Computations of Absolute Solvation Free Energies of Small Molecules Using Explicit and Implicit Solvent Model

Insights and Challenges in Correcting Force Field Based Solvation Free Energies Using a Neural Network Potential

We present a comprehensive study investigating the potential gain in accuracy for calculating absolute solvation free energies (ASFE) using a neural network potential to describe the intramolecular energy of the solute. We calculated the ASFE for most compounds from the FreeSolv database using the Open Force Field (OpenFF) and compared them to earlier results obtained with the CHARMM General Force Field (CGenFF). By applying a nonequilibrium (NEQ) switching approach between the molecular mechanics (MM) description (either OpenFF or CGenFF) and the neural net potential (NNP)/MM level of theory (using ANI-2x as the NNP potential), we attempted to improve the accuracy of the calculated ASFEs. The predictive performance of the results did not change when this approach was applied to all 589 small molecules in the FreeSolv database that ANI-2x can describe. When selecting a subset of 156 molecules, focusing on compounds where the force fields performed poorly, we saw a slight improvement in the root-mean-square error (RMSE) and mean absolute error (MAE). The majority of our calculations utilized unidirectional NEQ protocols based on Jarzynski's equation. Additionally, we conducted bidirectional NEQ switching for a subset of 156 solutes. Notably, only a small fraction (10 out of 156) exhibited statistically significant discrepancies between unidirectional and bidirectional NEQ switching free energy estimates.

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.

Assessment of Halogen Off-Center Point-Charge Models Using Explicit Solvent Simulations

Compounds containing halogens can form halogen bonds (XBs) with biological targets such as proteins and membranes due to their anisotropic electrostatic potential. To accurately describe this anisotropy, off-center point-charge (EP) models are commonly used in force field methods, allowing the description of XBs at the molecular mechanics and molecular dynamics level. Various EP implementations have been documented in the literature, and despite being efficient in reproducing protein-ligand geometries and sampling of XBs, it is unclear how well these EP models predict experimental properties such as hydration free energies (ΔGhyd), which are often used to validate force field performance. In this work, we report the first assessment of three EP models using alchemical free energy calculations to predict ΔGhyd values. We show that describing the halogen anisotropy using some EP models can lead to a slight improvement in the prediction of the ΔGhyd when compared with the models without EP, especially for the chlorinated compounds; however, this improvement is not related to the establishment of XBs but is most likely due to the improvement of the sampling of hydrogen bonds. We also highlight the importance of the choice of the EP model, especially for the iodinated molecules, since a slight tendency to improve the prediction is observed for compounds with a larger σ-hole but significantly worse results were obtained for compounds that are weaker XB donors.

Calculations of Absolute Solvation Free Energies with Transformato─Application to the FreeSolv Database Using the CGenFF Force Field

We recently introduced transformato, an open-source Python package for the automated setup of large-scale calculations of relative solvation and binding free energy differences. Here, we extend the capabilities of transformato to the calculation of absolute solvation free energy differences. After careful validation against the literature results and reference calculations with the PERT module of CHARMM, we used transformato to compute absolute solvation free energies for most molecules in the FreeSolv database (621 out of 642). The force field parameters were obtained with the program cgenff (v2.5.1), which derives missing parameters from the CHARMM general force field (CGenFF v4.6). A long-range correction for the Lennard-Jones interactions was added to all computed solvation free energies. The mean absolute error compared to the experimental data is 1.12 kcal/mol. Our results allow a detailed comparison between the AMBER and CHARMM general force fields and provide a more in-depth understanding of the capabilities and limitations of the CGenFF small molecule parameters.

Fast calculation of hydrogen-bond strengths and free energy of hydration of small molecules

Hydrogen bonding is an interaction of great importance in drug discovery and development as it may significantly affect chemical and biological processes including the interaction of small molecules with other molecules, proteins, and membranes. In particular, hydrogen bonding can impact drug-like properties such as target affinity and oral availability which are critical to developing effective pharmaceuticals, and therefore, numerous methods for the calculation of properties such as hydrogen-bond strengths, free energy of hydration, or water solubility have been proposed over time. However, the accessibility to efficient methods for the predictions of such properties is still limited. Here, we present the development of Jazzy, an open-source tool for the prediction of hydrogen-bond strengths and free energies of hydration of small molecules. Jazzy also allows the visualisation of hydrogen-bond strengths with atomistic resolution to support the design of compounds with desired properties and the interpretation of existing data. The tool is described in its implementation, parameter fitting, and validation against two data sets of experimental hydration free energies. Jazzy is also applied against two chemical series of bioactive compounds to show that hydrogen-bond strengths can be used to understand their structure-activity relationships. Results from the validations highlight the strengths and limitations of Jazzy, and suggest its suitability for interactive design, screening, and machine-learning featurisation.

Conformations and Solvation of Synthetic Polymers in Water by Generalized Born Implicit-Solvent Molecular Dynamics Simulations: Stereoisomers of Poly(acrylic acid) and Poly(methacrylic acid)

