Converging free energies of binding in cucurbit[7]uril and octa-acid host-guest systems from SAMPL4 using expanded ensemble simulations

Replica Exchange of Expanded Ensembles: A Generalized Ensemble Approach with Enhanced Flexibility and Parallelizability

Generalized ensemble methods such as Hamiltonian replica exchange (HREX) and expanded ensemble (EE) have been shown effective in free energy calculations for various contexts, given their ability to circumvent free energy barriers via nonphysical pathways defined by states with different modified Hamiltonians. However, both HREX and EE methods come with drawbacks, such as limited flexibility in parameter specification or the lack of parallelizability for more complicated applications. To address this challenge, we present the method of replica exchange of expanded ensembles (REXEE), which integrates the principles of HREX and EE methods by periodically exchanging coordinates of EE replicas sampling different yet overlapping sets of alchemical states. With the solvation free energy calculation of anthracene and binding free energy calculation of the CB7-10 binding complex, we show that the REXEE method achieves the same level of accuracy in free energy calculations as the HREX and EE methods, while offering enhanced flexibility and parallelizability. Additionally, we examined REXEE simulations with various setups to understand how different exchange frequencies and replica configurations influence the sampling efficiency in the fixed-weight phase and the weight convergence in the weight-updating phase. The REXEE approach can be further extended to support asynchronous parallelization schemes, allowing looser communications between larger numbers of loosely coupled processors such as cloud computing and therefore promising much more scalable and adaptive executions of alchemical free energy calculations. All algorithms for the REXEE method are available in the Python package ensemble_md, which offers an interface for REXEE simulation management without modifying the source code in GROMACS.

Enhanced Sampling of Buried Charges in Free Energy Calculations Using Replica Exchange with Charge Tempering

Buried ionizable groups in proteins often play important structural and functional roles. However, it is generally challenging to study the detailed molecular mechanisms solely based on experimental measurements. Free energy calculations using atomistic simulations, on the other hand, complement experimental studies and can provide high temporal and spatial resolution information that can lead to mechanistic insights. Nevertheless, it is also well recognized that sufficient sampling of such atomistic simulations can be challenging, considering that structural changes related to the buried charges may be very slow. In the present study, we describe a simple but effective enhanced sampling technique called replica exchange with charge tempering (REChgT) with a novel free energy method, multisite λ dynamics (MSλD), to study two systems containing buried charges, pKa prediction of a small molecule, orotate, in complex with the dihydroorotate dehydrogenase, and relative stability of a Glu-Lys pair buried in the hydrophobic core of two variants of Staphylococcal nuclease. Compared to the original MSλD simulations, the usage of REChgT dramatically increases sampling in both conformational and alchemical spaces, which directly translates into a significant reduction of wall time to converge the free energy calculations. This study highlights the importance of sufficient sampling toward developing improved free energy methods.

Exploring the impact of taurine on the biochemical properties of urate oxidase: response surface methodology and molecular dynamics simulation

This paper investigates the impact of taurine as an additive on the structural and functional stability of urate oxidase. First, the effect of the processing parameters for the stabilization of Urate Oxidase (UOX) using taurine was examined using the response surface methodology (RSM) and the central composite design (CCD) model. Also, the study examines thermodynamic and kinetic parameters as well as structural changes of urate oxidase with and without taurine. Fluorescence intensity changes indicated static quenching during taurine binding. The obtained result indicates that taurine has the ability to preserve the native structural conformation of UOX. Furthermore, molecular dynamics simulation is conducted in order to get insights into the alterations in the structure of urate oxidase in the absence and presence of taurine under optimal conditions. The molecular dynamics simulation section investigated the formation of hydrogen bonds (H-bonds) between different components as well as analysis of root mean square deviation (RMSD), root mean square fluctuations (RMSF) and secondary structure. Lower Cα-RMSD and RMSF values indicate greater stabilization of the taurine-treated UOX structure compared to the free enzyme. The results of molecular docking indicate that the binding of taurine to the UOX enzyme through hydrophobic interactions is associated with a negative value for the Gibbs free energy.

