Free Energies Of Small Molecules Research Articles

Exploring the Limits of the Generalized CHARMM and AMBER Force Fields through Predictions of Hydration Free Energy of Small Molecules.

Accurate force field parameters, potential energy functions, and receptor-ligand models are essential for modeling the solvation and binding of drug-like molecules to a receptor. A large and ever-growing chemical space of medicinally relevant scaffolds has also required these factors, especially force field parameters, to be highly transferable. Generalized force fields such as the CHARMM General Force Field (CGenFF) and the generalized AMBER force field (GAFF) have accomplished this feat along with other contemporaneous ones like OPLS. Here, we analyze the limits in the parametrization of drug-like small molecules by CGenFF and GAFF in terms of the various functional groups represented within them. Specifically, we link the presence of specific functional groups to the error in the absolute hydration free energy of over 600 small molecules, predicted by alchemical free energy methods implemented in the CHARMM program. Our investigation reveals that molecules with (i) a nitro group in CGenFF and GAFF are, respectively, over- or undersolubilized in aqueous medium, (ii) amine groups are undersolubilized more so in CGenFF than in GAFF, and (iii) carboxyl groups are more oversolubilized in GAFF than in CGenFF. We present our analyses of the potential factors underlying these trends. We also showcase the use of a machine-learning-based approach combined with the SHapley Additive exPlanations framework to attribute these trends to specific functional groups, which can be easily adopted to explore the limits of other general force fields.

Predicting Solvation Free Energies from the Minnesota Solvation Database Using Classical Density Functional Theory Based on the PC-SAFT Equation of State.

We critically assess the capabilities of classical density functional theory (DFT) based on the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state to predict the solvation free energies of small molecules in various hydrocarbon solvents. We compare DFT results with experimental data from the Minnesota solvation database and utilize statistical methods to analyze the accuracy of our approach, as well as its weaknesses. The mean absolute error of the solvation free energies is 3.7 kJ mol-1 for n-alkane solvents, ranging from pentane to hexadecane, with 473 solute-solvent systems. For solvents consisting of cyclic hydrocarbons (cyclohexane, benzene, toluene, and ethylbenzene) with 245 solute-solvent systems, we report a slightly larger mean absolute error of 4.2 kJ mol-1. We identify three possible sources of errors: (i) the neglect of solute-solvent and solvent-solvent Coulomb interactions, which limits the applicability of PC-SAFT DFT to nonpolar and weakly polar molecules; (ii) the solute's Lennard-Jones parameters supplied by the general AMBER force field, which are not parametrized toward solvation free energies; and (iii) the application of the Lorentz-Berthelot combining rules to the dispersive interactions between a segment of the PC-SAFT solvent and a Lennard-Jones interaction site of the solute. The approach is more accurate than standard implementations of phenomenological models in common chemistry software packages, which exhibit mean absolute errors larger than 9.12 kJ mol-1, even though newer phenomenological models achieve a mean absolute error of about 2 kJ mol-1. PC-SAFT DFT is more computationally efficient than state of the art explicit molecular simulations in combination with free energy perturbation methods. It is predictive with respect to solvation free energies, i.e., the input for the model is the (element-specific) molecular force field, the solute configuration from molecular dynamics simulations, and the (substance-specific) PC-SAFT parameters. The PC-SAFT parametrization uses pure-component data and does not require experimental solvation free energies. The PC-SAFT equation of state, without applying a DFT formalism, can also be used to calculate solvation free energies, provided that the PC-SAFT parameters for the solute are available. A large number of substances was recently parametrized by members of our group (Esper, T.; Bauer, G.; Rehner, P.; Gross, J. Ind. Eng. Chem. Res. 2023, 62), which enables a comparison to the DFT approach for 103 substances. Accurate results are obtained from the PC-SAFT equation of state with an MAE below 2.51 kJ mol-1. The DFT approach does not require PC-SAFT parameters for the solute and can be applied to all solutes that can be represented by the molecular force field.

Structure of the Bacterial Cell Envelope and Interactions with Antimicrobials: Insights from Molecular Dynamics Simulations.

