Free-energy perturbation and quantum mechanical study of SAMPL4 octa-acid host–guest binding energies

Application of molecular dynamic simulations in modeling the excited state behavior of confined molecules

Relative to isotropic organic solvent medium, the structure and conformation of a reactant molecule in an organized and confining medium are often different. In addition, because of the rigidity of the immediate environment, the reacting molecule have a little freedom to undergo large changes even upon gaining energy or modifications in the electronic structure. These alterations give rise to differences in the photochemistry of a molecular and supramolecular species. In this study, one such example is presented. α-Alkyl dibenzylketones upon excitation in isotropic solvents give products via Norrish type I and type II reactions that are independent of the chain length of the alkyl substituent. On the other hand, when these molecules are enclosed within an organic capsule of volume ~ 550 Å3, they give products that are strikingly dependent on the length of the α-alkyl substitution. These previously reported experimental observations are rationalized based on the structures generated by molecular modeling (docking and molecular dynamics (MD) simulations). It is shown that MD simulations that are utilized extensively in biologically important macromolecules can also be useful to understand the excited state behavior of reactive molecules that are part of supramolecular assemblies. These simulations can provide structural information of the reactant molecule and the surroundings complementing that with the one obtained from 1 and 2D NMR experiments. MD simulated structures of seven α-alkyl dibenzylketones encapsulated within the octa acid capsule provide a clear understanding of their unique behavior in this restricted medium. Because of the rigidity of the medium, these structures although generated in the ground state can rationalize the photochemical behavior of the molecules in the excited state.

Computational methods for calculation of protein-ligand binding affinities in structure-based drug design

Drug design is an expensive and time-consuming process. Any method that allows reducing the time the costs of the drug development project can have great practical value for the pharmaceutical industry. In structure-based drug design, affinity prediction methods are of great importance. The majority of methods used to predict binding free energy in protein-ligand complexes use molecular mechanics methods. However, many limitations of these methods in describing interactions exist. An attempt to go beyond these limits is the application of quantum-mechanical description for all or only part of the analyzed system. However, the extensive use of quantum mechanical (QM) approaches in drug discovery is still a demanding challenge. This chapter briefly reviews selected methods used to calculate protein-ligand binding affinity applied in virtual screening (VS), rescoring of docked poses, and lead optimization stage, including QM methods based on molecular simulations.

Seeding the multi-dimensional nonequilibrium pulling for Hamiltonian variation: indirect nonequilibrium free energy simulations at QM levels

The combination of free energy simulations in the alchemical and configurational spaces provides a feasible route to access the thermodynamic profiles under a computationally demanding target Hamiltonian. Normally, due to the significant differences between the computational cost of ab initio quantum mechanics (QM) calculations and those of semi-empirical quantum mechanics (SQM) and molecular mechanics (MM), this indirect method could be used to obtain the QM thermodynamics by combining the SQM or MM results and the SQM-to-QM or MM-to-QM corrections. In our previous work, a multi-dimensional nonequilibrium pulling framework for Hamiltonian variations was introduced based on bidirectional pulling and bidirectional reweighting. The method performs nonequilibrium free energy simulations in the configurational space to obtain the thermodynamic profile along the conformational change pathway under a selected computationally efficient Hamiltonian, and uses the nonequilibrium alchemical method to correct or perturb the thermodynamic profile to that under the target Hamiltonian. The BAR-based method is designed to achieve the best generality and transferability and thus leads to modest (∼20 fold) speedup. In this work, we explore the possibility of further accelerating the nonequilibrium free energy simulation by employing unidirectional pulling and using the selection criterion to obtain the initial configurations used to initiate nonequilibrium trajectories following the idea of adaptive steered molecular dynamics (ASMD). A single initial condition is used to seed the whole multi-dimensional nonequilibrium free energy simulation and the sampling is performed fully in the nonequilibrium ensemble. Introducing very short ps-length equilibrium sampling to grab more initial seeds could also be helpful. The ASMD scheme estimates the free energy difference with the unidirectional exponential average (EXP), but it does not follow exactly the requirements of the EXP estimator. Another deficiency of the seeding simulation is the inherently sequential or serial pulling due to the inter-segment dependency, which triggers some problems in the parallelizability of the simulation. Numerical tests are performed to grasp some insights and guidelines for using this selection-criterion-based ASMD scheme. The presented selection-criterion-based multi-dimensional ASMD scheme follows the same perturbation network of the BAR-based method, and thus could be used in various Hamiltonian-variation cases.

A General Picture of Cucurbit[8]uril Host-Guest Binding

Describing, understanding, and designing complex interaction networks within macromolecular systems remain challenging in modern chemical research. Host-guest systems, despite their relative simplicity in both the structural feature and interaction patterns, still pose problems in theoretical modeling. The barrel-shaped supramolecular container cucurbit[8]uril (CB8) shows promising functionalities in various areas, e.g., catalysis and molecular recognition. It can stably coordinate a series of structurally diverse guests with high affinities. In this work, we examine the binding of seven commonly abused drugs to the CB8 host, aiming at providing a general picture of CB8-guest binding. Extensive sampling of the configurational space of these host-guest systems is performed, and the binding pathway and interaction patterns of CB8-guest complexes are investigated. A thorough comparison of widely used fixed-charge models for drug-like molecules is presented. Iterative refitting of the atomic charges suggests significant conformation dependence of charge generation. The initial model generated at the original conformation could be inaccurate for new conformations explored during conformational search, and the newly fitted charge set improves the prediction-experiment correlation significantly. Our investigations of the configurational space of CB8-drug complexes suggest that the host-guest interactions are more complex than expected. Despite the structural simplicities of these molecules, the conformational fluctuations of the host and the guest molecules and orientations of functional groups lead to the existence of an ensemble of binding modes. The insights of the binding thermodynamics, performance of fixed-charge models, and binding patterns of the CB8-guest systems are useful for studying and elucidating the binding mechanism of other host-guest complexes.

