Assessing the performance of the MM/PBSA and MM/GBSA methods. 1. The accuracy of binding free energy calculations based on molecular dynamics simulations

The Molecular Mechanics/Poisson-Boltzmann Surface Area (MM/PBSA) and the Molecular Mechanics/Generalized Born Surface Area (MM/GBSA) methods calculate binding free energies for macromolecules by combining molecular mechanics calculations and continuum solvation models. To systematically evaluate the performance of these methods, we report here an extensive study of 59 ligands interacting with six different proteins. First, we explored the effects of the length of the molecular dynamics (MD) simulation, ranging from 400 to 4800 ps, and the solute dielectric constant (1, 2, or 4) on the binding free energies predicted by MM/PBSA. The following three important conclusions could be observed: (1) MD simulation length has an obvious impact on the predictions, and longer MD simulation is not always necessary to achieve better predictions. (2) The predictions are quite sensitive to the solute dielectric constant, and this parameter should be carefully determined according to the characteristics of the protein/ligand binding interface. (3) Conformational entropy often show large fluctuations in MD trajectories, and a large number of snapshots are necessary to achieve stable predictions. Next, we evaluated the accuracy of the binding free energies calculated by three Generalized Born (GB) models. We found that the GB model developed by Onufriev and Case was the most successful model in ranking the binding affinities of the studied inhibitors. Finally, we evaluated the performance of MM/GBSA and MM/PBSA in predicting binding free energies. Our results showed that MM/PBSA performed better in calculating absolute, but not necessarily relative, binding free energies than MM/GBSA. Considering its computational efficiency, MM/GBSA can serve as a powerful tool in drug design, where correct ranking of inhibitors is often emphasized.     

The Normal-Mode Entropy in the MM/GBSA Method: Effect of System Truncation, Buffer Region, and Dielectric Constant

We have performed a systematic study of the entropy term in the MM/GBSA (molecular mechanics combined with generalized Born and surface-area solvation) approach to calculate ligand-binding affinities. The entropies are calculated by a normal-mode analysis of harmonic frequencies from minimized snapshots of molecular dynamics simulations. For computational reasons, these calculations have normally been performed on truncated systems. We have studied the binding of eight inhibitors of blood clotting factor Xa, nine ligands of ferritin, and two ligands of HIV-1 protease and show that removing protein residues with distances larger than 8-16 ? to the ligand, including a 4 ? shell of fixed protein residues and water molecules, change the absolute entropies by 1-5 kJ/mol on average. However, the change is systematic, so relative entropies for different ligands change by only 0.7-1.6 kJ/mol on average. Consequently, entropies from truncated systems give relative binding affinities that are identical to those obtained for the whole protein within statistical uncertainty (1-2 kJ/mol). We have also tested to use a distance-dependent dielectric constant in the minimization and frequency calculation (ε = 4r), but it typically gives slightly different entropies and poorer binding affinities. Therefore, we recommend entropies calculated with the smallest truncation radius (8 ?) and ε =1. Such an approach also gives an improved precision for the calculated binding free energies.     

Rapid and accurate prediction of binding free energies for saquinavir-bound HIV-1 proteases

To explain drug resistance by computer simulations at the molecular level, we first have to assess the accuracy of theoretical predictions. Herein we report an application of the molecular mechanics Poisson-Boltzmann surface area (MM/PBSA) technique to the ranking of binding affinities of the inhibitor saquinavir with the wild type (WT) and three resistant mutants of HIV-1 protease: L90M, G48V, and G48V/L90M. For each ligand-protein complex we report 10 ns of fully unrestrained molecular dynamics (MD) simulations with explicit solvent. We investigate convergence, internal consistency, and model dependency of MM/PBSA ligand binding energies. Converged enthalpy and entropy estimates produce ligand binding affinities within 1.5 kcal/mol of experimental values, with a remarkable level of correlation to the experimentally observed ranking of resistance levels. A detailed analysis of the enthalpic/entropic balance of drug-protease interactions explains resistance in L90M in terms of a higher vibrational entropy than in the WT complex, while G48V disrupts critical hydrogen bonds at the inhibitor's binding site and produces an altered, more unfavorable balance of Coulomb and polar desolvation energies.     

