Binding Free Energy Estimation Research Articles

Calculation of binding free energies for non-zinc chelating pyrimidine dicarboxamide inhibitors with MMP-13

All-atom molecular dynamics (MD) simulations in both explicit and implicit solvent, followed by MM-GBSA energy analysis, have been used to estimate binding free energies of four pyrimidine dicarboxamide inhibitors with human collagenase-3 (MMP-13) for comparison with experimental activities. Energetic analysis reveals that affinity is driven primarily by favorable van der Waals interactions and burial of total surface area. The computed effects of desolvation, as a function of ligand structure, quantitatively show that hydrophilic derivatives pay greater penalties upon binding than their related more hydrophobic analogs.

Computational modeling and surface plasmon resonance analyses in the assessment of peptide ligands interacting with fibrin γ(312–324) epitope

Fibrin represents a suitable target for addressing delivery systems loaded by fibrinolytic drugs. Selective ligands capable to recognize fibrin could be used as targeting moieties for such systems. In this study the interactions between the γ(312–324) epitope of human fibrin and peptidic ligands were analyzed by using experimental and computational methods. Binding free energies were calculated through the molecular mechanics/generalized born surface area approach. Good qualitative agreements between the experimental and calculated data were obtained. The binding affinity seems to be well correlated ( R 2 = 0.69) with the changes of the nonpolar solvation energy term computed from solvent-accessible surface area calculation. These results indicate that current methods of estimating binding free energies are efficient for achieving information on protein–ligand interactions.

Investigation of MM-PBSA Rescoring of Docking Poses

Target-based virtual screening is increasingly used to generate leads for targets for which high quality three-dimensional (3D) structures are available. To allow large molecular databases to be screened rapidly, a tiered scoring scheme is often employed whereby a simple scoring function is used as a fast filter of the entire database and a more rigorous and time-consuming scoring function is used to rescore the top hits to produce the final list of ranked compounds. Molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) approaches are currently thought to be quite effective at incorporating implicit solvation into the estimation of ligand binding free energies. In this paper, the ability of a high-throughput MM-PBSA rescoring function to discriminate between correct and incorrect docking poses is investigated in detail. Various initial scoring functions are used to generate docked poses for a subset of the CCDC/Astex test set and to dock one set of actives/inactives from the DUD data set. The effectiveness of each of these initial scoring functions is discussed. Overall, the ability of the MM-PBSA rescoring function to (i) regenerate the set of X-ray complexes when docking the bound conformation of the ligand, (ii) regenerate the X-ray complexes when docking conformationally expanded databases for each ligand which include "conformation decoys" of the ligand, and (iii) enrich known actives in a virtual screen for the mineralocorticoid receptor in the presence of "ligand decoys" is assessed. While a pharmacophore-based molecular docking approach, PhDock, is used to carry out the docking, the results are expected to be general to use with any docking method.

Resurveying the Tris buffer solution: The specific interaction between tris(hydroxymethyl)aminomethane and lysozyme

An unusual phenomenon, the specific interaction between tris(hydroxymethyl)aminomethane (Tris) and lysozyme (LZM), was demonstrated for the first time by rapid screen analysis of interactions using a quartz crystal microbalance (QCM) biosensor. This phenomenon was also observed in a surface plasmon resonance (SPR) system. Further study using high-performance affinity chromatography (HPAC) confirmed this specific interaction between LZM and immobilized Tris with an apparent dissociation constant ( K D) of 6.7 × 10 −5 M. Molecular docking was carried out to identify possible modes of binding between LZM and Tris linked to a binding arm. The estimated binding free energy was −6.34 kcal mol −1, corresponding to a K D of 2.3 × 10 −5 M, which correlated well with the experimental value. Based on the docking model, the three hydroxyl groups of Tris form intermolecular H bonds with Asp52, Glu35, and Ala107 in LZM. This study reinforces the importance of buffer selection in quantitative biochemical investigations. For a lysozyme ligand binding study, it is better to avoid using Tris when the ligands under study are weak binders.

