Binding affinities in the SAMPL3 trypsin and host-guest blind tests estimated with the MM/PBSA and LIE methods

Revisiting MMPBSA by Adoption of MC-Based Surface Area/Volume, ANI-ML Potentials, and Two-Valued Interior Dielectric Constant

Here, we report the accuracy improvements of molecular mechanics Poisson-Boltzmann surface area (MMPBSA) calculations by adoption of ANI-ML potentials in replacement of MM terms, the use of solvent-accessible surface area (SASA) and volume (SAV) values from the Monte Carlo sampling of the probe, and introducing two different interior dielectric constants for electrostatic interactions of protein-ligand (P-L) and polar solvation term in the MMPBSA calculations. Our results show that the Pearson correlation coefficients of MMPBSA-calculated values with respect to experimental binding free energies can be drastically improved from 0.48 to 0.90 by adoption of ANI-ML potentials in replacement of MM energy terms in the equation, referred to as ANI-PBSA. Moreover, we show that the SASA/SAV-combined equation in the scaled particle theory (SPT) can be a better choice to model nonpolar solvation term, reaching nearly the same accuracy by ANI-PBSA calculations. Finally, we introduce two different values of interior dielectric constants, which could be an alternative strategy between the single and variable constant definitions.

Quantum Biochemistry and MM-PBSA Description of the ZIKV NS2B-NS3 Protease: Insights into the Binding Interactions beyond the Catalytic Triad Pocket

The Zika virus protease NS2B-NS3 has a binding site formed with the participation of a H51-D75-S135 triad presenting two forms, active and inactive. Studies suggest that the inactive conformation is a good target for the design of inhibitors. In this paper, we evaluated the co-crystallized structures of the protease with the inhibitors benzoic acid (5YOD) and benzimidazole-1-ylmethanol (5H4I). We applied a protocol consisting of two steps: first, classical molecular mechanics energy minimization followed by classical molecular dynamics were performed, obtaining stabilized molecular geometries; second, the optimized/relaxed geometries were used in quantum biochemistry and molecular mechanics/Poisson-Boltzmann surface area (MM-PBSA) calculations to estimate the ligand interactions with each amino acid residue of the binding pocket. We show that the quantum-level results identified essential residues for the stabilization of the 5YOD and 5H4I complexes after classical energy minimization, matching previously published experimental data. The same success, however, was not observed for the MM-PBSA simulations. The application of quantum biochemistry methods seems to be more promising for the design of novel inhibitors acting on NS2B-NS3.

Exploring the Binding Mechanism of a Supramolecular Tweezer CLR01 to 14-3-3σ Protein via Well-Tempered Metadynamics

Using supramolecules for protein function regulation is an effective strategy in chemical biology and drug discovery. However, due to the presence of multiple binding sites on protein surfaces, protein function regulation via selective binding of supramolecules is challenging. Recently, the functions of 14-3-3 proteins, which play an important role in regulating intracellular signaling pathways via protein–protein interactions, have been modulated using a supramolecular tweezer, CLR01. However, the binding mechanisms of the tweezer molecule to 14-3-3 proteins are still unclear, which has hindered the development of novel supramolecules targeting the 14-3-3 proteins. Herein, the binding mechanisms of the tweezer to the lysine residues on 14-3-3σ (an isoform in 14-3-3 protein family) were explored by well-tempered metadynamics. The results indicated that the inclusion complex formed between the protein and supramolecule is affected by both kinetic and thermodynamic factors. In particular, simulations confirmed that K214 could form a strong binding complex with the tweezer; the binding free energy was calculated to be −10.5 kcal·mol⁻¹ with an association barrier height of 3.7 kcal·mol⁻¹. In addition, several other lysine residues on 14-3-3σ were identified as being well-recognized by the tweezer, which agrees with experimental results, although only K214/tweezer was co-crystallized. Additionally, the binding mechanisms of the tweezer to all lysine residues were analyzed by exploring the representative conformations during the formation of the inclusion complex. This could be helpful for the development of new inhibitors based on tweezers with more functions against 14-3-3 proteins via modifications of CLR01. We also believe that the proposed computational strategies can be extended to understand the binding mechanism of multi-binding sites proteins with supramolecules and will, thus, be useful toward drug design.