Analyzing the robustness of the MM/PBSA free energy calculation method: application to DNA conformational transitions

The ability to predict and characterize free energy differences associated with conformational equilibria or the binding of biomolecules is vital to understanding the molecular basis of many important biological functions. As biological studies focus on larger molecular complexes and properties of the genome, proteome, and interactome, the development and characterization of efficient methods for calculating free energy becomes increasingly essential. The aim of this study is to examine the robustness of the end-point free energy method termed the molecular mechanics Poisson-Boltzmann solvent accessible surface area (MM/PBSA) method. Specifically, applications of MM/PBSA to the conformational equilibria of nucleic acid (NA) systems are explored. This is achieved by comparing A to B form DNA conformational free energy differences calculated using MM/PBSA with corresponding free energy differences determined with a more rigorous and time-consuming umbrella sampling algorithm. In addition, the robustness of NA MM/PBSA calculations is also evaluated in terms of the sensitivity towards the choice of force field and the choice of solvent model used during conformational sampling. MM/PBSA calculations of the free energy difference between A-form and B-form DNA are shown to be in very close agreement with the PMF result determined using an umbrella sampling approach. Further, it is found that the MM/PBSA conformational free energy differences were also in agreement using either the CHARMM or AMBER force field. The influence of ionic strength on conformational stability was particularly insensitive to the choice of force field. Finally, it is also shown that the use of a generalized Born implicit solvent during conformational sampling results in free energy estimates that deviate slightly from those obtained using explicitly solvated MD simulations in these NA systems.     

Protein‐specific force field derived from the fragment molecular orbital method can improve protein–ligand binding interactions

Accurate computational estimate of the protein–ligand binding affinity is of central importance in rational drug design. To improve accuracy of the molecular mechanics (MM) force field (FF) for protein–ligand simulations, we use a protein‐specific FF derived by the fragment molecular orbital (FMO) method and by the restrained electrostatic potential (RESP) method. Applying this FMO‐RESP method to two proteins, dodecin, and lysozyme, we found that protein‐specific partial charges tend to differ more significantly from the standard AMBER charges for isolated charged atoms. We did not see the dependence of partial charges on the secondary structure. Computing the binding affinities of dodecin with five ligands by MM PBSA protocol with the FMO‐RESP charge set as well as with the standard AMBER charges, we found that the former gives better correlation with experimental affinities than the latter. While, for lysozyme with five ligands, both charge sets gave similar and relatively accurate estimates of binding affinities. © 2013 Wiley Periodicals, Inc.     

Assessing the performance of the molecular mechanics/Poisson Boltzmann surface area and molecular mechanics/generalized Born surface area methods. II. The accuracy of ranking poses generated from docking

In molecular docking, it is challenging to develop a scoring function that is accurate to conduct high-throughput screenings. Most scoring functions implemented in popular docking software packages were developed with many approximations for computational efficiency, which sacrifices the accuracy of prediction. With advanced technology and powerful computational hardware nowadays, it is feasible to use rigorous scoring functions, such as molecular mechanics/Poisson Boltzmann surface area (MM/PBSA) and molecular mechanics/generalized Born surface area (MM/GBSA) in molecular docking studies. Here, we systematically investigated the performance of MM/PBSA and MM/GBSA to identify the correct binding conformations and predict the binding free energies for 98 protein-ligand complexes. Comparison studies showed that MM/GBSA (69.4%) outperformed MM/PBSA (45.5%) and many popular scoring functions to identify the correct binding conformations. Moreover, we found that molecular dynamics simulations are necessary for some systems to identify the correct binding conformations. Based on our results, we proposed the guideline for MM/GBSA to predict the binding conformations. We then tested the performance of MM/GBSA and MM/PBSA to reproduce the binding free energies of the 98 protein-ligand complexes. The best prediction of MM/GBSA model with internal dielectric constant 2.0, produced a Spearman's correlation coefficient of 0.66, which is better than MM/PBSA (0.49) and almost all scoring functions used in molecular docking. In summary, MM/GBSA performs well for both binding pose predictions and binding free-energy estimations and is efficient to re-score the top-hit poses produced by other less-accurate scoring functions.     

Lessons learned from participating in D3R 2016 Grand Challenge 2: compounds targeting the farnesoid X receptor

D3R 2016 Grand Challenge 2 focused on predictions of binding modes and affinities for 102 compounds against the farnesoid X receptor (FXR). In this challenge, two distinct methods, a docking-based method and a template-based method, were employed by our team for the binding mode prediction. For the new template-based method, 3D ligand similarities were calculated for each query compound against the ligands in the co-crystal structures of FXR available in Protein Data Bank. The binding mode was predicted based on the co-crystal protein structure containing the ligand with the best ligand similarity score against the query compound. For the FXR dataset, the template-based method achieved a better performance than the docking-based method on the binding mode prediction. For the binding affinity prediction, an in-house knowledge-based scoring function ITScore2 and MM/PBSA approach were employed. Good performance was achieved for MM/PBSA, whereas the performance of ITScore2 was sensitive to ligand composition, e.g. the percentage of carbon atoms in the compounds. The sensitivity to ligand composition could be a clue for the further improvement of our knowledge-based scoring function.     

