Predicting hydration free energies using all-atom molecular dynamics simulations and multiple starting conformations

Comparative assessment of physics-based in silico methods to calculate relative solubilities

Relative solubilities, i.e. whether a given molecule is more soluble in one solvent compared to others, is a critical parameter for pharmaceutical and agricultural formulation development and chemical synthesis, material science, and environmental chemistry. In silico predictions of this crucial variable can help reducing experiments, waste of solvents and synthesis optimization. In this study, we evaluate the performance of different physics-based methods for predicting relative solubilities. Our assessment involves quantum mechanics-based COSMO-RS and molecular dynamics-based free energy methods using OPLS4, the open-source OpenFF Sage, and GAFF force fields, spanning over 200 solvent-solute combinations. Our investigation highlights the important role of compound multimerization, an effect which must be accounted for to obtain accurate relative solubility predictions. The performance landscape of these methods is varied, with significant differences in precision depending on both the method used and the solute considered, thereby offering an improved understanding of the predictive power of physics-based methods in chemical research.

Surface Engineering of Migratory Corrosion Inhibitors: Controlling the Wettability of Calcium Silicate Hydrate in the Nanoscale

Migratory corrosion inhibitors (MCIs) are regarded as effective additives to prevent harmful ion transmission and improve concrete durability, but their behavior in the porosity of concrete is still unclarified. This paper proposes a unique perspective to evaluate the effects of surfactant-like MCIs in calcium silicate hydrate (C-S-H) nanoporosity through molecular and electronic structural information. Advanced enhanced sampling methods and perturbation theory methods were applied to evaluate the role of different MCIs. The reduced density gradient of MCI molecules was obtained by using quantum chemical calculations. This calculation is instrumental in elucidating the intensity of interactions among distinct MCI molecule head groups and the C-S-H matrix. It is found that MCIs can effectively improve the interfacial tension (IFT) between C-S-H and water, which corresponds to the inhibitory ability of transmission. Free energy indicates that the MCI has the properties of strong adsorption and weak dissolution, facilitating the improvement of IFT. The relationship between the MCI functional group and the ability of adsorption and dissolution is revealed. This study suggests that MCIs work as surface controllers of C-S-H pores and that their properties can be assessed on the nanoscale.

Understanding Drug Skin Permeation Enhancers Using Molecular Dynamics Simulations

Our skin constitutes an effective permeability barrier that protects the body from exogenous substances but concomitantly severely limits the number of pharmaceutical drugs that can be delivered transdermally. In topical formulation design, chemical permeation enhancers (PEs) are used to increase drug skin permeability. In vitro skin permeability experiments can measure net effects of PEs on transdermal drug transport, but they cannot explain the molecular mechanisms of interactions between drugs, permeation enhancers, and skin structure, which limits the possibility to rationally design better new drug formulations. Here we investigate the effect of the PEs water, lauric acid, geraniol, stearic acid, thymol, ethanol, oleic acid, and eucalyptol on the transdermal transport of metronidazole, caffeine, and naproxen. We use atomistic molecular dynamics (MD) simulations in combination with developed molecular models to calculate the free energy difference between 11 PE-containing formulations and the skin's barrier structure. We then utilize the results to calculate the final concentration of PEs in skin. We obtain an RMSE of 0.58 log units for calculated partition coefficients from water into the barrier structure. We then use the modified PE-containing barrier structure to calculate the PEs' permeability enhancement ratios (ERs) on transdermal metronidazole, caffeine, and naproxen transport and compare with the results obtained from in vitro experiments. We show that MD simulations are able to reproduce rankings based on ERs. However, strict quantitative correlation with experimental data needs further refinement, which is complicated by significant deviations between different measurements. Finally, we propose a model for how to use calculations of the potential of mean force of drugs across the skin's barrier structure in a topical formulation design.

Predicting octanol/water partition coefficients and pKa for the SAMPL7 challenge using the SM12, SM8 and SMD solvation models

Blind predictions of octanol/water partition coefficients and pKa at 298.15 K for 22 drug-like compounds were made for the SAMPL7 challenge. Octanol/water partition coefficients were predicted from solvation free energies computed using electronic structure calculations with the SM12, SM8 and SMD solvation models. Within these calculations we compared the use of gas- and solution-phase optimized geometries of the solute. Based on these calculations we found that in general the use of solution phase-optimized geometries increases the affinity of the solutes for water as compared to octanol, with the use of gas-phase optimized geometries resulting in the better agreement with experiment. The pKa is computed using the direct approach, scaled solvent-accessible surface model, and the inclusion of an explicit water molecule, where the latter two methods have previously been shown to offer improved predictions as compared to the direct approach. We find that the use of an explicit water molecule provides superior predictions, and that the predicted macroscopic pKa is sensitive to the employed microstates.