We present the GB-OBC model as an approach for implicit-solvent MD simulations of a synthetic macromolecule in water. The model is tested and found to be successful in reproducing the chain dimensions and predicting the free energy of solvation of carboxylic acid vinyl polymers. The influence of stereochemistry and the hydrophobic nature of the polymer was investigated as a function of chain length (20 < N < 600) for poly(acrylic acid) (PAA) and poly(methacrylic acid) (PMA). The dimensionless parameters of the GB-OBC model were parameterized to be applicable to PAA and PMA. Scaling relations for chain dimensions obtained using implicit-solvent MD simulations in this study are in good agreement with those from experiments, theory of solvated chains in good solvents, and all-atom MD simulations in explicit water. Results show that ⟨R_g²⟩/NL² is greater for the atactic chain as compared to the isotactic chain, for PAA as well as PMA. ⟨R_g²⟩/NL² values of chains attain constancy in water for N = 200, with the values being greater for PMA. The PMA chain is conformationally more perturbed than the PAA chain, for both isotactic and atactic stereochemistry. The solvation free energy ΔG_hyd of PAA and PMA in water is negative for all chain lengths (N = 20-600) and becomes more favorable with an increase in molecular weight. The ΔG_hyd values for isotactic and atactic chains are identical at lower values of N but differ slightly for N > 300. Irrespective of the hydrophobic nature of the polymer, the atactic chain is thermodynamically more soluble in water as compared to the isotactic chain. The isotactic chain is less hydrophilic as compared to the atactic chain due to the closer proximity of the COOH groups along the backbone. This implicit solvent method is an effective way to accurately simulate the configurational properties and solvation of synthetic polymers in water.

Quantum-based machine learning and AI models to generate force field parameters for drug-like small molecules

Force fields for drug-like small molecules play an essential role in molecular dynamics simulations and binding free energy calculations. In particular, the accurate generation of partial charges on small molecules is critical to understanding the interactions between proteins and drug-like molecules. However, it is a time-consuming process. Thus, we generated a force field for small molecules and employed a machine learning (ML) model to rapidly predict partial charges on molecules in less than a minute of time. We performed density functional theory (DFT) calculation for 31770 small molecules that covered the chemical space of drug-like molecules. The partial charges for the atoms in a molecule were predicted using an ML model trained on DFT-based atomic charges. The predicted values were comparable to the charges obtained from DFT calculations. The ML model showed high accuracy in the prediction of atomic charges for external test data sets. We also developed neural network (NN) models to assign atom types, phase angles and periodicities. All the models performed with high accuracy on test data sets. Our code calculated all the descriptors that were needed for the prediction of force field parameters and produced topologies for small molecules by combining results from ML and NN models. To assess the accuracy of the predicted force field parameters, we calculated solvation free energies for small molecules, and the results were in close agreement with experimental free energies. The AI-generated force field was effective in the fast and accurate generation of partial charges and other force field parameters for small drug-like molecules.

A dynamical view of protein-protein complexes: Studies by molecular dynamics simulations

Protein-protein interactions are at the basis of many protein functions, and the knowledge of 3D structures of protein-protein complexes provides structural, mechanical and dynamical pieces of information essential to understand these functions. Protein-protein interfaces can be seen as stable, organized regions where residues from different partners form non-covalent interactions that are responsible for interaction specificity and strength. They are commonly described as a peripheral region, whose role is to protect the core region that concentrates the most contributing interactions, from the solvent. To get insights into the dynamics of protein-protein complexes, we carried out all-atom molecular dynamics simulations in explicit solvent on eight different protein-protein complexes of different functional class and interface size by taking into account the bound and unbound forms. On the one hand, we characterized structural changes upon binding of the proteins, and on the other hand we extensively analyzed the interfaces and the structural waters involved in the binding. Based on our analysis, in 6 cases out of 8, the interfaces rearranged during the simulation time, in stable and long-lived substates with alternative residue-residue contacts. These rearrangements are not restricted to side-chain fluctuations in the periphery but also affect the core interface. Finally, the analysis of the waters at the interface and involved in the binding pointed out the importance to take into account their role in the estimation of the interaction strength.

Energy barrier for ion field emission from a dielectric liquid sphere

Ion field emission from the surface of a dielectric liquid is commonly modeled as a kinetic process with an energy barrier lowered by the strength of the electric field. Expressions for the energy barrier exist for simplified cases such as a planar surface and a conducting sphere. This article derives an analytical expression for the more general case of a dielectric sphere, which is the continuum model and geometry for most cases of interest. The energy barrier is computed using the method of image charges, and compared to existing expressions for simpler models. The energy barrier increases at decreasing dielectric constant and decreasing radius of curvature. Ion emission from typical systems (the ideal Taylor cone and charged nanodroplets) differs substantially when calculated with either our model or with existing simpler models.

Optimizing Multisite λ-Dynamics Throughput with Charge Renormalization

With the ability to sample combinations of alchemical perturbations at multiple sites off a small molecule core, multisite λ-dynamics (MSλD) has become an attractive alternative to conventional alchemical free energy methods for exploring large combinatorial chemical spaces. However, current software implementations dictate that combinatorial sampling with MSλD must be performed with a multiple topology model (MTM), which is nontrivial to create by hand, especially for a series of ligand analogues which may have diverse functional groups attached. This work introduces an automated workflow, referred to as msld_py_prep, to assist in the creation of a MTM for use with MSλD. One approach for partitioning partial atomic charges between ligands to create a MTM, called charge renormalization, is also presented and rigorously evaluated. We find that msld_py_prep greatly accelerates the preparation of MSλD ready-to-use files and that charge renormalization can provide a successful approach for MTM generation, as long as bookending calculations are applied to correct small differences introduced by charge renormalization. Charge renormalization also facilitates the use of many different force field parameters with MSλD, broadening the applicability of MSλD for computer-aided drug design.