Assessment of programs for ligand binding affinity prediction

The prediction of the binding free energy between a ligand and a protein is an important component in the virtual screening and lead optimization of ligands for drug discovery. To determine the quality of current binding free energy estimation programs, we examined FlexX, X-Score, AutoDock, and BLEEP for their performance in binding free energy prediction in various situations including cocrystallized complex structures, cross docking of ligands to their non-cocrystallized receptors, docking of thermally unfolded receptor decoys to their ligands, and complex structures with "randomized" ligand decoys. In no case was there a satisfactory correlation between the experimental and estimated binding free energies over all the datasets tested. Meanwhile, a strong correlation between ligand molecular weight-binding affinity correlation and experimental predicted binding affinity correlation was found. Sometimes the programs also correctly ranked ligands' binding affinities even though native interactions between the ligands and their receptors were essentially lost because of receptor deformation or ligand randomization, and the programs could not decisively discriminate randomized ligand decoys from their native ligands; this suggested that the tested programs miss important components for the accurate capture of specific ligand binding interactions.

Polyomaviridae Assembly Polymorphism from an Energy Landscape Perspective

Polyomaviridae assemblein vitrointo different aggregates depending on experimental conditions. We use an energy landscape approach using empirical energy calculations to quantify how the formation of these different aggregates depends on pH, the presence of bound calcium ions and disulfide linkages. Computations are carried out for SV40, a member of the Polyomaviridae family and are based on the binding free energy landscape of three distinct trimers of pentamers that correspond to the different bonding configurations between the capsid proteins observed in its crystal structure. Our computational analysis shows that the energetics of one of these environments is pivotal for the polymorphic assembly behaviour of SV40, whilst the binding energy landscapes of the other two environments are broadly funnel-shaped and thus contribute little to the formation of particles other than virus-like particles (VLP). We have quantified how the existence of bound calcium ions in the absence of disulfide linkages enhances the binding free energies of all three environments and hence, favours the assembly of VLPs. Moreover, estimation of the relative binding free energies of the three environments at pH 5 and pH 8 reveals that they are destabilized at pH 5 relative to pH 8. The extent of this destabilization is dependent on the presence of disulfide linkages and bound calcium ions and accounts for the experimentally observed polymorphic behaviour of VP1 proteins at pH 5. Interestingly, concurrent existence of bound calcium ions and disulfide linkages is found to be destabilizing and thus may disrupt the assembly of VLPs at pH 8.

Estimation of Ligand Binding Free Energies of F-ATPase by Using Molecular Dynamics/Free Energy Calculation

ATP 合成酵素であるF 型ATPase は, ほとんどの生物に存在する膜貫通型タンパク質であり, ATPの加水分解反応に共役した分子の回転が観察されている. ATPase活性を持つ最小単位はα3β3γ複合体であり, 触媒部位である3つのβサブユニットはATP結合型(βTP), ADP結合型(βDP),空の構造(βE)の3つの異なる構造が解明されている. それらβサブユニットの3つの構造は異なる基質親和性を持つとされ,実験的に基質親和性の測定がされてきた. しかし, ADPの親和性に関しては未知であり, γサブユニットの回転をもたらすβサブユニットの構造変化も解明されていない. そこで, 分子動力学法/自由エネルギー計算により触媒部位の基質ATPとADPを相互変換したときの自由エネルギー差を見積もり,さらにその基質変化に伴うβ サブユニットの構造変化を観察した. その結果, βDP の構造が最もADP との結合親和性が高いことが解った. この算出値は一分子観察の結果から推測された加水分解反応モデルを熱力学的知見から裏付けるものであった. さらに, βサブユニットの構造変化とγサブユニットの回転を共役する役目を持つと考えられているDELSEED配列(Asp394∼Asp400)付近の構造を観察したところ, 基質変換に伴い構造変化が確認された. すなわち, DELSEED配列近傍のPhe418∼Gly426 は, 触媒反応と構造変化, 回転を共役するのに重要な残基であることが示唆された. 以上の結果から, ATP加水分解・Piの放出に伴い, DELSEED 配列付近の構造が変化し, それがγサブユニットの回転をもたらすという分子機構の様子が明らかになった.

Molecular dynamics simulation study for LRH‐1: Interaction with fragments of SHP and function of phospholipid ligand

The liver receptor homolog-1 (LRH-1) is an important transcriptional factor in the process of cholesterol and bile acids metabolism. In this article, molecular dynamics simulation for six systems with total 60 ns is employed to study LRH-1. LRH-1/phospholipid and LRH-1/SHP (fragments) interactions are analyzed by counting atomic contact number, identifying hydrogen bonds, and estimating binding free energies (by MM-PB/SA and N-mode analysis). Through integrating our modeling result with previous experimental data, deeper understandings to LRH-1/SHP interaction are obtained, and functions of the phospholipid ligand in LRH-1 are proposed.