Best Practices in Constant pH MD Simulations: Accuracy and Sampling

Various approaches have been proposed to include the effect of pH in molecular dynamics (MD) simulations. Among these, the λ-dynamics approach proposed by Brooks and co-workers [Kong, X.; Brooks III, C. L. J. Chem. Phys.1996, 105, 2414−2423] can be performed with little computational overhead and hfor each typeence be used to routinely perform MD simulations at microsecond time scales, as shown in the accompanying paper [Aho, N. et al. J. Chem. Theory Comput.2022, DOI: 10.1021/acs.jctc.2c00516]. At such time scales, however, the accuracy of the molecular mechanics force field and the parametrization becomes critical. Here, we address these issues and provide the community with guidelines on how to set up and perform long time scale constant pH MD simulations. We found that barriers associated with the torsions of side chains in the CHARMM36m force field are too high for reaching convergence in constant pH MD simulations on microsecond time scales. To avoid the high computational cost of extending the sampling, we propose small modifications to the force field to selectively reduce the torsional barriers. We demonstrate that with such modifications we obtain converged distributions of both protonation and torsional degrees of freedom and hence consistent pK_a estimates, while the sampling of the overall configurational space accessible to proteins is unaffected as compared to normal MD simulations. We also show that the results of constant pH MD depend on the accuracy of the correction potentials. While these potentials are typically obtained by fitting a low-order polynomial to calculated free energy profiles, we find that higher order fits are essential to provide accurate and consistent results. By resolving problems in accuracy and sampling, the work described in this and the accompanying paper paves the way to the widespread application of constant pH MD beyond pK_a prediction.

Replica-Exchange Enveloping Distribution Sampling Using Generalized AMBER Force-Field Topologies: Application to Relative Hydration Free-Energy Calculations for Large Sets of Molecules

Free-energy differences between pairs of end-states can be estimated based on molecular dynamics (MD) simulations using standard pathway-dependent methods such as thermodynamic integration (TI), free-energy perturbation, or Bennett’s acceptance ratio. Replica-exchange enveloping distribution sampling (RE-EDS), on the other hand, allows for the sampling of multiple end-states in a single simulation without the specification of any pathways. In this work, we use the RE-EDS method as implemented in GROMOS together with generalized AMBER force-field (GAFF) topologies, converted to a GROMOS-compatible format with a newly developed GROMOS++ program amber2gromos, to compute relative hydration free energies for a series of benzene derivatives. The results obtained with RE-EDS are compared to the experimental data as well as calculated values from the literature. In addition, the estimated free-energy differences in water and in vacuum are compared to values from TI calculations carried out with GROMACS. The hydration free energies obtained using RE-EDS for multiple molecules are found to be in good agreement with both the experimental data and the results calculated using other free-energy methods. While all considered free-energy methods delivered accurate results, the RE-EDS calculations required the least amount of total simulation time. This work serves as a validation for the use of GAFF topologies with the GROMOS simulation package and the RE-EDS approach. Furthermore, the performance of RE-EDS for a large set of 28 end-states is assessed with promising results.

O-Methylation in Carbohydrates: An NMR and MD Simulation Study with Application to Methylcellulose

Methylated carbohydrates are important from both biological and technical perspectives. Specifically, methylcellulose is an interesting cellulose derivative that has applications in foods, materials, cosmetics, and many other fields. While the molecular dynamics simulation technique has the potential for both advancing the fundamental understanding of this polymer and aiding in the development of specific applications, a general drawback is the lack of experimentally validated interaction potentials for the methylated moieties. In the present study, simulations using the GROMOS 56 carbohydrate force field are compared to NMR spin–spin coupling constants related to the conformation of the exocyclic torsion angle ω in d-glucopyranose and derivatives containing a 6-O-methyl substituent and a ¹³C-isotopologue thereof. A ³J_CC Karplus-type relationship is proposed for the C5–C6–O6–C_Me torsion angle. Moreover, solvation free energies are compared to experimental data for small model compounds. Alkylation in the form of 6-O-methylation affects exocyclic torsion only marginally. Computed solvation free energies between nonmethylated and methylated molecules were internally consistent, which validates the application of these interaction potentials for more specialized purposes.

Alkane/Water Partition Coefficient Calculation Based on the Modified AM1 Method and Internal Hydrogen Bonding Sampling Using COSMO-RS

We introduce a physics-based model for calculating partition coefficients of solutes between water and alkanes, using a combination of a semi-empirical method for COSMO charge density calculation and statistical sampling of internal hydrogen bonds (IHBs). We validate the model on the experimental partition data (∼3500 molecules) of small organics, drug-like molecules, and statistical assessment of modeling of proteins and ligand drugs. The model combines two novel algorithms: a bond-correction method for improving the calculation of COSMO charge density from AM1 calculations and a sampling method to deal with IHBs. From a comparison of simulated and experimental partition coefficients, we find a root-mean-square deviation of roughly one log 10 unit. From IHB analysis, we know that IHBs can be present in two states: open (in water) and closed (in apolar solvent). The difference can lead to a shift of as much as two log 10 units per IHB; not taking this effect into account can lead to substantial errors. The method takes a few minutes of calculation time on a single core, per molecule. Although this is still much slower than quantitative structure–activity relationship, it is much faster than molecular simulations and can be readily incorporated into any screening method.

Determining the hydration free energies of selected small molecules with MP2 and local MP2 through adaptive force matching

Force fields for seven small solute molecules, ethanol, 2-methyl-1-propanol, 2-butanol, cyclohexene, tetrahydropyran, 1,4-dioxane, and 1,4-butanediol, in dilute aqueous solutions were created with the adaptive force matching (AFM) method using MP2 or local MP2 as reference. The force fields provide a way to predict the hydration free energies (HFEs) of these molecules with only electronic structure calculations as reference. For six of the seven molecules, the predicted HFEs are in very good agreement with experiments. For 1,4-butanediol, the model created by force matching LMP2 provides a HFE that is too positive. Further investigation suggests that LMP2 may not be sufficiently accurate for computing HFEs for alcohols with AFM. Other properties, such as enthalpy of hydration, diffusion constants, and vibrational spectra, are also computed with the force field developed. The force fields developed by AFM provide a bridge for computing ensemble properties of the reference electronic structure method. With MP2 and LMP2 as reference methods, the computed properties of the small molecular solutes are found to be in good agreement with experiments.