Evaluation of nine condensed-phase force fields of the GROMOS, CHARMM, OPLS, AMBER, and OpenFF families against experimental cross-solvation free energies

Experimental solvation free energies are nowadays commonly included as target properties in the validation of condensed-phase force fields, sometimes even in their calibration. In a previous article [Kashefolgheta et al., J. Chem. Theory. Comput., 2020, 16, 7556-7580], we showed how the involved comparison between experimental and simulation results could be made more systematic by considering a full matrix of cross-solvation free energies . For a set of N molecules that are all in the liquid state under ambient conditions, such a matrix encompasses N×N entries for considering each of the N molecules either as solute (A) or as solvent (B). In the quoted study, a cross-solvation matrix of 25 × 25 experimental value was introduced, considering 25 small molecules representative for alkanes, chloroalkanes, ethers, ketones, esters, alcohols, amines, and amides. This experimental data was used to compare the relative accuracies of four popular condensed-phase force fields, namely GROMOS-2016H66, OPLS-AA, AMBER-GAFF, and CHARMM-CGenFF. In the present work, the comparison is extended to five additional force fields, namely GROMOS-54A7, GROMOS-ATB, OPLS-LBCC, AMBER-GAFF2, and OpenFF. Considering these nine force fields, the correlation coefficients between experimental values and simulation results range from 0.76 to 0.88, the root-mean-square errors (RMSEs) from 2.9 to 4.8 kJ mol-1, and average errors (AVEEs) from -1.5 to +1.0 kJ mol-1. In terms of RMSEs, GROMOS-2016H66 and OPLS-AA present the best accuracy (2.9 kJ mol-1), followed by OPLS-LBCC, AMBER-GAFF2, AMBER-GAFF, and OpenFF (3.3 to 3.6 kJ mol-1), and then by GROMOS-54A7, CHARM-CGenFF, and GROMOS-ATB (4.0 to 4.8 kJ mol-1). These differences are statistically significant but not very pronounced, and are distributed rather heterogeneously over the set of compounds within the different force fields.

Generalizing the Discrete Gibbs Sampler-Based λ-Dynamics Approach for Multisite Sampling of Many Ligands

In this work, the discrete λ variant of the Gibbs sampler-based λ-dynamics (d-GSλD) method is developed to enable multiple functional group perturbations to be investigated at one or more sites of substitution off a common ligand core. The theoretical framework and special considerations for constructing discrete λ states for multisite d-GSλD are presented. The precision and accuracy of the d-GSλD method is evaluated with three test cases of increasing complexity. Specifically, methyl → methyl symmetric perturbations in water, 1,4-benzene hydration free energies and protein-ligand binding affinities for an example HIV-1 reverse transcriptase inhibitor series are computed with d-GSλD. Complementary MSλD calculations were also performed to compare with d-GSλD's performance. Excellent agreement between d-GSλD and MSλD is observed, with mean unsigned errors of 0.12 and 0.22 kcal/mol for computed hydration and binding free energy test cases, respectively. Good agreement with experiment is also observed, with errors of 0.5-0.7 kcal/mol. These findings support the applicability of the d-GSλD free energy method for a variety of molecular design problems, including structure-based drug design. Finally, a discussion of d-GSλD versus MSλD approaches is presented to compare and contrast features of both methods.

Artificial intelligence in drug design: algorithms, applications, challenges and ethics

The discovery paradigm of drugs is rapidly growing due to advances in machine learning (ML) and artificial intelligence (AI). This review covers myriad faces of AI and ML in drug design. There is a plethora of AI algorithms, the most common of which are summarized in this review. In addition, AI is fraught with challenges that are highlighted along with plausible solutions to them. Examples are provided to illustrate the use of AI and ML in drug discovery and in predicting drug properties such as binding affinities and interactions, solubility, toxicology, blood–brain barrier permeability and chemical properties. The review also includes examples depicting the implementation of AI and ML in tackling intractable diseases such as COVID-19, cancer and Alzheimer’s disease. Ethical considerations and future perspectives of AI are also covered in this review.

VAD-MM/GBSA: A Variable Atomic Dielectric MM/GBSA Model for Improved Accuracy in Protein-Ligand Binding Free Energy Calculations

The molecular mechanics/generalized Born surface area (MM/GBSA) has been widely used in end-point binding free energy prediction in structure-based drug design (SBDD). However, in practice, it is usually being treated as a disputed method mostly because of its system dependence. Here, combining with machine-learning optimization, we developed a novel version of MM/GBSA, named variable atomic dielectric MM/GBSA (VAD-MM/GBSA), by assigning variable dielectric constants directly to the protein/ligand atoms. The new strategy exhibits markedly improved accuracy in binding affinity calculations for various protein-ligand systems and is promising to be used in the postprocessing of structure-based virtual screening. Moreover, VAD-MM/GBSA outperformed prime MM/GBSA in Schrödinger software and showed remarkable predictive performance for specific protein targets, such as POL polyprotein, human immunodeficiency virus type 1 (HIV-1) protease, etc. Our study showed that the VAD-MM/GBSA method with little extra computational overhead provides a potential replacement of the MM/GBSA in AMBER software. An online web server of VAD-MMGBSA has been developed and is now available at http://cadd.zju.edu.cn/vdgb.

Quantum Chemical Microsolvation by Automated Water Placement

We developed a quantitative approach to quantum chemical microsolvation. Key in our methodology is the automatic placement of individual solvent molecules based on the free energy solvation thermodynamics derived from molecular dynamics (MD) simulations and grid inhomogeneous solvation theory (GIST). This protocol enabled us to rigorously define the number, position, and orientation of individual solvent molecules and to determine their interaction with the solute based on physical quantities. The generated solute-solvent clusters served as an input for subsequent quantum chemical investigations. We showcased the applicability, scope, and limitations of this computational approach for a number of small molecules, including urea, 2-aminobenzothiazole, (+)-syn-benzotriborneol, benzoic acid, and helicene. Our results show excellent agreement with the available ab initio molecular dynamics data and experimental results.

