Prediction of hydration free energies for the SAMPL4 diverse set of compounds using molecular dynamics simulations with the OPLS-AA force field

All-atom molecular dynamics computer simulations were used to blindly predict the hydration free energies of a range of small molecules as part of the SAMPL4 challenge. Compounds were parametrized on the basis of the OPLS-AA force field using three different protocols for deriving partial charges: (1) using existing OPLS-AA atom types and charges with minor adjustments of partial charges on equivalent connecting atoms and derivation of new parameters for a number of distinct chemical groups (N-alkyl imidazole, nitrate) that were not present in the published force field; (2) calculation of quantum mechanical charges via geometry optimization, followed by electrostatic potential (ESP) fitting, using Jaguar at the LMP2/cc-pVTZ(-F) level; and (3) via geometry optimization and CHelpG charges (Gaussian09 at the HF/6-31G* level), followed by two-stage RESP fitting. The absolute hydration free energy was computed by an established protocol including alchemical free energy perturbation with thermodynamic integration. The use of standard OPLS-AA charges (protocol 1) with a number of newly parametrized charges and the use of histidine derived parameters for imidazole yielded an overall root mean square deviation of the prediction from the experimental data of 1.75 kcal/mol. The precision of our results appears to be mainly limited by relatively poor reproducibility of the Lennard-Jones contribution towards the solvation free energy, for which we observed large variability that could be traced to a strong dependence on the initial system conditions.     

Absolute binding free energy calculations of CBClip host–guest systems in the SAMPL5 blind challenge

Herein, we report the absolute binding free energy calculations of CBClip complexes in the SAMPL5 blind challenge. Initial conformations of CBClip complexes were obtained using docking and molecular dynamics simulations. Free energy calculations were performed using thermodynamic integration (TI) with soft-core potentials and Bennett’s acceptance ratio (BAR) method based on a serial insertion scheme. We compared the results obtained with TI simulations with soft-core potentials and Hamiltonian replica exchange simulations with the serial insertion method combined with the BAR method. The results show that the difference between the two methods can be mainly attributed to the van der Waals free energies, suggesting that either the simulations used for TI or the simulations used for BAR, or both are not fully converged and the two sets of simulations may have sampled difference phase space regions. The penalty scores of force field parameters of the 10 guest molecules provided by CHARMM Generalized Force Field can be an indicator of the accuracy of binding free energy calculations. Among our submissions, the combination of docking and TI performed best, which yielded the root mean square deviation of 2.94 kcal/mol and an average unsigned error of 3.41 kcal/mol for the ten guest molecules. These values were best overall among all participants. However, our submissions had little correlation with experiments.     

Blind prediction of solvation free energies from the SAMPL4 challenge

Here, we give an overview of the small molecule hydration portion of the SAMPL4 challenge, which focused on predicting hydration free energies for a series of 47 small molecules. These gas-to-water transfer free energies have in the past proven a valuable test of a variety of computational methods and force fields. Here, in contrast to some previous SAMPL challenges, we find a relatively wide range of methods perform quite well on this test set, with RMS errors in the 1.2 kcal/mol range for several of the best performing methods. Top-performers included a quantum mechanical approach with continuum solvent models and functional group corrections, alchemical molecular dynamics simulations with a classical all-atom force field, and a single-conformation Poisson–Boltzmann approach. While 1.2 kcal/mol is still a significant error, experimental hydration free energies covered a range of nearly 20 kcal/mol, so methods typically showed substantial predictive power. Here, a substantial new focus was on evaluation of error estimates, as predicting when a computational prediction is reliable versus unreliable has considerable practical value. We found, however, that in many cases errors are substantially underestimated, and that typically little effort has been invested in estimating likely error. We believe this is an important area for further research.     