Expanded ensemble predictions of absolute binding free energies in the SAMPL9 host-guest challenge

As part of the SAMPL9 community-wide blind host-guest challenge, we implemented an expanded ensemble workflow to predict absolute binding free energies for 13 small molecules against pillar[6]arene. Notable features of our protocol include consideration of a variety of protonation and enantiomeric states for both host and guests, optimization of alchemical intermediates, and analysis of free energy estimates and their uncertainty using large numbers of simulation replicates performed using distributed computing. Our predictions of absolute binding free energies resulted in a mean absolute error of 2.29 kcal mol-1 and an R2 of 0.54. Overall, results show that expanded ensemble calculations using all-atom molecular dynamics simulations are a valuable and efficient computational tool in predicting absolute binding free energies.

Alchemical Metadynamics: Adding Alchemical Variables to Metadynamics to Enhance Sampling in Free Energy Calculations

Performing alchemical transformations, in which one molecular system is nonphysically changed to another system, is a popular approach adopted in performing free energy calculations associated with various biophysical processes, such as protein-ligand binding or the transfer of a molecule between environments. While the sampling of alchemical intermediate states in either parallel (e.g., Hamiltonian replica exchange) or serial manner (e.g., expanded ensemble) can bridge the high-probability regions in the configurational space between two end states of interest, alchemical methods can fail in scenarios where the most important slow degrees of freedom in the configurational space are, in large part, orthogonal to the alchemical variable, or if the system gets trapped in a deep basin extending in both the configurational and alchemical space. To alleviate these issues, we propose to use alchemical variables as an additional dimension in metadynamics, making it possible to both sample collective variables and to enhance sampling in free energy calculations simultaneously. In this study, we validate our implementation of "alchemical metadynamics" in PLUMED with test systems and alchemical processes with varying complexities and dimensionalities of collective variable space, including the interconversion between the torsional metastable states of a toy system and the methylation of a nucleoside both in the isolated form and in a duplex. We show that multidimensional alchemical metadynamics can address the challenges mentioned above and further accelerate sampling by introducing configurational collective variables. The method can trivially be combined with other metadynamics-based algorithms implemented in PLUMED. The necessary PLUMED code changes have already been released for general use in PLUMED 2.8.

Molecular Modelling of Ionic Liquids: Situations When Charge Scaling Seems Insufficient

Charge scaling as an effective solution to the experiment-computation disagreement in molecular modelling of ionic liquids (ILs) could bring the computational results close to the experimental reference for various thermodynamic properties. According to the large-scale benchmark calculations of mass density, solvation, and water-ILs transfer-free energies in our series of papers, the charge-scaling factor of 0.8 serves as a near-optimal option generally applicable to most ILs, although a system-dependent parameter adjustment could be attempted for further improved performance. However, there are situations in which such a charge-scaling treatment would fail. Namely, charge scaling cannot really affect the simulation outcome, or minimally perturbs the results that are still far from the experimental value. In such situations, the vdW radius as an additional adjustable parameter is commonly tuned to minimize the experiment-calculation deviation. In the current work, considering two ILs from the quinuclidinium family, we investigate the impacts of this vdW-scaling treatment on the mass density and the solvation/partition thermodynamics in a fashion similar to our previous charge-scaling works, i.e., scanning the vdW-scaling factor and computing physical properties under these parameter sets. It is observed that the mass density exhibits a linear response to the vdW-scaling factor with slopes close to -1.8 g/mL. By further investigating a set of physiochemically relevant temperatures between 288 K and 348 K, we confirm the robustness of the vdW-scaling treatment in the estimation of bulk properties. The best vdW-scaling parameter for mass density would worsen the computation of solvation/partition thermodynamics, and a marginal decrease in the vdW-scaling factor is considered as an intermediate option balancing the reproductions of bulk properties and solvation thermodynamics. These observations could be understood in a way similar to the charge-scaling situation. i.e., overfitting some properties (e.g., mass density) would degrade the accuracy of the other properties (e.g., solvation free energies). Following this principle, the general guideline for applying this vdW-tuning protocol is by using values between the density-derived choice and the solvation/partition-derived solution. The charge and current vdW scaling treatments cover commonly encountered ILs, completing the protocol for accurate modelling of ILs with fixed-charge force fields.

