The SAMPL5 host–guest challenge: computing binding free energies and enthalpies from explicit solvent simulations by the attach-pull-release (APR) method

The absolute binding free energies and binding enthalpies of twelve host–guest systems in the SAMPL5 blind challenge were computed using our attach-pull-release (APR) approach. This method has previously shown good correlations between experimental and calculated binding data in retrospective studies of cucurbit[7]uril (CB7) and β-cyclodextrin (βCD) systems. In the present work, the computed binding free energies for host octa acid (OA or OAH) and tetra-endo-methyl octa-acid (TEMOA or OAMe) with guests are in good agreement with prospective experimental data, with a coefficient of determination (R²) of 0.8 and root-mean-squared error of 1.7 kcal/mol using the TIP3P water model. The binding enthalpy calculations achieve moderate correlations, with R² of 0.5 and RMSE of 2.5 kcal/mol, for TIP3P water. Calculations using the newly developed OPC water model also show good performance. Furthermore, the present calculations semi-quantitatively capture the experimental trend of enthalpy-entropy compensation observed, and successfully predict guests with the strongest and weakest binding affinity. The most populated binding poses of all twelve systems, based on clustering analysis of 750 ns molecular dynamics (MD) trajectories, were extracted and analyzed. Computational methods using MD simulations and explicit solvent models in a rigorous statistical thermodynamic framework, like APR, can generate reasonable predictions of binding thermodynamics. Especially with continuing improvement in simulation force fields, such methods hold the promise of making substantial contributions to hit identification and lead optimization in the drug discovery process.     

A comparison of conformational energies calculated by several molecular mechanics methods

Several commonly used molecular mechanics force fields have been tested for accuracy in conformational energy calculations. Differences in performance between the force fields are discussed for different classes of structures. MMFF93 and force fields based on the MM2 or MM3 functional form are found to perform significantly better than other force fields in the test, with average conformational energy errors around 0.5 kcal/mol. CFF91 also reaches this accuracy for the subset in which fully determined parameters are used, but it doubles the overall error due to use of estimated parameters. Harmonic force fields generally have average errors exceeding 1 kcal/mol. Factors influencing accuracy are identified and discussed. © 1996 by John Wiley & Son s, Inc.     

Prediction of SAMPL3 host–guest binding affinities: evaluating the accuracy of generalized force-fields

We used the second-generation mining minima method (M2) to compute the binding affinities of the novel host-guest complexes in the SAMPL3 blind prediction challenge. The predictions were in poor agreement with experiment, and we conjectured that much of the error might derive from the force field, CHARMm with Vcharge charges. Repeating the calculations with other generalized force-fields led to no significant improvement, and we observed that the predicted affinities were highly sensitive to the choice of force-field. We therefore embarked on a systematic evaluation of a set of generalized force fields, based upon comparisons with PM6-DH2, a fast yet accurate semi-empirical quantum mechanics method. In particular, we compared gas-phase interaction energies and entropies for the host-guest complexes themselves, as well as for smaller chemical fragments derived from the same molecules. The mean deviations of the force field interaction energies from the quantum results were greater than 3 kcal/mol and 9 kcal/mol, for the fragments and host-guest systems respectively. We further evaluated the accuracy of force-fields for computing the vibrational entropies and found the mean errors to be greater than 4 kcal/mol. Given these errors in energy and entropy, it is not surprising in retrospect that the predicted binding affinities deviated from the experiment by several kcal/mol. These results emphasize the need for improvements in generalized force-fields and also highlight the importance of systematic evaluation of force-field parameters prior to evaluating different free-energy methods.     

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.     

Tautomerism of oxopyridines and oxopyrimidines: Theoretical study with complete optimization of geometry

The semiempirical MINDO /3 method is employed to calculate the energies of various tautomers of model tautomeric compounds— 2-oxo- and 4-oxopyridines and pyrimidines. The results are compared with experimental data in the gas phase, where the solute–solvent interactions not included in theoretical calculations are absent. Although the relative energies obtained by the MINDO /3 method appear to be superior to other semiempirical and ab initio calculations, the accuracy of the method was determined to be as low as 3–4 kcal/mol. It indicates that it is exceedingly difficult to account theoretically for intrinsic stabilities of the tautomers. The importance of various factors influencing calculated free-energy differences is discussed. Particular attention is paid to the problem of geometry optimization.     