Extended solvent-contact model approach to SAMPL4 blind prediction challenge for hydration free energies

Extended solvent-contact model was applied to the blind prediction of the hydration free energies of 47 organic molecules included in the SAMPL4 data set. To obtain a suitable prediction tool, we constructed a hydration free energy function involving three kinds of atomic parameters. With respect to total 34 atom types introduced to describe all SAMPL4 molecules, 102 atomic parameters were defined and optimized with a standard genetic algorithm in such a way to minimize the difference between the experimental hydration free energies and those calculated with the hydration free energy function. In this parameterization, we used a training set comprising 77 organic molecules with varying sizes and shapes. The estimated hydration free energies for the SAMPL4 molecules compared reasonably well with the experimental results with the associated squared correlation coefficient and root mean square deviation of 0.89 and 1.46 kcal/mol, respectively. Based on the comparative analysis of experimental and computational hydration free energies of the SAMPL4 molecules, the methods for further improvement of the present hydration model are suggested.     

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

Molecular dynamics simulations in explicit solvent were applied to predict the hydration free energies for 23 small organic molecules in blind SAMPL2 test. We found good agreement with experimental results, with an RMS error of 2.82 kcal/mol over the whole set and 1.86 kcal/mol over all the molecules except several hydroxyl-rich compounds where we find evidence for a systematic error in the force field. We tested two different solvent models, TIP3P and TIP4P-Ew, and obtained very similar hydration free energies for these two models; the RMS difference was 0.64 kcal/mol. We found that preferred conformation of the carboxylic acids in water differs from that in vacuum. Surprisingly, this conformational change is not adequately sampled on simulation timescales, so we apply an umbrella sampling technique to include free energies associated with the conformational change. Overall, the results of this test reveal that the force field parameters for some groups of molecules (such as hydroxyl-rich compounds) still need to be improved, but for most compounds, accuracy was consistent with that seen in our previous tests.     

Predicting hydration free energies with a hybrid QM/MM approach: an evaluation of implicit and explicit solvation models in SAMPL4

The correct representation of solute-water interactions is essential for the accurate simulation of most biological phenomena. Several highly accurate quantum methods are available to deal with solvation by using both implicit and explicit solvents. So far, however, most evaluations of those methods were based on a single conformation, which neglects solute entropy. Here, we present the first test of a novel approach to determine hydration free energies that uses molecular mechanics (MM) to sample phase space and quantum mechanics (QM) to evaluate the potential energies. Free energies are determined by using re-weighting with the Non-Boltzmann Bennett (NBB) method. In this context, the method is referred to as QM-NBB. Based on snapshots from MM sampling and accounting for their correct Boltzmann weight, it is possible to obtain hydration free energies that incorporate the effect of solute entropy. We evaluate the performance of several QM implicit solvent models, as well as explicit solvent QM/MM for the blind subset of the SAMPL4 hydration free energy challenge. While classical free energy simulations with molecular dynamics give root mean square deviations (RMSD) of 2.8 and 2.3 kcal/mol, the hybrid approach yields an improved RMSD of 1.6 kcal/mol. By selecting an appropriate functional and basis set, the RMSD can be reduced to 1 kcal/mol for calculations based on a single conformation. Results for a selected set of challenging molecules imply that this RMSD can be further reduced by using NBB to reweight MM trajectories with the SMD implicit solvent model.     

All-atom/coarse-grained hybrid predictions of distribution coefficients in SAMPL5

We present blind predictions submitted to the SAMPL5 challenge on calculating distribution coefficients. The predictions were based on estimating the solvation free energies in water and cyclohexane of the 53 compounds in the challenge. These free energies were computed using alchemical free energy simulations based on a hybrid all-atom/coarse-grained model. The compounds were treated with the general Amber force field, whereas the solvent molecules were treated with the Elba coarse-grained model. Considering the simplicity of the solvent model and that we approximate the distribution coefficient with the partition coefficient of the neutral species, the predictions are of good accuracy. The correlation coefficient, R is 0.64, 82 % of the predictions have the correct sign and the mean absolute deviation is 1.8 log units. This is on a par with or better than the other simulation-based predictions in the challenge. We present an analysis of the deviations to experiments and compare the predictions to another submission that used all-atom solvent.     