An Approach to Computing Solvent Reorganization Energy

A method for accurate calculation of reorganization free energy of an explicit solvent solvating a solute molecule is presented. The method relies on the knowledge of solvation free energy known either from experimental measurement or from accurate calculation. An important part of this approach lies in the calculation of entropy in solute-solvent interaction free energy using the interaction entropy method, combined with the calculation of enthalpy of solvent reorganization based on a finite number of solvent molecules near the solute molecule. This interaction entropy-solvent reorganization or IESR method enables one to compute both enthalpy and entropy components of the solvent reorganization energy from MD simulation of the solvated system. The calculated results are determined by the molecular force field only without any empirical parameter. The current method is applied to computing the reorganization energies of water solvent solvating a wide range of solute molecules including both hydrophilic and hydrophobic ones. The accuracy of the approach is indirectly verified by the excellent agreement of individual enthalpies and entropies of the solvation energies between theory and experiment.

Best Practices for Alchemical Free Energy Calculations [Article v1.0]

Alchemical free energy calculations are a useful tool for predicting free energy differences associated with the transfer of molecules from one environment to another. The hallmark of these methods is the use of "bridging" potential energy functions representing alchemical intermediate states that cannot exist as real chemical species. The data collected from these bridging alchemical thermodynamic states allows the efficient computation of transfer free energies (or differences in transfer free energies) with orders of magnitude less simulation time than simulating the transfer process directly. While these methods are highly flexible, care must be taken in avoiding common pitfalls to ensure that computed free energy differences can be robust and reproducible for the chosen force field, and that appropriate corrections are included to permit direct comparison with experimental data. In this paper, we review current best practices for several popular application domains of alchemical free energy calculations performed with equilibrium simulations, in particular relative and absolute small molecule binding free energy calculations to biomolecular targets.

Sublimation thermodynamics of nucleobases derived from fast scanning calorimetry

Fast scanning calorimetry was utilized to measure the sublimation thermodynamics of nucleobases. The results were rationalized at the molecular level.

Assessing the Conformational Equilibrium of Carboxylic Acid via Quantum Mechanical and Molecular Dynamics Studies on Acetic Acid

Accurate hydrogen placement in molecular modeling is crucial for studying the interactions and dynamics of biomolecular systems. The carboxyl functional group is a prototypical example of a functional group that requires protonation during structure preparation. To our knowledge, when in their neutral form, carboxylic acids are typically protonated in the syn conformation by default in classical molecular modeling packages, with no consideration of alternative conformations, though we are not aware of any careful examination of this topic. Here, we investigate the general belief that carboxylic acids should always be protonated in the syn conformation. We calculate and compare the relative energetic stabilities of syn and anti acetic acid using ab initio quantum mechanical calculations and atomistic molecular dynamics simulations. We focus on the carboxyl torsional potential and configurations of microhydrated acetic acid from molecular dynamics simulations, probing the effects of solvent, force field (GAFF vs GAFF2), and partial charge assignment of acetic acid. We show that while the syn conformation is the preferred state, the anti state may in some cases also be present under normal NPT conditions in solution.

Challenges in the use of atomistic simulations to predict solubilities of drug-like molecules

Background: Solubility is a physical property of high importance to the pharmaceutical industry, the prediction of which for potential drugs has so far been a hard task. We attempted to predict the solubility of acetylsalicylic acid (ASA) by estimating the absolute chemical potentials of its most stable polymorph and of solutions with different concentrations of the drug molecule. Methods: Chemical potentials were estimated from all-atom molecular dynamics simulations.  We used the Einstein molecule method (EMM) to predict the absolute chemical potential of the solid and solvation free energy calculations to predict the excess chemical potentials of the liquid-phase systems. Results: Reliable estimations of the chemical potentials for the solid and for a single ASA molecule using the EMM required an extremely large number of intermediate states for the free energy calculations, meaning that the calculations were extremely demanding computationally. Despite the computational cost, however, the computed value did not agree well with the experimental value, potentially due to limitations with the underlying energy model. Perhaps better values could be obtained with a better energy model; however, it seems likely computational cost may remain a limiting factor for use of this particular approach to solubility estimation.    Conclusions: Solubility prediction of drug-like solids remains computationally challenging, and it appears that both the underlying energy model and the computational approach applied may need improvement before the approach is suitable for routine use.