Absolute binding free energies for the SAMPL6 cucurbit[8]uril host–guest challenge via the AMOEBA polarizable force field

As part of the SAMPL6 host–guest blind challenge, the AMOEBA force field was applied to calculate the absolute binding free energy for a cucurbit[8]uril host complexed with 14 diverse guests, ranging from small, rigid structures to drug molecules. The AMOEBA results from the initial submission prompted an investigation into aspects of the methodology and parameterization employed. Lessons learned from the blind challenge include: a double annihilation scheme (electrostatics and van der Waals) is needed to obtain proper sampling of guest conformations, annihilation of key torsion parameters of the guest are recommended for flexible guests, and a more thorough analysis of torsion parameters is warranted. When put in to practice with the AMOEBA model, the lessons learned improved the MUE from 2.63 to 1.20 kcal/mol and the RMSE from 3.62 to 1.68 kcal/mol, respectively. Overall, the AMOEBA protocol for determining absolute binding free energies benefitted from participation in the SAMPL6 host–guest blind challenge and the results suggest the implementation of the methodology in future host–guest calculations.     

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.     

Can free energy calculations be fast and accurate at the same time? Binding of low-affinity,non-peptide inhibitors to the SH2 domain of the src protein

The usefulness of free-energy calculations in non-academic environments, in general, and in the pharmaceutical industry, in particular, is a long-time debated issue, often considered from the angle of cost/performance criteria. In the context of the rational drug design of low-affinity, non-peptide inhibitors to the SH2 domain of the (pp60)src tyrosine kinase, the continuing difficulties encountered in an attempt to obtain accurate free-energy estimates are addressed. free-energy calculations can provide a convincing answer, assuming that two key-requirements are fulfilled: (i) thorough sampling of the configurational space is necessary to minimize the statistical error, hence raising the question: to which extent can we sacrifice the computational effort, yet without jeopardizing the precision of the free-energy calculation? (ii) the sensitivity of binding free-energies to the parameters utilized imposes an appropriate parametrization of the potential energy function, especially for non-peptide molecules that are usually poorly described by multipurpose macromolecular force fields. Employing the free-energy perturbation method, accurate ranking, within +/-0.7 kcal/mol, is obtained in the case of four non-peptide mimes of a sequence recognized by the (pp60)src SH2 domain.     

Quantum mechanical and molecular mechanics approach with a multilayered-quantum representation study of solvent effects and potentials of mean force for the CH<Subscript>3</Subscript>CH<Subscript>2</Subscript>Cl + ClO<Superscript>−</Superscript> S<Subscript>N</Subscript>2 reaction in aqueous solution

The bimolecular nucleophilic substitution reaction of CH₃CH₂Cl + ClO^? in aqueous solution was investigated using a multilayered-quantum representation, quantum mechanical and molecular mechanics approach with an explicit water model. Ten configurations along the reaction pathway including reactant complex, transition state and product complex were analyzed in the presence of the aqueous solution. The obtained free energy activation barrier under the CCSD(T)/MM representation is 13.2 kcal/mol, while it is 11.7 kcal/mol under the DFT/MM representation which agrees very well with the DFT calculation, at 11.0 kcal/mol, with a polarizable continuum solvent model. The solvent effects including the solvation free energy contribution and the polarization effect raise the free activation barrier by 9.8 kcal/mol. The rate constant, at 298 K, is 5.27 × 10^?17 cm³/molecule/s which is about seven orders of magnitude smaller than that in the gas phase (1.10 × 10^?10 cm³/molecule/s). All in all, the aqueous solution plays an essential role in shaping the reaction pathway for this reaction in water.     

