A molecular reconstruction approach to site-based 3D-RISM and comparison to GIST hydration thermodynamic maps in an enzyme active site

Free Energy Density of a Fluid and Its Role in Solvation and Binding

The concept that a fluid has a position-dependent free energy density appears in the literature but has not been fully developed or accepted. We set this concept on an unambiguous theoretical footing via the following strategy. First, we set forth four desiderata that should be satisfied by any definition of the position-dependent free energy density, f(R), in a system comprising only a fluid and a rigid solute: its volume integral, plus the fixed internal energy of the solute, should be the system free energy; it deviates from its bulk value, fbulk, near a solute but should asymptotically approach fbulk with increasing distance from the solute; it should go to zero where the solvent density goes to zero; and it should be well-defined in the most general case of a fluid made up of flexible molecules with an arbitrary interaction potential. Second, we use statistical thermodynamics to formulate a definition of the free energy density that satisfies these desiderata. Third, we show how any free energy density satisfying the desiderata may be used to analyze molecular processes in solution. In particular, because the spatial integral of f(R) equals the free energy of the system, it can be used to compute free energy changes that result from the rearrangement of solutes as well as the forces exerted on the solutes by the solvent. This enables the use of a thermodynamic analysis of water in protein binding sites to inform ligand design. Finally, we discuss related literature and address published concerns regarding the thermodynamic plausibility of a position-dependent free energy density. The theory presented here has applications in theoretical and computational chemistry and may be further generalizable beyond fluids, such as to solids and macromolecules.

Advances in the discovery of new chemotypes through ultra-large library docking

INTRODUCTION

The size and complexity of virtual screening libraries in drug discovery have skyrocketed in recent years, reaching up to multiple billions of accessible compounds. However, virtual screening of such ultra-large libraries poses several challenges associated with preparing the libraries, sampling, and pre-selection of suitable compounds. The utilization of artificial intelligence (AI)-assisted screening approaches, such as deep learning, poses a promising countermeasure to deal with this rapidly expanding chemical space. For example, various AI-driven methods were recently successfully used to identify novel small molecule inhibitors of the SARS-CoV-2 main protease (M^pro).

AREAS COVERED

This review focuses on presenting various kinds of virtual screening methods suitable for dealing with ultra-large libraries. Challenges associated with these computational methodologies are discussed, and recent advances are highlighted in the example of the discovery of novel M^pro inhibitors targeting the SARS-CoV-2 virus.

EXPERT OPINION

With the rapid expansion of the virtual chemical space, the methodologies for docking and screening such quantities of molecules need to keep pace. Employment of AI-driven screening compounds has already been shown to be effective in a range from a few thousand to multiple billion compounds, furthered by de novo generation of drug-like molecules without human interference.

Total free energy analysis of fully hydrated proteins

The total free energy of a hydrated biomolecule and its corresponding decomposition of energy and entropy provides detailed information about regions of thermodynamic stability or instability. The free energies of four hydrated globular proteins with different net charges are calculated from a molecular dynamics simulation, with the energy coming from the system Hamiltonian and entropy using multiscale cell correlation. Water is found to be most stable around anionic residues, intermediate around cationic and polar residues, and least stable near hydrophobic residues, especially when more buried, with stability displaying moderate entropy-enthalpy compensation. Conversely, anionic residues in the proteins are energetically destabilized relative to singly solvated amino acids, while trends for other residues are less clear-cut. Almost all residues lose intraresidue entropy when in the protein, enthalpy changes are negative on average but may be positive or negative, and the resulting overall stability is moderate for some proteins and negligible for others. The free energy of water around single amino acids is found to closely match existing hydrophobicity scales. Regarding the effect of secondary structure, water is slightly more stable around loops, of intermediate stability around β strands and turns, and least stable around helices. An interesting asymmetry observed is that cationic residues stabilize a residue when bonded to its N-terminal side but destabilize it when on the C-terminal side, with a weaker reversed trend for anionic residues.