Molecular Environment-Specific Atomic Charges Improve Binding Affinity Predictions of SAMPL5 Host-Guest Systems

Host-guest systems are widely used in benchmarks as model systems to improve computational methods for absolute binding free energy predictions. Recent advances in sampling algorithms for alchemical free energy calculations and the increase in computational power have made their binding affinity prediction primarily dependent on the quality of the force field. Here, we propose a new methodology to derive the atomic charges of host-guest systems based on quantum mechanics/molecular mechanics calculations and minimal basis iterative stockholder (MBIS) partitioning of the polarized electron density. A newly developed interface between the OpenMM and ORCA software packages provides D-MBIS charges that represent the guest's average electrostatic interactions in the hosts or the solvent. The simulation workflow also calculates the average energy required to polarize the guest in the bound and unbound state. Alchemical free energy calculations using the general Amber force field parameters with D-MBIS charges improve the binding affinity prediction of six guests bound to two octa acid hosts compared to the AM1-BCC charge set after correction with the average energetic polarization cost. This correction originates from the difference in potential energy that is required to polarize the guest in the bound and unbound state and contributes significantly to the binding affinity of anionic guests.

On the Use of Interaction Entropy and Related Methods to Estimate Binding Entropies

Molecular mechanics combined with Poisson-Boltzmann or generalized Born and solvent-accessible area solvation energies (MM/PBSA and MM/GBSA) are popular methods to estimate the free energy for the binding of small molecules to biomacromolecules. However, the estimation of the entropy has been problematic and time-consuming. Traditionally, normal-mode analysis has been used to estimate the entropy, but more recently, alternative approaches have been suggested. In particular, it has been suggested that exponential averaging of the electrostatic and Lennard-Jones interaction energies may provide much faster and more accurate entropies, the interaction entropy (IE) approach. In this study, we show that this exponential averaging is extremely poorly conditioned. Using stochastic simulations, assuming that the interaction energies follow a Gaussian distribution, we show that if the standard deviation of the interaction energies (σIE) is larger than 15 kJ/mol, it becomes practically impossible to converge the interaction entropies (more than 10 million energies are needed, and the number increases exponentially). A cumulant approximation to the second order of the exponential average shows a better convergence, but for σIE > 25 kJ/mol, it gives entropies that are unrealistically large. Moreover, in practical applications, both methods show a steady increase in the entropy with the number of energies considered.

Thermochemical and Quantum Descriptor Calculations for Gaining Insight into Ricin Toxin A (RTA) Inhibitors

In this work, we performed a study to assess the interactions between the ricin toxin A (RTA) subunit of ricin and some of its inhibitors using modern semiempirical quantum chemistry and ONIOM quantum mechanics/molecular mechanics (QM/MM) methods. Two approaches were followed (calculation of binding enthalpies, ΔH _bind, and reactivity quantum chemical descriptors) and compared with the respective half-maximal inhibitory concentration (IC₅₀) experimental data, to gain insight into RTA inhibitors and verify which quantum chemical method would better describe RTA-ligand interactions. The geometries for all RTA-ligand complexes were obtained after running classical molecular dynamics simulations in aqueous media. We found that single-point energy calculations of ΔH _bind with the PM6-DH+, PM6-D3H4, and PM7 semiempirical methods and ONIOM QM/MM presented a good correlation with the IC₅₀ data. We also observed, however, that the correlation decreased significantly when we calculated ΔH _bind after full-atom geometry optimization with all semiempirical methods. Based on the results from reactivity descriptors calculations for the cases studied, we noted that both types of interactions, molecular overlap and electrostatic interactions, play significant roles in the overall affinity of these ligands for the RTA binding pocket.

Computation of host-guest binding free energies with a new quantum mechanics based mining minima algorithm

A new method called QM-VM2 is presented that efficiently combines statistical mechanics with quantum mechanical (QM) energy potentials in order to calculate noncovalent binding free energies of host-guest systems. QM-VM2 efficiently couples the use of semi-empirical QM (SEQM) energies and geometry optimizations with an underlying molecular mechanics (MM) based conformational search, to find low SEQM energy minima, and allows for processing of these minima at higher levels of ab initio QM theory. A progressive geometry optimization scheme is introduced as a means to increase conformational sampling efficiency. The newly implemented QM-VM2 is used to compute the binding free energies of the host molecule cucurbit[7]uril and a set of 15 guest molecules. The results are presented along with comparisons to experimentally determined binding affinities. For the full set of 15 host-guest complexes, which have a range of formal charges from +1 to +3, SEQM-VM2 based binding free energies show poor correlation with experiment, whereas for the ten +1 complexes only, a significant correlation (R2 = 0.8) is achieved. SEQM-VM2 generation of conformers followed by single-point ab initio QM calculations at the dispersion corrected restricted Hartree-Fock-D3(BJ) and TPSS-D3(BJ) levels of theory, as post-processing corrections, yields a reasonable correlation with experiment for the full set of host-guest complexes (R2 = 0.6 and R2 = 0.7, respectively) and an excellent correlation for the +1 formal charge set (R2 = 1.0 and R2 = 0.9, respectively), as long as a sufficiently large basis set (triple-zeta quality) is employed. The importance of the inclusion of configurational entropy, even at the MM level, for the achievement of good correlation with experiment was demonstrated by comparing the calculated ΔE values with experiment and finding a considerably poorer correlation with experiment than for the calculated free energy ΔE - TΔS. For the complete set of host-guest systems with the range of formal charges, it was observed that the deviation of the predicted binding free energy from experiment correlates somewhat with the net charge of the systems. This observation leads to a simple empirical interpolation scheme to improve the linear regression of the full set.

