Absolute binding free energy calculations: On the accuracy of computational scoring of protein–ligand interactions

Calculating the absolute binding free energies is a challenging task. Reliable estimates of binding free energies should provide a guide for rational drug design. It should also provide us with deeper understanding of the correlation between protein structure and its function. Further applications may include identifying novel molecular scaffolds and optimizing lead compounds in computer‐aided drug design. Available options to evaluate the absolute binding free energies range from the rigorous but expensive free energy perturbation to the microscopic linear response approximation (LRA/β version) and related approaches including the linear interaction energy (LIE) to the more approximated and considerably faster scaled protein dipoles Langevin dipoles (PDLD/S‐LRA version) as well as the less rigorous molecular mechanics Poisson–Boltzmann/surface area (MM/PBSA) and generalized born/surface area (MM/GBSA) to the less accurate scoring functions. There is a need for an assessment of the performance of different approaches in terms of computer time and reliability. We present a comparative study of the LRA/β, the LIE, the PDLD/S‐LRA/β, and the more widely used MM/PBSA and assess their abilities to estimate the absolute binding energies. The LRA and LIE methods perform reasonably well but require specialized parameterization for the nonelectrostatic term. The PDLD/S‐LRA/β performs effectively without the need of reparameterization. Our assessment of the MM/PBSA is less optimistic. This approach appears to provide erroneous estimates of the absolute binding energies because of its incorrect entropies and the problematic treatment of electrostatic energies. Overall, the PDLD/S‐LRA/β appears to offer an appealing option for the final stages of massive screening approaches. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

FastContact: rapid estimate of contact and binding free energies

Interaction free energies are crucial for analyzing binding propensities in proteins. Although the problem of computing binding free energies remains open, approximate estimates have become very useful for filtering potential binding complexes. We report on the implementation of a fast computational estimate of the binding free energy based on a statistically determined desolvation contact potential and Coulomb electrostatics with a distance-dependent dielectric constant, and validated in the Critical Assessment of PRotein Interactions experiment. The application also reports residue contact free energies that rapidly highlight the hotspots of the interaction. AVAILABILITY: The program was written in Fortran. The executable and full documentation is freely available at http://structure.pitt.edu/software/FastContact     

What determines the van der Waals coefficient beta in the LIE (linear interaction energy) method to estimate binding free energies using molecular dynamics simulations?

Recently a semiempirical method has been proposed by Aqvist et al. to calculate absolute and relative binding free energies. In this method, the absolute binding free energy of a ligand is estimated as deltaGbind = alpha + beta, where Vel(bound) and Vvdw(bound) are the electrostatic and van der Waals interaction energies between the ligand and the solvated protein from an molecular dynamics (MD) trajectory with ligand bound to protein and Vel(free) and Vel(free) and Vvdw(free) are the electrostatic and van der Waals interaction energies between the ligand and the water from an MD trajectory with the ligand in water. A set of values, alpha = 0.5 and beta = 0.16, was found to give results in good agreement with experimental data. Later, however, different optimal values of beta were found in studies of compounds binding to P450cam and avidin. The present work investigates how the optimal value of beta depends on the nature of binding sites for different protein-ligand interactions. By examining seven ligands interacting with five proteins, we have discovered a linear correlation between the value of beta and the weighted non-polar desolvation ratio (WNDR), with a correlation coefficient of 0.96. We have also examined the ability of this correlation to predict optimal values of beta for different ligands binding to a single protein. We studied twelve neutral compounds bound to avidin. In this case, the WNDR approach gave a better estimate of the absolute binding free energies than results obtained using the fixed value of beta found for biotin-avidin. In terms of reproducing the relative binding free energy to biotin, the fixed-beta value gave better results for compounds similar to biotin, but for compounds less similar to biotin, the WNDR approach led to better relative binding free energies.     