An Alternative to Conventional λ-Intermediate States in Alchemical Free Energy Calculations: λ-Enveloping Distribution Sampling

Alchemical free energy calculations typically rely on intermediate states to bridge between the relevant phase spaces of the two end states. These intermediate states are usually created by mixing the energies or parameters of the end states according to a coupling parameter λ. The choice of the procedure has a strong impact on the efficiency of the calculation, as it affects both the encountered energy barriers and the phase space overlap between the states. The present work builds on the connection between the minimum variance pathway (MVP) and enveloping distribution sampling (EDS). It is shown that both methods can be regarded as special cases of a common scheme referred to as λ-EDS, which can also reproduce the behavior of conventional λ-intermediate states. A particularly attractive feature of λ-EDS is its ability to emulate the use of soft core potentials (SCP) while avoiding the associated computational overhead when applying efficient free energy estimators such as the multistate Bennett's acceptance ratio (MBAR). The method is illustrated for both relative and absolute free energy calculations considering five benchmark systems. The first two systems (charge inversion and cavity creation in a dipolar solvent) demonstrate the use of λ-EDS as an alternative coupling scheme in the context of thermodynamic integration (TI). The three other systems (change of bond length, change of dihedral angles, and cavity creation in water) investigate the efficiency and optimal choice of parameters in the context of free energy perturbation (FEP) and Bennett's acceptance ratio (BAR). It is shown that λ-EDS allows larger steps along the alchemical pathway than conventional intermediate states.

Prediction of aqueous free energies of solvation using coupled QM and MM explicit solvent simulations

A method based on molecular dynamics simulations which employ two distinct levels of theory is proposed and tested for the prediction of Gibbs free energies of solvation for non-ionic solutes in water. The method consists of two additive contributions: (i) an evaluation of the free energy of solvation predicted by a computationally efficient molecular mechanics (MM) method; and (ii) an evaluation of the free energy difference between the potential energy surface of the MM method and that of a more computationally intensive first-principles quantum-mechanical (QM) method. The latter is computed by a thermodynamic integration method based on a series of shorter molecular dynamics simulations that employ weighted averages of the QM and MM force evaluations. The combined computational approach is tested against the experimental free energies of aqueous solvation for four solutes. For solute-solvent interactions that are found to be described qualitatively well by the MM method, the QM correction makes a modest improvement in the predicted free energy of aqueous solvation. However, for solutes that are found to not be adequately described by the MM method, the QM correction does not improve agreement with experiment. These preliminary results provide valuable insights into the novel concept of implementing thermodynamic integration between two model chemistries, suggesting that it is possible to use QM methods to improve upon the MM predictions of free energies of aqueous solvation.

Adapting free energy perturbation simulations for large macrocyclic ligands: how to dissect contributions from direct binding and free ligand flexibility

Large and flexible ligands gain increasing interest in the development of bioactive agents. They challenge the applicability of computational ligand optimization strategies originally developed for small molecules. Free energy perturbation (FEP) is often used for predicting binding affinities of small molecule ligands, however, its use for more complex ligands remains limited. Herein, we report the structure-based design of peptide macrocycles targeting the protein binding site of human adaptor protein 14-3-3. We observe a surprisingly strong dependency of binding affinities on relatively small variations in substituent size. FEP was performed to rationalize observed trends. To account for insufficient convergence of FEP, restrained calculations were performed and complemented with extensive REST MD simulations of the free ligands. These calculations revealed that changes in affinity originate both from altered direct interactions and conformational changes of the free ligand. In addition, MD simulations provided the basis to rationalize unexpected trends in ligand lipophilicity. We also verified the anticipated interaction site and binding mode for one of the high affinity ligands by X-ray crystallography. The introduced fully-atomistic simulation protocol can be used to rationalize the development of structurally complex ligands which will support future ligand maturation efforts.

The Dependence of Implicit Solvent Model Parameters and Electronic Absorption Spectra and Photoinduced Charge Transfer

In this work, the relationship between multiple solvent parameters and charge transfer index was analyzed by multi-factor multi-variate partial least squares regression (PLSR). The charge transfer of the molecule is visualized by the analysis of the excited state wave function. Hydrogen bond basicity and surface tension can significantly affect charge transfer by studying the solvation model parameters and charge transfer index. Finally, a method in which a solvent regulates charge transfer strength and migration length is proposed.

Physics-Based Method for Modeling Passive Membrane Permeability and Translocation Pathways of Bioactive Molecules

Assessment of permeability is a critical step in the drug development process for selection of drug candidates with favorable ADME properties. We have developed a novel physics-based method for fast computational modeling of passive permeation of diverse classes of molecules across lipid membranes. The method is based on heterogeneous solubility-diffusion theory and operates with all-atom 3D structures of solutes and the anisotropic solvent model of the lipid bilayer characterized by transbilayer profiles of dielectric and hydrogen bonding capacity parameters. The optimal translocation pathway of a solute is determined by moving an ensemble of representative conformations of the molecule through the dioleoyl-phosphatidylcholine (DOPC) bilayer and optimizing their rotational orientations in every point of the transmembrane trajectory. The method calculates (1) the membrane-bound state of the solute molecule; (2) free energy profile of the solute along the permeation pathway; and (3) the permeability coefficient obtained by integration over the transbilayer energy profile and assuming a constant size-dependent diffusivity along the membrane normal. The accuracy of the predictions was evaluated against experimental permeability coefficients measured in pure lipid membranes (for 78 compounds, R² was 0.88 and rmse was 1.15 log units), PAMPA-DS (for 280 compounds, R² was 0.75 and rmse was 1.59 log units), BBB (for 182 compounds, R² was 0.69 and rmse was 0.87 log units), and Caco-2/MDCK assays (for 165 compounds, R² was 0.52 and rmse was 0.89 log units).