Predicting Conserved Water Molecules in Binding Sites of Proteins Using Machine Learning Methods and Combining Features

Water molecules play an important role in many biological processes in terms of stabilizing protein structures, assisting protein folding, and improving binding affinity. It is well known that, due to the impacts of various environmental factors, it is difficult to identify the conserved water molecules (CWMs) from free water molecules (FWMs) directly as CWMs are normally deeply embedded in proteins and form strong hydrogen bonds with surrounding polar groups. To circumvent this difficulty, in this work, the abundance of spatial structure information and physicochemical properties of water molecules in proteins inspires us to adopt machine learning methods for identifying the CWMs. Therefore, in this study, a machine learning framework to identify the CWMs in the binding sites of the proteins was presented. First, by analyzing water molecules' physicochemical properties and spatial structure information, six features (i.e., atom density, hydrophilicity, hydrophobicity, solvent-accessible surface area, temperature B-factors, and mobility) were extracted. Those features were further analyzed and combined to reach a higher CWM identification rate. As a result, an optimal feature combination was determined. Based on this optimal combination, seven different machine learning models (including support vector machine (SVM), K-nearest neighbor (KNN), decision tree (DT), logistic regression (LR), discriminant analysis (DA), naïve Bayes (NB), and ensemble learning (EL)) were evaluated for their abilities in identifying two categories of water molecules, i.e., CWMs and FWMs. It showed that the EL model was the desired prediction model due to its comprehensive advantages. Furthermore, the presented methodology was validated through a case study of crystal 3skh and extensively compared with Dowser++. The prediction performance showed that the optimal feature combination and the desired EL model in our method could achieve satisfactory prediction accuracy in identifying CWMs from FWMs in the proteins' binding sites.

GalaxyWater-CNN: Prediction of Water Positions on the Protein Structure by a 3D-Convolutional Neural Network

Proteins interact with numerous water molecules to perform their physiological functions in biological organisms. Most water molecules act as solvent media; hence, their roles may be considered implicitly in theoretical treatments of protein structure and function. However, some water molecules interact intimately with proteins and require explicit treatment to understand their effects. Most physics-based computational methods are limited in their ability to accurately locate water molecules on protein surfaces because of inaccurate energy functions. Instead of relying on an energy function, this study attempts to learn the locations of water molecules from structural data. GalaxyWater-convolutional neural network (CNN) predicts water positions on protein chains, protein-protein interfaces, and protein-compound binding sites using a 3D-CNN model that is trained to generate a water score map on a given protein structure. The training data are compiled from high-resolution protein crystal structures resolved together with water molecules. GalaxyWater-CNN shows improved water prediction performance both in the coverage of crystal water molecules and in the accuracy of the predicted water positions when compared with previous energy-based methods. This method shows a superior performance in predicting water molecules that form hydrogen-bond networks precisely. The web service and the source code of this water prediction method are freely available at https://galaxy.seoklab.org/gwcnn and https://github.com/seoklab/GalaxyWater-CNN, respectively.

Reaction Entropies in Solution from Analytical Three-Dimensional Reference Interaction Site Model Derivatives with Application to Redox and Spin-Crossover Processes

An analytical approach to compute the excess entropy of solvation at constant pressure in three-dimensional reference interaction site model (3D-RISM) calculations is presented. It includes the changes in the macroscopic dielectric constant of the solvent upon variation of temperature and density. The approach is exact within the framework of force-field descriptions of the solute and gives reasonable results for self-consistently determined electrostatics as used in the 3D-RISM-self-consistent field approach, particularly for entropy differences. The new method is applied to simple examples of reaction entropies of iron complexes in aqueous solution, for which simple gas-phase calculations and many other approaches give unreliable estimates. For both redox half-reactions and spin-crossover processes, (semi)quantitative agreement with experimental reaction entropies can be achieved out of the box.