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.     

Fast and accurate predictions of binding free energies using MM‐PBSA and MM‐GBSA

In the drug discovery process, accurate methods of computing the affinity of small molecules with a biological target are strongly needed. This is particularly true for molecular docking and virtual screening methods, which use approximated scoring functions and struggle in estimating binding energies in correlation with experimental values. Among the various methods, MM‐PBSA and MM‐GBSA are emerging as useful and effective approaches. Although these methods are typically applied to large collections of equilibrated structures of protein‐ligand complexes sampled during molecular dynamics in water, the possibility to reliably estimate ligand affinity using a single energy‐minimized structure and implicit solvation models has not been explored in sufficient detail. Herein, we thoroughly investigate this hypothesis by comparing different methods for the generation of protein‐ligand complexes and diverse methods for free energy prediction for their ability to correlate with experimental values. The methods were tested on a series of structurally diverse inhibitors of Plasmodium falciparum DHFR with known binding mode and measured affinities. The results showed that correlations between MM‐PBSA or MM‐GBSA binding free energies with experimental affinities were in most cases excellent. Importantly, we found that correlations obtained with the use of a single protein‐ligand minimized structure and with implicit solvation models were similar to those obtained after averaging over multiple MD snapshots with explicit water molecules, with consequent save of computing time without loss of accuracy. When applied to a virtual screening experiment, such an approach proved to discriminate between true binders and decoy molecules and yielded significantly better enrichment curves. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

基于分子动力学模拟和连续介质模型的自由能计算方法*

近些年,基于分子动力学模拟和连续介质模型的自由能计算方法受到了越来越多的关注,其中MM/PBSA就是最具代表性的方法.在MM/PBSA中,体系的焓变采用分子力学(MM)的方法计算得到;溶剂效应中极性部分对自由能的贡献通过解Poisson-Boltzmann(PB)方程的方法计算得到;溶液效应中非极性部分对自由能的贡献则通过分子表面积(SA)计算得到.本文结合我们科研组的工作,就近几年MM/PBSA方法的最新进展做了较为详细的阐述,同时对MM/PBSA的发展前景进行了展望.     

EGFR和4-苯胺喹唑啉类抑制剂之间相互作用模式的研究

采用分子动力学和MM/PBSA相结合的方法预测了表皮生长因子受体和4-苯胺喹 啉类抑制剂的相互作用模式。在分子动力学采样的基础上,采用MM/PBSA的方法分 别预测了四种可能结合模式下表皮生长因子受体和4-苯胺喹唑啉类抑制剂间的结合 自由能。在MM/PBSA计算中,受体和抑制剂之间的非键相互作用能采用分子力学 (MM)的方法得到;溶剂效应中极性部分对自由能的贡献通过解Possion- Boltzmanne (PB)方程的方法得到;溶液效应中非极性部分对自由能的贡献则通过 分子表面积计算(SA)的方法得到。计算表明,在四种结合模式下,表皮生长因子受 体和4-苯胺喹唑啉类抑制剂之间的结合自由能有较大的差别。在最佳的相互作用模 式中,抑制剂的苯胺部分位于活性口袋的底部,能够与受体残基的非极性侧链产生 很强的范德华和疏水相互作用。抑制剂喹唑啉环上的N(1)原子能够和Met-769上的 NH形成稳定的氢键,而抑制剂上的N(3)原子则和周围的一个水分子形成氢键。同时 ,抑制剂双环上的取代基团也能和活性口袋外部的部分残基形成一定的范德华和疏 水相互作用。最佳结合模式能够很好地解释已有抑制剂结构和活性间的关系。     

Fragment‐based quantum mechanical calculation of protein–protein binding affinities