Heterogeneous Dielectric Implicit Membrane Model for the Calculation of MMPBSA Binding Free Energies

Membrane-bound protein receptors are a primary biological drug target, but the computational analysis of membrane proteins has been limited. In order to improve molecular mechanics Poisson-Boltzmann surface area (MMPBSA) binding free energy calculations for membrane protein-ligand systems, we have optimized a new heterogeneous dielectric implicit membrane model, with respect to free energy simulations in explicit membrane and explicit water, and implemented it into the Amber software suite. This new model supersedes our previous uniform, single dielectric implicit membrane model by allowing the dielectric constant to vary with depth within the membrane. We calculated MMPBSA binding free energies for the human purinergic platelet receptor (P2Y₁₂R) and two of the muscarinic acetylcholine receptors (M2R and M3R) bound to various antagonist ligands using both membrane models, and we found that the heterogeneous dielectric membrane model has a stronger correlation with experimental binding affinities compared to the older model under otherwise identical conditions. This improved membrane model increases the utility of MMPBSA calculations for the rational design and improvement of future drug candidates.

Solvation Free Energy Calculation Using a Fixed-Charge Model: Implicit and Explicit Treatments of the Polarization Effect

In this work, IPolQ-Mod charges and the reference potential scheme are used to calculate the solvation free energies of a set of organic molecules. Both methods could capture the phase transfer of a solute with accompanying polarization cost utilizing a fixed-charge model. The IPolQ-Mod charges, which are the average of two charge sets fitted in a vacuum state and a condensed phase, take account of the polarization effect implicitly. For the reference potential method, the quantum mechanics polarization corrections are calculated explicitly by thermodynamic perturbation. The polarization effect captured by the IPolQ-Mod charges is an approximation to that of the reference potential method theoretically. In the present study, the reference potential method shows a slight improvement over the classical restrained electrostatic potential (RESP) charges, which perform pretty well in predicting the solvation free energy. However, IPolQ-Mod(MP2) shows a poor agreement with the experimental data. Compared with IPolQ-Mod(MP2), IPolQ-Mod(M06-2X) or IPolQ-Mod(ωB97X) is found to give more appropriate prediction of the molecule's dipole and the solvation free energies calculated by IPolQ-Mod(M06-2X) or IPolQ-Mod(ωB97X) are more compatible with those of the RESP charges. If the other force field parameters remain unchanged, M06-2X or ωB97X is recommended to derive the IPolQ-Mod charges.

Solvation Free Energy Calculations with Quantum Mechanics/Molecular Mechanics and Machine Learning Models

For exploration of chemical and biological systems, the combined quantum mechanics and molecular mechanics (QM/MM) and machine learning (ML) models have been developed recently to achieve high accuracy and efficiency for molecular dynamics (MD) simulations. Despite its success on reaction free energy calculations, how to identify new configurations on insufficiently sampled regions during MD and how to update the current ML models with the growing database on the fly are both very important but still challenging. In this article, we apply the QM/MM ML method to solvation free energy calculations and address these two challenges. We employ three approaches to detect new data points and introduce the gradient boosting algorithm to reoptimize efficiently the ML model during ML-based MD sampling. The solvation free energy calculations on several typical organic molecules demonstrate that our developed method provides a systematic, robust, and efficient way to explore new chemistry using ML-based QM/MM MD simulations.

Unexpected trends in the hydrophobicity of fluorinated amino acids reflect competing changes in polarity and conformation

The hydration free energy of fluorinated amino acids is calculated with molecular simulations and explained with an analytical model.

Robustness and Efficiency of Poisson-Boltzmann Modeling on Graphics Processing Units

Poisson-Boltzmann equation (PBE) based continuum electrostatics models have been widely used in modeling electrostatic interactions in biochemical processes, particularly in estimating protein-ligand binding affinities. Fast convergence of PBE solvers is crucial in binding affinity computations as numerous snapshots need to be processed. Efforts have been reported to develop PBE solvers on graphics processing units (GPUs) for efficient modeling of biomolecules, though only relatively simple successive over-relaxation and conjugate gradient methods were implemented. However, neither convergence nor scaling properties of the two methods are optimal for large biomolecules. On the other hand, geometric multigrid (MG) has been shown to be an optimal solver on CPUs, though no MG have been reported for biomolecular applications on GPUs. This is not a surprise as it is a more complex method and depends on simpler but limited iterative methods such as Gauss-Seidel in its core relaxation procedure. The robustness and efficiency of MG on GPUs are also unclear. Here we present an implementation and a thorough analysis of MG on GPUs. Our analysis shows that robustness is a more pronounced issue than efficiency for both MG and other tested solvers when the single precision is used for complex biomolecules. We further show how to balance robustness and efficiency utilizing MG's overall efficiency and conjugate gradient's robustness, pointing to a hybrid GPU solver with a good balance of efficiency and accuracy. The new PBE solver will significantly improve the computational throughput for a range of biomolecular applications on the GPU platforms.

Refining evERdock: Improved selection of good protein-protein complex models achieved by MD optimization and use of multiple conformations

A method for evaluating binding free energy differences of protein-protein complex structures generated by protein docking was recently developed by some of us. The method, termed evERdock, combined short (2 ns) molecular dynamics (MD) simulations in explicit water and solution theory in the energy representation (ER) and succeeded in selecting the near-native complex structures from a set of decoys. In the current work, we performed longer (up to 100 ns) MD simulations before employing ER analysis in order to further refine the structures of the decoy set with improved binding free energies. Moreover, we estimated the binding free energies for each complex structure based on an average value from five individual MD snapshots. After MD simulations, all decoys exhibit a decrease in binding free energy, suggesting that proper equilibration in explicit solvent resulted in more favourably bound complexes. During the MD simulations, non-native structures tend to become unstable and in some cases dissociate, while near-native structures maintain a stable interface. The energies after the MD simulations show an improved correlation between similarity criteria (such as interface root-mean-square distance) to the native (crystal) structure and the binding free energy. In addition, calculated binding free energies show sensitivity to the number of contacts, which was demonstrated to reflect the relative stability of structures at earlier stages of the MD simulation. We therefore conclude that the additional equilibration step along with the use of multiple conformations can make the evERdock scheme more versatile under low computational cost.