Benchmark Study of Redox Potential Calculations for Iron-Sulfur Clusters in Proteins

Redox potentials have been calculated for 12 different iron–sulfur sites of 6 different types with 1–4 iron ions. Structures were optimized with combined quantum mechanical and molecular mechanical (QM/MM) methods, and the redox potentials were calculated using the QM/MM energies, single-point QM methods in a continuum solvent or by QM/MM thermodynamic cycle perturbations. We show that the best results are obtained with a large QM system (∼300 atoms, but a smaller QM system, ∼150 atoms, can be used for the QM/MM geometry optimization) and a large value of the dielectric constant (80). For absolute redox potentials, the B3LYP density functional method gives better results than TPSS, and the results are improved with a larger basis set. However, for relative redox potentials, the opposite is true. The results are insensitive to the force field (charges of the surroundings) used for the QM/MM calculations or whether the protein and solvent outside the QM system are relaxed or kept fixed at the crystal structure. With the best approach for relative potentials, mean absolute and maximum deviations of 0.17 and 0.44 V, respectively, are obtained after removing a systematic error of −0.55 V. Such an approach can be used to identify the correct oxidation states involved in a certain redox reaction.

We have studied redox potentials of 12 iron−sulfur sites of 6 types with 1−4 iron ions. Structures were optimized with combined quantum mechanical and molecular mechanical (QM/MM) methods, and the redox potentials were calculated with QM/MM, QM calculations in a continuum solvent or by QM/MM thermodynamic cycle perturbations. The best results are obtained with the second approach using ∼300 atoms in the QM model and a large dielectric constant.

VAD-MM/GBSA: A Variable Atomic Dielectric MM/GBSA Model for Improved Accuracy in Protein-Ligand Binding Free Energy Calculations

The molecular mechanics/generalized Born surface area (MM/GBSA) has been widely used in end-point binding free energy prediction in structure-based drug design (SBDD). However, in practice, it is usually being treated as a disputed method mostly because of its system dependence. Here, combining with machine-learning optimization, we developed a novel version of MM/GBSA, named variable atomic dielectric MM/GBSA (VAD-MM/GBSA), by assigning variable dielectric constants directly to the protein/ligand atoms. The new strategy exhibits markedly improved accuracy in binding affinity calculations for various protein-ligand systems and is promising to be used in the postprocessing of structure-based virtual screening. Moreover, VAD-MM/GBSA outperformed prime MM/GBSA in Schrödinger software and showed remarkable predictive performance for specific protein targets, such as POL polyprotein, human immunodeficiency virus type 1 (HIV-1) protease, etc. Our study showed that the VAD-MM/GBSA method with little extra computational overhead provides a potential replacement of the MM/GBSA in AMBER software. An online web server of VAD-MMGBSA has been developed and is now available at http://cadd.zju.edu.cn/vdgb.

Accurate Receptor-Ligand Binding Free Energies from Fast QM Conformational Chemical Space Sampling

Small molecule receptor-binding is dominated by weak, non-covalent interactions such as van-der-Waals hydrogen bonding or electrostatics. Calculating these non-covalent ligand-receptor interactions is a challenge to computational means in terms of accuracy and efficacy since the ligand may bind in a number of thermally accessible conformations. The conformational rotamer ensemble sampling tool (CREST) uses an iterative scheme to efficiently sample the conformational space and calculates energies using the semi-empirical 'Geometry, Frequency, Noncovalent, eXtended Tight Binding' (GFN2-xTB) method. This combined approach is applied to blind predictions of the modes and free energies of binding for a set of 10 drug molecule ligands to the cucurbit[n]urils CB[8] receptor from the recent 'Statistical Assessment of the Modeling of Proteins and Ligands' (SAMPL) challenge including morphine, hydromorphine, cocaine, fentanyl, and ketamine. For each system, the conformational space was sufficiently sampled for the free ligand and the ligand-receptor complexes using the quantum chemical Hamiltonian. A multitude of structures makes up the final conformer-rotamer ensemble, for which then free energies of binding are calculated. For those large and complex molecules, the results are in good agreement with experimental values with a mean error of 3 kcal/mol. The GFN2-xTB energies of binding are validated by advanced density functional theory calculations and found to be in good agreement. The efficacy of the automated QM sampling workflow allows the extension towards other complex molecular interaction scenarios.

Computational insights into the role of calcium ions in protein–glycosaminoglycan systems

The prediction power of computational methodologies for studying the role of ions in protein–glycosaminoglycan interactions was critically assessed.