Bacteria have evolved over 3 billion years, shaping our intrinsic and symbiotic coexistence with these single-celled organisms. With rising populations of drug-resistant strains, the search for novel antimicrobials is an ongoing area of research. Advances in high-performance computing platforms have led to a variety of molecular dynamics simulation strategies to study the interactions of antimicrobial molecules with different compartments of the bacterial cell envelope of both Gram-positive and Gram-negative species. In this review, we begin with a detailed description of the structural aspects of the bacterial cell envelope. Simulations concerned with the transport and associated free energy of small molecules and ions through the outer membrane, peptidoglycan, inner membrane and outer membrane porins are discussed. Since surfactants are widely used as antimicrobials, a section is devoted to the interactions of surfactants with the cell wall and inner membranes. The review ends with a discussion on antimicrobial peptides and the insights gained from the molecular simulations on the free energy of translocation. Challenges involved in developing accurate molecular models and coarse-grained strategies that provide a trade-off between atomic details with a gain in sampling time are highlighted. The need for efficient sampling strategies to obtain accurate free energies of translocation is also discussed. Molecular dynamics simulations have evolved as a powerful tool that can potentially be used to design and develop novel antimicrobials and strategies to effectively treat bacterial infections.

Routine Molecular Dynamics Simulations Including Nuclear Quantum Effects: From Force Fields to Machine Learning Potentials.

We report the implementation of a multi-CPU and multi-GPU massively parallel platform dedicated to the explicit inclusion of nuclear quantum effects (NQEs) in the Tinker-HP molecular dynamics (MD) package. The platform, denoted Quantum-HP, exploits two simulation strategies: the Ring-Polymer Molecular Dynamics (RPMD) that provides exact structural properties at the cost of a MD simulation in an extended space of multiple replicas and the adaptive Quantum Thermal Bath (adQTB) that imposes the quantum distribution of energy on a classical system via a generalized Langevin thermostat and provides computationally affordable and accurate (though approximate) NQEs. We discuss some implementation details, efficient numerical schemes, and parallelization strategies and quickly review the GPU acceleration of our code. Our implementation allows an efficient inclusion of NQEs in MD simulations for very large systems, as demonstrated by scaling tests on water boxes with more than 200,000 atoms (simulated using the AMOEBA polarizable force field). We test the compatibility of the approach with Tinker-HP's recently introduced Deep-HP machine learning potentials module by computing water properties using the DeePMD potential with adQTB thermostatting. Finally, we show that the platform is also compatible with the alchemical free energy estimation capabilities of Tinker-HP and fast enough to perform simulations. Therefore, we study how NQEs affect the hydration free energy of small molecules solvated with the recently developed Q-AMOEBA water force field. Overall, the Quantum-HP platform allows users to perform routine quantum MD simulations of large condensed-phase systems and will help to shed new light on the quantum nature of important interactions in biological matter.

Identifying Systematic Force Field Errors Using a 3D-RISM Element Counting Correction.

Hydration free energies of small molecules are commonly used as benchmarks for solvation models. However, errors in predicting hydration free energies are partially due to the force fields used and not just the solvation model. To address this, we have used the 3D reference interaction site model (3D-RISM) of molecular solvation and existing benchmark explicit solvent calculations with a simple element count correction (ECC) to identify problems with the non-bond parameters in the general AMBER force field (GAFF). 3D-RISM was used to calculate hydration free energies of all 642 molecules in the FreeSolv database, and a partial molar volume correction (PMVC), ECC, and their combination (PMVECC) were applied to the results. The PMVECC produced a mean unsigned error of 1.01±0.04kcal/mol and root mean squared error of 1.44±0.07kcal/mol, better than the benchmark explicit solvent calculations from FreeSolv, and required less than 15 s of computing time per molecule on a single CPU core. Importantly, parameters for PMVECC showed systematic errors for molecules containing Cl, Br, I, and P. Applying ECC to the explicit solvent hydration free energies found the same systematic errors. The results strongly suggest that some small adjustments to the Lennard-Jones parameters for GAFF will lead to improved hydration free energy calculations for all solvent models.

Robust and Efficient Implicit Solvation Model for Fast Semiempirical Methods.