The electrostatically embedded generalized molecular fractionation with conjugate caps (EE‐GMFCC) method has been successfully utilized for efficient linear‐scaling quantum mechanical (QM) calculation of protein energies. In this work, we applied the EE‐GMFCC method for calculation of binding affinity of Endonuclease colicin–immunity protein complex. The binding free energy changes between the wild‐type and mutants of the complex calculated by EE‐GMFCC are in good agreement with experimental results. The correlation coefficient (R) between the predicted binding energy changes and experimental values is 0.906 at the B3LYP/6‐31G*‐D level, based on the snapshot whose binding affinity is closest to the average result from the molecular mechanics/Poisson–Boltzmann surface area (MM/PBSA) calculation. The inclusion of the QM effects is important for accurate prediction of protein–protein binding affinities. Moreover, the self‐consistent calculation of PB solvation energy is required for accurate calculations of protein–protein binding free energies. This study demonstrates that the EE‐GMFCC method is capable of providing reliable prediction of relative binding affinities for protein–protein complexes. © 2018 Wiley Periodicals, Inc.     

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

We have estimated affinities for the binding of 34 ligands to trypsin and nine guest molecules to three different hosts in the SAMPL3 blind challenge, using the MM/PBSA, MM/GBSA, LIE, continuum LIE, and Glide score methods. For the trypsin challenge, none of the methods were able to accurately predict the experimental results. For the MM/GB(PB)SA and LIE methods, the rankings were essentially random and the mean absolute deviations were much worse than a null hypothesis giving the same affinity to all ligand. Glide scoring gave a Kendall's τ index better than random, but the ranking is still only mediocre, τ = 0.2. However, the range of affinities is small and most of the pairs of ligands have an experimental affinity difference that is not statistically significant. Removing those pairs improves the ranking metric to 0.4-1.0 for all methods except CLIE. Half of the trypsin ligands were non-binders according to the binding assay. The LIE methods could not separate the inactive ligands from the active ones better than a random guess, whereas MM/GBSA and MM/PBSA were slightly better than random (area under the receiver-operating-characteristic curve, AUC = 0.65-0.68), and Glide scoring was even better (AUC = 0.79). For the first host, MM/GBSA and MM/PBSA reproduce the experimental ranking fairly good, with τ = 0.6 and 0.5, respectively, whereas the Glide scoring was considerably worse, with a τ = 0.4, highlighting that the success of the methods is system-dependent.     

Binding energies of tyrosine kinase inhibitors: Error assessment of computational methods for imatinib and nilotinib binding

The binding energies of imatinib and nilotinib to tyrosine kinase have been determined by quantum mechanical (QM) computations, and compared with literature binding energy studies using molecular mechanics (MM). The potential errors in the computational methods include these critical factors:

• •Errors in X-ray structures such as structural distortions and steric clashes give unrealistically high van der Waals energies, and erroneous binding energies.
• •MM optimization gives a very different configuration to the QM optimization for nilotinib, whereas the imatinib ion gives similar configurations
• •Solvation energies are a major component of the overall binding energy. The QM based solvent model (PCM/SMD) gives different values from those used in the implicit PBSA solvent MM models. A major error in inhibitor—kinase binding lies in the non-polar solvation terms.
• •Solvent transfer free energies and the required empirical solvent accessible surface area factors for nilotinib and imatinib ion to give the transfer free energies have been reverse calculated. These values differ from those used in the MM PBSA studies.
• •An intertwined desolvation—conformational binding selectivity process is a balance of thermodynamic desolvation and intramolecular conformational kinetic control.
• •The configurational entropies (TΔS) are minor error sources.

     

Crystal molecular dynamics simulations to speed up MM/PB(GB)SA evaluation of binding free energies of di-mannose deoxy analogs with P51G-m4-Cyanovirin-N

Complexes of two Cyanovirin-N (CVN) mutants, m4-CVN and P51G-m4-CVN, with deoxy di-mannose analogs were employed as models to generate conformational ensembles using explicit water Molecular Dynamics (MD) simulations in solution and in crystal environment. The results were utilized for evaluation of binding free energies with the molecular mechanics Poisson-Boltzmann (or Generalized Born) surface area, MM/PB(GB)SA, methods. The calculations provided the ranking of deoxy di-mannose ligands affinity in agreement with available qualitative experimental evidences. This confirms the importance of the hydrogen-bond network between di-mannose 3'- and 4'-hydroxyl groups and the protein binding site B(M) as a basis of the CVN activity as an effective HIV fusion inhibitor. Comparison of binding free energies averaged over snapshots from the solution and crystal simulations showed high promises in the use of the crystal matrix for acceleration of the conformational ensemble generation, the most time consuming step in MM/PB(GB)SA approach. Correlation between energy values based on solution versus crystal ensembles is 0.95 for both MM/PBSA and MM/GBSA methods.     