Insights into drug resistance of mutations D30N and I50V to HIV-1 protease inhibitor TMC-114: Free energy calculation and molecular dynamic simulation

The single mutations D30N and I50V are considered as the key residue mutations of the HIV-1 protease drug resistance to inhibitors in clinical use. In this work, molecular dynamics (MD) simulations combined with the molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) method have been performed to investigate the drug-resistant mechanisms of D30N and I50V to an inhibitor TMC-114. The analyses of absolute binding free energies using the separate trajectory approach suggests that the decrease in the van der Waals energy and electrostatic energy in the gas phase results in the drug resistance of D30N to TMC-114, while for I50V, the decrease in the electrostatic energy mainly drive its drug resistance to TMC-114. Detailed binding free energies between TMC-114 and individual protein residues are computed by using a per-residue basis decomposition method, which provides insights into the inhibitor-protein binding mechanism and also explains the drug-resistant mechanisms of mutations D30N and I50V to TMC-114. The study shows that the loss of the hydrogen bond between TMC-114 and the side chain of Asn30′ is the main driving force of the resistance of D30N to TMC-114, and in the case of I50V, the increase in the polar solvation energies between TMC-114 and two residues Val50′ and Asp30′ definitively drives the resistance of I50V to TMC-114. We expect that this work can provide some helpful insights into the nature of mutational effect and aid the future design of better inhibitors.     

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.     

Calculations of antibody-antigen interactions: microscopic and semi-microscopic evaluation of the free energies of binding of phosphorylcholine analogs to McPC603.

The study of antibody-antigen interactions should greatly benefit from the development of quantitative models for the evaluation of binding free energies in proteins. The present work addresses this challenge by considering the test case of the binding free energies of phosphorylcholine analogs to the murine myeloma protein McPC603. This includes the evaluation of the differential binding energy as well as the absolute binding energies and their corresponding electrostatic contributions. Four different approaches are examined: the Protein Dipoles Langevin Dipoles (PDLD) method, the semi-microscopic PDLD (PDLD/S) method, a free energy perturbation (FEP) method based on an adiabatic charging procedure and a linear response approximation that accelerates the FEP calculation. The PDLD electrostatic calculations are augmented by estimates of the relevant hydrophobic and steric contributions. The determination of the hydrophobic energy involves an approach which considers the modification of the effective surface area of the solute by local field effects. The steric contributions are analyzed in terms of the corresponding reorganization energies. This treatment, which considers the protein as a harmonic system, views the steric forces as the restoring forces for the electrostatic interactions. The FEP method is found to give unreliable results with regular cut-off radii and starts to give quantitative results only in very expensive treatment with very large cut-off radii. The PDLD and PDLD/S methods are much faster than the FEP approach and give reasonable results for both the relative and absolute binding energies. The speed and simplicity of the PDLD/S method make it an effective strategy for interactive docking studies and indeed such an option is incorporated in the program MOLARIS. A component analysis of the different energy contributions of the FEP treatment and a similar PDLD analysis indicate that electrostatic effects provide the largest contribution to the differential binding energy, while the hydrophobic and steric contributions are much smaller. This finding lends further support to the idea that electrostatic interactions play a major role in determining the antigen specificity of McPC603.     

Validating the vitality strategy for fighting drug resistance

The current challenge in designing effective drugs against HIV-1 is to find novel candidates with high potency, but with a lower susceptibility to mutations associated with drug resistance. Trying to address this challenge, we developed in our previous study (Ishikita and Warshel, Angew Chem Int Ed Engl 2008; 47:697-700) a novel computational strategy for fighting drug resistance by predicting the likely moves of the virus through constraints on binding and catalysis. This has been based on calculating the ratio between the vitality values ((K(i) k(cat)/K(M))(mutant)/(K(i) k(cat)/K(M))(wild-type)) and using it as a guide for predicting the moves of the virus. The corresponding calculations of the binding affinity, K(i), were carried out using the semi-macroscopic version of the protein dipole Langevin dipole (PDLD/S) in its linear response approximation (LRA) in its β version (PDLD/S-LRA/β). We also calculate the proteolytic efficiency, k(cat)/K(M), by evaluating the transition state (TS) binding free energies using the PDLD/S-LRA/β method. Here we provide an extensive validation of our strategy by calculating the vitality of six existing clinical and experimental drug candidates. It is found that the computationally determined vitalities correlate reasonably well with those derived from the corresponding experimental data. This indicates that the calculated vitality may be used to identify mutations that would be most effective for the survival of the virus. Thus, it should be possible to use our approach in screening for mutations that would provide the most effective resistance to any proposed antiviral drug. This ability should be very useful in guiding the design of drug molecules that will lead to the slowest resistance.     