Computational insights into factor affecting the potency of diaryl sulfone analogs as Escherichia coli dihydropteroate synthase inhibitors

Dihydropteroate synthase (DHPS) is an alluring target for designing novel drug candidates to prevent infections caused by pathogenic Escherichia coli strains. Diaryl Sulfone (SO) compounds are found to inhibit DHPS competitively with respect to the substrate pABA (p-aminobenzoate). The extra aromatic ring of diaryl sulfone compounds found to stabilize them in highly flexible pABA binding loops. In this present study, a statistically significant 3D-QSAR model was developed using a data set of diaryl sulfone compounds. The favourable and unfavourable contributions of substitutions in sulfone compounds were illustrated by contour plot obtained from the developed 3D-QSAR model. Molecular docking calculations were performed to investigate the putative binding mode of diaryl sulfone compounds at the catalytic pocket. DFT calculations were carried out using SCF approach, B3LYP- 6-31 G (d) basis set to compute the HOMO, LUMO energies and their respective location at pABA binding pocket. Further, the developed model was validated by FEP (Free Energy Perturbation) calculations. The calculated relative free energy of binding between the highly potent and less potent sulfone compound was found to be -3.78 kcal/ mol which is comparable to the experimental value of -5.85 kcal/mol. A 10 ns molecular dynamics simulation of inhibitor and DHPS confirmed its stability at pABA catalytic site. Outcomes of the present work provide deeper insight in designing novel drug candidates for pathogenic Escherichia coli strains.

Automated Topology Builder Version 3.0: Prediction of Solvation Free Enthalpies in Water and Hexane

The ability of atomic interaction parameters generated using the Automated Topology Builder and Repository version 3.0 (ATB3.0) to predict experimental hydration free enthalpies (Δ G^water) and solvation free enthalpies in the apolar solvent hexane (Δ G^hexane) is presented. For a validation set of 685 molecules the average unsigned error (AUE) between Δ G^water values calculated using the ATB3.0 and experiment is 3.8 kJ·mol^-1. The slope of the line of best fit is 1.00, the intercept -1.0 kJ·mol^-1, and the R² 0.90. For the more restricted set of 239 molecules used to validate OPLS3 ( J. Chem. Theory Comput. 2016 , 12 , 281 - 296 , DOI: 10.1021/acs.jctc.5b00864 ) the AUE using the ATB3.0 is just 2.7 kJ·mol^-1 and the R² 0.93. A roadmap for further improvement of the ATB parameters is presented together with a discussion of the challenges of validating force fields against the available experimental data.

Hydration Free Energies in the FreeSolv Database Calculated with Polarized Iterative Hirshfeld Charges

Computer simulations of biomolecular systems often use force fields, which are combinations of simple empirical atom-based functions to describe the molecular interactions. Even though polarizable force fields give a more detailed description of intermolecular interactions, nonpolarizable force fields, developed several decades ago, are often still preferred because of their reduced computation cost. Electrostatic interactions play a major role in biomolecular systems and are therein described by atomic point charges. In this work, we address the performance of different atomic charges to reproduce experimental hydration free energies in the FreeSolv database in combination with the GAFF force field. Atomic charges were calculated by two atoms-in-molecules approaches, Hirshfeld-I and Minimal Basis Iterative Stockholder (MBIS). To account for polarization effects, the charges were derived from the solute's electron density computed with an implicit solvent model, and the energy required to polarize the solute was added to the free energy cycle. The calculated hydration free energies were analyzed with an error model, revealing systematic errors associated with specific functional groups or chemical elements. The best agreement with the experimental data is observed for the AM1-BCC and the MBIS atomic charge methods. The latter includes the solvent polarization and presents a root-mean-square error of 2.0 kcal mol-1 for the 613 organic molecules studied. The largest deviation was observed for phosphorus-containing molecules and the molecules with amide, ester and amine functional groups.

Optimized Lennard-Jones Parameters for Druglike Small Molecules

Meaningful efforts in computer-aided drug design (CADD) require accurate molecular mechanical force fields to quantitatively characterize protein-ligand interactions, ligand hydration free energies, and other ligand physical properties. Atomic models of new compounds are commonly generated by analogy from the predefined tabulated parameters of a given force field. Two widely used approaches following this strategy are the General Amber Force Field (GAFF) and the CHARMM General Force Field (CGenFF). An important limitation of using pretabulated parameter values is that they may be inadequate in the context of a specific molecule. To resolve this issue, we previously introduced the General Automated Atomic Model Parameterization (GAAMP) for automatically generating the parameters of atomic models of small molecules, using the results from ab initio quantum mechanical (QM) calculations as target data. The GAAMP protocol uses QM data to optimize the bond, valence angle, and dihedral angle internal parameters, and atomic partial charges. However, since the treatment of van der Waals interactions based on QM is challenging and may often be unreliable, the Lennard-Jones 6-12 parameters are kept unchanged from the initial atom types assignments (GAFF or CGenFF), which limits the accuracy that can be achieved by these models. To address this issue, a new set of Lennard-Jones 6-12 parameters was systematically optimized to reproduce experimental neat liquid densities and enthalpies of vaporization for a large set of 430 compounds, covering a wide range of chemical functionalities. Calculations of the hydration free energy indicate that optimal accuracy for these models is achieved when the molecule-water van der Waals dispersion is rescaled by a factor of 1.115. The final optimized model yields an average unsigned error of 0.79 kcal/mol in the hydration free energies.