Inhibitory mechanism of two homoisoflavonoids from Ophiopogon japonicus on tyrosinase activity: insight from spectroscopic analysis and molecular docking

The inhibition mechanism of two homoisoflavonoids from Ophiopogon japonicus including methylophiopogonanone A (MO-A) and methylophiopogonanone B (MO-B) on tyrosinase (Tyr) was studied by multiple spectroscopic techniques and molecular docking. The results showed that the two homoisoflavonoids both inhibited Tyr activity via a reversible mixed-inhibition, with a half inhibitory concentration (IC50) of (10.87 ± 0.25) × 10-5 and (18.76 ± 0.14) × 10-5 mol L-1, respectively. The fluorescence quenching and secondary structure change of Tyr caused by MO-A and B are mainly driven by hydrophobic interaction and hydrogen bonding. Molecular docking analysis indicated that phenylmalandioxin in MO-A and methoxy in MO-B could coordinate with a Cu ion in the active center of Tyr, and interacted with amino acid Glu322 to form hydrogen bonding, occupying the catalytic center to block the entry of the substrate and consequently inhibit Tyr activity. This study may provide new perspectives on the inhibition mechanism of MO-A and MO-B on Tyr and serve a scientific basis for screening effective Tyr inhibitors.

Expanded Ensemble Methods Can be Used to Accurately Predict Protein-Ligand Relative Binding Free Energies

Alchemical free energy methods have become indispensable in computational drug discovery for their ability to calculate highly accurate estimates of protein-ligand affinities. Expanded ensemble (EE) methods, which involve single simulations visiting all of the alchemical intermediates, have some key advantages for alchemical free energy calculation. However, there have been relatively few examples published in the literature of using expanded ensemble simulations for free energies of protein-ligand binding. In this paper, as a test of expanded ensemble methods, we compute relative binding free energies using the Open Force Field Initiative force field (codename "Parsley") for 24 pairs of Tyk2 inhibitors derived from a congeneric series of 16 compounds. The EE predictions agree well with the experimental values (root-mean-square error (RMSE) of 0.94 ± 0.13 kcal mol^-1 and mean unsigned error (MUE) of 0.75 ± 0.12 kcal mol^-1). We find that while increasing the number of alchemical intermediates can improve the phase space overlap, faster convergence can be obtained with fewer intermediates, as long as acceptance rates are sufficient. We also find that convergence can be improved using more aggressive updating of biases, and that estimates can be improved by performing multiple independent EE calculations. This work demonstrates that EE is a viable option for alchemical free energy calculation. We discuss the implications of these findings for rational drug design, as well as future directions for improvement.

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 Challenge Overview: assessing the reliability of polarizable and non-polarizable methods for binding free energy calculations

The SAMPL challenges focus on testing and driving progress of computational methods to help guide pharmaceutical drug discovery. However, assessment of methods for predicting binding affinities is often hampered by computational challenges such as conformational sampling, protonation state uncertainties, variation in test sets selected, and even lack of high quality experimental data. SAMPL blind challenges have thus frequently included a component focusing on host-guest binding, which removes some of these challenges while still focusing on molecular recognition. Here, we report on the results of the SAMPL7 blind prediction challenge for host-guest affinity prediction. In this study, we focused on three different host-guest categories-a familiar deep cavity cavitand series which has been featured in several prior challenges (where we examine binding of a series of guests to two hosts), a new series of cyclodextrin derivatives which are monofunctionalized around the rim to add amino acid-like functionality (where we examine binding of two guests to a series of hosts), and binding of a series of guests to a new acyclic TrimerTrip host which is related to previous cucurbituril hosts. Many predictions used methods based on molecular simulations, and overall success was mixed, though several methods stood out. As in SAMPL6, we find that one strategy for achieving reasonable accuracy here was to make empirical corrections to binding predictions based on previous data for host categories which have been studied well before, though this can be of limited value when new systems are included. Additionally, we found that alchemical free energy methods using the AMOEBA polarizable force field had considerable success for the two host categories in which they participated. The new TrimerTrip system was also found to introduce some sampling problems, because multiple conformations may be relevant to binding and interconvert only slowly. Overall, results in this challenge tentatively suggest that further investigation of polarizable force fields for these challenges may be warranted.

