An optimized MM/PBSA virtual screening approach applied to an HIV-1 gp41 fusion peptide inhibitor

VIRus Inhibitory Peptide (VIRIP), a 20 amino acid peptide, binds to the fusion peptide (FP) of human immunodeficiency virus type 1 (HIV-1) gp41 and blocks viral entry. VIRIP derivatives with improved antiviral activity have been developed, and one of those derivatives has recently proven effective and safe in a phase 1/2 clinical trial. Here, molecular dynamics were executed in combination with molecular mechanics/Poisson-Boltzmann surface area (MM/PBSA) free energy calculations to explore the binding interaction between VIRIP derivatives and gp41 FP. A promising correlation between antiviral activity and simulated binding free energy was established thanks to restriction of the flexibility of the peptides, inclusion of configurational entropy calculations, and the use of multiple internal dielectric constants for the MM/PBSA calculations depending on the amino acid sequence. Based on these results, a virtual screening experiment was carried out to design VIRIP analogs with further improved antiretroviral activity. A selection of peptides was tested for inhibitory activity and several VIRIP derivatives were identified with significantly enhanced activity compared to the reference peptides. The results demonstrate that computational modeling strategies using an adapted MM/PBSA methodology improve the accuracy of binding free energy calculations of peptide complexes compared to the classic MM/PBSA protocol. As such, this virtual screening approach generated HIV-1 gp41 FP inhibitors with improved antiviral activity that could be useful for future clinical applications.     

Anti-cooperativity and cooperativity in hydrophobic interactions: Three-body free energy landscapes and comparison with implicit-solvent potential functions for proteins

Potentials of mean force (PMFs) of three-body hydrophobic association are investigated to gain insight into similar processes in protein folding. Free energy landscapes obtained from explicit simulations of three methanes in water are compared with that predicted by popular implicit-solvent effective potentials for the study of proteins. Explicit-water simulations show that for an extended range of three-methane configurations, hydrophobic association at 25 degrees C under atmospheric pressure is mostly anti-cooperative, that is, less favorable than if the interaction free energies were pairwise additive. Effects of free energy nonadditivity on the kinetic path of association and the temperature dependence of additivity are explored by using a three-methane system and simplified chain models. The prevalence of anti-cooperativity under ambient conditions suggests that driving forces other than hydrophobicity also play critical roles in protein thermodynamic cooperativity. We evaluate the effectiveness of several implicit-solvent potentials in mimicking explicit water simulated three-body PMFs. The favorability of the contact free energy minimum is found to be drastically overestimated by solvent accessible surface area (SASA). Both the SASA and a volume-based Gaussian solvent exclusion model fail to predict the desolvation barrier. However, this barrier is qualitatively captured by the molecular surface area model and a recent "hydrophobic force field." None of the implicit-solvent models tested are accurate for the entire range of three-methane configurations and several other thermodynamic signatures considered.     

Application of MM/PBSA colony free energy to loop decoy discrimination: toward correlation between energy and root mean square deviation

Accurate free energy estimation is needed in many predictive tasks. The molecular mechanics/Poisson-Boltzmann solvent accessible surface area (MM/PBSA) approach has proven to be accurate. However, the correlation between the estimated free energy and the distance (e.g., root mean square deviation [RMSD]) from the most stable conformation is hindered by the strong free energy dependence on minor conformational variations. In this paper, a protocol for MM/PBSA free energy estimation is designed and tested on several loop decoy sets. We show that further integration of MM/PBSA free energy estimator with the colony energy approach makes the correlation between the free energy and RMSD from the native structure apparent, for the test sets on which it could be applied. Our results suggest that (1) the MM/PBSA free energy estimator is able to detect native-like structures for most decoy sets, and (2) application of the colony energy approach greatly hampers the MM/energy strong dependence on minor conformational changes.     