Exploring a multi-scale method for molecular simulation in continuum solvent model: Explicit simulation of continuum solvent as an incompressible fluid

We explored a multi-scale algorithm for the Poisson-Boltzmann continuum solvent model for more robust simulations of biomolecules. In this method, the continuum solvent/solute interface is explicitly simulated with a numerical fluid dynamics procedure, which is tightly coupled to the solute molecular dynamics simulation. There are multiple benefits to adopt such a strategy as presented below. At this stage of the development, only nonelectrostatic interactions, i.e., van der Waals and hydrophobic interactions, are included in the algorithm to assess the quality of the solvent-solute interface generated by the new method. Nevertheless, numerical challenges exist in accurately interpolating the highly nonlinear van der Waals term when solving the finite-difference fluid dynamics equations. We were able to bypass the challenge rigorously by merging the van der Waals potential and pressure together when solving the fluid dynamics equations and by considering its contribution in the free-boundary condition analytically. The multi-scale simulation method was first validated by reproducing the solute-solvent interface of a single atom with analytical solution. Next, we performed the relaxation simulation of a restrained symmetrical monomer and observed a symmetrical solvent interface at equilibrium with detailed surface features resembling those found on the solvent excluded surface. Four typical small molecular complexes were then tested, both volume and force balancing analyses showing that these simple complexes can reach equilibrium within the simulation time window. Finally, we studied the quality of the multi-scale solute-solvent interfaces for the four tested dimer complexes and found that they agree well with the boundaries as sampled in the explicit water simulations.

Accuracy Comparison of Generalized Born Models in the Calculation of Electrostatic Binding Free Energies

The need for accurate yet efficient representation of the aqueous environment in biomolecular modeling has led to the development of a variety of generalized Born (GB) implicit solvent models. While many studies have focused on the accuracy of available GB models in predicting solvation free energies, a systematic assessment of the quality of these models in binding free energy calculations, crucial for rational drug design, has not been undertaken. Here, we evaluate the accuracies of eight common GB flavors (GB-HCT, GB-OBC, GB-neck2, GBNSR6, GBSW, GBMV1, GBMV2, and GBMV3), available in major molecular dynamics packages, in predicting the electrostatic binding free energies ( ΔΔ G_el) for a diverse set of 60 biomolecular complexes belonging to four main classes: protein-protein, protein-drug, RNA-peptide, and small complexes. The GB flavors are examined in terms of their ability to reproduce the results from the Poisson-Boltzmann (PB) model, commonly used as accuracy reference in this context. We show that the agreement with the PB of ΔΔ G_el estimates varies widely between different GB models and also across different types of biomolecular complexes, with R² correlations ranging from 0.3772 to 0.9986. A surface-based "R6" GB model recently implemented in AMBER shows the closest overall agreement with reference PB ( R² = 0.9949, RMSD = 8.75 kcal/mol). The RNA-peptide and protein-drug complex sets appear to be most challenging for all but one model, as indicated by the large deviations from the PB in ΔΔ G_el. Small neutral complexes present the least challenge for most of the GB models tested. The quantitative demonstration of the strengths and weaknesses of the GB models across the diverse complex types provided here can be used as a guide for practical computations and future development efforts.

Reproducing the Ensemble Average Polar Solvation Energy of a Protein from a Single Structure: Gaussian-Based Smooth Dielectric Function for Macromolecular Modeling

Typically, the ensemble average polar component of solvation energy (ΔG_polar^solv) of a macromolecule is computed using molecular dynamics (MD) or Monte Carlo (MC) simulations to generate conformational ensemble and then single/rigid conformation solvation energy calculation is performed on each snapshot. The primary objective of this work is to demonstrate that Poisson-Boltzmann (PB)-based approach using a Gaussian-based smooth dielectric function for macromolecular modeling previously developed by us (Li et al. J. Chem. Theory Comput. 2013, 9 (4), 2126-2136) can reproduce that ensemble average (ΔG_polar^solv) of a protein from a single structure. We show that the Gaussian-based dielectric model reproduces the ensemble average ΔG_polar^solv(⟨ΔG_polar^solv⟩) from an energy-minimized structure of a protein regardless of the minimization environment (structure minimized in vacuo, implicit or explicit waters, or crystal structure); the best case, however, is when it is paired with an in vacuo-minimized structure. In other minimization environments (implicit or explicit waters or crystal structure), the traditional two-dielectric model can still be selected with which the model produces correct solvation energies. Our observations from this work reflect how the ability to appropriately mimic the motion of residues, especially the salt bridge residues, influences a dielectric model's ability to reproduce the ensemble average value of polar solvation free energy from a single in vacuo-minimized structure.

Generalized Born implicit solvent models for small molecule hydration free energies

Hydration free energy estimation of small molecules from all-atom simulations was widely investigated in recent years, as it provides an essential test of molecular force fields and our understanding of solvation effects. While explicit solvent representations result in highly accurate models, they also require extensive sampling due to the high number of solvent degrees of freedom. Implicit solvent models, such as those based on the generalized Born model for electrostatic solvation effects and a solvent accessible surface area term for nonpolar contributions (GBSA), significantly reduce the number of degrees of freedom and the computational cost to estimate hydration free energies. However, a recent survey revealed a gap in the accuracy between explicit TIP3P solvent estimates and those computed with many common GBSA models. Here we address this shortcoming by providing a thorough comparison of the performance of three implicit solvent models with different nonpolar contributions and a generalized Born term to estimate experimental hydration free energies. Starting with a minimal set of only ten atom types, we demonstrate that a nonpolar term with atom type dependent surface tension coefficients in combination with an accurate generalized Born term and fully optimized parameters performs best in estimating hydration free energies, even yielding comparable results to the explicit TIP3P water model. Analysis of our results provides evidence that the asymmetric behavior of water around oppositely charged atoms is one of the main sources of error for two of the three implicit solvent models. Explicitly accounting for this effect in the parameterization reduces the corresponding errors, suggesting this as a general strategy for improving implicit solvent models. The findings presented here will help to improve the existing generalized Born based implicit solvent models implemented in state-of-the-art molecular simulation packages.