SAMPL7 TrimerTrip host-guest binding affinities from extensive alchemical and end-point free energy calculations

The prediction of host-guest binding affinities with computational modelling is still a challenging task. In the 7th statistical assessment of the modeling of proteins and ligands (SAMPL) challenge, a new host named TrimerTrip was synthesized and the thermodynamic parameters of 16 structurally diverse guests binding to the host were characterized. In the TrimerTrip-guest challenge, only structures of the host and the guests are provided, which indicates that the predictions of both the binding poses and the binding affinities are under assessment. In this work, starting from the binding poses obtained from our previous enhanced sampling simulations in the configurational space, we perform extensive alchemical and end-point free energy calculations to calculate the host-guest binding affinities retrospectively. The alchemical predictions with two widely accepted charge schemes (i.e. AM1-BCC and RESP) are in good agreement with the experimental reference, while the end-point estimates perform poorly in reproducing the experimental binding affinities. Aside from the absolute value of the binding affinity, the rank of binding free energies is also crucial in drug design. Surprisingly, the end-point MM/PBSA method seems very powerful in reproducing the experimental rank of binding affinities. Although the length of our simulations is long and the intermediate spacing is dense, the convergence behavior is not very good, which may arise from the flexibility of the host molecule. Enhanced sampling techniques in the configurational space may be required to obtain fully converged sampling. Further, as the length of sampling in alchemical free energy calculations already achieves several hundred ns, performing direct simulations of the binding/unbinding event in the physical space could be more useful and insightful. More details about the binding pathway and mechanism could be obtained in this way. The nonequilibrium method could also be a nice choice if one insists to use the alchemical method, as the intermediate sampling is avoided to some extent.

New insight into the molecular mechanism of the trehalose effect on urate oxidase stability

Urate oxidase (EC 1.7.3.3) is a key enzyme in the purine metabolism which is applied in the treatment of gout and also, as a diagnostic reagent for uric acid detection. In the current study, the trehalose (TRE) effects as an additive on the structural stability and function of uricase were investigated. For recombinant expression of UOX in E. coli BL21 cells, firstly the coding sequence was subcloned into the pET-28a vector and after induction with IPTG, the recombinant UOX was purified by affinity chromatography using a Ni-NTA agarose column. To specify the trehalose effects on the urate oxidase (UOX) structure, optimum pH, optimum temperature, kinetic and thermodynamic parameters and also, the intrinsic fluorescence of UOX in the absence and presence of trehalose were examined. The UOX half-life is 24.32 min at 40 °C, whereas the UOX-TRE has a higher half-life (32.09 min) at this temperature. Generally, our findings confirm that trehalose has a protective effect on the enzyme structure. Optimum pH and temperature were 9 and 25 °C, respectively for both the naked and treated enzymes and their activity retained 42.18 and 64.80%, respectively after 48 h of incubation at room temperature. Also, theoretical results indicate that the random coil of the enzyme was converted to α-helix and β-sheet in the presence of trehalose which may preserve the integrity of the active site of the enzyme and increased the enzymatic activity. The MD simulation results indicated greater stability of the uricase structure in the presence of trehalose.Communicated by Ramaswamy H. Sarma.