Escaping Atom Types in Force Fields Using Direct Chemical Perception

Traditional approaches to specifying a molecular mechanics force field encode all the information needed to assign force field parameters to a given molecule into a discrete set of atom types. This is equivalent to a representation consisting of a molecular graph comprising a set of vertices, which represent atoms labeled by atom type, and unlabeled edges, which represent chemical bonds. Bond stretch, angle bend, and dihedral parameters are then assigned by looking up bonded pairs, triplets, and quartets of atom types in parameter tables to assign valence terms and using the atom types themselves to assign nonbonded parameters. This approach, which we call indirect chemical perception because it operates on the intermediate graph of atom-typed nodes, creates a number of technical problems. For example, atom types must be sufficiently complex to encode all necessary information about the molecular environment, making it difficult to extend force fields encoded this way. Atom typing also results in a proliferation of redundant parameters applied to chemically equivalent classes of valence terms, needlessly increasing force field complexity. Here, we describe a new approach to assigning force field parameters via direct chemical perception. Rather than working through the intermediary of the atom-typed graph, direct chemical perception operates directly on the unmodified chemical graph of the molecule to assign parameters. In particular, parameters are assigned to each type of force field term (e.g., bond stretch, angle bend, torsion, and Lennard-Jones) based on standard chemical substructure queries implemented via the industry-standard SMARTS chemical perception language, using SMIRKS extensions that permit labeling of specific atoms within a chemical pattern. We use this to implement a new force field format, called the SMIRKS Native Open Force Field (SMIRNOFF) format. We demonstrate the power and generality of this approach using examples of specific molecules that pose problems for indirect chemical perception and construct and validate a minimalist yet very general force field, SMIRNOFF99Frosst. We find that a parameter definition file only ∼300 lines long provides coverage of all but <0.02% of a 5 million molecule drug-like test set. Despite its simplicity, the accuracy of SMIRNOFF99Frosst for small molecule hydration free energies and selected properties of pure organic liquids is similar to that of the General Amber Force Field, whose specification requires thousands of parameters. This force field provides a starting point for further optimization and refitting work to follow.

Reproducibility of Free Energy Calculations across Different Molecular Simulation Software Packages

Alchemical free energy calculations are an increasingly important modern simulation technique to calculate free energy changes on binding or solvation. Contemporary molecular simulation software such as AMBER, CHARMM, GROMACS, and SOMD include support for the method. Implementation details vary among those codes, but users expect reliability and reproducibility, i.e., for a given molecular model and set of force field parameters, comparable free energy differences should be obtained within statistical bounds regardless of the code used. Relative alchemical free energy (RAFE) simulation is increasingly used to support molecule discovery projects, yet the reproducibility of the methodology has been less well tested than its absolute counterpart. Here we present RAFE calculations of hydration free energies for a set of small organic molecules and demonstrate that free energies can be reproduced to within about 0.2 kcal/mol with the aforementioned codes. Absolute alchemical free energy simulations have been carried out as a reference. Achieving this level of reproducibility requires considerable attention to detail and package-specific simulation protocols, and no universally applicable protocol emerges. The benchmarks and protocols reported here should be useful for the community to validate new and future versions of software for free energy calculations.

A Comparison of QM/MM Simulations with and without the Drude Oscillator Model Based on Hydration Free Energies of Simple Solutes

Maintaining a proper balance between specific intermolecular interactions and non-specific solvent interactions is of critical importance in molecular simulations, especially when predicting binding affinities or reaction rates in the condensed phase. The most rigorous metric for characterizing solvent affinity are solvation free energies, which correspond to a transfer from the gas phase into solution. Due to the drastic change of the electrostatic environment during this process, it is also a stringent test of polarization response in the model. Here, we employ both the CHARMM fixed charge and polarizable force fields to predict hydration free energies of twelve simple solutes. The resulting classical ensembles are then reweighted to obtain QM/MM hydration free energies using a variety of QM methods, including MP2, Hartree⁻Fock, density functional methods (BLYP, B3LYP, M06-2X) and semi-empirical methods (OM2 and AM1 ). Our simulations test the compatibility of quantum-mechanical methods with molecular-mechanical water models and solute Lennard⁻Jones parameters. In all cases, the resulting QM/MM hydration free energies were inferior to purely classical results, with the QM/MM Drude force field predictions being only marginally better than the QM/MM fixed charge results. In addition, the QM/MM results for different quantum methods are highly divergent, with almost inverted trends for polarizable and fixed charge water models. While this does not necessarily imply deficiencies in the QM models themselves, it underscores the need to develop consistent and balanced QM/MM interactions. Both the QM and the MM component of a QM/MM simulation have to match, in order to avoid artifacts due to biased solute⁻solvent interactions. Finally, we discuss strategies to improve the convergence and efficiency of multi-scale free energy simulations by automatically adapting the molecular-mechanics force field to the target quantum method.

High accuracy quantum-chemistry-based calculation and blind prediction of macroscopic pKa values in the context of the SAMPL6 challenge

Recent advances in the development of low-cost quantum chemical methods have made the prediction of conformational preferences and physicochemical properties of medium-sized drug-like molecules routinely feasible, with significant potential to advance drug discovery. In the context of the SAMPL6 challenge, macroscopic pKa values were blindly predicted for a set of 24 of such molecules. In this paper we present two similar quantum chemical based approaches based on the high accuracy calculation of standard reaction free energies and the subsequent determination of those pKa values via a linear free energy relationship. Both approaches use extensive conformational sampling and apply hybrid and double-hybrid density functional theory with continuum solvation to calculate free energies. The blindly calculated macroscopic pKa values were in excellent agreement with the experiment.

Biosolvation Nature of Ionic Liquids: Molecular Dynamics Simulation of Methylated Nucleobases in Hydrated 1-Ethyl-3-methylimidazolium Acetate

Solvation free energies of methylated nucleobases were calculated in pure and hydrated 1-ethyl-3-methylimidazolium acetate, [Emim][Ac], ionic liquid, and pure water using classical molecular dynamics simulations using multistate Bennett's acceptance ratio method. The calculated solvation free energies in pure water were compared with the previous experimental and theoretical findings and found to be in agreement. We observe that the solvation free energy of methylated nucleobases is more in the pure ionic liquid compared to that in the pure water and on changing the mole fraction of water in the ionic liquid, the solvation free energy decreases gradually. Comparing the Coulombic and van der Waals contribution to the solvation free energy, electrostatic contribution is more compared to that of the latter for all nucleobases. To obtain the atomistic details and explain the solvation mechanism, we calculated radial distribution functions (RDFs), spatial distribution functions (SDFs), and stacking angle distribution of cations to the nucleobases. From RDFs and SDFs, we find that the acetate anions of the ionic liquid are forming strong hydrogen bonds with the amine hydrogen atoms of the nucleobases. These hydrogen bonds contribute to the major part of the Coulombic contribution to the solvation free energy. Stacking of cations to the nucleobases is primarily due to the van der Waals contribution to the solvation free energy.