Comparison of two simulation methods to compute solvation free energies and partition coefficients

The thermodynamic integration (TI) and expanded ensemble (EE) methods are used here to calculate the hydration free energy in water, the solvation free energy in 1‐octanol, and the octanol‐water partition coefficient for a six compounds of varying functionality using the optimized potentials for liquid simulations (OPLS) all‐atom (AA) force field parameters and atomic charges. Both methods use the molecular dynamics algorithm as a primary component of the simulation protocol, and both have found wide applications in fields such as the calculation of activity coefficients, phase behavior, and partition coefficients. Both methods result in solvation free energies and 1‐octanol/water partition coefficients with average absolute deviations (AAD) from experimental data to within 4 kJ/mol and 0.5 log units, respectively. Here, we find that in simulations the OPLS‐AA force field parameters (with fixed charges) can reproduce solvation free energies of solutes in 1‐octanol with AAD of about half that for the solute hydration free energies using a extended simple point charge (SPC/E) model of water. The computational efficiency of the two simulation methods are compared based on the time (in nanoseconds) required to obtain similar standard deviations in the solvation free energies and 1‐octanol/water partition coefficients. By this analysis, the EE method is found to be a factor of nine more efficient than the TI algorithm. For both methods, solvation free energy calculations in 1‐octanol consume roughly an order of magnitude more CPU hours than the hydration free energy calculations. © 2012 Wiley Periodicals, Inc.     

Box size effects are negligible for solvation free energies of neutral solutes

Hydration free energy calculations in explicit solvent have become an integral part of binding free energy calculations and a valuable test of force fields. Most of these simulations follow the conventional norm of keeping edge length of the periodic solvent box larger than twice the Lennard-Jones (LJ) cutoff distance, with the rationale that this should be sufficient to keep the interactions between copies of the solute to a minimum. However, for charged solutes, hydration free energies can exhibit substantial box size-dependence even at typical box sizes. Here, we examine whether similar size-dependence affects hydration of neutral molecules. Thus, we focused on two strongly polar molecules with large dipole moments, where any size-dependence should be most pronounced, and determined how their hydration free energies vary as a function of simulation box size. In addition to testing a variety of simulation box sizes, we also tested two LJ cut-off distances, 0.65 and 1.0 nm. We show from these simulations that the calculated hydration free energy is independent of the box-size as well as the LJ cut-off distance, suggesting that typical hydration free energy calculations of neutral compounds indeed need not be particularly concerned with finite-size effects as long as standard good practices are followed.     

Solvation free energies of amino acid side chain analogs for common molecular mechanics water models

Quantitative free energy computation involves both using a model that is sufficiently faithful to the experimental system under study (accuracy) and establishing statistically meaningful measures of the uncertainties resulting from finite sampling (precision). In order to examine the accuracy of a range of common water models used for protein simulation for their solute/solvent properties, we calculate the free energy of hydration of 15 amino acid side chain analogs derived from the OPLS-AA parameter set with the TIP3P, TIP4P, SPC, SPC/E, TIP3P-MOD, and TIP4P-Ew water models. We achieve a high degree of statistical precision in our simulations, obtaining uncertainties for the free energy of hydration of 0.02-0.06 kcal/mol, equivalent to that obtained in experimental hydration free energy measurements of the same molecules. We find that TIP3P-MOD, a model designed to give improved free energy of hydration for methane, gives uniformly the closest match to experiment; we also find that the ability to accurately model pure water properties does not necessarily predict ability to predict solute/solvent behavior. We also evaluate the free energies of a number of novel modifications of TIP3P designed as a proof of concept that it is possible to obtain much better solute/solvent free energetic behavior without substantially negatively affecting pure water properties. We decrease the average error to zero while reducing the root mean square error below that of any of the published water models, with measured liquid water properties remaining almost constant with respect to our perturbations. This demonstrates there is still both room for improvement within current fixed-charge biomolecular force fields and significant parameter flexibility to make these improvements. Recent research in computational efficiency of free energy methods allows us to perform simulations on a local cluster that previously required large scale distributed computing, performing four times as much computational work in approximately a tenth of the computer time as a similar study a year ago.     