Molecular Dynamics Simulations Predict That rSNP Located in the HNF‑1α Gene Promotor Region Linked with MODY3 and Hepatocellular Carcinoma Promotes Stronger Binding of the HNF‑4α Transcription Factor

Our study aims to investigate the impact of the Maturity-onset diabetes of the young 3 disease-linked rSNP rs35126805 located in the HNF-1α gene promotor on the binding of the transcription factor HNF-4α and consequently on the regulation of HNF-1α gene expression. Our focus is to calculate the change in the binding affinity of the transcription factor HNF-4α to the DNA, caused by the regulatory single nucleotide polymorphism (rSNP) through molecular dynamics simulations and thermodynamic analysis of acquired results. Both root-mean-square difference (RMSD) and the relative binding free energy ΔΔG_bind reveal that the HNF-4α binds slightly more strongly to the DNA containing the mutation (rSNP) making the complex more stable/rigid, and thereby influencing the expression of the HNF-1α gene. The resulting disruption of the HNF-4α/HNF-1α pathway is also linked to hepatocellular carcinoma metastasis and enhanced apoptosis in pancreatic cancer cells. To the best of our knowledge, this represents the first study where thermodynamic analysis of the results obtained from molecular dynamics simulations is performed to uncover the influence of rSNP on the protein binding to DNA. Therefore, our approach can be generally applied for studying the impact of regulatory single nucleotide polymorphisms on the binding of transcription factors to the DNA.

D3R Grand Challenge 4: ligand similarity and MM-GBSA-based pose prediction and affinity ranking for BACE-1 inhibitors

The Drug Design Data Resource (D3R) Grand Challenges present an opportunity to assess, in the context of a blind predictive challenge, the accuracy and the limits of tools and methodologies designed to help guide pharmaceutical drug discovery projects. Here, we report the results of our participation in the D3R Grand Challenge 4 (GC4), which focused on predicting the binding poses and affinity ranking for compounds targeting the [Formula: see text]-amyloid precursor protein (BACE-1). Our ligand similarity-based protocol using HYBRID (OpenEye Scientific Software) successfully identified poses close to the native binding mode for most of the ligands with less than 2 Å RMSD accuracy. Furthermore, we compared the performance of our HYBRID-based approach to that of AutoDock Vina and DOCK 6 and found that using a reference ligand to guide the docking process is a better strategy for pose prediction and helped HYBRID to perform better here. We also conducted end-point free energy estimates on molecules dynamics based ensembles of protein-ligand complexes using molecular mechanics combined with generalized Born surface area method (MM-GBSA). We found that the binding affinity ranking based on MM-GBSA scores have poor correlation with the experimental values. Finally, the main lessons from our participation in D3R GC4 are: (i) the generation of the macrocyclic conformers is a key step for successful pose prediction, (ii) the protonation states of the BACE-1 binding site should be treated carefully, (iii) the MM-GBSA method could not discriminate well between different predicted binding poses, and (iv) the MM-GBSA method does not perform well at predicting protein-ligand binding affinities here.

Assessing the performance of the MM/PBSA and MM/GBSA methods. 10. Impacts of enhanced sampling and variable dielectric model on protein-protein Interactions

Enhanced sampling has been extensively used to capture the conformational transitions in protein folding, but it attracts much less attention in the studies of protein-protein recognition. In this study, we evaluated the impact of enhanced sampling methods and solute dielectric constants on the overall accuracy of the molecular mechanics/Poisson-Boltzmann surface area (MM/PBSA) and molecular mechanics/generalized Born surface area (MM/GBSA) approaches for the protein-protein binding free energy calculations. Here, two widely used enhanced sampling methods, including aMD and GaMD, and conventional molecular dynamics (cMD) simulations with two AMBER force fields (ff03 and ff14SB) were used to sample the conformations for 21 protein-protein complexes. The MM/PBSA and MM/GBSA calculation results illustrate that the standard MM/GBSA based on the cMD simulations yields the best Pearson correlation (r_p = -0.523) between the predicted binding affinities and the experimental data, which is much higher than that given by MM/PBSA (r_p = -0.212). Two enhanced sampling methods (aMD and GaMD) are indeed more efficient for conformational sampling, but they did not improve the binding affinity predictions for protein-protein systems, suggesting that the aMD or GaMD sampling (at least in short timescale simulations) may not be a good choice for the MM/PBSA and MM/GBSA predictions of protein-protein complexes. The solute dielectric constant of 1.0 is recommended to MM/GBSA, but a higher solute dielectric constant is recommended to MM/PBSA, especially for the systems with higher polarity on the protein-protein binding interfaces. Then, a preliminary assessment of the MM/GBSA calculations based on a variable dielectric generalized Born (VDGB) model was conducted. The results highlight the potential power of VDGB in the free energy predictions for protein-protein systems, but more thorough studies should be done in the future.