1-Butanol as a Solvent for Efficient Extraction of Polar Compounds from Aqueous Medium: Theoretical and Practical Aspects

The extraction of polar molecules from aqueous solution is a challenging task in organic synthesis. 1-Butanol has been used sporadically as an eluent for polar molecules, but it is unclear which molecular features drive its efficiency. Here, we employ free energy simulations to study the partitioning of 15 solutes between water and 1-butanol. The simulations demonstrate that the high affinity of polar molecules to the wet 1-butanol phase is associated with its nanostructure. Small inverse micelles of water are able to accommodate polar solutes and locally mimic an aqueous environment. We verify the simulations based on partition coefficients between water and 1-octanol, and include a blind prediction of the water/1-butanol partition coefficient of cyclohexane-1,2-diol. The calculations are in excellent agreement with experiment, reaching root-mean-square deviations below 0.7 kcal/mol. Actual extractions of cyclohexane-1,2-diol from buffer solutions that mimic cell lysates and suspensions in biocatalytic reactions further exemplify our findings. The yields highlight that extractions with 1-butanol can be significantly more efficient than the conventional protocol based on ethyl acetate.

Approaches for calculating solvation free energies and enthalpies demonstrated with an update of the FreeSolv database

Solvation free energies can now be calculated precisely from molecular simulations, providing a valuable test of the energy functions underlying these simulations. Here, we briefly review "alchemical" approaches for calculating the solvation free energies of small, neutral organic molecules from molecular simulations, and illustrate by applying them to calculate aqueous solvation free energies (hydration free energies). These approaches use a non-physical pathway to compute free energy differences from a simulation or set of simulations and appear to be a particularly robust and general-purpose approach for this task. We also present an update (version 0.5) to our FreeSolv database of experimental and calculated hydration free energies of neutral compounds and provide input files in formats for several simulation packages. This revision to FreeSolv provides calculated values generated with a single protocol and software version, rather than the heterogeneous protocols used in the prior version of the database. We also further update the database to provide calculated enthalpies and entropies of hydration and some experimental enthalpies and entropies, as well as electrostatic and nonpolar components of solvation free energies.

Bayesian Model Averaging for Ensemble-Based Estimates of Solvation-Free Energies

This paper applies the Bayesian Model Averaging statistical ensemble technique to estimate small molecule solvation free energies. There is a wide range of methods available for predicting solvation free energies, ranging from empirical statistical models to ab initio quantum mechanical approaches. Each of these methods is based on a set of conceptual assumptions that can affect predictive accuracy and transferability. Using an iterative statistical process, we have selected and combined solvation energy estimates using an ensemble of 17 diverse methods from the fourth Statistical Assessment of Modeling of Proteins and Ligands (SAMPL) blind prediction study to form a single, aggregated solvation energy estimate. Methods that possess minimal or redundant information are pruned from the ensemble and the evaluation process repeats until aggregate predictive performance can no longer be improved. We show that this process results in a final aggregate estimate that outperforms all individual methods by reducing estimate errors by as much as 91% to 1.2 kcal mol^-1 accuracy. This work provides a new approach for accurate solvation free energy prediction and lays the foundation for future work on aggregate models that can balance computational cost with prediction accuracy.

Blind prediction of cyclohexane-water distribution coefficients from the SAMPL5 challenge

In the recent SAMPL5 challenge, participants submitted predictions for cyclohexane/water distribution coefficients for a set of 53 small molecules. Distribution coefficients (log D) replace the hydration free energies that were a central part of the past five SAMPL challenges. A wide variety of computational methods were represented by the 76 submissions from 18 participating groups. Here, we analyze submissions by a variety of error metrics and provide details for a number of reference calculations we performed. As in the SAMPL4 challenge, we assessed the ability of participants to evaluate not just their statistical uncertainty, but their model uncertainty-how well they can predict the magnitude of their model or force field error for specific predictions. Unfortunately, this remains an area where prediction and analysis need improvement. In SAMPL4 the top performing submissions achieved a root-mean-squared error (RMSE) around 1.5 kcal/mol. If we anticipate accuracy in log D predictions to be similar to the hydration free energy predictions in SAMPL4, the expected error here would be around 1.54 log units. Only a few submissions had an RMSE below 2.5 log units in their predicted log D values. However, distribution coefficients introduced complexities not present in past SAMPL challenges, including tautomer enumeration, that are likely to be important in predicting biomolecular properties of interest to drug discovery, therefore some decrease in accuracy would be expected. Overall, the SAMPL5 distribution coefficient challenge provided great insight into the importance of modeling a variety of physical effects. We believe these types of measurements will be a promising source of data for future blind challenges, especially in view of the relatively straightforward nature of the experiments and the level of insight provided.