Rapid Estimation of Relative Protein—Ligand Binding Affinities Using a High‐Throughput Version of MM‐PBSA.

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Calculation of binding affinities of HIV-1 RT and β-secretase inhibitors using the linear interaction energy method with explicit and continuum solvation approaches

The linear interaction energy (LIE) approach has been applied to estimate the binding free energies of representative sets of HIV-1 RT and beta-Secretase inhibitors, using both molecular dynamics (MD) and tethered energy minimization sampling protocols with the OPLS-AA potential, using a range of solvation methodologies. Generalized Born (GB), 'shell' and periodic boundary condition (PBC) solvation were used, the latter with reaction field (RF) electrostatics. Poisson-Boltzmann (PB) and GB continuum electrostatics schemes were applied to the simulation trajectories for each solvation type to estimate the electrostatic ligand-water interaction energy in both the free and bound states. Reasonable agreement of the LIE predictions was obtained with respect to experimental binding free energy estimates for both systems: for instance, 'PB' fits on MD trajectories carried out with PBC solvation and RF electrostatics led to models with standard errors of 1.11 and 1.03 kcal mol(-1) and coefficients of determination, r (2) of 0.76 and 0.75 for the HIV-1 RT and beta-Secretase sets. However, it was also found that results from MD sampling using PBC solvation provided only slightly better fits than from simulations using shell or Born solvation or tethered energy minimization sampling.

Rapid Estimation of Relative Protein−Ligand Binding Affinities Using a High-Throughput Version of MM-PBSA

By employing a modified protocol of the Molecular Mechanics with Poisson-Boltzmann Surface Area (MM-PBSA) methodology we substantially decrease the required computation time for calculating relative estimates of protein-ligand binding affinities. The modified method uses a generalized Born implicit solvation model during molecular dynamics to enhance conformational sampling as well as a very efficient Poisson-Boltzmann solver and a computational design based on a distributed-computing paradigm. This construction allows for reduction of the computational cost of the calculations by roughly 2 orders of magnitude compared to the traditional formulation of MM-PBSA. With this high-throughput version of MM-PBSA we show that one can produce efficient physics-based estimates of relative binding free energies with reasonable correlation to experimental data and a total computation time that is sufficiently low such that an industrially relevant throughput can be realized given currently accessible computing resources. We demonstrate this approach by performing a comparison of different MM-PBSA implementations on a set of 18 ligands for the protein target urokinase.

Molecular modeling of anti-parallel G-quadruplex DNA/TMPyP complexes

We carried out the molecular modeling of anti-parallel G-quadruplex/TMPyP complex, molecular dynamics simulation and estimation of binding free energy using MM-PBSA method to validate groove binding model in addition to external stacking one. We found that not total electrostatic but van der Waals energy contributes to the negative binding free energies in both models.

Dynamics and assembly of the cytolethal distending toxin

The cytolethal distending toxin (CDT) is a widespread bacterial toxin that consists of an active subunit CdtB with nuclease activity and two ricin-like lectin domains, CdtA and CdtC, that are involved in the delivery of CdtB into the host cell. The three subunits form a tripartite complex that is required to achieve the fully active holotoxin. In the present study we investigate the assembly and dynamic properties of the CDT holotoxin using molecular dynamics simulations and binding free energy calculations. The results have revealed that CdtB likely adopts a different conformation in the unbound state with a closed DNA binding site. The two characterized structural elements of the aromatic patch and groove on the CdtA and CdtC protein surfaces exhibit high mobility, and free energy calculations show that the heterodimeric complex CdtA-CdtC, as well as the CdtA-CdtB and CdtB-CdtC sub-complexes are less energetically stable as compared to the binding in the tripartite complex. Analysis of the dynamical cross-correlation map reveals information on the correlated motions and long-range interplay among the CDT subunits associated with complex formation. Finally, the estimated binding free energies of subunit interactions are presented, together with the free energy decomposition to determine the contributions of residues for both binding partners, providing insight into the protein-protein interactions in the CDT holotoxin.