First principle and ReaxFF molecular dynamics investigations of formaldehyde dissociation on Fe(100) surface

Detailed formaldehyde adsorption and dissociation reactions on Fe(100) surface were studied using first principle calculations and molecular dynamics (MD) simulations, and results were compared with available experimental data. The study includes formaldehyde, formyl radical (HCO), and CO adsorption and dissociation energy calculations on the surface, adsorbate vibrational frequency calculations, density of states analysis of clean and adsorbed surfaces, complete potential energy diagram construction from formaldehyde to atomic carbon (C), hydrogen (H), and oxygen (O), simulation of formaldehyde adsorption and dissociation reaction on the surface using reactive force field, ReaxFF MD, and reaction rate calculations of adsorbates using transition state theory (TST). Formaldehyde and HCO were adsorbed most strongly at the hollow (fourfold) site. Adsorption energies ranged from ?22.9 to ?33.9 kcal/mol for formaldehyde, and from ?44.3 to ?66.3 kcal/mol for HCO, depending on adsorption sites and molecular direction. The dissociation energies were investigated for the dissociation paths: formaldehyde → HCO + H, HCO → H + CO, and CO → C + O, and the calculated energies were 11.0, 4.1, and 26.3 kcal/mol, respectively. ReaxFF MD simulation results were compared with experimental surface analysis using high resolution electron energy loss spectrometry (HREELS) and TST based reaction rates. ReaxFF simulation showed less reactivity than HREELS observation at 310 and 523 K. ReaxFF simulation showed more reactivity than the TST based rate for formaldehyde dissociation and less reactivity than TST based rate for HCO dissociation at 523 K. TST‐based rates are consistent with HREELS observation. © 2013 Wiley Periodicals, Inc.     

On the fly estimation of host–guest binding free energies using the movable type method: participation in the SAMPL5 blind challenge

We review our performance in the SAMPL5 challenge for predicting host–guest binding affinities using the movable type (MT) method. The challenge included three hosts, acyclic Cucurbit[2]uril and two octa-acids with and without methylation at the entrance to their binding cavities. Each host was associated with 6–10 guest molecules. The MT method extrapolates local energy landscapes around particular molecular states and estimates the free energy by Monte Carlo integration over these landscapes. Two blind submissions pairing MT with variants of the KECSA potential function yielded mean unsigned errors of 1.26 and 1.53 kcal/mol for the non-methylated octa-acid, 2.83 and 3.06 kcal/mol for the methylated octa-acid, and 2.77 and 3.36 kcal/mol for Cucurbit[2]uril host. While our results are in reasonable agreement with experiment, we focused on particular cases in which our estimates gave incorrect results, particularly with regard to association between the octa-acids and an adamantane derivative. Working on the hypothesis that differential solvation effects play a role in effecting computed binding affinities for the parent octa-acid and the methylated octa-acid and that the ligands bind inside the pockets (rather than on the surface) we devised a new solvent accessible surface area term to better quantify solvation energy contributions in MT based studies. To further explore this issue a, molecular dynamics potential of mean force (PMF) study indicates that, as found by our docking calculations, the stable binding mode for this ligand is inside (rather than surface bound) the octa-acid cavity whether the entrance is methylated or not. The PMF studies also obtained the correct order for the methylation-induced change in binding affinities and associated the difference, to a large extent to differential solvation effects. Overall, the SAMPL5 challenge yielded in improvements our solvation modeling and also demonstrated the need for thorough validation of input data integrity prior to any computational analysis.     

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.     

Transition-state characterization of the ammonia ionization process in aqueous solution via the free-energy gradient method

For the ionization process of ammonia in aqueous solution, the transition-state (TS) structure was fully optimized for the first time on the free-energy surface (FES) by applying the free-energy gradient (FEG) method combined with a hybrid quantum mechanical and molecular mechanical molecular dynamics (QM/MM-MD) method. In aqueous solution, the ionization process was found to proceed by way of a clear TS (R(N1-H5) = 1.512 A), which does not exist in the gas phase. The free-energy (FE) of activation for ionization obtained was 14.7 kcal/mol, within the classical approximation, via the QM/MM-MD FEG method, and is found to be in good agreement with 9.57 kcal/mol estimated from the TS theory using the experimental value of the rate constant. Apart from the dynamic correction, it is indicated that the theoretical value would be improved to be 10.28 kcal/mol if the electronic-state calculation could be executed at the B3LYP/6-31G(d) level of theory.     