Binding free energy calculation with QM/MM hybrid methods for Abl-Kinase inhibitor

We report a Quantum mechanics/Molecular Mechanics–Poisson-Boltzmann/ Surface Area (QM/MM-PB/SA) method to calculate the binding free energy of c-Abl human tyrosine kinase by combining the QM and MM principles where the ligand is treated quantum mechanically and the rest of the receptor by classical molecular mechanics. To study the role of entropy and the flexibility of the protein ligand complex in a solvated environment, molecular dynamics calculations are performed using a hybrid QM/MM approach. This work shows that the results of the QM/MM approach are strongly correlated with the binding affinity. The QM/MM interaction energy in our reported study confirms the importance of electronic and polarization contributions, which are often neglected in classical MM-PB/SA calculations. Moreover, a comparison of semi-empirical methods like DFTB-SCC, PM3, MNDO, MNDO-PDDG, and PDDG-PM3 is also performed. The results of the study show that the implementation of a DFTB-SCC semi-empirical Hamiltonian that is derived from DFT gives better results than other methods. We have performed such studies using the AMBER molecular dynamic package for the first time. The calculated binding free energy is also in agreement with the experimentally determined binding affinity for c-Abl tyrosine kinase complex with Imatinib.     

Thermodynamics calculation of protein–ligand interactions by QM/MM polarizable charge parameters

The calculation of protein–ligand binding free energy (ΔG) is of great importance for virtual screening and drug design. Molecular dynamics (MD) simulation has been an attractive tool to investigate this scientific problem. However, the reliability of such approach is affected by many factors including electrostatic interaction calculation. Here, we present a practical protocol using quantum mechanics/molecular mechanics (QM/MM) calculations to generate polarizable QM protein charge (QMPC). The calculated QMPC of some atoms in binding pockets was obviously different from that calculated by AMBER ff03, which might significantly affect the calculated ΔG. To evaluate the effect, the MD simulations and MM/GBSA calculation with QMPC for 10 protein–ligand complexes, and the simulation results were then compared to those with the AMBER ff03 force field and experimental results. The correlation coefficient between the calculated ΔΔG using MM/GBSA under QMPC and the experimental data is .92, while that with AMBER ff03 force field is .47 for the complexes formed by streptavidin or its mutants and biotin. Moreover, the calculated ΔΔG with QMPC for the complexes formed by ERβ and five ligands is positively related to experimental result with correlation coefficient of .61, while that with AMBER ff03 charge is negatively related to experimental data with correlation coefficient of .42. The detailed analysis shows that the electrostatic polarization introduced by QMPC affects the electrostatic contribution to the binding affinity and thus, leads to better correlation with experimental data. Therefore, this approach should be useful to virtual screening and drug design.     

Predicting binding modes of reversible peptide‐based inhibitors of falcipain‐2 consistent with structure–activity relationships

Falcipain‐2 (FP‐2) is a major hemoglobinase of Plasmodium falciparum, considered an important drug target for the development of antimalarials. A previous study reported a novel series of 20 reversible peptide‐based inhibitors of FP‐2. However, the lack of tridimensional structures of the complexes hinders further optimization strategies to enhance the inhibitory activity of the compounds. Here we report the prediction of the binding modes of the aforementioned inhibitors to FP‐2. A computational approach combining previous knowledge on the determinants of binding to the enzyme, docking, and postdocking refinement steps, is employed. The latter steps comprise molecular dynamics simulations and free energy calculations. Remarkably, this approach leads to the identification of near‐native ligand conformations when applied to a validation set of protein‐ligand structures. Overall, we proposed substrate‐like binding modes of the studied compounds fulfilling the structural requirements for FP‐2 binding and yielding free energy values that correlated well with the experimental data. Proteins 2017; 85:1666–1683. © 2017 Wiley Periodicals, Inc.     

Binding free energy calculations between bovine β‐lactoglobulin and four fatty acids using the MMGBSA method

The bovine dairy protein β‐lactoglobulin (βlg) is a promiscuous protein that has the ability to bind several hydrophobic ligands. In this study, based on known experimental data, the dynamic interaction mechanism between bovine βlg and four fatty acids was investigated by a protocol combining molecular dynamics (MD) simulations and molecular mechanics generalized Born surface area (MMGBSA) binding free energy calculations. Energetic analyses revealed binding free energy trends that corroborated known experimental findings; larger ligand size corresponded to greater binding affinity. Finally, binding free energy decomposition provided detailed information about the key residues stabilizing the complex. © 2014 Wiley Periodicals, Inc. Biopolymers 101: 1010–1018, 2014.     