Rational in silico design of aptamers for organophosphates based on the example of paraoxon

Poisoning by organophosphates (OPs) takes one of the leading places in the total number of exotoxicoses. Detoxication of OPs at the first stage of the poison entering the body could be achieved with the help of DNA- or RNA-aptamers, which are able to bind poisons in the bloodstream. The aim of the research was to develop an approach to rational in silico design of aptamers for OPs based on the example of paraoxon. From the published sequence of an aptamer binding organophosphorus pesticides, its three-dimensional model has been constructed. The most probable binding site for paraoxon was determined by molecular docking and molecular dynamics (MD) methods. Then the nucleotides of the binding site were mutated consequently and the values of free binding energy have been calculated using MD trajectories and MM-PBSA approach. On the basis of the energy values, two sequences that bind paraoxon most efficiently have been selected. The value of free binding energy of paraoxon with peripheral anionic site of acetylcholinesterase (AChE) has been calculated as well. It has been revealed that the aptamers found bind paraoxon more effectively than AChE. The peculiarities of paraoxon interaction with the aptamers nucleotides have been analyzed. The possibility of improving in silico approach for aptamer selection is discussed.

Machine learning accelerates MD-based binding pose prediction between ligands and proteins

Motivation

Fast and accurate prediction of protein–ligand binding structures is indispensable for structure-based drug design and accurate estimation of binding free energy of drug candidate molecules in drug discovery. Recently, accurate pose prediction methods based on short Molecular Dynamics (MD) simulations, such as MM-PBSA and MM-GBSA, among generated docking poses have been used. Since molecular structures obtained from MD simulation depend on the initial condition, taking the average over different initial conditions leads to better accuracy. Prediction accuracy of protein–ligand binding poses can be improved with multiple runs at different initial velocity.

Results

This paper shows that a machine learning method, called Best Arm Identification, can optimally control the number of MD runs for each binding pose. It allows us to identify a correct binding pose with a minimum number of total runs. Our experiment using three proteins and eight inhibitors showed that the computational cost can be reduced substantially without sacrificing accuracy. This method can be applied for controlling all kinds of molecular simulations to obtain best results under restricted computational resources.

Availability and implementation

Code and data are available on GitHub at https://github.com/tsudalab/bpbi.

Supplementary information

Supplementary data are available at Bioinformatics online.

Accuracy Comparison of Generalized Born Models in the Calculation of Electrostatic Binding Free Energies

The need for accurate yet efficient representation of the aqueous environment in biomolecular modeling has led to the development of a variety of generalized Born (GB) implicit solvent models. While many studies have focused on the accuracy of available GB models in predicting solvation free energies, a systematic assessment of the quality of these models in binding free energy calculations, crucial for rational drug design, has not been undertaken. Here, we evaluate the accuracies of eight common GB flavors (GB-HCT, GB-OBC, GB-neck2, GBNSR6, GBSW, GBMV1, GBMV2, and GBMV3), available in major molecular dynamics packages, in predicting the electrostatic binding free energies ( ΔΔ G_el) for a diverse set of 60 biomolecular complexes belonging to four main classes: protein-protein, protein-drug, RNA-peptide, and small complexes. The GB flavors are examined in terms of their ability to reproduce the results from the Poisson-Boltzmann (PB) model, commonly used as accuracy reference in this context. We show that the agreement with the PB of ΔΔ G_el estimates varies widely between different GB models and also across different types of biomolecular complexes, with R² correlations ranging from 0.3772 to 0.9986. A surface-based "R6" GB model recently implemented in AMBER shows the closest overall agreement with reference PB ( R² = 0.9949, RMSD = 8.75 kcal/mol). The RNA-peptide and protein-drug complex sets appear to be most challenging for all but one model, as indicated by the large deviations from the PB in ΔΔ G_el. Small neutral complexes present the least challenge for most of the GB models tested. The quantitative demonstration of the strengths and weaknesses of the GB models across the diverse complex types provided here can be used as a guide for practical computations and future development efforts.

Recent Developments and Applications of the MMPBSA Method

The Molecular Mechanics Poisson-Boltzmann Surface Area (MMPBSA) approach has been widely applied as an efficient and reliable free energy simulation method to model molecular recognition, such as for protein-ligand binding interactions. In this review, we focus on recent developments and applications of the MMPBSA method. The methodology review covers solvation terms, the entropy term, extensions to membrane proteins and high-speed screening, and new automation toolkits. Recent applications in various important biomedical and chemical fields are also reviewed. We conclude with a few future directions aimed at making MMPBSA a more robust and efficient method.

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.

Can System Truncation Speed up Ligand-Binding Calculations with Periodic Free-Energy Simulations?

