity for all subpockets. Therefore, we generated conformational ensembles using molecular dynamics simulations. We identified representative binding site conformations using distance-based hierarchical agglomerative clustering and determined subpocket interaction potentials for each representative conformation of the binding site. Considering the differences in subpocket interaction potentials for these representative conformations as well as their abundance allowed us to quantitatively explain subpocket specificity for the nonprime side for all three example proteases on a molecular level. The methods to identify key regions determining subpocket specificity introduced in this study are directly applicable to other serine proteases, and the results provide starting points for new strategies in rational drug design.