The SAMPL4 hydration challenge: evaluation of partial charge sets with explicit-water molecular dynamics simulations

We used blind predictions of the 47 hydration free energies in the SAMPL4 challenge to test multiple partial charge models in the context of explicit solvent free energy simulations with the general AMBER force field. One of the partial charge models, IPolQ-Mod, is a fast continuum solvent-based implementation of the IPolQ approach. The AM1-BCC, restrained electrostatic potential (RESP) and IpolQ-Mod approaches all perform reasonably well (R² > 0.8), while VCharge, though faster, gives less accurate results (R² of 0.5). The AM1-BCC results are more accurate than those of RESP for tertiary amines and nitrates, but the overall difference in accuracy between these methods is not statistically significant. Interestingly, the IPolQ-Mod method is found to yield partial charges in very close agreement with RESP. This observation suggests that the success of RESP may be attributed to its fortuitously approximating the arguably more rigorous IPolQ approach.     

An atomistic model for simulations of nilotinib and nilotinib/kinase binding

Nilotinib is a novel anticancer drug, which specifically binds to the Abl kinase and blocks its signaling activity. In order to model the nilotinib/protein interactions, we have developed a molecular mechanics force field for nilotinib, consistent with the CHARMM force field for proteins and nucleic acids. Atomic charges were derived by utilizing a supermolecule ab initio approach. We considered the ab initio energies and geometries of a probe water molecule that interacts with nilotinib fragments at six different positions. We investigated both neutral and protonated states of nilotinib. The final rms deviation between the ab initio and the force field energies, averaged over both forms, was equal 0.2 kcal/mol. The model reproduces the ab initio geometry and flexibility of nilotinib. To apply the force field to nilotinib/Abl simulations, it is also necessary to determine the most likely protein and nilotinib protonation state when it binds to Abl. This task was carried out using molecular dynamics free energy simulations. The simulations indicate that nilotinib can interact with Abl in protonated and deprotonated forms, with the protonated form more favoured for the interaction. In the course of our calculations, we established that the His361, a titratable amino acid residue that mediates the interaction, prefers to be neutral. These insights and models should be of interest for drug design.     

Amine hydration: a united-atom force-field solution.

The free energies of hydration for ammonia and mono-, di-, and trimethylated amines experimentally show an unexpected trend that has, in the past, been difficult to reproduce computationally. Absolute and relative free energies of hydration of these compounds were calculated using the OPLS all-atom and the united-atom GROMOS force fields. Both force fields reproduce the relative free energy of hydration, but the absolute free energies of hydration were only reproduced within kBT when using the recently developed GROMOS parameter set 53A6. Relative free energies of solvation in chloroform could also be reproduced indicating a proper partitioning of the compounds between polar and apolar media. Overall we conclude that it is possible to resolve the amine hydration problem using a simple united-atom force field.     

Comparison of charge models for fixed-charge force fields: small-molecule hydration free energies in explicit solvent

In molecular simulations with fixed-charge force fields, the choice of partial atomic charges influences numerous computed physical properties, including binding free energies. Many molecular mechanics force fields specify how nonbonded parameters should be determined, but various choices are often available for how these charges are to be determined for arbitrary small molecules. Here, we compute hydration free energies for a set of 44 small, neutral molecules in two different explicit water models (TIP3P and TIP4P-Ew) to examine the influence of charge model on agreement with experiment. Using the AMBER GAFF force field for nonbonded parameters, we test several different methods for obtaining partial atomic charges, including two fast methods exploiting semiempirical quantum calculations and methods deriving charges from the electrostatic potentials computed with several different levels of ab initio quantum calculations with and without a continuum reaction field treatment of solvent. We find that the best charge sets give a root-mean-square error from experiment of roughly 1 kcal/mol. Surprisingly, agreement with experimental hydration free energies does not increase substantially with increasing level of quantum theory, even when the quantum calculations are performed with a reaction field treatment to better model the aqueous phase. We also find that the semiempirical AM1-BCC method for computing charges works almost as well as any of the more computationally expensive ab initio methods and that the root-mean-square error reported here is similar to that for implicit solvent models reported in the literature. Further, we find that the discrepancy with experimental hydration free energies grows substantially with the polarity of the compound, as does its variation across theory levels.     