Prediction of hydration free energies for the SAMPL4 data set with the AMOEBA polarizable force field

Hydration free energy calculations are often used to validate molecular simulation methodologies and molecular mechanics force fields. We use the free-energy perturbation method together with the AMOEBA polarizable force field and the Poltype parametrization protocol to predict the hydration free energies of 52 molecules as part of the SAMPL4 blind challenge. For comparison, similar calculations are performed using the non-polarizable General Amber force field. Against our expectations, the latter force field gives the better results compared to experiment. One possible explanation is the sensitivity of the AMOEBA results to the conformation used for parametrization.     

Force field parameters for sulfates and sulfamates based on ab initio calculations: Extensions of AMBER and CHARMm fields

Ab initio self-consistent field (SCF) Hartree-Fock calculations of sulfates R? O? SO₃(?1) (R = Me, Et, i-Pr) and sulfamates R? NHSO₃(?1) (R = H, Me, Et, i-Pr) were performed at the 4-31G(*S*N) //3-21G(*S*N) basis set levels, where asterisks indicate d functions on sulfur and nitrogen atoms. These standard levels were determined by comparing calculation results with several basis sets up to MP2/6-31G*//6-31G*. Several conformations per compound were studied to obtain molecular geometries, rotational barriers, and potential derived point charges. In methyl sulfate, the rotational barrier around the C? O bond is 1.6 kcal/mol at the MP2 level and 1.4 kcal/mol at the standard level. Its ground state has one of three HCOS torsion angles trans and one of three COSO torsion angles trans. Rotation over 60° around the single O? S bond in the sulfate group costs 2.5 kcal/mol at the MP2 and 2.1 kcal/mol at the standard level. For ethyl sulfate, the calculated rotational barrier in going from the ground state, which has its CCOS torsion angle trans, to the syn-periplanar conformation (CCOS torsion angle cis) is 4.8 kcal/mol. However, a much lower barrier of 0.7 kcal/mol leads to a secondary gauchelike conformation about 0.4 kcal/mol above the ground state, with the CCOS torsion angle at 87.6°. Again, one of the COSO torsion angles is trans in the ground state, and the rotational barrier for a 60° rotation of the sulfate group amounts to 1.8 kcal/mol. For methyl sulfamate, the rotational barriers are 2.5 kcal/mol around the C? N bond and 3.3 kcal/mol around the N? S bond. This is noteworthy because sulfamate itself has a calculated rotational barrier around the N? S bond of only 1.7 kcal/mol. These and other data were used to parameterize the well-known empirical force fields AMBER and CHARMm. When the new fields were tested by means of vibrational frequency calculations at the 6-31G*//6-31G* level for methyl sulfate, sulfamate, and methyl sulfamate ground states, the frequencies compared favorably with the AMBER and CHARMm calculated frequencies. The transferability of the force parameters to β-D -glucose-6-sulfate and isopropyl sulfate appears to be better than to isopropyl sulfamate. © 1995 by John Wiley & Sons, Inc.     

Influence of insertion of a noble gas atom on halogen bonding in H2O···XCCNgF and H3N···XCCNgF (X = Cl and Br; Ng = Ar, Kr, and Xe) complexes

The H₂O···XCCNgF and H₃N···XCCNgF (X = Cl and Br; Ng = Ar, Kr, and Xe) complexes have been studied with quantum chemical calculations at the MP2/aug-cc-pVTZ level. The results show that the inserted noble gas atom has an enhancing effect on the strength of halogen bond, and this enhancement is weakened with the increase of noble gas atomic number. The methyl and Li substituents in the electron donor strengthen the halogen bond. The interaction energy increases from ?3.75 kcal/mol in H₃N–BrCCF complex to ?9.66 kcal/mol in H₂LiN–BrCCArF complex. These complexes have been analyzed with atoms in molecules, natural bond orbital, molecular electrostatic potentials, and energy decomposition calculations.     