Structural insights into the effect of isonucleosides on B-DNA duplexes using molecular-dynamics simulations

Some structural insights into the conformations of the isonucleosides containing duplexes have been provided. Unrestrained molecular-dynamics simulations on 18-mer duplexes with isonucleosides incorporated at the 3'-end or in the center of one strand have been carried out with explicit solvent under periodic boundary conditions using the AMBER force field and the particle mesh Ewald method. The Watson–Crick hydrogen-bonding patterns of the duplexes studied remained intact throughout the simulation. For the modified duplexes, the changes observed in the inter-base pair parameters and backbone torsional angles were primarily localized at the isonucleoside-inserted area. All five structures studied remained in the B-form family. The decreased stacking abilities indicated by the large changes in inter-base pair parameters and the large changes in backbones made the modified duplexes show a minor thermal destabilization in comparison with native DNA. The MM_PBSA method for estimating binding free energies on two complementary strands was used. The results showed that the binding free energies of isonucleoside-incorporated DNA duplexes were lower than the native DNA duplex, which is in good agreement with experimental observations.

Prediction of Binding Sites of Peptide Recognition Domains: An Application on Grb2 and SAP SH2 Domains

Determination of the binding motif and identification of interaction partners of the modular domains such as SH2 domains can enhance our understanding of the regulatory mechanism of protein-protein interactions. We propose here a new computational method to achieve this goal by integrating the orthogonal information obtained from binding free energy estimation and peptide sequence analysis. We performed a proof-of-concept study on the SH2 domains of SAP and Grb2 proteins. The method involves the following steps: (1) estimating the binding free energy of a set of randomly selected peptides along with a sample of known binders; (2) clustering all these peptides using sequence and energy characteristics; (3) extracting a sequence motif, which is represented by a hidden Markov model (HMM), from the cluster of peptides containing the sample of known binders; and (4) scanning the human proteome to identify binding sites of the domain. The binding motifs of the SAP and Grb2 SH2 domains derived by the method agree well with those determined through experimental studies. Using the derived binding motifs, we have predicted new possible interaction partners for the Grb2 and SAP SH2 domains as well as possible interaction sites for interaction partners already known. We also suggested novel roles for the proteins by reviewing their top interaction candidates.

Estimating protein-ligand binding free energy: atomic solvation parameters for partition coefficient and solvation free energy calculation.

Solvation energy calculation is one of the main difficulties for the estimation of protein-ligand binding free energy and the correct scoring in docking studies. We have developed a new solvation energy estimation method for protein-ligand binding based on atomic solvation parameter (ASP), which has been shown to improve the power of protein-ligand binding free energy predictions. The ASP set, designed to handle both proteins and organic compounds and derived from experimental n-octanol/water partition coefficient (log P) data, contains 100 atom types (united model that treats hydrogen atoms implicitly) or 119 atom types (all-atom model that treats hydrogen atoms explicitly). By using this unified ASP set, an algorithm was developed for solvation energy calculation and was further integrated into a score function for predicting protein-ligand binding affinity. The score function reproduced the absolute binding free energies of a test set of 50 protein-ligand complexes with a standard error of 8.31 kJ/mol. As a byproduct, a conformation-dependent log P calculation algorithm named ASPLOGP was also implemented. The predictive results of ASPLOGP for a test set of 138 compounds were r = 0.968, s = 0.344 for the all-atom model and r = 0.962, s = 0.367 for the united model, which were better than previous conformation-dependent approaches and comparable to fragmental and atom-based methods. ASPLOGP also gave good predictive results for small peptides. The score function based on the ASP model can be applied widely in protein-ligand interaction studies and structure-based drug design.

A Free Energy Based Computational Pathway from Chemical Templates to Lead Compounds: A Case Study of COX-2 Inhibitors

Automation of lead compound design in silico given the structure of the protein target and a definition of its active site vies for the top of the wish list in any drug discovery programme. We present here an enumeration of steps starting from chemical templates and propose a solution at the state of the art, in the form of a system independent comprehensive computational pathway. This methodology is illustrated with cyclooxygenase-2 (COX-2) as a target. We built candidate molecules including a few Non Steroidal Anti-inflammatory Drugs (NSAIDs) from chemical templates, passed them through empirical filters to assess drug-like properties, optimized their geometries, derived partial atomic charges via quantum calculations, performed Monte Carlo docking, carried out molecular mechanics and developed free energy estimates with Molecular Mechanics Generalized Born Solvent Accessibility (MMGBSA) methodology for each of the candidate molecules. For the case of aspirin, we also conducted molecular dynamics on the enzyme, the drug and the complex with explicit solvent followed by binding free energy analysis. Collectively, the results obtained from the above studies viz. sorting of drugs from non-drugs, semi-quantitative estimates of binding free energies, amply demonstrate the viability of the strategy proposed for lead selection/design for biomolecular targets.