Grid inhomogeneous solvation theory for cross-solvation in rigid solvents

Grid Inhomogeneous Solvation Theory (GIST) has proven useful to calculate localized thermodynamic properties of water around a solute. Numerous studies have leveraged this information to enhance structure-based binding predictions. We have recently extended GIST toward chloroform as a solvent to allow the prediction of passive membrane permeability. Here, we further generalize the GIST algorithm toward all solvents that can be modeled as rigid molecules. This restriction is inherent to the method and is already present in the inhomogeneous solvation theory. Here, we show that our approach can be applied to various solvent molecules by comparing the results of GIST simulations with thermodynamic integration (TI) calculations and experimental results. Additionally, we analyze and compare a matrix consisting of 100 entries of ten different solvent molecules solvated within each other. We find that the GIST results are highly correlated with TI calculations as well as experiments. For some solvents, we find Pearson correlations of up to 0.99 to the true entropy, while others are affected by the first-order approximation more strongly. The enthalpy-entropy splitting provided by GIST allows us to extend a recently published approach, which estimates higher order entropies by a linear scaling of the first-order entropy, to solvents other than water. Furthermore, we investigate the convergence of GIST in different solvents. We conclude that our extension to GIST reliably calculates localized thermodynamic properties for different solvents and thereby significantly extends the applicability of this widely used method.

Spatially Resolved Hydration Thermodynamics in Biomolecular Systems

Water is essential for the structure, dynamics, energetics, and thus the function of biomolecules. It is a formidable challenge to elicit, in microscopic detail, the role of the solvation-related driving forces of biomolecular processes, such as the enthalpy and entropy contributions to the underlying free-energy landscape. In this Perspective, we discuss recent developments and applications of computational methods that provide a spatially resolved map of hydration thermodynamics in biomolecular systems and thus yield atomic-level insights to guide the interpretation of experimental observations. An emphasis is on the challenge of quantifying the hydration entropy, which requires characterization of both the motions of the biomolecules and of the water molecules in their surrounding.

Developing end-point methods for absolute binding free energy calculation using the Boltzmann-quasiharmonic model

Understanding the physical forces underlying receptor-ligand binding requires robust methods for analyzing the binding thermodynamics. In end-point binding free energy methods the binding free energy is naturally decomposable into physically intuitive contributions such as the solvation free energy and configurational entropy that can provide insights. Here we present a new end-point method called EE-BQH (Effective Energy-Boltzmann-Quasiharmonic) which combines the Boltzmann-Quasiharmonic model for configurational entropy with different solvation free energy methods, such as the continuum solvent PBSA model and the integral equation-based 3D-RISM, to estimate the absolute binding free energy. We compare EE-BQH with other treatments of configurational entropy such as Quasiharmonic models in internal coordinates (QHIC) and in Cartesian coordinates (QHCC), and Normal Mode analysis (NMA), by testing them on the octa acids host-guest complexes from the SAMPL8 blind challenge. The accuracies in the calculated absolute binding free energies strongly depend on the configurational entropy and solvation free energy methods used. QHIC and BQH yield the best agreements with the established potential of mean force (PMF) estimates, with R² of ∼0.7 and mean unsigned error of ∼1.7 kcal mol^-1. These results from the end-point calculations are also in similar agreement with experiments. While 3D-RISM in combination with QHIC or BQH lead to reasonable correlations with the PMF results and experiments, the calculated absolute binding free energies are underestimated by ∼5 kcal mol^-1. While the binding is accompanied by a significant reduction in the ligand translational/rotational entropy, the change in the torsional entropy in these host-guest systems is slightly positive. Compared with BQH, QHIC underestimates the reduction of configurational entropy because of the non-Gaussian probability distributions in the ligand rotation and a small number of torsions. The study highlights the crucial role of configurational entropy in determining binding and demonstrates the potential of using the new end-point method to provide insights in more complex protein-ligand systems.