We have investigated whether alchemical free-energy perturbation calculations of relative binding energies can be sped up by simulating a truncated protein. Previous studies with spherical nonperiodic systems showed that the number of simulated atoms could be reduced by a factor of 26 without affecting the calculated binding free energies by more than 0.5 kJ/mol on average ( Genheden, S.; Ryde, U. J. Chem. Theory Comput. 2012 , 8 , 1449 ), leading to a 63-fold decrease in the time consumption. However, such simulations are rather slow, owing to the need of a large cutoff radius for the nonbonded interactions. Periodic simulations with the electrostatics treated by Ewald summation are much faster. Therefore, we have investigated if a similar speed-up can be obtained also for periodic simulations. Unfortunately, our results show that it is harder to truncate periodic systems and that the truncation errors are larger for these systems. In particular, residues need to be removed from the calculations, which means that atoms have to be restrained to avoid that they move in an unrealistic manner. The results strongly depend on the strength on this restraint. For the binding of seven ligands to dihydrofolate reductase and ten inhibitors of blood-clotting factor Xa, the best results are obtained with a small restraining force constant. However, the truncation errors were still significant (e.g., 1.5-2.9 kJ/mol at a truncation radius of 10 Å). Moreover, the gain in computer time was only modest. On the other hand, if the snapshots are truncated after the MD simulations, the truncation errors are small (below 0.9 kJ/mol even for a truncation radius of 10 Å). This indicates that postprocessing with a more accurate energy function (e.g., with quantum chemistry) on truncated snapshots may be a viable approach.

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.

Interpreting Thermodynamic Profiles of Aminoadamantane Compounds Inhibiting the M2 Proton Channel of Influenza A by Free Energy Calculations

The development of novel anti-influenza drugs is of great importance because of the capability of influenza viruses to occasionally cross interspecies barriers and to rapidly mutate. One class of anti-influenza agents, aminoadamantanes, including the drugs amantadine and rimantadine now widely abandoned due to virus resistance, bind to and block the pore of the transmembrane domain of the M2 proton channel (M2TM) of influenza A. Here, we present one of the still rare studies that interprets thermodynamic profiles from isothermal titration calorimetry (ITC) experiments in terms of individual energy contributions to binding, calculated by the computationally inexpensive implicit solvent/implicit membrane molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) approach, for aminoadamantane compounds binding to M2TM of the avian "Weybridge" strain. For all eight pairs of aminoadamantane compounds considered, the trend of the predicted relative binding free energies and their individual components, effective binding energies and changes in the configurational entropy, agrees with experimental measures (ΔΔG, ΔΔH, TΔΔS) in 88, 88, and 50% of the cases. In addition, information yielded by the MM-PBSA approach about determinants of binding goes beyond that available in component quantities (ΔH, ΔS) from ITC measurements. We demonstrate how one can make use of such information to link thermodynamic profiles from ITC with structural causes on the ligand side and, ultimately, to guide decision making in lead optimization in a prospective manner, which results in an aminoadamantane derivative with improved binding affinity against M2TM(Weybridge).

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.

Assessing the performance of MM/PBSA and MM/GBSA methods. 4. Accuracies of MM/PBSA and MM/GBSA methodologies evaluated by various simulation protocols using PDBbind data set