Molecular modelling studies unveil potential binding sites on human serum albumin for selected experimental and in silico COVID-19 drug candidate molecules

Human serum albumin (HSA) is the most prevalent protein in the blood plasma which binds an array of exogenous compounds. Drug binding to HSA is an important consideration when developing new therapeutic molecules, and it also aids in understanding the underlying mechanisms that govern their pharmacological effects. This study aims to investigate the molecular binding of coronavirus disease 2019 (COVID-19) therapeutic candidate molecules to HSA and to identify their putative binding sites. Binding energies and interacting residues were used to evaluate the molecular interaction. Four drug candidate molecules (β-D-N4-hydroxycytidine, Chloroquine, Disulfiram, and Carmofur) demonstrate weak binding to HSA, with binding energies ranging from −5 to −6.7 kcal/mol. Ivermectin, Hydroxychloroquine, Remdesivir, Arbidol, and other twenty drug molecules with binding energies ranging from −6.9 to −9.5 kcal/mol demonstrated moderate binding to HSA. The strong HSA binding drug candidates consist of fourteen molecules (Saquinavir, Ritonavir, Dihydroergotamine, Daclatasvir, Paritaprevir etc.) with binding energies ranging from −9.7 to −12.1 kcal/mol. All these molecules bind to different HSA subdomains (IA, IB, IIA, IIB, IIIA, and IIIB) through molecular forces such as hydrogen bonds and hydrophobic interactions. Various pharmacokinetic properties (gastrointestinal absorption, blood-brain barrier permeation, P-glycoprotein substrate, and cytochrome P450 inhibitor) of each molecule were determined using SwissADME program. Further, the stability of the HSA-ligand complexes was analyzed through 100 ns molecular dynamics simulations considering various geometric properties. The binding free energy between free HSA and compounds were calculated using Molecular mechanics Poisson–Boltzmann surface area (MM/PBSA) and molecular mechanics generalized Born surface area (MM/GBSA) approach. The findings of this study might be useful in understanding the mechanism of COVID-19 drug candidates binding to serum albumin protein, as well as their pharmacodynamics and pharmacokinetics.Keyword: Human serum albumin, HAS, Serum protein, COVID-19, Molecular docking, Molecular dynamics simulation, Pharmacokinetics, Pharmacodynamics     

BEAR, a novel virtual screening methodology for drug discovery

BEAR (binding estimation after refinement) is a new virtual screening technology based on the conformational refinement of docking poses through molecular dynamics and prediction of binding free energies using accurate scoring functions. Here, the authors report the results of an extensive benchmark of the BEAR performance in identifying a smaller subset of known inhibitors seeded in a large (1.5 million) database of compounds. BEAR performance proved strikingly better if compared with standard docking screening methods. The validations performed so far showed that BEAR is a reliable tool for drug discovery. It is fast, modular, and automated, and it can be applied to virtual screenings against any biological target with known structure and any database of compounds.     

Theoretical calculation of the binding free energies for pyruvate dehydrogenase E1 binding with ligands

We have tested a computational protocol based on molecular mechanics-Poisson-Boltzmann surface area (MM-PBSA) free-energy calculations to examine the detailed microscopic structures and binding free energies for the pyruvate dehydrogenase multienzyme complex (PDHc) E1 binding with its ligands (cofactor and inhibitors). The calculated binding free energies are all in good agreement with available experimental data, with an average absolute deviation of approximately 0.7 kcal/mol, suggesting that the computational protocol tested may be valuable in future rational design of new, more potent inhibitors of PDHc E1.     