Explicit solvation thermodynamics in ionic solution: extending grid inhomogeneous solvation theory to solvation free energy of salt-water mixtures

Hydration thermodynamics play a fundamental role in fields ranging from the pharmaceutical industry to environmental research. Numerous methods exist to predict solvation thermodynamics of compounds ranging from small molecules to large biomolecules. Arguably the most precise methods are those based on molecular dynamics (MD) simulations in explicit solvent. One theory that has seen increased use is inhomogeneous solvation theory (IST). However, while many applications require accurate description of salt-water mixtures, no implementation of IST is currently able to estimate solvation properties involving more than one solvent species. Here, we present an extension to grid inhomogeneous solvation theory (GIST) that can take salt contributions into account. At the example of carbazole in 1 M NaCl solution, we compute the solvation energy as well as first and second order entropies. While the effect of the first order ion entropy is small, both the water-water and water-ion entropies contribute strongly. We show that the water-ion entropies are efficiently approximated using the Kirkwood superposition approximation. However, this approach cannot be applied to the water-water entropy. Furthermore, we test the quantitative validity of our method by computing salting-out coefficients and comparing them to experimental data. We find a good correlation to experimental salting-out constants, while the absolute values are overpredicted due to the approximate second order entropy. Since ions are frequently used in MD, either to neutralize the system or as a part of the investigated process, our method greatly extends the applicability of GIST. The use-cases range from biopharmaceuticals, where many assays require high salt concentrations, to environmental research, where solubility in sea water is important to model the fate of organic substances.

Contributions of higher-order proximal distribution functions to solvent structure around proteins

The proximal distribution function (pDF) quantifies the probability of finding a solvent molecule in the vicinity of solutes. The approach constitutes a hierarchically organized theory for constructing approximate solvation structures around solutes. Given the assumption of universality of atom cluster-specific solvation, reconstruction of the solvent distribution around arbitrary molecules provides a computationally convenient route to solvation thermodynamics. Previously, such solvent reconstructions usually considered the contribution of the nearest-neighbor distribution only. We extend the pDF reconstruction algorithm to terms including next-nearest-neighbor contribution. As a test, small molecules (alanine and butane) are examined. The analysis is then extended to include the protein myoglobin in the P6 crystal unit cell. Molecular dynamics simulations are performed, and solvent density distributions around the solute molecules are compared with the results from different pDF reconstruction models. It is shown that the next-nearest-neighbor modification significantly improves the reconstruction of the solvent number density distribution in concave regions and between solute molecules. The probability densities are then used to calculate the solute-solvent non-bonded interaction energies including van der Waals and electrostatic, which are found to be in good agreement with the simulated values.

Accurate prediction of hydration free energies and solvation structures using molecular density functional theory with a simple bridge functional

This paper assesses the ability of molecular density functional theory to predict efficiently and accurately the hydration free energies of molecular solutes and the surrounding microscopic water structure. A wide range of solutes were investigated, including hydrophobes, water as a solute, and the FreeSolv database containing 642 drug-like molecules having a variety of shapes and sizes. The usual second-order approximation of the theory is corrected by a third-order, angular-independent bridge functional. The overall functional is parameter-free in the sense that the only inputs are bulk water properties, independent of the solutes considered. These inputs are the direct correlation function, compressibility, liquid-gas surface tension, and excess chemical potential of the solvent. Compared to molecular simulations with the same force field and the same fixed solute geometries, the present theory is shown to describe accurately the solvation free energy and structure of both hydrophobic and hydrophilic solutes. Overall, the method yields a precision of order 0.5 k_BT for the hydration free energies of the FreeSolv database, with a computer speedup of 3 orders of magnitude. The theory remains to be improved for a better description of the H-bonding structure and the hydration free energy of charged solutes.