SAMPL7: Host-guest binding prediction by molecular dynamics and quantum mechanics

Statistical Assessment of Modeling of Proteins and Ligands (SAMPL) challenges provide routes to compare chemical quantities determined using computational chemistry approaches to experimental measurements that are shared after the competition. For this effort, several computational methods have been used to calculate the binding energies of Octa Acid (OA) and exo-Octa Acid (exoOA) host-guest systems for SAMPL7. The initial poses for molecular dynamics (MD) were generated by molecular docking. Binding free energy calculations were performed using molecular mechanics combined with Poisson-Boltzmann or generalized Born surface area solvation (MMPBSA/MMGBSA) approaches. The factors that affect the utility of the MMPBSA/MMGBSA approaches including solvation, partial charge, and solute entropy models were also analyzed. In addition to MD calculations, quantum mechanics (QM) calculations were performed using several different density functional theory (DFT) approaches. From SAMPL6 results, B3PW91-D3 was found to overestimate binding energies though it was effective for geometry optimizations, so it was considered for the DFT geometry optimizations in the current study, with single-point energy calculations carried out with B2PLYP-D3 with double-, triple-, and quadruple-ζ level basis sets. Accounting for dispersion effects, and solvation models was deemed essential for the predictions. MMGBSA and MMPBSA correlated better to experiment when used in conjunction with an empirical/linear correction.

BAR-based multi-dimensional nonequilibrium pulling for indirect construction of QM/MM free energy landscapes: from semi-empirical to ab initio

The indirect method for the construction of quantum mechanics (QM)/molecular mechanics (MM) free energy landscapes provides a cheaper alternative for free energy simulations at the QM level. The indirect method features a direct calculation of the free energy profile with a computationally efficient but less accurate Hamiltonian (i.e. low-level Hamiltonian) and a low-level-to-high-level correction. In the thermodynamic cycle, the direct low-level calculation along the physically meaningful reaction coordinate is corrected via the alchemical method, which is often achieved with perturbation-based techniques. In our previous work, a multi-dimensional nonequilibrium pulling framework is proposed for the indirect construction of QM/MM free energy landscapes. Previously, we focused on obtaining semi-empirical QM (SQM) results indirectly from direct MM simulations and MM to SQM corrections. In this work, we apply this method to obtain results under ab initio QM Hamiltonians by combining direct SQM results and SQM to QM corrections. A series of SQM and QM Hamiltonians are benchmarked. It is observed that PM6 achieves the best performance among the low-level Hamiltonians. Therefore, we recommend using PM6 as the low-level theory in the indirect free energy simulation. Considering its higher similarity to the high-level Hamiltonians, PM6 corrected with the bond charge correction could be more accurate than the existing AM1-BCC model. Another central result in the current work is a basic protocol of choosing the strength of restraints and an appropriate time step in nonequilibrium free energy simulation at the stiff spring limit. We provide theoretical derivations to emphasize the importance of using a sufficiently large force constant and choosing an appropriate time step. It is worth noting that a general rule of thumb for choosing the time step, according to our derivation, is that a time step of 1 fs or smaller should be used, as long as the stiff spring approximation is employed, even in simulations with constraints on bonds involving hydrogen atoms.

Use of Interaction Energies in QM/MM Free Energy Simulations

The use of the most accurate (i.e., QM or QM/MM) levels of theory for free energy simulations (FES) is typically not possible. Primarily, this is because the computational cost associated with the extensive configurational sampling needed for converging FES is prohibitive. To ensure the feasibility of QM-based FES, the "indirect" approach is generally taken, necessitating a free energy calculation between the MM and QM/MM potential energy surfaces. Ideally, this step is performed with standard free energy perturbation (Zwanzig's equation) as it only requires simulations be carried out at the low level of theory; however, work from several groups over the past few years has conclusively shown that Zwanzig's equation is ill-suited to this task. As such, many approximations have arisen to mitigate difficulties with Zwanzig's equation. One particularly popular notion is that the convergence of Zwanzig's equation can be improved by using interaction energy differences instead of total energy differences. Although problematic numerical fluctuations (a major problem when using Zwanzig's equation) are indeed reduced, our results and analysis demonstrate that this "interaction energy approximation" (IEA) is theoretically incorrect, and the implicit approximation invoked is spurious at best. Herein, we demonstrate this via solvation free energy calculations using IEA from two different low levels of theory to the same target high level. Results from this proof-of-concept consistently yield the wrong results, deviating by ∼1.5 kcal/mol from the rigorously obtained value.

BAR-based multi-dimensional nonequilibrium pulling for indirect construction of a QM/MM free energy landscape

Construction of free energy landscapes at the quantum mechanics (QM) level is computationally demanding. As shown in previous studies, by employing an indirect scheme (i.e. constructing a thermodynamic cycle connecting QM states via an alchemical pathway), simulations are converged with much less computational burden. The indirect scheme makes QM/molecular mechanics (MM) free energy simulation orders of magnitude faster than the direct QM/MM schemes. However, the indirect QM/MM simulations were mostly equilibrium sampling based and the nonequilibrium methods were merely exploited in one-dimensional alchemical QM/MM end-state correction at two end states. In this work, we represent a multi-dimensional nonequilibrium pulling scheme for indirect QM/MM free energy simulations, where the whole free energy simulation is performed only with nonequilibrium methods. The collective variable (CV) space we explore is a combination of one alchemical CV and one physically meaningful CV. The current nonequilibrium indirect QM/MM simulation method can be seen as the generalization of equilibrium perturbation based indirect QM/MM methods. The test systems include one backbone dihedral case and one distance case. The two cases are significantly different in size, enabling us to investigate the dependence of the speedup of the indirect scheme on the size of the system. It is shown that the speedup becomes larger when the size of the system becomes larger, which is consistent with the scaling behavior of QM Hamiltonians.