The configurational dependence of binding free energies: A Poisson–Boltzmann study of Neuraminidase inhibitors

The linear finite difference Poisson-Boltzmann (FDPB) equation is applied to the calculation of the electrostatic binding free energies of a group of inhibitors to the Neuraminidase enzyme. An ensemble of enzyme-inhibitor complex conformations was generated using Monte Carlo simulations and the electrostatic binding free energies of subtly different configurations of the enzyme-inhibitor complexes were calculated. It was seen that the binding free energies calculated using FDPB depend strongly on the configuration of the complex taken from the ensemble. This configurational dependence was investigated in detail in the electrostatic hydration free energies of the inhibitors. Differences in hydration energies of up to 7 kcal mol^–1 were obtained for root mean square (RMS) structural deviations of only 0.5 Å. To verify the result, the grid size and parameter dependence of the calculated hydration free energies were systematically investigated. This showed that the absolute hydration free energies calculated using the FDPB equation were very sensitive to the values of key parameters, but that the configurational dependence of the free energies was independent of the parameters chosen. Thus just as molecular mechanics energies are very sensitive to configuration, and single-structure values are not typically used to score binding free energies, single FDPB energies should be treated with the same caution.     

A molecular dynamics study of alkaline earth metal-chloride complexation in aqueous solution

The relative stability of alkaline earth metals (M2+ = Mg2+, Ca2+, Sr2+, and Ba2+) and their chloride complexes in aqueous solution is examined through molecular dynamics simulations using a flexible SPC water model with an internally consistent set of metal ion force field parameters. For each metal-chloride ion pair in aqueous solution, the free energy profile was calculated via potential of mean force simulations. The simulations provide detailed thermodynamic information regarding the relative stability of the different types of metal-chloride pairs. The free energy profiles indicate that the preference for contact ion pair formation increases with ionic radius and is closely related to the metal hydration free energies. The water residence times within the first hydration shells are in agreement with residence times reported in other computational studies. Calculated association constants suggest an increase in metal-chloride complexation with increasing cation radii that is inconsistent with experimentally observed trends. Possible explanations for this discrepancy are discussed.     

Hydration free energies of monovalent ions in transferable intermolecular potential four point fluctuating charge water: an assessment of simulation methodology and force field performance and transferability

Hydration free energies of nonpolarizable monovalent atomic ions in transferable intermolecular potential four point fluctuating charge (TIP4P-FQ) are computed using several commonly employed ion-water force fields including two complete model sets recently developed for use with the simple water model with four sites and Drude polarizability and TIP4P water models. A simulation methodology is presented which incorporates a number of finite-system free energy corrections within the context of constant pressure molecular dynamics simulations employing the Ewald method and periodic boundary conditions. The agreement of the computed free energies and solvation structures with previously reported results for these models in finite droplet systems indicates good transferability of ion force fields from these water models to TIP4Q-FQ even when ion polarizability is neglected. To assess the performance of the ion models in TIP4P-FQ, we compare with consensus values for single-ion hydration free energies arising from recently improved cluster-pair estimates and a reevaluation of commonly cited, experimentally derived single-ion hydration free energies; we couple the observed consistency of these energies with a justification of the cluster-pair approximation in assigning single-ion hydration free energies to advocate the use of these consensus energies as a benchmark set in the parametrization of future ion force fields.     