Absolute binding free energy calculations using molecular dynamics simulations with restraining potentials

The absolute (standard) binding free energy of eight FK506-related ligands to FKBP12 is calculated using free energy perturbation molecular dynamics (FEP/MD) simulations with explicit solvent. A number of features are implemented to improve the accuracy and enhance the convergence of the calculations. First, the absolute binding free energy is decomposed into sequential steps during which the ligand-surrounding interactions as well as various biasing potentials restraining the translation, orientation, and conformation of the ligand are turned "on" and "off." Second, sampling of the ligand conformation is enforced by a restraining potential based on the root mean-square deviation relative to the bound state conformation. The effect of all the restraining potentials is rigorously unbiased, and it is shown explicitly that the final results are independent of all artificial restraints. Third, the repulsive and dispersive free energy contribution arising from the Lennard-Jones interactions of the ligand with its surrounding (protein and solvent) is calculated using the Weeks-Chandler-Andersen separation. This separation also improves convergence of the FEP/MD calculations. Fourth, to decrease the computational cost, only a small number of atoms in the vicinity of the binding site are simulated explicitly, while all the influence of the remaining atoms is incorporated implicitly using the generalized solvent boundary potential (GSBP) method. With GSBP, the size of the simulated FKBP12/ligand systems is significantly reduced, from approximately 25,000 to 2500. The computations are very efficient and the statistical error is small ( approximately 1 kcal/mol). The calculated binding free energies are generally in good agreement with available experimental data and previous calculations (within approximately 2 kcal/mol). The present results indicate that a strategy based on FEP/MD simulations of a reduced GSBP atomic model sampled with conformational, translational, and orientational restraining potentials can be computationally inexpensive and accurate.     

An efficient computational method for calculating ligand binding affinities

Virtual compound screening using molecular docking is widely used in the discovery of new lead compounds for drug design. However, the docking scores are not sufficiently precise to represent the protein-ligand binding affinity. Here, we developed an efficient computational method for calculating protein-ligand binding affinity, which is based on molecular mechanics generalized Born/surface area (MM-GBSA) calculations and Jarzynski identity. Jarzynski identity is an exact relation between free energy differences and the work done through non-equilibrium process, and MM-GBSA is a semimacroscopic approach to calculate the potential energy. To calculate the work distribution when a ligand is pulled out of its binding site, multiple protein-ligand conformations are randomly generated as an alternative to performing an explicit single-molecule pulling simulation. We assessed the new method, multiple random conformation/MM-GBSA (MRC-MMGBSA), by evaluating ligand-binding affinities (scores) for four target proteins, and comparing these scores with experimental data. The calculated scores were qualitatively in good agreement with the experimental binding affinities, and the optimal docking structure could be determined by ranking the scores of the multiple docking poses obtained by the molecular docking process. Furthermore, the scores showed a strong linear response to experimental binding free energies, so that the free energy difference of the ligand binding (ΔΔG) could be calculated by linear scaling of the scores. The error of calculated ΔΔG was within ≈±1.5 kcal•mol⁻¹ of the experimental values. Particularly, in the case of flexible target proteins, the MRC-MMGBSA scores were more effective in ranking ligands than those generated by the MM-GBSA method using a single protein-ligand conformation. The results suggest that, owing to its lower computational costs and greater accuracy, the MRC-MMGBSA offers efficient means to rank the ligands, in the post-docking process, according to their binding affinities, and to compare these directly with the experimental values.     

Binding free energy calculations of N-sulphonyl-glutamic acid inhibitors of MurD ligase

The increasing incidence of bacterial resistance to most available antibiotics has underlined the urgent need for the discovery of novel efficacious antibacterial agents. The biosynthesis of bacterial peptidoglycan, where the MurD enzyme is involved in the intracellular phase of UDP-MurNAc-pentapeptide formation, represents a collection of highly selective targets for novel antibacterial drug design. Structural studies of N-sulfonyl-glutamic acid inhibitors of MurD have made possible the examination of binding modes of this class of compounds, providing valuable information for the lead optimization phase of the drug discovery cycle. Binding free energies were calculated for a series of MurD N-sulphonyl-Glu inhibitors using the linear interaction energy (LIE) method. Analysis of interaction energy during the 20-ns MD trajectories revealed non-polar van der Waals interactions as the main driving force for the binding of these inhibitors, and excellent agreement with the experimental free energies was obtained. Calculations of binding free energies for selected moieties of compounds in this structural class substantiated even deeper insight into the source of inhibitory activity. These results constitute new valuable information to further assist the lead optimization process. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.