Calculating distribution coefficients based on multi-scale free energy simulations: an evaluation of MM and QM/MM explicit solvent simulations of water-cyclohexane transfer in the SAMPL5 challenge

One of the central aspects of biomolecular recognition is the hydrophobic effect, which is experimentally evaluated by measuring the distribution coefficients of compounds between polar and apolar phases. We use our predictions of the distribution coefficients between water and cyclohexane from the SAMPL5 challenge to estimate the hydrophobicity of different explicit solvent simulation techniques. Based on molecular dynamics trajectories with the CHARMM General Force Field, we compare pure molecular mechanics (MM) with quantum-mechanical (QM) calculations based on QM/MM schemes that treat the solvent at the MM level. We perform QM/MM with both density functional theory (BLYP) and semi-empirical methods (OM1, OM2, OM3, PM3). The calculations also serve to test the sensitivity of partition coefficients to solute polarizability as well as the interplay of the quantum-mechanical region with the fixed-charge molecular mechanics environment. Our results indicate that QM/MM with both BLYP and OM2 outperforms pure MM. However, this observation is limited to a subset of cases where convergence of the free energy can be achieved.

An efficient protocol for obtaining accurate hydration free energies using quantum chemistry and reweighting from molecular dynamics simulations

The non-Boltzmann Bennett (NBB) free energy estimator method is applied to 21 molecules from the blind subset of the SAMPL4 challenge. When NBB is applied with the SMD implicit solvent model, and the OLYP/DZP level of quantum chemistry, highly accurate hydration free energy calculations are obtained with respect to experiment (RMSD=0.89kcal·mol^-1). Other quantum chemical methods are also tested, and the effects of solvent model, density functional, basis set are explored in this benchmarking study, providing a framework for improvements in calculating hydration free energies. We provide a practical guide for using the best QM-NBB protocols that are consistently more accurate than either pure QM or pure MM alone. In situations where high accuracy hydration free energy predictions are needed, the QM-NBB method with SMD implicit solvent should be the first choice of quantum chemists.

Calculating Partition Coefficients of Small Molecules in Octanol/Water and Cyclohexane/Water

Partition coefficients describe how a solute is distributed between two immiscible solvents. They are used in drug design as a measure of a solute's hydrophobicity and a proxy for its membrane permeability. We calculate partition coefficients from transfer free energies using molecular dynamics simulations in explicit solvent. Setup is done by our new Solvation Toolkit which automates the process of creating input files for any combination of solutes and solvents for many popular molecular dynamics software packages. We calculate partition coefficients between octanol/water and cyclohexane/water with the Generalized AMBER Force Field (GAFF) and the Dielectric Corrected GAFF (GAFF-DC). With similar methods in the past we found a root-mean-squared error (RMSE) of 6.3 kJ/mol in hydration free energies which would correspond to an error of around 1.6 log units in partition coefficients if solvation free energies in both solvents were estimated with comparable accuracy. Here we find an overall RMSE of about 1.2 log units with both force fields. Results from GAFF and GAFF-DC seem to exhibit systematic biases in opposite directions for calculated cyclohexane/water partition coefficients.

KECSA-Movable Type Implicit Solvation Model (KMTISM)

Computation of the solvation free energy for chemical and biological processes has long been of significant interest. The key challenges to effective solvation modeling center on the choice of potential function and configurational sampling. Herein, an energy sampling approach termed the “Movable Type” (MT) method, and a statistical energy function for solvation modeling, “Knowledge-based and Empirical Combined Scoring Algorithm” (KECSA) are developed and utilized to create an implicit solvation model: KECSA-Movable Type Implicit Solvation Model (KMTISM) suitable for the study of chemical and biological systems. KMTISM is an implicit solvation model, but the MT method performs energy sampling at the atom pairwise level. For a specific molecular system, the MT method collects energies from prebuilt databases for the requisite atom pairs at all relevant distance ranges, which by its very construction encodes all possible molecular configurations simultaneously. Unlike traditional statistical energy functions, KECSA converts structural statistical information into categorized atom pairwise interaction energies as a function of the radial distance instead of a mean force energy function. Within the implicit solvent model approximation, aqueous solvation free energies are then obtained from the NVT ensemble partition function generated by the MT method. Validation is performed against several subsets selected from the Minnesota Solvation Database v2012. Results are compared with several solvation free energy calculation methods, including a one-to-one comparison against two commonly used classical implicit solvation models: MM-GBSA and MM-PBSA. Comparison against a quantum mechanics based polarizable continuum model is also discussed (Cramer and Truhlar’s Solvation Model 12).

Comparison of Methods To Reweight from Classical Molecular Simulations to QM/MM Potentials

We examine methods to reweight classical molecular mechanics solvation calculations to more expensive QM/MM energy functions. We first consider the solvation free energy difference between ethane and methanol in a QM/MM Hamiltonian from configurations generated in a cheaper MM potential. The solute molecules in the QM/MM Hamiltonian are treated with B3LYP/6-31G*, and the solvent water molecules are treated classically. The free energy difference in the QM/MM Hamiltonian is estimated using Boltzmann reweighting with both the non-Boltzmann Bennett method (NBB) and the multistate Bennett acceptance ratio (MBAR), and the variance of each method is directly compared for an identical data set. For this system, MBAR-derived methods are found to produce smaller overall uncertainties than NBB-based methods. Additionally, we show that to reduce the variance in the overall free energy difference estimate in this system for a fixed amount of QM/MM calculations, the energy re-evaluations in the Boltzmann reweighting step should be concentrated on the physical MM states with the highest overlap to the QM/MM states, rather than allocated equally over all sampled MM states. We also show that reallocating the QM/MM re-evaluations can be used to diagnose poor overlap between the sampled and target state. The solvation free energies for molecules in the SAMPL4 solvation data set are also calculated in the QM/MM Hamiltonian with NBB and MBAR, and the variances are marginally smaller for MBAR. Overall, NBB and MBAR produce similar variances for systems with poor sampling efficiency, and MBAR provides smaller variances than NBB in systems with high sampling efficiency. Both NBB and MBAR converge to identical solvation free energy estimates in the QM/MM Hamiltonian, and the RMSD to experimental values for molecules in the SAMPL4 solvation data set decreases by approximately 28% when switching from the MM Hamiltonian to the QM/MM Hamiltonian.