SAMPL7 TrimerTrip host-guest binding poses and binding affinities from spherical-coordinates-biased simulations

Host-guest binding remains a major challenge in modern computational modelling. The newest 7th statistical assessment of the modeling of proteins and ligands (SAMPL) challenge contains a new series of host-guest systems. The TrimerTrip host binds to 16 structurally diverse guests. Previously, we have successfully employed the spherical coordinates as the collective variables coupled with the enhanced sampling technique metadynamics to enhance the sampling of the binding/unbinding event, search for possible binding poses and calculate the binding affinities in all three host-guest binding cases of the 6th SAMPL challenge. In this work, we report a retrospective study on the TrimerTrip host-guest systems by employing the same protocol to investigate the TrimerTrip host in the SAMPL7 challenge. As no binding pose is provided by the SAMPL7 host, our simulations initiate from randomly selected configurations and are proceeded long enough to obtain converged free energy estimates and search for possible binding poses. The calculated binding affinities are in good agreement with the experimental reference, and the obtained binding poses serve as a nice starting point for end-point or alchemical free energy calculations. Note that as the work is performed after the close of the SAMPL7 challenge, we do not participate in the challenge and the results are not formally submitted to the SAMPL7 challenge.

The SAMPL6 SAMPLing challenge: assessing the reliability and efficiency of binding free energy calculations

Approaches for computing small molecule binding free energies based on molecular simulations are now regularly being employed by academic and industry practitioners to study receptor-ligand systems and prioritize the synthesis of small molecules for ligand design. Given the variety of methods and implementations available, it is natural to ask how the convergence rates and final predictions of these methods compare. In this study, we describe the concept and results for the SAMPL6 SAMPLing challenge, the first challenge from the SAMPL series focusing on the assessment of convergence properties and reproducibility of binding free energy methodologies. We provided parameter files, partial charges, and multiple initial geometries for two octa-acid (OA) and one cucurbit[8]uril (CB8) host-guest systems. Participants submitted binding free energy predictions as a function of the number of force and energy evaluations for seven different alchemical and physical-pathway (i.e., potential of mean force and weighted ensemble of trajectories) methodologies implemented with the GROMACS, AMBER, NAMD, or OpenMM simulation engines. To rank the methods, we developed an efficiency statistic based on bias and variance of the free energy estimates. For the two small OA binders, the free energy estimates computed with alchemical and potential of mean force approaches show relatively similar variance and bias as a function of the number of energy/force evaluations, with the attach-pull-release (APR), GROMACS expanded ensemble, and NAMD double decoupling submissions obtaining the greatest efficiency. The differences between the methods increase when analyzing the CB8-quinine system, where both the guest size and correlation times for system dynamics are greater. For this system, nonequilibrium switching (GROMACS/NS-DS/SB) obtained the overall highest efficiency. Surprisingly, the results suggest that specifying force field parameters and partial charges is insufficient to generally ensure reproducibility, and we observe differences between seemingly converged predictions ranging approximately from 0.3 to 1.0 kcal/mol, even with almost identical simulations parameters and system setup (e.g., Lennard-Jones cutoff, ionic composition). Further work will be required to completely identify the exact source of these discrepancies. Among the conclusions emerging from the data, we found that Hamiltonian replica exchange-while displaying very small variance-can be affected by a slowly-decaying bias that depends on the initial population of the replicas, that bidirectional estimators are significantly more efficient than unidirectional estimators for nonequilibrium free energy calculations for systems considered, and that the Berendsen barostat introduces non-negligible artifacts in expanded ensemble simulations.

SAMPL6 host-guest binding affinities and binding poses from spherical-coordinates-biased simulations

Host-guest binding is a challenging problem in computer simulation. The prediction of binding affinities between hosts and guests is an important part of the statistical assessment of the modeling of proteins and ligands (SAMPL) challenges. In this work, the volume-based variant of well-tempered metadynamics is employed to calculate the binding affinities of the host-guest systems in the SAMPL6 challenge. By biasing the spherical coordinates describing the relative position of the host and the guest, the initial-configuration-induced bias vanishes and all possible binding poses are explored. The agreement between the predictions and the experimental results and the observation of new binding poses indicate that the volume-based technique serves as a nice candidate for the calculation of binding free energies and the search of the binding poses.