We present a robust and efficient method to implicitly account for solvation effects in modern semiempirical quantum mechanics and force fields. A computationally efficient yet accurate solvation model based on the analytical linearized Poisson-Boltzmann (ALPB) model is parameterized for the extended tight binding (xTB) and density functional tight binding (DFTB) methods as well as for the recently proposed GFN-FF general force field. The proposed methods perform well over a broad range of systems and applications, from conformational energies over transition-metal complexes to large supramolecular association reactions of charged species. For hydration free energies of small molecules, GFN1-xTB(ALPB) is reaching the accuracy of sophisticated explicitly solvated approaches, with a mean absolute deviation of only 1.4 kcal/mol compared to the experiment. Logarithmic octanol-water partition coefficients (log Kow) are computed with a mean absolute deviation of about 0.65 using GFN2-xTB(ALPB) compared to experimental values indicating a consistent description of differential solvent effects. Overall, more than twenty solvents for each of the six semiempirical methods are parameterized and tested. They are readily available in the xtb and dftb+ programs for diverse computational applications.

Predicting Small Molecule Transfer Free Energies by Combining Molecular Dynamics Simulations and Deep Learning.

Accurately predicting small molecule partitioning and hydrophobicity is critical in the drug discovery process. There are many heterogeneous chemical environments within a cell and entire human body. For example, drugs must be able to cross the hydrophobic cellular membrane to reach their intracellular targets, and hydrophobicity is an important driving force for drug-protein binding. Atomistic molecular dynamics (MD) simulations are routinely used to calculate free energies of small molecules binding to proteins, crossing lipid membranes, and solvation but are computationally expensive. Machine learning (ML) and empirical methods are also used throughout drug discovery but rely on experimental data, limiting the domain of applicability. We present atomistic MD simulations calculating 15,000 small molecule free energies of transfer from water to cyclohexane. This large data set is used to train ML models that predict the free energies of transfer. We show that a spatial graph neural network model achieves the highest accuracy, followed closely by a 3D-convolutional neural network, and shallow learning based on the chemical fingerprint is significantly less accurate. A mean absolute error of ∼4 kJ/mol compared to the MD calculations was achieved for our best ML model. We also show that including data from the MD simulation improves the predictions, tests the transferability of each model to a diverse set of molecules, and show multitask learning improves the predictions. This work provides insight into the hydrophobicity of small molecules and ML cheminformatics modeling, and our data set will be useful for designing and testing future ML cheminformatics methods.

3D Convolutional Neural Network for Predicting Free Energies of Partitioning

Accurate predictions of small molecule hydrophobicity and oil/water partitioning is a critical part of drug discovery. The hydrophobicity of a drug will determine how effectively it can cross the hydrophobic cellular membrane to reach their intracellular targets. In addition to traversing the many heterogenous chemical environments within a cell, hydrophobicity is also an important driving force for drug-protein binding. Traditionally, atomistic molecular dynamics simulations are used to calculate free energies of small molecules crossing lipid membranes and solvation. Machine learning models and empirical methods have also been used, but simulations are expensive and machine learning models trained on experimental data have limited domains of applicability. Here, we combine data generated from atomistic molecular dynamics simulations with machine learning to predict free energy of partitioning. We’ve simulated over 15,000 small molecules to calculate the relative free energy in three environments: water, at an interface, and in bulk hydrocarbon. The simulation data is fed into a 3D convolutional neural network to predict free energies for transfer. To ensure a large domain of applicability, we compare random splits of the data with scaffold splitting. Our trained models are tested on previously unseen, and reasonably different, set of data generated from a subset of world approved drugs. We compare our results against shallow models trained using chemical fingerprints. This work is a step towards integrating molecular dynamics simulations and machine learning, with many new avenues of research to pursue. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. Release number: LLNL-ABS-792042.

Computing Relative Binding Affinity of Ligands to Receptor: An Effective Hybrid Single-Dual-Topology Free-Energy Perturbation Approach in NAMD.