Host-Guest Relative Binding Affinities at Density-Functional Theory Level from Semiempirical Molecular Dynamics Simulations

Relative free energies for the binding of nine cyclic carboxylate ligands to the octa-acid deep-cavity host were calculated at the combined density-functional theory and molecular mechanics (DFT/MM) level of theory. The DFT calculations employed the BLYP functional and the 6-31G* basis set for the ligand. We employed free-energy perturbations (FEP) with the reference-potential approach and used molecular dynamics (MD) simulations with the semiempirical quantum mechanical (SQM) PM6-DH+ method for the ligand as an intermediate level between MM and DFT/MM to improve the convergence. Thus, the relative binding free energy of two ligands was first calculated at the MM level by an alchemical transformation from one ligand to another in both the bound and unbound states. Then, for each ligand the free-energy correction for going from the MM to the SQM/MM potentials was calculated using explicit SQM/MM MD simulations. Finally, the free-energy correction for going from the SQM/MM to the DFT/MM potentials was estimated with FEP without running any DFT/MM simulations. Instead, the free energy was calculated by single-step exponential averaging (ssEA) or employing the cumulant approximation to the second order (CA). The results show that CA converges much better than ssEA, and with 500-4500 DFT/MM single-point energy calculations, converged free energies with a precision of 0.3 kJ/mol can be obtained. These free energies reproduce the experimental binding free energy differences with a mean absolute deviation of 3.4 kJ/mol, a correlation ( R²) of 0.97, and correct signs for all of the eight free-energy differences. This is appreciably better than the results obtained at the SQM/MM level of theory and also slightly better than those obtained with MM. We show that the convergence of the SQM/MM → DFT/MM perturbations can be monitored by the use of Wu and Kofke's bias metric Π and by the standard deviation of the difference between the SQM/MM and DFT/MM energies. Finally, we show that the use of the intermediate SQM/MM MD simulations improves the convergence of the free energies by a factor of at least two, compared to doing direct MM → DFT/MM perturbations.

Predicting protein-ligand binding affinity and correcting crystal structures with quantum mechanical calculations: lactate dehydrogenase A

Accurately computing the geometry and energy of host-guest and protein-ligand interactions requires a physically accurate description of the forces in action. Quantum mechanics can provide this accuracy but the calculations can require a prohibitive quantity of computational resources. The size of the calculations can be reduced by including only the atoms of the receptor that are in close proximity to the ligand. We show that when combined with log P values for the ligand (which can be computed easily) this approach can significantly improve the agreement between computed and measured binding energies. When the approach is applied to lactate dehydrogenase A, it can make quantitative predictions about conformational, tautomeric and protonation state preferences as well as stereoselectivity and even identifies potential errors in structures deposited in the Protein Data Bank for this enzyme. By broadening the evidence base for these structures from only the diffraction data, more chemically realistic structures can be proposed.

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.

Overview of the SAMPL6 host-guest binding affinity prediction challenge

Accurately predicting the binding affinities of small organic molecules to biological macromolecules can greatly accelerate drug discovery by reducing the number of compounds that must be synthesized to realize desired potency and selectivity goals. Unfortunately, the process of assessing the accuracy of current computational approaches to affinity prediction against binding data to biological macromolecules is frustrated by several challenges, such as slow conformational dynamics, multiple titratable groups, and the lack of high-quality blinded datasets. Over the last several SAMPL blind challenge exercises, host-guest systems have emerged as a practical and effective way to circumvent these challenges in assessing the predictive performance of current-generation quantitative modeling tools, while still providing systems capable of possessing tight binding affinities. Here, we present an overview of the SAMPL6 host-guest binding affinity prediction challenge, which featured three supramolecular hosts: octa-acid (OA), the closely related tetra-endo-methyl-octa-acid (TEMOA), and cucurbit[8]uril (CB8), along with 21 small organic guest molecules. A total of 119 entries were received from ten participating groups employing a variety of methods that spanned from electronic structure and movable type calculations in implicit solvent to alchemical and potential of mean force strategies using empirical force fields with explicit solvent models. While empirical models tended to obtain better performance than first-principle methods, it was not possible to identify a single approach that consistently provided superior results across all host-guest systems and statistical metrics. Moreover, the accuracy of the methodologies generally displayed a substantial dependence on the system considered, emphasizing the need for host diversity in blind evaluations. Several entries exploited previous experimental measurements of similar host-guest systems in an effort to improve their physical-based predictions via some manner of rudimentary machine learning; while this strategy succeeded in reducing systematic errors, it did not correspond to an improvement in statistical correlation. Comparison to previous rounds of the host-guest binding free energy challenge highlights an overall improvement in the correlation obtained by the affinity predictions for OA and TEMOA systems, but a surprising lack of improvement regarding root mean square error over the past several challenge rounds. The data suggests that further refinement of force field parameters, as well as improved treatment of chemical effects (e.g., buffer salt conditions, protonation states), may be required to further enhance predictive accuracy.