Density functional theory calculations on entire proteins for free energies of binding: Application to a model polar binding site

In drug optimization calculations, the molecular mechanics Poisson‐Boltzmann surface area (MM‐PBSA) method can be used to compute free energies of binding of ligands to proteins. The method involves the evaluation of the energy of configurations in an implicit solvent model. One source of errors is the force field used, which can potentially lead to large errors due to the restrictions in accuracy imposed by its empirical nature. To assess the effect of the force field on the calculation of binding energies, in this article we use large‐scale density functional theory (DFT) calculations as an alternative method to evaluate the energies of the configurations in a “QM‐PBSA” approach. Our DFT calculations are performed with a near‐complete basis set and a minimal parameter implicit solvent model, within the self‐consistent calculation, using the ONETEP program on protein–ligand complexes containing more than 2600 atoms. We apply this approach to the T4‐lysozyme double mutant L99A/M102Q protein, which is a well‐studied model of a polar binding site, using a set of eight small aromatic ligands. We observe that there is very good correlation between the MM and QM binding energies in vacuum but less so in the solvent. The relative binding free energies from DFT are more accurate than the ones from the MM calculations, and give markedly better agreement with experiment for six of the eight ligands. Furthermore, in contrast to MM‐PBSA, QM‐PBSA is able to correctly predict a nonbinder. Proteins 2014; 82:3335–3346. © 2014 Wiley Periodicals, Inc.     

Molecular modelling methods for prediction of sequence-selectivity in DNA recognition

We describe how one can apply molecular modelling methods, based on the molecular mechanics/generalised Born (MM/GB) approach, to the prediction of the relative affinity of DNA minor groove binding ligands for different DNA sequences. We discuss the theoretical background to the technique, some variations in the methodology that can be employed, and illustrate its application through a case study: analysis of the energetics of binding of Hoechst 33258 to the minor groove of various A/T-rich DNA duplexes. We show how the underpinning molecular dynamics (MD) simulations can be set up, how they can be analysed for satisfactory behaviour, and various approaches to extracting thermodynamics of drug binding from them. We find that while certain elaborations to the basic MM/GB method can improve the agreement with experimental data (e.g., calculating the DNA perturbation energy), others have to be analysed with more caution (e.g., calculating configurational entropy changes). Overall, these methodologies can rank the affinity of a ligand for the minor groove of different DNA sequences fairly well, but the calculation of absolute binding affinities is not very reliable.     

Detailed microscopic study of the full zipA:FtsZ interface

Protein-protein interaction networks are very important for a wide range of biological processes. Crystallographic structures and mutational studies have generated a large number of information that allowed the discovery of energetically important determinants of specificity at intermolecular protein interfaces and the understanding of the structural and energetic characteristics of the binding hot spots. In this study we have used the improved MMPB/SA (molecular mechanics/Poisson-Boltzmann surface area) approach that combining molecular mechanics and continuum solvent permits to calculate the free energy differences upon alanine mutation. For a better understanding of the binding determinants of the complex formed between the FtsZ fragment and ZipA we extended the alanine scanning mutagenesis study to all interfacial residues of this complex. As a result, we present new mutations that allowed the discovery of residues for which the binding free energy differences upon alanine mutation are higher than 2.0 kcal/mol. We also observed the formation of a hydrophobic pocket with a high warm spot spatial complementarity between FtsZ and ZipA. Small molecules could be designed to bind to these amino acid residues hindering the binding of FtsZ to ZipA. Hence, these mutational data can be used to design new drugs to control more efficiently bacterial infections.     

Computational investigation of the HIV-1 Rev multimerization using molecular dynamics simulations and binding free energy calculations

The HIV Rev protein mediates the nuclear export of viral mRNA, and is thereby essential for the production of late viral proteins in the replication cycle. Rev forms a large organized multimeric protein-protein complex for proper functioning. Recently, the three-dimensional structures of a Rev dimer and tetramer have been resolved and provide the basis for a thorough structural analysis of the binding interaction. Here, molecular dynamics (MD) and binding free energy calculations were performed to elucidate the forces thriving dimerization and higher order multimerization of the Rev protein. It is found that despite the structural differences between each crystal structure, both display a similar behavior according to our calculations. Our analysis based on a molecular mechanics-generalized Born surface area (MM/GBSA) and a configurational entropy approach demonstrates that the higher order multimerization site is much weaker than the dimerization site. In addition, a quantitative hot spot analysis combined with a mutational analysis reveals the most contributing amino acid residues for protein interactions in agreement with experimental results. Additional residues were found in each interface, which are important for the protein interaction. The investigation of the thermodynamics of the Rev multimerization interactions performed here could be a further step in the development of novel antiretrovirals using structure based drug design. Moreover, the variability of the angle between each Rev monomer as measured during the MD simulations suggests a role of the Rev protein in allowing flexibility of the arginine rich domain (ARM) to accommodate RNA binding.     