An effective hybrid single-dual-topology protocol is designed for the calculation of relative binding affinities of small ligands to a receptor. The protocol was developed as an extension of the NAMD molecular dynamics program, which exclusively supports a dual-topology framework for relative alchemical free-energy perturbation (FEP) calculations. In this protocol, the alchemical end states are represented as two separate molecules sharing a common substructure identified through maximum structural mapping. Within the substructure, an atom-to-atom correspondence is established, and each pair of corresponding atoms is holonomically constrained to share identical coordinates at all time throughout the simulation. The forces are projected and combined at each step for propagation. Following this formulation, a set of illustrative calculations of reliable experiment/simulation data, including relative solvation free energies of small molecules and relative binding affinities of drug compounds to proteins, are presented. To enhance sampling of the dual-topology region, the FEP calculations were carried out within a replica-exchange MD scheme supported by the multiple-copy algorithm module of NAMD, with periodically attempted swapping of the thermodynamic coupling parameter λ between neighboring states. The results are consistent with experiments and benchmarks reported in the literature, lending support to the validity of the current protocol. In summary, this hybrid single-dual-topology approach combines the conceptual simplicity of the dual-topology paradigm with the advantageous sampling efficiency of the single-topology approach, making it an ideal strategy for high-throughput in silico drug design.

New Hybrid Method for the Calculation of the Solvation Free Energy of Small Molecules in Aqueous Solutions.

The ability to accurately predict the solvation free energies of ionic species using the appropriate thermodynamic cycle is of great importance in many areas of chemistry and biochemistry. To improve the accuracy of calculating solvation free energies, we devised a hybrid cluster-continuum approach, where explicit solvent molecules are added to the traditionally employed continuum model. Our computational workflow consists of the following steps: First, the minimum number of explicit water molecules beyond which additional water molecules no longer improve the accuracy of the cluster-continuum model is carefully established. Next, the convergence values for fully relaxed molecular configurations are compared with those obtained by sampling thermally disordered configurations using single-point calculations. We find that the dielectric constant does not have a significant influence on the solvation free energy, while accounting for the placement of a counterion is necessary for the accurate calculation of the solvation free energy.

Method Evaluations for Adsorption Free Energy Calculations at the Solid/Water Interface through Metadynamics, Umbrella Sampling, and Jarzynski's Equality.

Considerable interest in characterizing protein/peptide-surface interactions has prompted extensive computational studies on calculations of adsorption free energy. However, in many cases, each individual study has focused on the application of free energy calculations to a specific system; therefore, it is difficult to combine the results into a general picture for choosing an appropriate strategy for the system of interest. Herein, three well-established computational algorithms are systemically compared and evaluated to compute the adsorption free energy of small molecules on two representative surfaces. The results clearly demonstrate that the characteristics of studied interfacial systems have crucial effects on the accuracy and efficiency of the adsorption free energy calculations. For the hydrophobic surface, steered molecular dynamics exhibits the highest efficiency, which appears to be a favorable method of choice for enhanced sampling simulations. However, for the charged surface, only the umbrella sampling method has the ability to accurately explore the adsorption free energy surface. The affinity of the water layer to the surface significantly affects the performance of free energy calculation methods, especially at the region close to the surface. Therefore, a general principle of how to discriminate between methodological and sampling issues based on the interfacial characteristics of the system under investigation is proposed.

Binding mode prediction and MD/MMPBSA-based free energy ranking for agonists of REV-ERBα/NCoR.

The knowledge of the free energy of binding of small molecules to a macromolecular target is crucial in drug design as is the ability to predict the functional consequences of binding. We highlight how a molecular dynamics (MD)-based approach can be used to predict the free energy of small molecules, and to provide priorities for the synthesis and the validation via in vitro tests. Here, we study the dynamics and energetics of the nuclear receptor REV-ERBα with its co-repressor NCoR and 35 novel agonists. Our in silico approach combines molecular docking, molecular dynamics (MD), solvent-accessible surface area (SASA) and molecular mechanics poisson boltzmann surface area (MMPBSA) calculations. While docking yielded initial hints on the binding modes, their stability was assessed by MD. The SASA calculations revealed that the presence of the ligand led to a higher exposure of hydrophobic REV-ERB residues for NCoR recruitment. MMPBSA was very successful in ranking ligands by potency in a retrospective and prospective manner. Particularly, the prospective MMPBSA ranking-based validations for four compounds, three predicted to be active and one weakly active, were confirmed experimentally.