QM/MM Calculations on Protein-RNA Complexes: Understanding Limitations of Classical MD Simulations and Search for Reliable Cost-Effective QM Methods

Although atomistic explicit-solvent Molecular Dynamics (MD) is a popular tool to study protein-RNA recognition, satisfactory MD description of protein-RNA complexes is not always achieved. Unfortunately, it is often difficult to separate MD simulation instabilities primarily caused by the simple point-charge molecular mechanics (MM) force fields from problems related to the notorious uncertainties in the starting structures. Herein, we report a series of large-scale QM/MM calculations on the U1A protein-RNA complex. This experimentally well-characterized system has an intricate protein-RNA interface, which is very unstable in MD simulations. The QM/MM calculations identify several H-bonds poorly described by the MM method and thus indicate the sources of instabilities of the U1A interface in MD simulations. The results suggest that advanced QM/MM computations could be used to indirectly rationalize problems seen in MM-based MD simulations of protein-RNA complexes. As the most accurate QM method, we employ the computationally demanding meta-GGA density functional TPSS-D3(BJ)/def2-TZVP level of theory. Because considerably faster methods would be needed to extend sampling and to study even larger protein-RNA interfaces, a set of low-cost QM/MM methods is compared to the TPSS-D3(BJ)/def2-TZVP data. The PBEh-3c and B97-3c density functional composite methods appear to be suitable for protein-RNA interfaces. In contrast, HF-3c and the tight-binding Hamiltonians DFTB3-D3 and GFN-xTB perform unsatisfactorily and do not provide any advantage over the MM description. These conclusions are supported also by similar analysis of a simple HutP protein-RNA interface, which is well-described by MD with the exception of just one H-bond. Some other methodological aspects of QM/MM calculations on protein-RNA interfaces are discussed.

SAMPL6 host-guest challenge: binding free energies via a multistep approach

In this effort in the SAMPL6 host-guest binding challenge, a combination of molecular dynamics and quantum mechanical methods were used to blindly predict the host-guest binding free energies of a series of cucurbit[8]uril (CB8), octa-acid (OA), and tetramethyl octa-acid (TEMOA) hosts bound to various guest molecules in aqueous solution. Poses for host-guest systems were generated via molecular dynamics (MD) simulations and clustering analyses. The binding free energies for the structures obtained via cluster analyses of MD trajectories were calculated using the MMPBSA method and density functional theory (DFT) with the inclusion of Grimme's dispersion correction, an implicit solvation model to model the aqueous solution, and the resolution-of-the-identity (RI) approximation (MMPBSA, RI-B3PW91-D3, and RI-B3PW91, respectively). Among these three methods tested, the results for OA and TEMOA systems showed MMPBSA and RI-B3PW91-D3 methods can be used to qualitatively rank binding energies of small molecules with an overbinding by 7 and 37 kcal/mol respectively, and RI-B3PW91 gave the poorest quality results, indicating the importance of dispersion correction for the binding free energy calculations. Due to the complexity of the CB8 systems, all of the methods tested show poor correlation with the experimental results. Other quantum mechanical approaches used for the calculation of binding free energies included DFT without the RI approximation, utilizing truncated basis sets to reduce the computational cost (memory, disk space, CPU time), and a corrected dielectric constant to account for ionic strength within the implicit solvation model.

Binding free energies in the SAMPL6 octa-acid host-guest challenge calculated with MM and QM methods

We have estimated free energies for the binding of eight carboxylate ligands to two variants of the octa-acid deep-cavity host in the SAMPL6 blind-test challenge (with or without endo methyl groups on the four upper-rim benzoate groups, OAM and OAH, respectively). We employed free-energy perturbation (FEP) for relative binding energies at the molecular mechanics (MM) and the combined quantum mechanical (QM) and MM (QM/MM) levels, the latter obtained with the reference-potential approach with QM/MM sampling for the MM → QM/MM FEP. The semiempirical QM method PM6-DH+ was employed for the ligand in the latter calculations. Moreover, binding free energies were also estimated from QM/MM optimised structures, combined with COSMO-RS estimates of the solvation energy and thermostatistical corrections from MM frequencies. They were performed at the PM6-DH+ level of theory with the full host and guest molecule in the QM system (and also four water molecules in the geometry optimisations) for 10-20 snapshots from molecular dynamics simulations of the complex. Finally, the structure with the lowest free energy was recalculated using the dispersion-corrected density-functional theory method TPSS-D3, for both the structure and the energy. The two FEP approaches gave similar results (PM6-DH+/MM slightly better for OAM), which were among the five submissions with the best performance in the challenge and gave the best results without any fit to data from the SAMPL5 challenge, with mean absolute deviations (MAD) of 2.4-5.2 kJ/mol and a correlation coefficient (R²) of 0.77-0.93. This is the first time QM/MM approaches give binding free energies that are competitive to those obtained with MM for the octa-acid host. The QM/MM-optimised structures gave somewhat worse performance (MAD = 3-8 kJ/mol and R² = 0.1-0.9), but the results were improved compared to previous studies of this system with similar methods.

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.

Bind3P: Optimization of a Water Model Based on Host-Guest Binding Data

We report a water model, Bind3P (Version 0.1), which was obtained by using sensitivity analysis to readjust the Lennard-Jones parameters of the TIP3P model against experimental binding free energies for six host-guest systems, along with pure liquid properties. Tests of Bind3P against >100 experimental binding free energies and enthalpies for host-guest systems distinct from the training set show a consistent drop in the mean signed error, relative to matched calculations with TIP3P. Importantly, Bind3P also yields some improvement in the hydration free energies of small organic molecules and preserves the accuracy of bulk water properties, such as density and the heat of vaporization. The same approach can be applied to more sophisticated water models that can better represent pure water properties. These results lend further support to the concept of integrating host-guest binding data into force field parametrization.

On the convergence of multi-scale free energy simulations

In this work we employ simple model systems to evaluate the relative performance of two of the most important free energy methods: The Zwanzig equation (also known as "Free energy perturbation") and Bennett's acceptance ratio method (BAR). Although our examples should be transferable to other kinds of free energy simulations, we focus on applications of multi-scale free energy simulations. Such calculations are especially complex, since they connect two different levels of theory with very different requirements in terms of speed, accuracy, sampling and parallelizability. We try to reconcile all those different factors by developing some simple criteria to guide the early stages of the development of a free energy protocol. This is accomplished by quantifying how many λ intermediate steps and how many potential energy evaluations are necessary in order to reach a certain level of convergence.