Biomolecular Simulations with the Three-Dimensional Reference Interaction Site Model with the Kovalenko-Hirata Closure Molecular Solvation Theory

The statistical mechanics-based 3-dimensional reference interaction site model with the Kovalenko-Hirata closure (3D-RISM-KH) molecular solvation theory has proven to be an essential part of a multiscale modeling framework, covering a vast region of molecular simulation techniques. The successful application ranges from the small molecule solvation energy to the bulk phase behavior of polymers, macromolecules, etc. The 3D-RISM-KH successfully predicts and explains the molecular mechanisms of self-assembly and aggregation of proteins and peptides related to neurodegeneration, protein-ligand binding, and structure-function related solvation properties. Upon coupling the 3D-RISM-KH theory with a novel multiple time-step molecular dynamic (MD) of the solute biomolecule stabilized by the optimized isokinetic Nosé-Hoover chain thermostat driven by effective solvation forces obtained from 3D-RISM-KH and extrapolated forward by generalized solvation force extrapolation (GSFE), gigantic outer time-steps up to picoseconds to accurately calculate equilibrium properties were obtained in this new quasidynamics protocol. The multiscale OIN/GSFE/3D-RISM-KH algorithm was implemented in the Amber package and well documented for fully flexible model of alanine dipeptide, miniprotein 1L2Y, and protein G in aqueous solution, with a solvent sampling rate ~150 times faster than a standard MD simulation in explicit water. Further acceleration in computation can be achieved by modifying the extent of solvation layers considered in the calculation, as well as by modifying existing closure relations. This enhanced simulation technique has proven applications in protein-ligand binding energy calculations, ligand/solvent binding site prediction, molecular solvation energy calculations, etc. Applications of the RISM-KH theory in molecular simulation are discussed in this work.

GalaxyWater-wKGB: Prediction of Water Positions on Protein Structure Using wKGB Statistical Potential

Proteins fold and function in water, and protein-water interactions play important roles in protein structure and function. In computational studies on protein structure and interaction, the effect of water is considered either implicitly or explicitly. Implicit water models are frequently used in protein structure prediction and docking because they are computationally much more efficient than explicit water models, which are often employed in molecular dynamics (MD) simulations. However, implicit water models that treat water as a continuous solvent medium cannot account for specific atomistic protein-water interactions that are critical for structure formation and interactions with other molecules. Various methods for predicting water molecules that form specific atomistic interactions with proteins have been developed. Methods involving MD simulations or the integral equation theory tend to produce more accurate results at a higher computational cost than simple geometry- or energy-based methods. Here, we present a novel method for predicting water positions on a protein surface called GalaxyWater-wKGB, which is based on a statistical potential, a water knowledge-based potential based on the generalized Born model (wKGB). This method is accurate and rapid because it does not require conformational sampling or iterative computation owing to the effective statistical treatment employed to derive the potential. The statistical potential describes specific protein atom-water interactions more accurately than conventional potentials by considering the dependence on the degree of solvent accessibility of protein atoms as well as on protein atom-water distances and orientations. The introduction of solvent accessibility allows effective consideration of competing nonspecific protein-water and intraprotein interactions. When tested on high-resolution protein crystal structures, this method could recover similar or larger fractions of crystallographic water 180 times faster than the sophisticated integral equation theory, 3D-RISM. A web service of this water prediction method is freely available at http://galaxy.seoklab.org/wkgb.

An online repository of solvation thermodynamic and structural maps of SARS-CoV-2 targets

SARS-CoV-2 recently jumped species and rapidly spread via human-to-human transmission to cause a global outbreak of COVID-19. The lack of effective vaccine combined with the severity of the disease necessitates attempts to develop small molecule drugs to combat the virus. COVID19_GIST_HSA is a freely available online repository to provide solvation thermodynamic maps of COVID-19-related protein small molecule drug targets. Grid inhomogeneous solvation theory maps were generated using AmberTools cpptraj-GIST, 3D reference interaction site model maps were created with AmberTools rism3d.snglpnt and hydration site analysis maps were created using SSTMap code. The resultant data can be applied to drug design efforts: scoring solvent displacement for docking, rational lead modification, prioritization of ligand- and protein- based pharmacophore elements, and creation of water-based pharmacophores. Herein, we demonstrate the use of the solvation thermodynamic mapping data. It is hoped that this freely provided data will aid in small molecule drug discovery efforts to defeat SARS-CoV-2.