Predicting the Effect of Amino Acid Single-Point Mutations on Protein Stability—Large-Scale Validation of MD-Based Relative Free Energy Calculations

The stability of folded proteins is critical to their biological function and for the efficacy of protein therapeutics. Predicting the energetic effects of protein mutations can improve our fundamental understanding of structural biology, the molecular basis of diseases, and possible routes to addressing those diseases with biological drugs. Identifying the effect of single amino acid point mutations on the thermodynamic equilibrium between the folded and unfolded states of a protein can pinpoint residues of critical importance that should be avoided in the process of improving other properties (affinity, solubility, viscosity, etc.) and suggest changes at other positions for increasing stability in protein engineering. Multiple computational tools have been developed for in silico predictions of protein stability in recent years, ranging from sequence-based empirical approaches to rigorous physics-based free energy methods. In this work, we show that FEP+, which is a free energy perturbation method based on all-atom molecular dynamics simulations, can provide accurate thermal stability predictions for a wide range of biologically relevant systems. Significantly, the FEP+ approach, while originally developed for relative binding free energies of small molecules to proteins and not specifically fitted for protein stability calculations, performs well compared to other methods that were fitted specifically to predict protein stability. Here, we present the broadest validation of a rigorous free energy-based approach applied to protein stability reported to date: 700+ single-point mutations spanning 10 different protein targets. Across the entire data set, we correctly classify the mutations as stabilizing or destabilizing in 84% of the cases, and obtain statistically significant predictions as compared with experiment [average error of ~1.6kcal/mol and coefficient of determination (R2) of 0.40]. This study demonstrates, for the first time in a large-scale validation, that rigorous free energy calculations can be used to predict changes in protein stability from point mutations without parameterization or system-specific customization, although further improvements should be possible with additional sampling and a better representation of the unfolded state of the protein. Here, we describe the FEP+ method as applied to protein stability calculations, summarize the large-scale retrospective validation results, and discuss limitations of the method, along with future directions for further improvements.

Evaluation of solvation free energies for small molecules with the AMOEBA polarizable force field.

The effects of electronic polarization in biomolecular interactions will differ depending on the local dielectric constant of the environment, such as in solvent, DNA, proteins, and membranes. Here the performance of the AMOEBA polarizable force field is evaluated under nonaqueous conditions by calculating the solvation free energies of small molecules in four common organic solvents. Results are compared with experimental data and equivalent simulations performed with the GAFF pairwise‐additive force field. Although AMOEBA results give mean errors close to “chemical accuracy,” GAFF performs surprisingly well, with statistically significantly more accurate results than AMOEBA in some solvents. However, for both models, free energies calculated in chloroform show worst agreement to experiment and individual solutes are consistently poor performers, suggesting non‐potential‐specific errors also contribute to inaccuracy. Scope for the improvement of both potentials remains limited by the lack of high quality experimental data across multiple solvents, particularly those of high dielectric constant. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Predicting binding poses and affinities for protein - ligand complexes in the 2015 D3R Grand Challenge using a physical model with a statistical parameter estimation.

The 2015 D3R Grand Challenge provided an opportunity to test our new model for the binding free energy of small molecules, as well as to assess our protocol to predict binding poses for protein-ligand complexes. Our pose predictions were ranked 3-9 for the HSP90 dataset, depending on the assessment metric. For the MAP4K dataset the ranks are very dispersed and equal to 2-35, depending on the assessment metric, which does not provide any insight into the accuracy of the method. The main success of our pose prediction protocol was the re-scoring stage using the recently developed Convex-PL potential. We make a thorough analysis of our docking predictions made with AutoDock Vina and discuss the effect of the choice of rigid receptor templates, the number of flexible residues in the binding pocket, the binding pocket size, and the benefits of re-scoring. However, the main challenge was to predict experimentally determined binding affinities for two blind test sets. Our affinity prediction model consisted of two terms, a pairwise-additive enthalpy, and a non pairwise-additive entropy. We trained the free parameters of the model with a regularized regression using affinity and structural data from the PDBBind database. Our model performed very well on the training set, however, failed on the two test sets. We explain the drawback and pitfalls of our model, in particular in terms of relative coverage of the test set by the training set and missed dynamical properties from crystal structures, and discuss different routes to improve it.

Building Water Models: A Different Approach.