Relative Ligand-Binding Free Energies Calculated from Multiple Short QM/MM MD Simulations

We have devised a new efficient approach to compute combined quantum mechanical (QM) and molecular mechanical (MM, i.e. QM/MM) ligand-binding relative free energies. Our method employs the reference-potential approach with free-energy perturbation both at the MM level (between the two ligands) and from MM to QM/MM (for each ligand). To ensure that converged results are obtained for the MM → QM/MM perturbations, explicit QM/MM molecular dynamics (MD) simulations are performed with two intermediate mixed states. To speed up the calculations, we utilize the fact that the phase space can be extensively sampled at the MM level. Therefore, we run many short QM/MM MD simulations started from snapshots of the MM simulations, instead of a single long simulation. As a test case, we study the binding of nine cyclic carboxylate ligands to the octa-acid deep cavitand. Only the ligand is in the QM system, treated with the semiempirical PM6-DH+ method. We show that for eight of the ligands, we obtain well converged results with short MD simulations (1-15 ps). However, in one case, the convergence is slower (∼50 ps) owing to a mismatch between the conformational preferences of the MM and QM/MM potentials. We test the effect of initial minimization, the need of equilibration, and how many independent simulations are needed to reach a certain precision. The results show that the present approach is about four times faster than using standard MM → QM/MM free-energy perturbations with the same accuracy and precision.

Assessing the stability of free-energy perturbation calculations by performing variations in the method

We have calculated relative binding affinities for eight tetrafluorophenyl-triazole-thiogalactoside inhibitors of galectin-3 with the alchemical free-energy perturbation approach. We obtain a mean absolute deviation from experimental estimates of only 2-3 kJ/mol and a correlation coefficient (R²) of 0.5-0.8 for seven relative affinities spanning a range of up to 11 kJ/mol. We also studied the effect of using different methods to calculate the charges of the inhibitor and different sizes of the perturbed group (the atoms that are described by soft-core potentials and are allowed to have differing coordinates). However, the various approaches gave rather similar results and it is not possible to point out one approach as consistently and significantly better than the others. Instead, we suggest that such small and reasonable variations in the computational method can be used to check how stable the calculated results are and to obtain a more accurate estimate of the uncertainty than if performing only one calculation with a single computational setup.

Binding affinities of the farnesoid X receptor in the D3R Grand Challenge 2 estimated by free-energy perturbation and docking

We have studied the binding of 102 ligands to the farnesoid X receptor within the D3R Grand Challenge 2016 blind-prediction competition. First, we employed docking with five different docking software and scoring functions. The selected docked poses gave an average root-mean-squared deviation of 4.2 Å. Consensus scoring gave decent results with a Kendall's τ of 0.26 ± 0.06 and a Spearman's ρ of 0.41 ± 0.08. For a subset of 33 ligands, we calculated relative binding free energies with free-energy perturbation. Five transformations between the ligands involved a change of the net charge and we implemented and benchmarked a semi-analytic correction (Rocklin et al., J Chem Phys 139:184103, 2013) for artifacts caused by the periodic boundary conditions and Ewald summation. The results gave a mean absolute deviation of 7.5 kJ/mol compared to the experimental estimates and a correlation coefficient of R 2 = 0.1. These results were among the four best in this competition out of 22 submissions. The charge corrections were significant (7-8 kJ/mol) and always improved the results. By employing 23 intermediate states in the free-energy perturbation, there was a proper overlap between all states and the precision was 0.1-0.7 kJ/mol. However, thermodynamic cycles indicate that the sampling was insufficient in some of the perturbations.

Replica-Exchange and Standard State Binding Free Energies with Grand Canonical Monte Carlo

The ability of grand canonical Monte Carlo (GCMC) to create and annihilate molecules in a given region greatly aids the identification of water sites and water binding free energies in protein cavities. However, acceptance rates without the application of biased moves can be low, resulting in large variations in the observed water occupancies. Here, we show that replica-exchange of the chemical potential significantly reduces the variance of the GCMC data. This improvement comes at a negligible increase in computational expense when simulations comprise of runs at different chemical potentials. Replica-exchange GCMC is also found to substantially increase the precision of water binding free energies as calculated with grand canonical integration, which has allowed us to address a missing standard state correction.

Extensive Assessment of Various Computational Methods for Aspartate's pKa Shift

A series of computational methods for pK_a shift prediction are extensively tested on a set of benchmark protein systems, aiming at identifying pitfalls and evaluating their performance on high variants. Including 19 ASP residues in 10 protein systems, the benchmark set consists of both residues with highly shifted pK_a values as well as those varying little from the reference value, with an experimental RMS free energy differences of 2.49 kcal/mol with respect to blocked amino acid, namely the RMS pK_a shift being 1.82 pK_a units. The constant pH molecular dynamics (MD), alchemical methods, PROPKA3.1, and multiconformation continuum electrostatics give RMSDs of 1.52, 2.58, 1.37, and 3.52 pK_a units, respectively, on the benchmark set. The empirical scoring method is the most accurate one with extremely low computational cost, and the pH-dependent model is also able to provide accurate results, while the accuracy of MD sampling incorporating alchemical free energy simulation is prohibited by convergence achievement and the performance of conformational search incorporating multiconformation continuum electrostatics is bad. Former research works did not define statistical uncertainty with care and yielded the questionable conclusion that alchemical methods perform well in most benchmarks. In this work the traditional alchemical methods are thoroughly tested for high variants. We also performed the first application of nonequilibrium alchemical methods to the pK_a cases.