Combining the polarizable Drude force field with a continuum electrostatic Poisson–Boltzmann implicit solvation model

In this work, we have combined the polarizable force field based on the classical Drude oscillator with a continuum Poisson–Boltzmann/solvent‐accessible surface area (PB/SASA) model. In practice, the positions of the Drude particles experiencing the solvent reaction field arising from the fixed charges and induced polarization of the solute must be optimized in a self‐consistent manner. Here, we parameterized the model to reproduce experimental solvation free energies of a set of small molecules. The model reproduces well‐experimental solvation free energies of 70 molecules, yielding a root mean square difference of 0.8 kcal/mol versus 2.5 kcal/mol for the CHARMM36 additive force field. The polarization work associated with the solute transfer from the gas‐phase to the polar solvent, a term neglected in the framework of additive force fields, was found to make a large contribution to the total solvation free energy, comparable to the polar solute–solvent solvation contribution. The Drude PB/SASA also reproduces well the electronic polarization from the explicit solvent simulations of a small protein, BPTI. Model validation was based on comparisons with the experimental relative binding free energies of 371 single alanine mutations. With the Drude PB/SASA model the root mean square deviation between the predicted and experimental relative binding free energies is 3.35 kcal/mol, lower than 5.11 kcal/mol computed with the CHARMM36 additive force field. Overall, the results indicate that the main limitation of the Drude PB/SASA model is the inability of the SASA term to accurately capture non‐polar solvation effects. © 2018 Wiley Periodicals, Inc.     

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.     

A multilayered representation,quantum mechanical and molecular mechanics study of the CH3F + OH− reaction in water

The bimolecular nucleophilic substitution (S_N2) reaction of CH₃F + OH^? in aqueous solution was investigated using a combined quantum mechanical and molecular mechanics approach. Reactant complex, transition state, and product complex along the reaction pathway were analyzed in water. The potentials of mean force were calculated using a multilayered representation with the DFT and CCSD(T) level of theory for the reactive region. The obtained free energy activation barrier for this reaction at the CCSD(T)/MM representation is 18.3 kcal/mol which agrees well with the experimental value at ～21.6 kcal/mol. Both the solvation effect and solute polarization effect play key roles on raising the activation barrier height in aqueous solution, with the former raising the barrier height by 3.1 kcal/mol, the latter 1.5 kcal/mol. © 2013 Wiley Periodicals, Inc.     

Prediction of SAMPL4 host–guest binding affinities using funnel metadynamics

Accurately predicting binding affinities between ligands and macromolecules has been a much sought-after goal. A tremendous amount of resources can be saved in the pharmaceutical industry through accurate binding-affinity prediction and hence correct decision-making for the drug discovery processes. Owing to the structural complexity of macromolecules, one of the issues in binding affinity prediction using molecular dynamics is the adequate sampling of the conformational space. Recently, the funnel metadynamics method (Limongelli et al. in Proc Natl Acad Sci USA 110:6358, 2013) was developed to enhance the sampling of the ligand at the binding site as well as in the solvated state, and offer the possibility to predict the absolute binding free energy. We apply funnel metadynamics to predict host–guest binding affinities for the cucurbit[7]uril host as part of the SAMPL4 blind challenge. Using total simulation times of 300–400 ns per ligand, we show that the errors due to inadequate sampling are below 1 kcal/mol. However, despite the large investment in terms of computational time, the results compared to experiment are not better than a random guess. As we obtain differences of up to 11 kcal/mol when switching between two commonly used force fields (with automatically generated parameters), we strongly believe that in the pursuit of accurate binding free energies a more careful force-field parametrization is needed to address this type of system.