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

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

Theoretical understanding of the thermodynamics and interactions in transcriptional regulator TtgR-ligand binding

The transcriptional regulator TtgR belongs to the TetR family of transcriptional repressors. It depresses the transcription of the TtgABC operon and itself and thus regulates the extrusion of noxious chemicals with efflux pumps in bacterial cells. As the ligand-binding domain of TtgR is rather flexible, it can bind with a number of structurally diverse ligands, such as antibiotics, flavonoids and aromatic solvents. In the current work, we perform equilibrium and nonequilibrium alchemical free energy simulation to predict the binding affinities of a series of ligands targeting the TtgR protein and an agreement between the theoretical prediction and the experimental result is observed. End-point methods MM/PBSA and MM/GBSA are also employed for comparison. We further study the interaction maps and contacts between the protein and the ligand and identify important interactions in the protein-ligand binding cases. The dynamics fluctuation and secondary structures are also investigated. The current work sheds light on atomic and thermodynamic understanding of the TtgR-ligand interactions.

A combined molecular dynamics simulation and quantum mechanics study on mercaptopurine interaction with the cucurbit [6,7] urils: Analysis of electronic structure

In the current study, the probability of complex formation between mercaptopurine drug with cucurbit[6]urils and cucurbit[7]urils has been investigated. The calculations for geometry optimization of complexes have been carried out by means of DFT (B3LYP), DFT-D (B3LYP-D) and M06-2X methods. The Atoms In Molecules (AIM), Natural Bond Orbital (NBO), NMR, the density of states (DOSs) and frontier molecular orbital (MO) analyses have been done on the inclusion complexes. In addition, the UV-Vis spectra of the first eight states have been obtained by CAM-B3LYP/TD-DFT calculation. The obtained results of the complexation process reveal that CB[7]-DRG complexes are more favorable than that of CB[6]-DRG interactions. Furthermore, our theoretical results show that configurations III and I are the most stable configurations related to the CB[6]/DRG and CB[7]/DRG interactions, respectively. The positive ∇²_ρ(r) and HC values at the bond critical points indicate that exist the weak H-bonds between CB[6] and CB[7] with H atoms of the drug molecule. The obtained negative binding energy values of CB[7]-DRG interaction in solution phase show the stability of these complexes in the aqueous medium. Also, all of the observed parameters of molecular dynamics simulation such as the number of contacts, hydrogen bonding, center-of-mass distance and van der Waals energy values confirm the encapsulation of mercaptopurine molecule inside the cucurbit[7]urils cavity at about 3.2ns.

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.

Lessons learned from comparing molecular dynamics engines on the SAMPL5 dataset

We describe our efforts to prepare common starting structures and models for the SAMPL5 blind prediction challenge. We generated the starting input files and single configuration potential energies for the host-guest in the SAMPL5 blind prediction challenge for the GROMACS, AMBER, LAMMPS, DESMOND and CHARMM molecular simulation programs. All conversions were fully automated from the originally prepared AMBER input files using a combination of the ParmEd and InterMol conversion programs. We find that the energy calculations for all molecular dynamics engines for this molecular set agree to better than 0.1 % relative absolute energy for all energy components, and in most cases an order of magnitude better, when reasonable choices are made for different cutoff parameters. However, there are some surprising sources of statistically significant differences. Most importantly, different choices of Coulomb's constant between programs are one of the largest sources of discrepancies in energies. We discuss the measures required to get good agreement in the energies for equivalent starting configurations between the simulation programs, and the energy differences that occur when simulations are run with program-specific default simulation parameter values. Finally, we discuss what was required to automate this conversion and comparison.

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.

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.