Predicting Binding Free Energies: Frontiers and Benchmarks

Binding free energy calculations based on molecular simulations provide predicted affinities for biomolecular complexes. These calculations begin with a detailed description of a system, including its chemical composition and the interactions among its components. Simulations of the system are then used to compute thermodynamic information, such as binding affinities. Because of their promise for guiding molecular design, these calculations have recently begun to see widespread applications in early-stage drug discovery. However, many hurdles remain in making them a robust and reliable tool. In this review, we highlight key challenges of these calculations, discuss some examples of these challenges, and call for the designation of standard community benchmark test systems that will help the research community generate and evaluate progress. In our view, progress will require careful assessment and evaluation of new methods, force fields, and modeling innovations on well-characterized benchmark systems, and we lay out our vision for how this can be achieved.

Binding free energies in the SAMPL5 octa-acid host-guest challenge calculated with DFT-D3 and CCSD(T)

We have tried to calculate the free energy for the binding of six small ligands to two variants of the octa-acid deep cavitand host in the SAMPL5 blind challenge. We employed structures minimised with dispersion-corrected density-functional theory with small basis sets and energies were calculated using large basis sets. Solvation energies were calculated with continuum methods and thermostatistical corrections were obtained from frequencies calculated at the HF-3c level. Care was taken to minimise the effects of the flexibility of the host by keeping the complexes as symmetric and similar as possible. In some calculations, the large net charge of the host was reduced by removing the propionate and benzoate groups. In addition, the effect of a restricted molecular dynamics sampling of structures was tested. Finally, we tried to improve the energies by using the DLPNO-CCSD(T) approach. Unfortunately, results of quite poor quality were obtained, with no correlation to the experimental data, systematically too positive affinities (by ~50 kJ/mol) and a mean absolute error (after removal of the systematic error) of 11-16 kJ/mol. DLPNO-CCSD(T) did not improve the results, so the accuracy is not limited by the energy function. Instead, four likely sources of errors were identified: first, the minimised structures were often incorrect, owing to the omission of explicit solvent. They could be partly improved by performing the minimisations in a continuum solvent with four water molecules around the charged groups of the ligands. Second, some ligands could bind in several different conformations, requiring sampling of reasonable structures. Third, there is an indication the continuum-solvation model has problems to accurately describe the binding of both the negatively and positively charged guest molecules. Fourth, different methods to calculate the thermostatistical corrections gave results that differed by up to 30 kJ/mol and there is an indication that HF-3c overestimates the entropy term. In conclusion, it is a challenge to calculate binding affinities for this octa-acid system with quantum-mechanical methods.

Absolute binding free energies for octa-acids and guests in SAMPL5 : Evaluating binding free energies for octa-acid and guest complexes in the SAMPL5 blind challenge

As part of the SAMPL5 blind prediction challenge, we calculate the absolute binding free energies of six guest molecules to an octa-acid (OAH) and to a methylated octa-acid (OAMe). We use the double decoupling method via thermodynamic integration (TI) or Hamiltonian replica exchange in connection with the Bennett acceptance ratio (HREM-BAR). We produce the binding poses either through manual docking or by using GalaxyDock-HG, a docking software developed specifically for this study. The root mean square deviations for our most accurate predictions are 1.4 kcal mol-1 for OAH with TI and 1.9 kcal mol-1 for OAMe with HREM-BAR. Our best results for OAMe were obtained for systems with ionic concentrations corresponding to the ionic strength of the experimental solution. The most problematic system contains a halogenated guest. Our attempt to model the σ-hole of the bromine using a constrained off-site point charge, does not improve results. We use results from molecular dynamics simulations to argue that the distinct binding affinities of this guest to OAH and OAMe are due to a difference in the flexibility of the host. We believe that the results of this extensive analysis of host-guest complexes will help improve the protocol used in predicting binding affinities for larger systems, such as protein-substrate compounds.

Calculating binding free energies of host-guest systems using the AMOEBA polarizable force field

Molecular recognition is of paramount interest in many applications. Here we investigate a series of host-guest systems previously used in the SAMPL4 blind challenge by using molecular simulations and the AMOEBA polarizable force field. The free energy results computed by Bennett's acceptance ratio (BAR) method using the AMOEBA polarizable force field ranked favorably among the entries submitted to the SAMPL4 host-guest competition [Muddana, et al., J. Comput.-Aided Mol. Des., 2014, 28, 305-317]. In this work we conduct an in-depth analysis of the AMOEBA force field host-guest binding thermodynamics by using both BAR and the orthogonal space random walk (OSRW) methods. The binding entropy-enthalpy contributions are analyzed for each host-guest system. For systems of inordinate binding entropy-enthalpy values, we further examine the hydrogen bonding patterns and configurational entropy contribution. The binding mechanism of this series of host-guest systems varies from ligand to ligand, driven by enthalpy and/or entropy changes. Convergence of BAR and OSRW binding free energy methods is discussed. Ultimately, this work illustrates the value of molecular modelling and advanced force fields for the exploration and interpretation of binding thermodynamics.

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.

Overview of the SAMPL5 host-guest challenge: Are we doing better?