Detailed potential of mean force studies on host–guest systems from the SAMPL6 challenge

Accurately predicting receptor–ligand binding free energies is one of the holy grails of computational chemistry with many applications in chemistry and biology. Many successes have been reported, but issues relating to sampling and force field accuracy remain significant issues affecting our ability to reliably calculate binding free energies. In order to explore these issues in more detail we have examined a series of small host–guest complexes from the SAMPL6 blind challenge, namely octa-acids (OAs)–guest complexes and Curcurbit[8]uril (CB8)–guest complexes. Specifically, potential of mean force studies using umbrella sampling combined with the weighted histogram method were carried out on both systems with both known and unknown binding affinities. We find that using standard force fields and straightforward simulation protocols we are able to obtain satisfactory results, but that simply scaling our results allows us to significantly improve our predictive ability for the unknown test sets: the overall RMSD of the binding free energy versus experiment is reduced from 5.59 to 2.36 kcal/mol; for the CB8 test system, the RMSD goes from 8.04 to 3.51 kcal/mol, while for the OAs test system, the RSMD goes from 2.89 to 0.95 kcal/mol. The scaling approach was inspired by studies on structurally related known benchmark sets: by simply scaling, the RMSD was reduced from 6.23 to 1.19 kcal/mol and from 2.96 to 0.62 kcal/mol for the CB8 benchmark system and the OA benchmark system, respectively. We find this scaling procedure to correct absolute binding affinities to be highly effective especially when working across a “congeneric” series with similar charge states. It is less successful when applied to mixed ligands with varied charges and chemical characteristics, but improvement is still realized in the present case. This approach suggests that there are large systematic errors in absolute binding free energy calculations that can be straightforwardly accounted for using a scaling procedure. Random errors are still an issue, but near chemical accuracy can be obtained using the present strategy in select cases.     

A molecular mechanics model for imatinib and imatinib:kinase binding

Imatinib is an important anticancer drug, which binds specifically to the Abl kinase and blocks its signalling activity. To model imatinib:protein interactions, we have developed a molecular mechanics force field for imatinib and four close analogues, which is consistent with the CHARMM force field for proteins and nucleic acids. Atomic charges and Lennard‐Jones parameters were derived from a supermolecule ab initio approach. We considered the ab initio energies and geometries of a probe water molecule interacting with imatinib fragments at 32 different positions. We considered both a neutral and a protonated imatinib. The final RMS deviation between the ab initio and force field energies, averaged over both forms, was 0.2 kcal/mol. The model also reproduces the ab initio geometry and flexibility of imatinib. To apply the force field to imatinib:Abl simulations, it is also necessary to determine the most likely imatinib protonation state when it binds to Abl. This was done using molecular dynamics free energy simulations, where imatinib is reversibly protonated during a series of MD simulations, both in solution and in complex with Abl. The simulations indicate that imatinib binds to Abl in its protonated, positively‐charged form. To help test the force field and the protonation prediction, we did MD free energy simulations that compare the Abl binding affinities of two imatinib analogs, obtaining good agreement with experiment. Finally, two new imatinib variants were considered, one of which is predicted to have improved Abl binding. This variant could be of interest as a potential drug. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Modifying the OPLS-AA force field to improve hydration free energies for several amino acid side chains using new atomic charges and an off-plane charge model for aromatic residues

The hydration free energies of amino acid side chains are an important determinant of processes that involve partitioning between different environments, including protein folding, protein complex formation, and protein-membrane interactions. Several recent papers have shown that calculated hydration free energies for polar and aromatic residues (Trp, His, Tyr, Asn, Gln, Asp, Glu) in several common molecular dynamics force fields differ significantly from experimentally measured values. We have attempted to improve the hydration energies for these residues by modifying the partial charges of the OPLS-AA force field based on natural population analysis of density functional theory calculations. The resulting differences between calculated hydration free energies and experimental results for the seven side chain analogs are less than 0.1 kcal/mol. Simulations of the synthetic Trp-rich peptide Trpzip2 show that the new charges lead to significantly improved geometries for interacting Trp-side chains. We also investigated an off-plane charge model for aromatic rings that more closely mimics their electronic configuration. This model results in an improved free energy of hydration for Trp and a somewhat altered benzene-sodium potential of mean force with a more favorable energy for direct benzene-sodium contact.