Evaluating thermodynamic integration performance of the new amber molecular dynamics package and assess potential halogen bonds of enoyl-ACP reductase (FabI) benzimidazole inhibitors

Thermodynamic integration (TI) can provide accurate binding free energy insights in a lead optimization program, but its high computational expense has limited its usage. In the effort of developing an efficient and accurate TI protocol for FabI inhibitors lead optimization program, we carefully compared TI with different Amber molecular dynamics (MD) engines (sander and pmemd), MD simulation lengths, the number of intermediate states and transformation steps, and the Lennard-Jones and Coulomb Softcore potentials parameters in the one-step TI, using eleven benzimidazole inhibitors in complex with Francisella tularensis enoyl acyl reductase (FtFabI). To our knowledge, this is the first study to extensively test the new AMBER MD engine, pmemd, on TI and compare the parameters of the Softcore potentials in the one-step TI in a protein-ligand binding system. The best performing model, the one-step pmemd TI, using 6 intermediate states and 1 ns MD simulations, provides better agreement with experimental results (RMSD = 0.52 kcal/mol) than the best performing implicit solvent method, QM/MM-GBSA from our previous study (RMSD = 3.00 kcal/mol), while maintaining similar efficiency. Briefly, we show the optimized TI protocol to be highly accurate and affordable for the FtFabI system. This approach can be implemented in a larger scale benzimidazole scaffold lead optimization against FtFabI. Lastly, the TI results here also provide structure-activity relationship insights, and suggest the parahalogen in benzimidazole compounds might form a weak halogen bond with FabI, which is a well-known halogen bond favoring enzyme.

Parameterization of an effective potential for protein-ligand binding from host-guest affinity data

Force field accuracy is still one of the "stalemates" in biomolecular modeling. Model systems with high quality experimental data are valuable instruments for the validation and improvement of effective potentials. With respect to protein-ligand binding, organic host-guest complexes have long served as models for both experimental and computational studies because of the abundance of binding affinity data available for such systems. Binding affinity data collected for cyclodextrin (CD) inclusion complexes, a popular model for molecular recognition, is potentially a more reliable resource for tuning energy parameters than hydration free energy measurements. Convergence of binding free energy calculations on CD host-guest systems can also be obtained rapidly, thus offering the opportunity to assess the robustness of these parameters. In this work, we demonstrate how implicit solvent parameters can be developed using binding affinity experimental data and the binding energy distribution analysis method (BEDAM) and validated using the Grid Inhomogeneous Solvation Theory analysis. These new solvation parameters were used to study protein-ligand binding in two drug targets against the HIV-1 virus and improved the agreement between the calculated and the experimental binding affinities. This work illustrates how benchmark sets of high quality experimental binding affinity data and physics-based binding free energy models can be used to evaluate and optimize force fields for protein-ligand systems. Copyright © 2015 John Wiley & Sons, Ltd.

Guidelines for the analysis of free energy calculations

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

The SAMPL4 host-guest blind prediction challenge: an overview

Prospective validation of methods for computing binding affinities can help assess their predictive power and thus set reasonable expectations for their performance in drug design applications. Supramolecular host-guest systems are excellent model systems for testing such affinity prediction methods, because their small size and limited conformational flexibility, relative to proteins, allows higher throughput and better numerical convergence. The SAMPL4 prediction challenge therefore included a series of host-guest systems, based on two hosts, cucurbit[7]uril and octa-acid. Binding affinities in aqueous solution were measured experimentally for a total of 23 guest molecules. Participants submitted 35 sets of computational predictions for these host-guest systems, based on methods ranging from simple docking, to extensive free energy simulations, to quantum mechanical calculations. Over half of the predictions provided better correlations with experiment than two simple null models, but most methods underperformed the null models in terms of root mean squared error and linear regression slope. Interestingly, the overall performance across all SAMPL4 submissions was similar to that for the prior SAMPL3 host-guest challenge, although the experimentalists took steps to simplify the current challenge. While some methods performed fairly consistently across both hosts, no single approach emerged as consistent top performer, and the nonsystematic nature of the various submissions made it impossible to draw definitive conclusions regarding the best choices of energy models or sampling algorithms. Salt effects emerged as an issue in the calculation of absolute binding affinities of cucurbit[7]uril-guest systems, but were not expected to affect the relative affinities significantly. Useful directions for future rounds of the challenge might involve encouraging participants to carry out some calculations that replicate each others' studies, and to systematically explore parameter options.