Theoretical study of the ligand-CYP2B4 complexes: effect of structure on binding free energies and heme spin state.

The molecular origins of temperature-dependent ligand-binding affinities and ligand-induced heme spin state conversion have been investigated using free energy analysis and DFT calculations for substrates and inhibitors of cytochrome P450 2B4 (CYP2B4), employing models of CYP2B4 based on CYP2C5(3LVdH)/CYP2C9 crystal structures, and the results compared with experiment. DFT calculations indicate that large heme-ligand interactions (ca. -15 kcal/mol) are required for inducing a high to low spin heme transition, which is correlated with large molecular electrostatic potentials (approximately -45 kcal/mol) at the ligand heteroatom. While type II ligands often contain oxygen and nitrogen heteroatoms that ligate heme iron, DFT results indicate that BP and MF heme complexes, with weak substrate-heme interactions (ca. -2 kcal/mol), and modest MEPS minima (>-35 kcal/mol) are high spin. In contrast, heme complexes of the CYP2B4 inhibitor, 4PI, the product of benzphetamine metabolism, DMBP, and water are low spin, have substantial heme-ligand interaction energies (<-15 kcal/mol) and deep MEPS minima (<-45 kcal/mol) near their heteroatoms. MMPBSA analysis of MD trajectories were made to estimate binding free energies of these ligands at the heme binding site of CYP2B4. In order to initially assess the realism of this approach, the binding free energy of 4PI inhibitor was computed and found to be a reasonable agreement with experiment: -7.7 kcal/mol [-7.2 kcal/mol (experiment)]. BP was determined to be a good substrate [-6.3 kcal/mol (with heme-ligand water), -7.3 kcal/mol (without ligand water)/-5.8 kcal/mol (experiment)], whereas the binding of MF was negligible, with only marginal binding binding free energy of -1.7 kcal/mol with 2-MF bound [-3.8 kcal/mol (experiment)], both with and without retained heme-ligand water. Analysis of the free energy components reveal that hydrophobic/nonpolar contributions account for approximately 90% of the total binding free energy of these substrates and are the source of their differential and temperature-dependent CYP2B4 binding. The results indicate the underlying origins of the experimentally observed differential binding affinities of BP and MF, and indicate the plausibility of the use of models derived from moderate sequence identity templates in conjunction with approximate free energy methods in the estimation of ligand-P450 binding affinities.

Protein-ligand binding free energy estimation using molecular mechanics and continuum electrostatics. Application to HIV-1 protease inhibitors.

A method is proposed for the estimation of absolute binding free energy of interaction between proteins and ligands. Conformational sampling of the protein-ligand complex is performed by molecular dynamics (MD) in vacuo and the solvent effect is calculated a posteriori by solving the Poisson or the Poisson-Boltzmann equation for selected frames of the trajectory. The binding free energy is written as a linear combination of the buried surface upon complexation, SASbur, the electrostatic interaction energy between the ligand and the protein, Eelec, and the difference of the solvation free energies of the complex and the isolated ligand and protein, deltaGsolv. The method uses the buried surface upon complexation to account for the non-polar contribution to the binding free energy because it is less sensitive to the details of the structure than the van der Waals interaction energy. The parameters of the method are developed for a training set of 16 HIV-1 protease-inhibitor complexes of known 3D structure. A correlation coefficient of 0.91 was obtained with an unsigned mean error of 0.8 kcal/mol. When applied to a set of 25 HIV-1 protease-inhibitor complexes of unknown 3D structures, the method provides a satisfactory correlation between the calculated binding free energy and the experimental pIC5o without reparametrization.

The Filling Potential Method: A Method for Estimating the Free Energy Surface for Protein−Ligand Docking

We developed a molecular simulation method suitable for estimation of binding free energy, called the filling potential method, based on the concept of the Taboo search, which is a type of self-avoiding random walk consisting of a cycle of local-minimum searches and transition state searches. The filling potential method is an umbrella potential sampling method, and enables the ligand molecule to drift from its local minima automatically. In the case of the filling potential method, the umbrella potential is a combination of Gaussian-type repulsive potentials, which are located on the trajectory of the ligand. Without setting the reaction coordinates a priori, this method searches for and determines the suitable reaction coordinates by successive generation of umbrella potentials based on its trajectory analysis. The weighted histogram analysis for these trajectories gives the binding free energy of the ligand to the receptor protein. It was applied to the complex of thermolysin and its inhibitors in expl...