Study of the insulin dimerization: binding free energy calculations and per-residue free energy decomposition

A calculation of the binding free energy for the dimerization of insulin has been performed using the molecular mechanics-generalized Born surface area approach. The calculated absolute binding free energy is -11.9 kcal/mol, in approximate agreement with the experimental value of -7.2 kcal/mol. The results show that the dimerization is mainly due to nonpolar interactions. The role of the hydrogen bonds between the 2 monomers appears to give the direction of the interactions. A per-atom decomposition of the binding free energy has been performed to identify the residues contributing most to the self association free energy. Residues B24-B26 are found to make the largest favorable contributions to the dimerization. Other residues situated at the interface between the 2 monomers were found to make favorable but smaller contributions to the dimerization: Tyr B16, Val B12, and Pro B28, and to an even lesser extent, Gly B23. The energy decomposition on a per-residue basis is in agreement with experimental alanine scanning data. The results obtained from a single trajectory (i.e., the dimer trajectory is also used for the monomer analysis) and 2 trajectories (i.e., separate trajectories are used for the monomer and dimer) are similar.     

A computational analysis of the binding affinities of FKBP12 inhibitors using the MM-PB/SA method

The FK506-binding proteins have been targets of pharmaceutical interests over years. We have studied the binding of a set of 12 nonimmunosuppressive small-molecule inhibitors to FKBP12 through molecular dynamics simulations. Each complex was subjected to 1-ns MD simulation conducted in an explicit solvent environment under constant temperature and pressure. The binding free energy of each complex was then computed by the MM-PB/SA method in the AMBER program. Our MM-PB/SA computation produced a good correlation between the experimentally determined and the computed binding free energies with a correlation coefficient (R(2)) of 0.93 and a standard deviation as low as 0.30 kcal/mol. The vibrational entropy term given by the normal mode analysis was found to be helpful for achieving this correlation. Moreover, an adjustment to one weight factor in the PB/SA model was essential to correct the absolute values of the final binding free energies to a reasonable range. A head-to-head comparison of our MM-PB/SA model with a previously reported Linear Response Approximation (LRA) model suggested that the MM-PB/SA method is more robust in binding affinity prediction for this class of compounds.     

MM/PBSA analysis of molecular dynamics simulations of bovine β‐lactoglobulin: Free energy gradients in conformational transitions?

The pH-driven opening and closure of beta-lactoglobulin EF loop, acting as a lid and closing the internal cavity of the protein, has been studied by molecular dynamics (MD) simulations and free energy calculations based on molecular mechanics/Poisson-Boltzmann (PB) solvent-accessible surface area (MM/PBSA) methodology. The forms above and below the transition pH differ presumably only in the protonation state of residue Glu89. MM/PBSA calculations are able to reproduce qualitatively the thermodynamics of the transition. The analysis of MD simulations using a combination of MM/PBSA methodology and the colony energy approach is able to highlight the driving forces implied in the transition. The analysis suggests that global rearrangements take place before the equilibrium local conformation is reached. This conclusion may bear general relevance to conformational transitions in all lipocalins and proteins in general.     

Validation of an automated procedure for the prediction of relative free energies of binding on a set of aldose reductase inhibitors

Among the available methods for predicting free energies of binding of ligands to a protein, the molecular mechanics Poisson–Boltzmann surface area (MM-PBSA) and molecular mechanics generalized Born surface area (MM-GBSA) approaches have been validated for a relatively limited number of targets and compounds in the training set. Here, we report the results of an extensive study on a series of 28 inhibitors of aldose reductase with experimentally determined crystal structures and inhibitory activities, in which we evaluate the ability of MM-PBSA and MM-GBSA methods in predicting binding free energies using a number of different simulation conditions. While none of the methods proved able to predict absolute free energies of binding in quantitative agreement with the experimental values, calculated and experimental free energies of binding were significantly correlated. Comparing the predicted and experimental ΔG of binding, MM-PBSA proved to perform better than MM-GBSA, and within the MM-PBSA methods, the PBSA of Amber performed similarly to Delphi. In particular, significant relationships between experimental and computed free energies of binding were obtained using Amber PBSA and structures minimized with a distance-dependent dielectric function. Importantly, while free energy predictions are usually made on large collections of equilibrated structures sampled during molecular dynamics in water, we have found that a single minimized structure is a reasonable approximation if relative free energies of binding are to be calculated. This finding is particularly relevant, considering that the generation of equilibrated MD ensembles and the subsequent free energy analysis on multiple snapshots is computationally intensive, while the generation and analysis of a single minimized structure of a protein–ligand complex is relatively fast, and therefore suited for high-throughput virtual screening studies. At this aim, we have developed an automated workflow that integrates all the necessary steps required to generate structures and calculate free energies of binding. The procedure is relatively fast and able to screen automatically and iteratively molecules contained in databases and libraries of compounds. Taken altogether, our results suggest that the workflow can be a valuable tool for ligand identification and optimization, being able to automatically and efficiently refine docking poses, which sometimes may not be accurate, and rank the compounds based on more accurate scoring functions.     