By using different evaluation strategies, we systemically evaluated the performance of Molecular Mechanics/Generalized Born Surface Area (MM/GBSA) and Molecular Mechanics/Poisson-Boltzmann Surface Area (MM/PBSA) methodologies based on more than 1800 protein-ligand crystal structures in the PDBbind database. The results can be summarized as follows: (1) for the one-protein-family/one-binding-ligand case which represents the unbiased protein-ligand complex sampling, both MM/GBSA and MM/PBSA methodologies achieve approximately equal accuracies at the interior dielectric constant of 4 (with rp = 0.408 ± 0.006 of MM/GBSA and rp = 0.388 ± 0.006 of MM/PBSA based on the minimized structures); while for the total dataset (1864 crystal structures), the overall best Pearson correlation coefficient (rp = 0.579 ± 0.002) based on MM/GBSA is better than that of MM/PBSA (rp = 0.491 ± 0.003), indicating that biased sampling may significantly affect the accuracy of the predicted result (some protein families contain too many instances and can bias the overall predicted accuracy). Therefore, family based classification is needed to evaluate the two methodologies; (2) the prediction accuracies of MM/GBSA and MM/PBSA for different protein families are quite different with rp ranging from 0 to 0.9, whereas the correlation and ranking scores (an averaged rp/rs over a list of protein folds and also representing the unbiased sampling) given by MM/PBSA (rp-score = 0.506 ± 0.050 and rs-score = 0.481 ± 0.052) are comparable to those given by MM/GBSA (rp-score = 0.516 ± 0.047 and rs-score = 0.463 ± 0.047) at the fold family level; (3) for the overall prediction accuracies, molecular dynamics (MD) simulation may not be quite necessary for MM/GBSA (rp-minimized = 0.579 ± 0.002 and rp-1ns = 0.564 ± 0.002), but is needed for MM/PBSA (rp-minimized = 0.412 ± 0.003 and rp-1ns = 0.491 ± 0.003). However, for the individual systems, whether to use MD simulation is depended. (4) both MM/GBSA and MM/PBSA may be unable to give successful predictions for the ligands with high formal charges, with the Pearson correlation coefficient ranging from 0.621 ± 0.003 (neutral ligands) to 0.125 ± 0.142 (ligands with a formal charge of 5). Therefore, it can be summarized that, although MM/GBSA and MM/PBSA perform similarly in the unbiased dataset, for the currently available crystal structures in the PDBbind database, compared with MM/GBSA, which may be used in multi-target comparisons, MM/PBSA is more sensitive to the investigated systems, and may be more suitable for individual-target-level binding free energy ranking. This study may provide useful guidance for the post-processing of docking based studies.

The MM/PBSA and MM/GBSA methods to estimate ligand-binding affinities

INTRODUCTION

The molecular mechanics energies combined with the Poisson-Boltzmann or generalized Born and surface area continuum solvation (MM/PBSA and MM/GBSA) methods are popular approaches to estimate the free energy of the binding of small ligands to biological macromolecules. They are typically based on molecular dynamics simulations of the receptor-ligand complex and are therefore intermediate in both accuracy and computational effort between empirical scoring and strict alchemical perturbation methods. They have been applied to a large number of systems with varying success.

AREAS COVERED

The authors review the use of MM/PBSA and MM/GBSA methods to calculate ligand-binding affinities, with an emphasis on calibration, testing and validation, as well as attempts to improve the methods, rather than on specific applications.

EXPERT OPINION

MM/PBSA and MM/GBSA are attractive approaches owing to their modular nature and that they do not require calculations on a training set. They have been used successfully to reproduce and rationalize experimental findings and to improve the results of virtual screening and docking. However, they contain several crude and questionable approximations, for example, the lack of conformational entropy and information about the number and free energy of water molecules in the binding site. Moreover, there are many variants of the method and their performance varies strongly with the tested system. Likewise, most attempts to ameliorate the methods with more accurate approaches, for example, quantum-mechanical calculations, polarizable force fields or improved solvation have deteriorated the results.

Improvements, trends, and new ideas in molecular docking: 2012-2013 in review

Molecular docking is a computational method for predicting the placement of ligands in the binding sites of their receptor(s). In this review, we discuss the methodological developments that occurred in the docking field in 2012 and 2013, with a particular focus on the more difficult aspects of this computational discipline. The main challenges and therefore focal points for developments in docking, covered in this review, are receptor flexibility, solvation, scoring, and virtual screening. We specifically deal with such aspects of molecular docking and its applications as selection criteria for constructing receptor ensembles, target dependence of scoring functions, integration of higher-level theory into scoring, implicit and explicit handling of solvation in the binding process, and comparison and evaluation of docking and scoring methods.

A large-scale test of free-energy simulation estimates of protein-ligand binding affinities

We have performed a large-scale test of alchemical perturbation calculations with the Bennett acceptance-ratio (BAR) approach to estimate relative affinities for the binding of 107 ligands to 10 different proteins. Employing 20-Å truncated spherical systems and only one intermediate state in the perturbations, we obtain an error of less than 4 kJ/mol for 54% of the studied relative affinities and a precision of 0.5 kJ/mol on average. However, only four of the proteins gave acceptable errors, correlations, and rankings. The results could be improved by using nine intermediate states in the simulations or including the entire protein in the simulations using periodic boundary conditions. However, 27 of the calculated affinities still gave errors of more than 4 kJ/mol, and for three of the proteins the results were not satisfactory. This shows that the performance of BAR calculations depends on the target protein and that several transformations gave poor results owing to limitations in the molecular-mechanics force field or the restricted sampling possible within a reasonable simulation time. Still, the BAR results are better than docking calculations for most of the proteins.