The ability to computationally predict protein-small molecule binding affinities with high accuracy would accelerate drug discovery and reduce its cost by eliminating rounds of trial-and-error synthesis and experimental evaluation of candidate ligands. As academic and industrial groups work toward this capability, there is an ongoing need for datasets that can be used to rigorously test new computational methods. Although protein-ligand data are clearly important for this purpose, their size and complexity make it difficult to obtain well-converged results and to troubleshoot computational methods. Host-guest systems offer a valuable alternative class of test cases, as they exemplify noncovalent molecular recognition but are far smaller and simpler. As a consequence, host-guest systems have been part of the prior two rounds of SAMPL prediction exercises, and they also figure in the present SAMPL5 round. In addition to being blinded, and thus avoiding biases that may arise in retrospective studies, the SAMPL challenges have the merit of focusing multiple researchers on a common set of molecular systems, so that methods may be compared and ideas exchanged. The present paper provides an overview of the host-guest component of SAMPL5, which centers on three different hosts, two octa-acids and a glycoluril-based molecular clip, and two different sets of guest molecules, in aqueous solution. A range of methods were applied, including electronic structure calculations with implicit solvent models; methods that combine empirical force fields with implicit solvent models; and explicit solvent free energy simulations. The most reliable methods tend to fall in the latter class, consistent with results in prior SAMPL rounds, but the level of accuracy is still below that sought for reliable computer-aided drug design. Advances in force field accuracy, modeling of protonation equilibria, electronic structure methods, and solvent models, hold promise for future improvements.

Blind prediction of distribution in the SAMPL5 challenge with QM based protomer and pK a corrections

The computation of distribution coefficients between polar and apolar phases requires both an accurate characterization of transfer free energies between phases and proper accounting of ionization and protomerization. We present a protocol for accurately predicting partition coefficients between two immiscible phases, and then apply it to 53 drug-like molecules in the SAMPL5 blind prediction challenge. Our results combine implicit solvent QM calculations with classical MD simulations using the non-Boltzmann Bennett free energy estimator. The OLYP/DZP/SMD method yields predictions that have a small deviation from experiment (RMSD = 2.3 [Formula: see text] D units), relative to other participants in the challenge. Our free energy corrections based on QM protomer and [Formula: see text] calculations increase the correlation between predicted and experimental distribution coefficients, for all methods used. Unfortunately, these corrections are overly hydrophilic, and fail to account for additional effects such as aggregation, water dragging and the presence of polar impurities in the apolar phase. We show that, although expensive, QM-NBB free energy calculations offer an accurate and robust method that is superior to standard MM and QM techniques alone.

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.

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.

Resolving the problem of trapped water in binding cavities: prediction of host-guest binding free energies in the SAMPL5 challenge by funnel metadynamics

The funnel metadynamics method enables rigorous calculation of the potential of mean force along an arbitrary binding path and thereby evaluation of the absolute binding free energy. A problem of such physical paths is that the mechanism characterizing the binding process is not always obvious. In particular, it might involve reorganization of the solvent in the binding site, which is not easily captured with a few geometrically defined collective variables that can be used for biasing. In this paper, we propose and test a simple method to resolve this trapped-water problem by dividing the process into an artificial host-desolvation step and an actual binding step. We show that, under certain circumstances, the contribution from the desolvation step can be calculated without introducing further statistical errors. We apply the method to the problem of predicting host–guest binding free energies in the SAMPL5 blind challenge, using two octa-acid hosts and six guest molecules. For one of the hosts, well-converged results are obtained and the prediction of relative binding free energies is the best among all the SAMPL5 submissions. For the other host, which has a narrower binding pocket, the statistical uncertainties are slightly higher; longer simulations would therefore be needed to obtain conclusive results.

Binding-affinity predictions of HSP90 in the D3R Grand Challenge 2015 with docking, MM/GBSA, QM/MM, and free-energy simulations

We have estimated the binding affinity of three sets of ligands of the heat-shock protein 90 in the D3R grand challenge blind test competition. We have employed four different methods, based on five different crystal structures: first, we docked the ligands to the proteins with induced-fit docking with the Glide software and calculated binding affinities with three energy functions. Second, the docked structures were minimised in a continuum solvent and binding affinities were calculated with the MM/GBSA method (molecular mechanics combined with generalised Born and solvent-accessible surface area solvation). Third, the docked structures were re-optimised by combined quantum mechanics and molecular mechanics (QM/MM) calculations. Then, interaction energies were calculated with quantum mechanical calculations employing 970-1160 atoms in a continuum solvent, combined with energy corrections for dispersion, zero-point energy and entropy, ligand distortion, ligand solvation, and an increase of the basis set to quadruple-zeta quality. Fourth, relative binding affinities were estimated by free-energy simulations, using the multi-state Bennett acceptance-ratio approach. Unfortunately, the results were varying and rather poor, with only one calculation giving a correlation to the experimental affinities larger than 0.7, and with no consistent difference in the quality of the predictions from the various methods. For one set of ligands, the results could be strongly improved (after experimental data were revealed) if it was recognised that one of the ligands displaced one or two water molecules. For the other two sets, the problem is probably that the ligands bind in different modes than in the crystal structures employed or that the conformation of the ligand-binding site or the whole protein changes.

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.

Blinded predictions of host-guest standard free energies of binding in the SAMPL5 challenge

In the context of the SAMPL5 blinded challenge standard free energies of binding were predicted for a dataset of 22 small guest molecules and three different host molecules octa-acids (OAH and OAMe) and a cucurbituril (CBC). Three sets of predictions were submitted, each based on different variations of classical molecular dynamics alchemical free energy calculation protocols based on the double annihilation method. The first model (model A) yields a free energy of binding based on computed free energy changes in solvated and host-guest complex phases; the second (model B) adds long range dispersion corrections to the previous result; the third (model C) uses an additional standard state correction term to account for the use of distance restraints during the molecular dynamics simulations. Model C performs the best in terms of mean unsigned error for all guests (MUE [Formula: see text]-95 % confidence interval) for the whole data set and in particular for the octa-acid systems (MUE [Formula: see text]). The overall correlation with experimental data for all models is encouraging ([Formula: see text]). The correlation between experimental and computational free energy of binding ranks as one of the highest with respect to other entries in the challenge. Nonetheless the large MUE for the best performing model highlights systematic errors, and submissions from other groups fared better with respect to this metric.