Can MM/GBSA calculations be sped up by system truncation?

We have studied whether calculations of the binding free energy of small ligands to a protein by the MM/GBSA approach (molecular mechanics combined with generalized Born and surface area solvation) can be sped up by including only a restricted number of atoms close to the ligand. If the protein is truncated before the molecular dynamics (MD) simulations, quite large changes are observed for the calculated binding energies, for example, 4 kJ/mol average difference for a radius of 19 Å for the binding of nine phenol derivatives to ferritin. The results are improved if no atoms are fixed in the simulations, with average and maximum errors of 2 and 3 kJ/mol at 19 Å and 3 and 6 kJ/mol at 7 Å. Similar results are obtained for two additional proteins, p38α MAP kinase and factor Xa. On the other hand, if energies are calculated on snapshots that are truncated after the MD simulation, all residues more than 8.5 Å from the ligand can be omitted without changing the energies by more than 1 kJ/mol on average (maximum error 1.4 kJ/mol). At the molecular mechanics level, the gain in computer time for such an approach is small. However, it shows what size of system should be used if the energies instead are calculated with a more demanding method, for example, quantum‐mechanics. © 2017 Wiley Periodicals, Inc.     

应用MM/PBSA方法研究CDK2活性口袋内溶剂水分子对CDK2-配体结合自由能的影响

应用MM/PBSA方法研究了CDK2活性口袋内溶剂水分子对CDK2-配体结合自由能的影响. 结果表明, 活性口袋内溶剂水分子对CDK2-配体相互作用自由能有一定的贡献, 其贡献的大小随配体不同而有所差异, 导致这种差异的主要原因是活性位点内溶剂水分子与蛋白残基和配体之间形成了不同的氢键相互作用网络.     

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

We have estimated free energies for the binding of nine cyclic carboxylate guest molecules to the octa-acid host in the SAMPL4 blind-test challenge with four different approaches. First, we used standard free-energy perturbation calculations of relative binding affinities, performed at the molecular-mechanics (MM) level with TIP3P waters, the GAFF force field, and two different sets of charges for the host and the guest, obtained either with the restrained electrostatic potential or AM1-BCC methods. Both charge sets give good and nearly identical results, with a mean absolute deviation (MAD) of 4 kJ/mol and a correlation coefficient (R ²) of 0.8 compared to experimental results. Second, we tried to improve these predictions with 28,800 density-functional theory (DFT) calculations for selected snapshots and the non-Boltzmann Bennett acceptance-ratio method, but this led to much worse results, probably because of a too large difference between the MM and DFT potential-energy functions. Third, we tried to calculate absolute affinities using minimised DFT structures. This gave intermediate-quality results with MADs of 5–9 kJ/mol and R ² = 0.6–0.8, depending on how the structures were obtained. Finally, we tried to improve these results using local coupled-cluster calculations with single and double excitations, and non-iterative perturbative treatment of triple excitations (LCCSD(T0)), employing the polarisable multipole interactions with supermolecular pairs approach. Unfortunately, this only degraded the predictions, probably because of a mismatch between the solvation energies obtained at the DFT and LCCSD(T0) levels.     

Conformational dependence of charges in protein simulations

We have studied the conformational dependence of molecular mechanics atomic charges for proteins by calculating the charges fitted to the quantum mechanical (QM) electrostatic potential (ESP) for all atoms in complexes between avidin and seven biotin analogues for 20 snapshots from molecular dynamics simulations. We have studied how various other charge sets reproduce those charges. The QM charges, even if averaged over all snapshots or all residues, in general have a larger magnitude than standard Amber charges, indicating that the restraint toward zero in the restrained ESP method is too strong. This has a significant influence on the electrostatic conformational energies and the interaction energy between the biotin ligand and the protein, giving a difference between the QM and Amber charges of 43 and 8 kJ/mol for the negatively charged and neutral biotin analogues, respectively (3-4%). However, this energy difference is strongly reduced if the solvation energy (calculated by the Poisson-Boltzmann or Generalized Born methods) is added, viz., to 7 kJ/mol for charged and 3 kJ/mol for uncharged ligand. In fact, charges need to be recalculated with a QM method only for residues within 7 or 4 A of the ligand, if the error should be less than 4 kJ/mol. Unfortunately, the QM charges do not give significantly better MM/PBSA estimates of ligand-binding affinities than standard Amber charges.