Binding Free Energy Calculations for Lead Optimization: Assessment of Their Accuracy in an Industrial Drug Design Context

Correctly ranking compounds according to their computed relative binding affinities will be of great value for decision making in the lead optimization phase of industrial drug discovery. However, the performance of existing computationally demanding binding free energy calculation methods in this context is largely unknown. We analyzed the performance of the molecular mechanics continuum solvent, the linear interaction energy (LIE), and the thermodynamic integration (TI) approach for three sets of compounds from industrial lead optimization projects. The data sets pose challenges typical for this early stage of drug discovery. None of the methods was sufficiently predictive when applied out of the box without considering these challenges. Detailed investigations of failures revealed critical points that are essential for good binding free energy predictions. When data set-specific features were considered accordingly, predictions valuable for lead optimization could be obtained for all approaches but LIE. Our findings lead to clear recommendations for when to use which of the above approaches. Our findings also stress the important role of expert knowledge in this process, not least for estimating the accuracy of prediction results by TI, using indicators such as the size and chemical structure of exchanged groups and the statistical error in the predictions. Such knowledge will be invaluable when it comes to the question which of the TI results can be trusted for decision making.

β-Amyloid and neprilysin computational studies identify critical residues implicated in binding specificity

The zinc metalloprotease neprilysin (NEP) promiscuously degrades small bioactive peptides. NEP is among a select group of metalloenzymes that degrade the amyloid beta-peptide (Aβ) in vivo and in situ. Since accumulation of neurotoxic Aβ aggregates in the brain appears to be a causative agent in the pathophysiology of Alzheimer's disease (AD), increased clearance of Aβ resulting from overexpression of NEP exhibits therapeutic potential for AD. However, higher NEP peptidase activity may be harmful without an increased specificity for Aβ over other competing substrates. Crystal structures of NEP-inhibitor complexes and their characterization have highlighted potential amino acid interactions involved in substrate binding and are used as templates to guide our methodology in docking Aβ in NEP. Results from protein-ligand docking calculations predict S2' subsite residues Arg 102 and Arg 110 of NEP participate in specific interactions with Aβ. These interactions provide insight into developing NEP specificity for Aβ.

Predicting hydration free energies with chemical accuracy: the SAMPL4 challenge

An implicit solvent model described by a non-simple dielectric medium is used for the prediction of hydration free energies on the dataset of 47 molecules in the SAMPL4 challenge. The solute is represented by a minimal parameter set model based on a new all atom force-field, named the liquid simulation force-field. The importance of a first solvation shell correction to the hydration free energy prediction is discussed and two different approaches are introduced to address it: either with an empirical correction to a few functional groups (alcohol, ether, ester, amines and aromatic nitrogen), or an ab initio correction based on the formation of a solute/explicit water complex. Both approaches give equally good predictions with an average unsigned error <1 kcal/mol. Chemical accuracy is obtained.

Comprehending renin inhibitor's binding affinity using structure-based approaches

The performance of several structure-based design (SBD) approaches in predicting the binding affinity of diverse small molecule inhibitors co-crystallized to human renin was assessed to ascertain the modeling tool and method of choice required when dealing with structure-based lead optimization projects. Most of the SBD approaches investigated here were able to provide qualitative guidance, but quantitative accuracy as well as decisive discrimination between [in]actives is still not within reach. Such an outcome suggests that the current methods need improvement to capture the overall physics of the binding phenomenon for consistent applications in a lead optimization setting.

Large scale affinity calculations of cyclodextrin host-guest complexes: Understanding the role of reorganization in the molecular recognition process

Host-guest inclusion complexes are useful models for understanding the structural and energetic aspects of molecular recognition. Due to their small size relative to much larger protein-ligand complexes, converged results can be obtained rapidly for these systems thus offering the opportunity to more reliably study fundamental aspects of the thermodynamics of binding. In this work, we have performed a large scale binding affinity survey of 57 β-cyclodextrin (CD) host guest systems using the binding energy distribution analysis method (BEDAM) with implicit solvation (OPLS-AA/AGBNP2). Converged estimates of the standard binding free energies are obtained for these systems by employing techniques such as parallel Hamitionian replica exchange molecular dynamics, conformational reservoirs and multistate free energy estimators. Good agreement with experimental measurements is obtained in terms of both numerical accuracy and affinity rankings. Overall, average effective binding energies reproduce affinity rank ordering better than the calculated binding affinities, even though calculated binding free energies, which account for effects such as conformational strain and entropy loss upon binding, provide lower root mean square errors when compared to measurements. Interestingly, we find that binding free energies are superior rank order predictors for a large subset containing the most flexible guests. The results indicate that, while challenging, accurate modeling of reorganization effects can lead to ligand design models of superior predictive power for rank ordering relative to models based only on ligand-receptor interaction energies.