A comprehensive examination of the contributions to the binding entropy of protein–ligand complexes

One of the most important requirements in computer‐aided drug design is the ability to reliably evaluate the binding free energies. However, the process of ligand binding is very complex because of the intricacy of the interrelated processes that are difficult to predict and quantify. In fact, the deeper understanding of the origin of the observed binding free energies requires the ability to decompose these free energies to their contributions from different interactions. Furthermore, it is important to evaluate the relative entropic and enthalpic contributions to the overall free energy. Such an evaluation is useful for assessing temperature effects and exploring specialized options in enzyme design. Unfortunately, calculations of binding entropies have been much more challenging than calculations of binding free energies. This work is probably the first to present microscopic evaluation of all of the relevant components to the binding entropy, namely configurational, polar solvation, and hydrophobic entropies. All of these contributions are evaluated by the restraint release approach. The calculated results shed an interesting light on major compensation effects in both the solvation and hydrophobic effect and, despite some overestimate, can provide very useful insight. This study also helps in analyzing some problems with the widely used molecular mechanics/Poisson‐Boltzmann surface area approach. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Structure and thermodynamics of RNA-protein binding: using molecular dynamics and free energy analyses to calculate the free energies of binding and conformational change

An adaptive binding mechanism, requiring large conformational rearrangements, occurs commonly with many RNA-protein associations. To explore this process of reorganization, we have investigated the conformational change upon spliceosomal U1A-RNA binding with molecular dynamics (MD) simulations and free energy analyses. We computed the energetic cost of conformational change in U1A-hairpin and U1A-internal loop binding using a hybrid of molecular mechanics and continuum solvent methods. Encouragingly, in all four free energy comparisons (two slightly different proteins, two different RNAs), the free macromolecule was more stable than the bound form by the physically reasonable value of approximately 10 kcal/mol. We calculated the absolute binding free energies for both complexes to be in the same range as that found experimentally.     

Computational analysis of binding of P1 variants to trypsin

The binding of P1 variants of bovine pancreatic trypsin inhibitor (BPTI) to trypsin has been investigated by means of molecular dynamics simulations. The specific interaction formed between the amino acid at the primary binding (P1) position of the binding loop of BPTI and the specificity pocket of trypsin was estimated by use of the linear interaction energy (LIE) method. Calculations for 13 of the naturally occurring amino acids at the P1 position were carried out, and the results obtained were found to correlate well with the experimental binding free energies. The LIE calculations rank the majority of the 13 variants correctly according to the experimental association energies and the mean error between calculated and experimental binding free energies is only 0.38 kcal/mole, excluding the Glu and Asp variants, which are associated with some uncertainties regarding protonation and the possible presence of counter-ions. The three-dimensional structures of the complex with three of the P1 variants (Asn, Tyr, and Ser) included in this study have not at present been solved by any experimental techniques and, therefore, were modeled on the basis of experimental data from P1 variants of similar size. Average structures were calculated from the MD simulations, from which specific interactions explaining the broad variation in association energies were identified. The present study also shows that explicit treatment of the complex water-mediated hydrogen bonding network at the protein-protein interface is of crucial importance for obtaining reliable binding free energies. The successful reproduction of relative binding energies shows that this type of methodology can be very useful as an aid in rational design and redesign of biologically active macromolecules.     

Estimation of the binding affinities of FKBP12 inhibitors using a linear response method.