Molecular docking study and development of an empirical binding free energy model for phosphodiesterase 4 inhibitors

In the present work, several computational methodologies were combined to develop a model for the prediction of PDE4B inhibitors' activity. The adequacy of applying the ligand docking approach, keeping the enzyme rigid, to the study of a series of PDE4 inhibitors was confirmed by a previous molecular dynamics analysis of the complete enzyme. An exhaustive docking procedure was performed to identify the most probable binding modes of the ligands to the enzyme, including the active site metal ions and the surrounding structural water molecules. The enzyme-inhibitor interaction enthalpies, refined by using the semiempirical molecular orbital approach, were combined with calculated solvation free energies and entropy considerations in an empirical free energy model that enabled the calculation of binding free energies that correlated very well with experimentally derived binding free energies. Our results indicate that both the inclusion of the structural water molecules close to the ions in the binding site and the use of a free energy model with a quadratic dependency on the ligand free energy of solvation are important aspects to be considered for molecular docking investigations involving the PDE4 enzyme family.     

Understanding the molecular basis of MK2-p38α signaling complex assembly: insights into protein-protein interaction by molecular dynamics and free energy studies

The formation of a p38 MAPK and MAPK-activated protein kinase 2 (MK2) signaling complex is physiologically relevant to cellular responses such as the proinflammatory cytokine production. The interaction between p38α isoform and MK2 is of great importance for this signaling. In this study, molecular dynamics simulation and binding free energy calculation were performed on the MK2-p38α signaling complex to investigate the protein-protein interaction between the two proteins. Dynamic domain motion analyses were performed to analyze the conformational changes between the unbound and bound states of proteins during the interaction. The activation loop, αF-I helices, and loops among α helices in the C-lobe of MK2 are found to be highly flexible and exhibit significant changes upon p38α binding. The results also show that after the binding of p38α, the N- and C-terminal domains of MK2 display an opening and twisting motion centered on the activation loop. The molecular mechanics Poisson-Boltzmann and generalized-Born surface area (MM-PB/GBSA) methods were used to calculate binding free energies between MK2 and p38α. The analysis of the components of binding free energy calculation indicates that the van der Waals interaction and the nonpolar solvation energy provide the driving force for the binding process, while the electrostatic interaction contributes critically to the specificity, rather than to MK2-p38α binding affinity. The contribution of each residue at the interaction interface to the binding affinity of MK2 with p38α was also analyzed by free energy decomposition. Several important residues responsible for the protein-protein interaction were also identified.     

Free energy calculations for theophylline binding to an RNA aptamer: Comparison of MM-PBSA and thermodynamic integration methods

We have applied the molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) method (J. Srinivasan, T. E. Cheatham, P. Cieplak, P. A. Kollman, and D. A. Case, Journal of the American Chemical Society, 1998, Vol. 120, pp. 9401-9409) to study the interaction of an RNA aptamer with theophylline and its analogs. The MM-PBSA free energy analysis provides a reasonable absolute binding free energy for the RNA aptamer-theophylline complex formation. Energetic analysis reveals that the van der Waals interaction and the nonpolar contribution to solvation provide the basis for the favorable absolute free energy of complex. This trend is similar to other protein-ligand interactions studied previously. The MM-PBSA method also ranks the relative binding energies of five theophylline analogs approximately correctly, but not as well as the more conventional thermodynamic integration calculations, which were carried out to convert theophylline into its analogs. The comparison of MM-PBSA with TI suggests that the MM-PBSA method has some difficulties with the first-solvation-shell energetics.