Using MD Simulations To Calculate How Solvents Modulate Solubility

Here, our interest is in predicting solubility in general, and we focus particularly on predicting how the solubility of particular solutes is modulated by the solvent environment. Solubility in general is extremely important, both for theoretical reasons - it provides an important probe of the balance between solute-solute and solute-solvent interactions - and for more practical reasons, such as how to control the solubility of a given solute via modulation of its environment, as in process chemistry and separations. Here, we study how the change of solvent affects the solubility of a given compound. That is, we calculate relative solubilities. We use MD simulations to calculate relative solubility and compare our calculated values with experiment as well as with results from several other methods, SMD and UNIFAC, the latter of which is commonly used in chemical engineering design. We find that straightforward solubility calculations based on molecular simulations using a general small-molecule force field outperform SMD and UNIFAC both in terms of accuracy and coverage of the relevant chemical space.

Free Energy Calculations using a Swarm-Enhanced Sampling Molecular Dynamics Approach

Free energy simulations are an established computational tool in modelling chemical change in the condensed phase. However, sampling of kinetically distinct substates remains a challenge to these approaches. As a route to addressing this, we link the methods of thermodynamic integration (TI) and swarm-enhanced sampling molecular dynamics (sesMD), where simulation replicas interact cooperatively to aid transitions over energy barriers. We illustrate the approach by using alchemical alkane transformations in solution, comparing them with the multiple independent trajectory TI (IT-TI) method. Free energy changes for transitions computed by using IT-TI grew increasingly inaccurate as the intramolecular barrier was heightened. By contrast, swarm-enhanced sampling TI (sesTI) calculations showed clear improvements in sampling efficiency, leading to more accurate computed free energy differences, even in the case of the highest barrier height. The sesTI approach, therefore, has potential in addressing chemical change in systems where conformations exist in slow exchange.

Is ring breaking feasible in relative binding free energy calculations?

Our interest is relative binding free energy (RBFE) calculations based on molecular simulations. These are promising tools for lead optimization in drug discovery, computing changes in binding free energy due to modifications of a lead compound. However, in the "alchemical" framework for RBFE calculations, some types of mutations have the potential to introduce error into the computed binding free energies. Here we explore the magnitude of this error in several different model binding calculations. We find that some of the calculations involving ring breaking have significant errors, and these errors are especially large in bridged ring systems. Since the error is a function of ligand strain, which is unpredictable in advance, we believe that ring breaking should be avoided when possible.

Guidelines for the analysis of free energy calculations

Free energy calculations based on molecular dynamics simulations show considerable promise for applications ranging from drug discovery to prediction of physical properties and structure-function studies. But these calculations are still difficult and tedious to analyze, and best practices for analysis are not well defined or propagated. Essentially, each group analyzing these calculations needs to decide how to conduct the analysis and, usually, develop its own analysis tools. Here, we review and recommend best practices for analysis yielding reliable free energies from molecular simulations. Additionally, we provide a Python tool, alchemical-analysis.py, freely available on GitHub as part of the pymbar package (located at http://github.com/choderalab/pymbar), that implements the analysis practices reviewed here for several reference simulation packages, which can be adapted to handle data from other packages. Both this review and the tool covers analysis of alchemical calculations generally, including free energy estimates via both thermodynamic integration and free energy perturbation-based estimators. Our Python tool also handles output from multiple types of free energy calculations, including expanded ensemble and Hamiltonian replica exchange, as well as standard fixed ensemble calculations. We also survey a range of statistical and graphical ways of assessing the quality of the data and free energy estimates, and provide prototypes of these in our tool. We hope this tool and discussion will serve as a foundation for more standardization of and agreement on best practices for analysis of free energy calculations.

Solution Properties of Hemicellulose Polysaccharides with Four Common Carbohydrate Force Fields

Hemicellulose polysaccharides play an important role in the swelling behavior of the primary plant cell wall, and molecular dynamics simulations provide the means of gaining a concise understanding of the interactions of hemicellulose polysaccharides with water. Here, we compare four of the main polysaccharide force fields (CHARMM36 TIP3P, GROMOS56A6(CARBO) SPC, GLYCAM06h TIP3P, and GLYCAM06h TIP5P) for the most abundant hemicellulose backbone components. In particular, we compare aggregation, diffusion coefficients, system density, and investigate the free energy of hydration of saccharides in water. We find that the saccharides show nonphysical aggregation at low concentrations with the GLYCAM06h TIP3P force field, which can be rectified by the use of the TIP5P water model. As a result of the aggregation, GLYCAM06h TIP3P does not lead to reasonable diffusion coefficients whereas the diffusion coefficients, as well as the system density, agrees best with experimental data for the GLYCAM06h TIP5P force field. Overall, GLYCAM06h TIP5P gives good agreement with experimental free energy of hydration data for small saccharides. In addition, the free energy of hydration for short polysaccharides calculated with the GLYCAM06h TIP5P force field is consistent with the radial distribution functions between the polysaccharides and water, the hydration number of the polysaccharides, and the hydrogen bonds formed in the system.