Recent Developments and Applications of the MMPBSA Method

The Molecular Mechanics Poisson-Boltzmann Surface Area (MMPBSA) approach has been widely applied as an efficient and reliable free energy simulation method to model molecular recognition, such as for protein-ligand binding interactions. In this review, we focus on recent developments and applications of the MMPBSA method. The methodology review covers solvation terms, the entropy term, extensions to membrane proteins and high-speed screening, and new automation toolkits. Recent applications in various important biomedical and chemical fields are also reviewed. We conclude with a few future directions aimed at making MMPBSA a more robust and efficient method.

Estimations of the thermodynamic properties of halogenated benzenes as they relate to their environment mobility

In this work, several simple new equations for predicting important environmental mobility properties, at T = 298.15 K, were derived for halogenated benzenes: standard Gibbs energy of hydration, aqueous solubility, octanol-water partition coefficients, and Henry's law constants. A discussion on our previous estimates of other related properties (standard Gibbs energy and vapor pressure of sublimation and of vaporization) and their relation with entropy of fusion is also presented. As we aimed to estimate these properties for any of the ca. 1500 halogenated benzenes that may exist theoretically, an equation for estimating the temperature of fusion was also derived, since some of the proposed predictive equations (solubility of solids and Gibbs energy of sublimation) require its knowledge. For the other estimated properties just the number of each halogen that replaces hydrogen atoms in the halogenated benzene is needed. It was found that the coefficients that multiply the number of halogen atoms in the predictive equations vary linearly with the volume of the halogen atom.

Efficient Implicit Solvation Method for Full Potential DFT

With the advent of efficient electronic structure methods, effective continuum solvation methods have emerged as a way to, at least partially, include solvent effects into simulations without the need for expensive sampling over solvent degrees of freedom. The multipole moment expansion (MPE) model, while based on ideas initially put forward almost 100 years ago, has recently been updated for the needs of modern electronic structure calculations. Indeed, for an all-electron code relying on localized basis sets and-more importantly-a multipole moment expansion of the electrostatic potential, the MPE method presents a particularly cheap way of solving the macroscopic Poisson equation to determine the electrostatic response of a medium surrounding a solute. In addition to our implementation of the MPE model in the FHI-aims electronic structure theory code [ Blum , V. ; Comput. Phys. Commun. 2009 , 180 , 2175 - 2196 , DOI: 10.1016/j.cpc.2009.06.022 ], we describe novel algorithms for determining equidistributed points on the solvation cavity-defined as a charge density isosurface-and the determination of cavity surface and volume from just this collection of points and their local density gradients. We demonstrate the efficacy of our model on an analytically solvable test case, against high-accuracy finite-element calculations for a set of ≈140000 2D test cases, and finally against experimental solvation free energies of a number of neutral and singly charged molecular test sets [ Andreussi , O. ; J. Chem. Phys. 2012 , 136 , 064102 , DOI: 10.1063/1.3676407 ; Marenich , A. V. ; Minnesota Solvation Database , Version 2012; University of Minnesota : Minneapolis, MN, USA , 2012 . ]. In all test cases we find that our MPE approach compares very well with given references at computational overheads < 20% and sometimes much smaller compared to a plain self-consistency cycle.

A Continuum Poisson-Boltzmann Model for Membrane Channel Proteins

Membrane proteins constitute a large portion of the human proteome and perform a variety of important functions as membrane receptors, transport proteins, enzymes, signaling proteins, and more. Computational studies of membrane proteins are usually much more complicated than those of globular proteins. Here, we propose a new continuum model for Poisson-Boltzmann calculations of membrane channel proteins. Major improvements over the existing continuum slab model are as follows: (1) The location and thickness of the slab model are fine-tuned based on explicit-solvent MD simulations. (2) The highly different accessibilities in the membrane and water regions are addressed with a two-step, two-probe grid-labeling procedure. (3) The water pores/channels are automatically identified. The new continuum membrane model is optimized (by adjusting the membrane probe, as well as the slab thickness and center) to best reproduce the distributions of buried water molecules in the membrane region as sampled in explicit water simulations. Our optimization also shows that the widely adopted water probe of 1.4 Å for globular proteins is a very reasonable default value for membrane protein simulations. It gives the best compromise in reproducing the explicit water distributions in membrane channel proteins, at least in the water accessible pore/channel regions. Finally, we validate the new membrane model by carrying out binding affinity calculations for a potassium channel, and we observe good agreement with the experimental results.

Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units

Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes. Though great efforts have been put into developing efficient PBE numerical models, challenges still remain due to the high dimensionality of typical biomolecular systems. In this study, we implemented and analyzed commonly used linear PBE solvers for the ever-improving graphics processing units (GPU) for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners. Our implementation utilizes the standard Nvidia CUDA libraries cuSPARSE, cuBLAS, and CUSP. Extensive tests show that good numerical accuracy can be achieved given that the single precision is often used for numerical applications on GPU platforms. The optimal GPU performance was observed with the Jacobi-preconditioned CG solver, with a significant speedup over standard CG solver on CPU in our diversified test cases. Our analysis further shows that different matrix storage formats also considerably affect the efficiency of different linear PBE solvers on GPU, with the diagonal format best suited for our standard finite-difference linear systems. Further efficiency may be possible with matrix-free operations and integrated grid stencil setup specifically tailored for the banded matrices in PBE-specific linear systems.