Distribution and Function of Glycosaminoglycans and Proteoglycans in the Development, Homeostasis and Pathology of the Ocular Surface

The ocular surface, which forms the interface between the eye and the external environment, includes the cornea, corneoscleral limbus, the conjunctiva and the accessory glands that produce the tear film. Glycosaminoglycans (GAGs) and proteoglycans (PGs) have been shown to play important roles in the development, hemostasis and pathology of the ocular surface. Herein we review the current literature related to the distribution and function of GAGs and PGs within the ocular surface, with focus on the cornea. The unique organization of ECM components within the cornea is essential for the maintenance of corneal transparency and function. Many studies have described the importance of GAGs within the epithelial and stromal compartment, while very few studies have analyzed the ECM of the endothelial layer. Importantly, GAGs have been shown to be essential for maintaining corneal homeostasis, epithelial cell differentiation and wound healing, and, more recently, a role has been suggested for the ECM in regulating limbal stem cells, corneal innervation, corneal inflammation, corneal angiogenesis and lymphangiogenesis. Reports have also associated genetic defects of the ECM to corneal pathologies. Thus, we also highlight the role of different GAGs and PGs in ocular surface homeostasis, as well as in pathology.

Solvation Free Energy as a Measure of Hydrophobicity: Application to Serine Protease Binding Interfaces

Solvation and hydrophobicity play a key role in a variety of biological mechanisms. In substrate binding, but also in structure-based drug design, the thermodynamic properties of water molecules surrounding a given protein are of high interest. One of the main algorithms devised in recent years to quantify thermodynamic properties of water is the grid inhomogeneous solvation theory (GIST), which calculates these features on a grid surrounding the protein. Despite the inherent advantages of GIST, the computational demand is a major drawback, as calculations for larger systems can take days or even weeks. Here, we present a GPU accelerated version of the GIST algorithm, which facilitates efficient estimates of solvation free energy even of large biomolecular interfaces. Furthermore, we show that GIST can be used as a reliable tool to evaluate protein surface hydrophobicity. We apply the approach on a set of nine different proteases calculating localized solvation free energies on the surface of the binding interfaces as a measure of their hydrophobicity. We find a compelling agreement with the hydrophobicity of their substrates, i.e., peptides, binding into the binding cleft, and thus our approach provides a reliable description of hydrophobicity characteristics of these biological interfaces.

Hydration of Aromatic Heterocycles as an Adversary of π-Stacking

Hydration is one of the key players in the protein-ligand binding process. It not only influences the binding process per se, but also the drug's absorption, distribution, metabolism, and excretion properties. To gain insights into the hydration of aromatic cores, the solvation thermodynamics of 40 aromatic mono- and bicyclic systems, frequently occurring in medicinal chemistry, are investigated. Thermodynamics is analyzed with two different methods: grid inhomogeneous solvation theory (GIST) and thermodynamic integration (TI). Our results agree well with previously published experimental and computational solvation free energies. The influence of adding heteroatoms to aromatic systems and how the position of these heteroatoms impacts the compound's interactions with water is studied. The solvation free energies of these heteroaromatics are highly correlated to their gas phase interaction energies with benzene: compounds showing a high interaction energy also have a high solvation free energy value. Therefore, replacing a compound with one having a higher gas phase interaction energy might not result in the expected improvement in affinity. The desolvation costs counteract the higher stacking interactions, hence weakening or even inverting the expected gain in binding free energy.