Predicting the excess solubility of acetanilide, acetaminophen, phenacetin, benzocaine, and caffeine in binary water/ethanol mixtures via molecular simulation

We present a general framework to predict the excess solubility of small molecular solids (such as pharmaceutical solids) in binary solvents via molecular simulation free energy calculations at infinite dilution with conventional molecular models. The present study used molecular dynamics with the General AMBER Force Field to predict the excess solubility of acetanilide, acetaminophen, phenacetin, benzocaine, and caffeine in binary water/ethanol solvents. The simulations are able to predict the existence of solubility enhancement and the results are in good agreement with available experimental data. The accuracy of the predictions in addition to the generality of the method suggests that molecular simulations may be a valuable design tool for solvent selection in drug development processes.

Bridging Calorimetry and Simulation through Precise Calculations of Cucurbituril-Guest Binding Enthalpies

We used microsecond time scale molecular dynamics simulations to compute, at high precision, binding enthalpies for cucurbit[7]uril (CB7) with eight guests in aqueous solution. The results correlate well with experimental data from previously published isothermal titration calorimetry studies, and decomposition of the computed binding enthalpies by interaction type provides plausible mechanistic insights. Thus, dispersion interactions appear to play a key role in stabilizing these complexes, due at least in part to the fact that their packing density is greater than that of water. On the other hand, strongly favorable Coulombic interactions between the host and guests are compensated by unfavorable solvent contributions, leaving relatively modest electrostatic contributions to the binding enthalpies. The better steric fit of the aliphatic guests into the circular host appears to explain why their binding enthalpies tend to be more favorable than those of the more planar aromatic guests. The present calculations also bear on the validity of the simulation force field. Somewhat unexpectedly, the TIP3P water yields better agreement with experiment than the TIP4P-Ew water model, although the latter is known to replicate the properties of pure water more accurately. More broadly, the present results demonstrate the potential for computational calorimetry to provide atomistic explanations for thermodynamic observations.

Origin of parameter degeneracy and molecular shape relationships in geometric-flow calculations of solvation free energies

Implicit solvent models are important tools for calculating solvation free energies for chemical and biophysical studies since they require fewer computational resources but can achieve accuracy comparable to that of explicit-solvent models. In past papers, geometric flow-based solvation models have been established for solvation analysis of small and large compounds. In the present work, the use of realistic experiment-based parameter choices for the geometric flow models is studied. We find that the experimental parameters of solvent internal pressure p = 172 MPa and surface tension γ = 72 mN/m produce solvation free energies within 1 RT of the global minimum root-mean-squared deviation from experimental data over the expanded set. Our results demonstrate that experimental values can be used for geometric flow solvent model parameters, thus eliminating the need for additional parameterization. We also examine the correlations between optimal values of p and γ which are strongly anti-correlated. Geometric analysis of the small molecule test set shows that these results are inter-connected with an approximately linear relationship between area and volume in the range of molecular sizes spanned by the data set. In spite of this considerable degeneracy between the surface tension and pressure terms in the model, both terms are important for the broader applicability of the model.

FreeSolv: a database of experimental and calculated hydration free energies, with input files

This work provides a curated database of experimental and calculated hydration free energies for small neutral molecules in water, along with molecular structures, input files, references, and annotations. We call this the Free Solvation Database, or FreeSolv. Experimental values were taken from prior literature and will continue to be curated, with updated experimental references and data added as they become available. Calculated values are based on alchemical free energy calculations using molecular dynamics simulations. These used the GAFF small molecule force field in TIP3P water with AM1-BCC charges. Values were calculated with the GROMACS simulation package, with full details given in references cited within the database itself. This database builds in part on a previous, 504-molecule database containing similar information. However, additional curation of both experimental data and calculated values has been done here, and the total number of molecules is now up to 643. Additional information is now included in the database, such as SMILES strings, PubChem compound IDs, accurate reference DOIs, and others. One version of the database is provided in the Supporting Information of this article, but as ongoing updates are envisioned, the database is now versioned and hosted online. In addition to providing the database, this work describes its construction process. The database is available free-of-charge via http://www.escholarship.org/uc/item/6sd403pz .

FreeSolv: a database of experimental and calculated hydration free energies, with input files

This work provides a curated database of experimental and calculated hydration free energies for small neutral molecules in water, along with molecular structures, input files, references, and annotations. We call this the Free Solvation Database, or FreeSolv. Experimental values were taken from prior literature and will continue to be curated, with updated experimental references and data added as they become available. Calculated values are based on alchemical free energy calculations using molecular dynamics simulations. These used the GAFF small molecule force field in TIP3P water with AM1-BCC charges. Values were calculated with the GROMACS simulation package, with full details given in references cited within the database itself. This database builds in part on a previous, 504-molecule database containing similar information. However, additional curation of both experimental data and calculated values has been done here, and the total number of molecules is now up to 643. Additional information is now included in the database, such as SMILES strings, PubChem compound IDs, accurate reference DOIs, and others. One version of the database is provided in the Supporting Information of this article, but as ongoing updates are envisioned, the database is now versioned and hosted online. In addition to providing the database, this work describes its construction process. The database is available free-of-charge via http://www.escholarship.org/uc/item/6sd403pz .