Structural modeling of HCV NS3/4A serine protease drug-resistance mutations using end-point continuum solvation and side-chain flexibility calculations

Computational methods of modeling protein-ligand interactions have gained widespread application in modern drug discovery. In continuum solvation-based methods of binding affinity estimation, limited description of solvent environment and protein flexibility is traded for a time scale that fits medicinal chemistry test cycles. The results of this speed-accuracy trade-off have been promising in terms of modeling structure-activity relationships of ligand series against protein targets. The potential of these approaches in recapitulating structural and energetic effects of resistance mutations, which involve large changes in binding affinity, remains relatively unexplored. We used continuum solvation binding affinity predictions and graph theory-based flexibility calculations to model thirteen drug resistance mutations in HCV NS3/4A serine protease, against three small-molecule inhibitors, with a 2-fold objective: quantitative assessment of binding energy predictions against experimental data and elucidation of structural/energetic determinants of resistance. The results show statistically significant correlation between predicted and experimental binding affinities, with R(2) and predictive index of up to 0.83 and 0.91, respectively. The level of accuracy was consistent with what has been reported for the inverse problem of binding affinity estimation of congeneric ligands against the same target. The quality of predictions was poor for mutations involving induced-fit effects, primarily, because of the lack of entropy terms. Flexibility analysis explained this discrepancy by indicating characteristic changes in side-chain mobility of a key binding site residue. The combined results from two approaches provide novel insights regarding the molecular mechanism of resistance. NS3/4A inhibitors, with large P2 substituents, derive high affinity with optimal van der Waals interactions in the S2 subsite, in order to overcome unfavorable desolvation and entropic cost of induced-fit effects. High-level resistance mutations tend to increase the desolvation and/or entropic barrier to ligand binding. The lead optimization strategies should, therefore, address the balance of these opposing energetic contributions in both the wild-type and mutant target.

Are homology models sufficiently good for free-energy simulations?

In this paper, I evaluate the usefulness of protein homology models in rigorous free-energy simulations to determine ligand affinities. Two templates were used to create models of the factor Xa protein and one template was used for dihydrofolate reductase from Plasmodium falciparum. Then, the relative free energies for several pairs of ligands were estimated using thermodynamic integration with the homology models as starting point of the simulation. These binding affinities were compared to affinities obtained when using published crystal structures as starting point of the simulations. Encouragingly, the differences between the affinities obtained when starting from either homology models or crystal structure were not statistical significant for a majority of the considered pairs of ligands. Differences between 1 and 2 kJ/mol were observed for the dihydrofolate reductase ligands and differences between 0 and 8 kJ/mol were observed for the factor Xa ligands. The largest difference for factor Xa was caused by an erroneous modeling of a loop region close to two of the ligands, and it was only observed when using one of the templates. Therefore, it is advisible to always use more than one template when creating homology models if they should be used in free-energy simulations.

Comparison of end-point continuum-solvation methods for the calculation of protein-ligand binding free energies

We have compared the predictions of ligand-binding affinities from several methods based on end-point molecular dynamics simulations and continuum solvation, that is, methods related to MM/PBSA (molecular mechanics combined with Poisson-Boltzmann and surface area solvation). Two continuum-solvation models were considered, viz., the Poisson-Boltzmann (PB) and generalised Born (GB) approaches. The nonelectrostatic energies were also obtained in two different ways, viz., either from the sum of the bonded, van der Waals, nonpolar solvation energies, and entropy terms (as in MM/PBSA), or from the scaled protein-ligand van der Waals interaction energy (as in the linear interaction energy approach, LIE). Three different approaches to calculate electrostatic energies were tested, viz., the sum of electrostatic interaction energies and polar solvation energies, obtained either from a single simulation of the complex or from three independent simulations of the complex, the free protein, and the free ligand, or the linear-response approximation (LRA). Moreover, we investigated the effect of scaling the electrostatic interactions by an effective internal dielectric constant of the protein (ϵ(int) ). All these methods were tested on the binding of seven biotin analogues to avidin and nine 3-amidinobenzyl-1H-indole-2-carboxamide inhibitors to factor Xa. For avidin, the best results were obtained with a combination of the LIE nonelectrostatic energies with the MM+GB electrostatic energies from a single simulation, using ϵ(int) = 4. For fXa, standard MM/GBSA, based on one simulation and using ϵ(int) = 4-10 gave the best result. The optimum internal dielectric constant seems to be slightly higher with PB than with GB solvation.