A series of non-immunosuppressive inhibitors of FK506 binding protein (FKBP12) are investigated using Monte Carlo statistical mechanics simulations. These small molecules may serve as scaffolds for chemical inducers of protein dimerization, and have recently been found to have FKBP12-dependent neurotrophic activity. A linear response model was developed for estimation of absolute binding free energies based on changes in electrostatic and van der Waals energies and solvent-accessible surface areas, which are accumulated during simulations of bound and unbound ligands. With average errors of 0.5 kcal/mol, this method provides a relatively rapid way to screen the binding of ligands while retaining the structural information content of more rigorous free energy calculations.     

Insights into protein-protein binding by binding free energy calculation and free energy decomposition for the Ras-Raf and Ras-RalGDS complexes

Absolute binding free energy calculations and free energy decompositions are presented for the protein-protein complexes H-Ras/C-Raf1 and H-Ras/RalGDS. Ras is a central switch in the regulation of cell proliferation and differentiation. In our study, we investigate the capability of the molecular mechanics (MM)-generalized Born surface area (GBSA) approach to estimate absolute binding free energies for the protein-protein complexes. Averaging gas-phase energies, solvation free energies, and entropic contributions over snapshots extracted from trajectories of the unbound proteins and the complexes, calculated binding free energies (Ras-Raf: -15.0(+/-6.3)kcal mol(-1); Ras-RalGDS: -19.5(+/-5.9)kcal mol(-1)) are in fair agreement with experimentally determined values (-9.6 kcal mol(-1); -8.4 kcal mol(-1)), if appropriate ionic strength is taken into account. Structural determinants of the binding affinity of Ras-Raf and Ras-RalGDS are identified by means of free energy decomposition. For the first time, computationally inexpensive generalized Born (GB) calculations are applied in this context to partition solvation free energies along with gas-phase energies between residues of both binding partners. For selected residues, in addition, entropic contributions are estimated by classical statistical mechanics. Comparison of the decomposition results with experimentally determined binding free energy differences for alanine mutants of interface residues yielded correlations with r(2)=0.55 and 0.46 for Ras-Raf and Ras-RalGDS, respectively. Extension of the decomposition reveals residues as far apart as 25A from the binding epitope that can contribute significantly to binding free energy. These "hotspots" are found to show large atomic fluctuations in the unbound proteins, indicating that they reside in structurally less stable regions. Furthermore, hotspot residues experience a significantly larger-than-average decrease in local fluctuations upon complex formation. Finally, by calculating a pair-wise decomposition of interactions, interaction pathways originating in the binding epitope of Raf are found that protrude through the protein structure towards the loop L1. This explains the finding of a conformational change in this region upon complex formation with Ras, and it may trigger a larger structural change in Raf, which is considered to be necessary for activation of the effector by Ras.     

Calculations of free-energy contributions to protein-RNA complex stabilization

The problem of calculating binding affinities of protein-RNA complexes is addressed by analyzing a computational strategy of modeling electrostatic free energies based on a nonlinear Poisson-Boltzmann (NLPB) model and linear response approximation (LRA). The underlying idea is to treat binding as a two-step process. Solutions to the NLPB equation calculate free energies arising from electronic polarizability and the LRA is constructed from molecular dynamics simulations to model reorganization free energies due to conformational transitions. By implementing a consistency condition of requiring the NLPB model to reproduce the solute-solvent free-energy transitions determined by the LRA, a "macromolecule dielectric constant" (epsilon(m)) for treating reorganization is obtained. The applicability of this hybrid approach was evaluated by calculating the absolute free energy of binding and free-energy changes for amino acid substitutions in the complex between the U1A spliceosomal protein and its cognate RNA hairpin. Depending on the residue substitution, epsilon(m) varied from 3 to 18, and reflected dipolar reorientation not included in the polarization modeled by epsilon(m) = 2. Although the changes in binding affinities from substitutions modeled strictly at the implicit level by the NLPB equation with epsilon(m) = 4 reproduced the experimental values with good overall agreement, substitutions problematic to this simple treatment showed significant improvement when solved by the NLPB-LRA approach.