Simplified classical water models are currently an indispensable component in practical atomistic simulations. Yet, despite several decades of intense research, these models are still far from perfect. Presented here is an alternative approach to constructing widely used point charge water models. In contrast to the conventional approach, we do not impose any geometry constraints on the model other than the symmetry. Instead, we optimize the distribution of point charges to best describe the “electrostatics” of the water molecule. The resulting “optimal” 3-charge, 4-point rigid water model (OPC) reproduces a comprehensive set of bulk properties significantly more accurately than commonly used rigid models: average error relative to experiment is 0.76%. Close agreement with experiment holds over a wide range of temperatures. The improvements in the proposed model extend beyond bulk properties: compared to common rigid models, predicted hydration free energies of small molecules using OPC are uniformly closer to experiment, with root-mean-square error <1 kcal/mol.

A transferable coarse-grained model for diphenylalanine: How to represent an environment driven conformational transition

One of the major challenges in the development of coarse grained (CG) simulation models that aim at biomolecular structure formation processes is the correct representation of an environment-driven conformational change, for example, a folding/unfolding event upon interaction with an interface or upon aggregation. In the present study, we investigate this transferability challenge for a CG model using the example of diphenylalanine. This dipeptide displays a transition from a trans-like to a cis-like conformation upon aggregation as well as upon transfer from bulk water to the cyclohexane/water interface. Here, we show that one can construct a single CG model that can reproduce both the bulk and interface conformational behavior and the segregation between hydrophobic/hydrophilic medium. While the general strategy to obtain nonbonded interactions in the present CG model is to reproduce solvation free energies of small molecules representing the CG beads in the respective solvents, the success of the model strongly depends on nontrivial decisions one has to make to capture the delicate balance between the bonded and nonbonded interactions. In particular, we found that the peptide's conformational behavior is qualitatively affected by the cyclohexane/water interaction potential, an interaction that does not directly involve the peptide at all but merely influences the properties of the hydrophobic/hydrophilic interface. Furthermore, we show that a small modification to improve the structural/conformational properties of the CG model could dramatically alter the thermodynamic properties.

High-Throughput Prediction of the Hydration Free Energies of Small Molecules from a Classical Density Functional Theory

The classical density functional theory (DFT) is proposed as an efficient computational tool for high-throughput prediction of the solvation free energies of small molecules in liquid water under the ambient condition. With the solute molecules represented by the AMBER force field and the TIP3P model for the solvent, the new theoretical method predicts the hydration free energies of 500 neutral molecules with average unsigned errors of 0.96 and 1.04 kcal/mol in comparison with the experimental and simulation data, respectively. The DFT predictions are orders of magnitude faster than conventional molecular dynamics simulations, and the theoretical performance can be further improved by taking into account the molecular flexibility of large solutes.

High performance computing for drug development on K computer

Massively parallel computations (MP-CAFEE) ware developed to calculate absolute binding free energies of small molecules bound to a protein by all-atom molecular dynamics. It uses the nonequilibrium work measurement and Bennett acceptance ratio methods to calculate the free energy difference between the bound and unbound states. The FUJI force field was developed in order to assign force field parameters to arbitrary organic molecules in a unified manner including proteins and nucleic acids. Its dihedral parameters agree with the torsion energy profiles calculated by high-level ab initio molecular orbital theory for the model systems of protein backbone. Comparing with various force fields it agrees well with recent observations by vibrational spectroscopy on Ramachandran angle's population of alanine dipeptide in water. MP-CAFEE with FUJI force field has an efficient parallel algorithm and enough accuracy for computer aided drug design.

The electrostatic response of water to neutral polar solutes: implications for continuum solvent modeling.

Continuum solvation models are widely used to estimate the hydration free energies of small molecules and proteins, in applications ranging from drug design to protein engineering, and most such models are based on the approximation of a linear dielectric response by the solvent. We used explicit-water molecular dynamics simulations with the TIP3P water model to probe this linear response approximation in the case of neutral polar molecules, using miniature cucurbituril and cyclodextrin receptors and protein side-chain analogs as model systems. We observe supralinear electrostatic solvent responses, and this nonlinearity is found to result primarily from waters' being drawn closer and closer to the solutes with increased solute-solvent electrostatic interactions; i.e., from solute electrostriction. Dielectric saturation and changes in the water-water hydrogen bonding network, on the other hand, play little role. Thus, accounting for solute electrostriction may be a productive approach to improving the accuracy of continuum solvation models.