Analysis of knowledge-based protein-ligand potentials using a self-consistent method

We propose a self-consistent approach to analyze knowledge-based atom-atom potentials used to calculate protein-ligand binding energies. Ligands complexed to actual protein structures were first built using the SMoG growth procedure (DeWitte & Shakhnovich, 1996) with a chosen input potential. These model protein-ligand complexes were used to construct databases from which knowledge-based protein-ligand potentials were derived. We then tested several different modifications to such potentials and evaluated their performance on their ability to reconstruct the input potential using the statistical information available from a database composed of model complexes. Our data indicate that the most significant improvement resulted from properly accounting for the following key issues when estimating the reference state: (1) the presence of significant nonenergetic effects that influence the contact frequencies and (2) the presence of correlations in contact patterns due to chemical structure. The most successful procedure was applied to derive an atom-atom potential for real protein-ligand complexes. Despite the simplicity of the model (pairwise contact potential with a single interaction distance), the derived binding free energies showed a statistically significant correlation (approximately 0.65) with experimental binding scores for a diverse set of complexes.     

Consistency in structural energetics of protein folding and peptide recognition.

We report a new free energy decomposition that includes structure-derived atomic contact energies for the desolvation component, and show that it applies equally well to the analysis of single-domain protein folding and to the binding of flexible peptides to proteins. Specifically, we selected the 17 single-domain proteins for which the three-dimensional structures and thermodynamic unfolding free energies are available. By calculating all terms except the backbone conformational entropy change and comparing the result to the experimentally measured free energy, we estimated that the mean entropy gain by the backbone chain upon unfolding (delta Sbb) is 5.3 cal/K per mole of residue, and that the average backbone entropy for glycine is 6.7 cal/K. Both numbers are in close agreement with recent estimates made by entirely different methods, suggesting a promising degree of consistency between data obtained from disparate sources. In addition, a quantitative analysis of the folding free energy indicates that the unfavorable backbone entropy for each of the proteins is balanced predominantly by favorable backbone interactions. Finally, because the binding of flexible peptides to receptors is physically similar to folding, the free energy function should, in principle, be equally applicable to flexible docking. By combining atomic contact energies, electrostatics, and sequence-dependent backbone entropy, we calculated a priori the free energy changes associated with the binding of four different peptides to HLA-A2, 1 MHC molecule and found agreement with experiment to within 10% without parameter adjustment.     

Pseudo-dynamic contact surface areas: estimation of apolar bonding

A new Monte Carlo based algorithm has been written for the computation of pseudo-dynamic contact surface areas. The linear correlation of this contact area with solute transfer free energies (water leads to organic liquid) is established for apolar amino acid side chains. The slope of these linear plots, deltaGosp, is a unitary free energy which has potential use in the estimation of apolar bond free energies in proteins. The magnitude of deltaGosp is dependent upon the nature of the organic solvent involved in the transfer process, varying from 86 to 130 cal/A2. Analogues linear correlations with the same range of deltaGosp values are observed for inhibitors of protein-catalyzed reactions.     

Entropy-enthalpy compensation in ionic interactions probed in a zinc finger peptide

Zinc(II) and cobalt(II) binding to a series of zinc finger peptides with different charged residue pairs across from one another in a beta-sheet were examined. Previous studies revealed a narrow range of interaction free energies (<0.5 kcal/mol) between these residues. Here, isothermal titration calorimetry studies were performed, revealing a range of over 3 kcal/mol in relative binding enthalpies. Double mutant cycle analysis revealed a range of interaction enthalpies ranging from -3.1 to -3.4 kcal/mol for the Arg-Asp pair to -0.8 kcal/mol for the Lys-Glu pair. The large range of interaction enthalpies coupled with the small range of interaction free energies reveals substantial entropy-enthalpy compensation. The magnitudes of the effects are consistent with the formation of a structurally rigid Arg-Asp contact ion pair but less direct and more mobile interactions involving the other combinations.     

Potential of mean force for protein-protein interaction studies.

Calculating protein-protein interaction energies is crucial for understanding protein-protein associations. On the basis of the methodology of mean-field potential, we have developed an empirical approach to estimate binding free energy for protein-protein interactions. This knowledge-based approach has been used to derive distance-dependent free energies of protein complexes from a nonredundant training set in the Protein Data Bank (PDB), with a careful treatment of homology. We calculate atom pair potentials for 16 pair interactions, which can reflect the importance of hydrophobic interactions and specific hydrogen-bonding interactions. The derived potentials for hydrogen-bonding interactions show a valley of favorable interactions at a distance of approximately 3 A, corresponding to that of an established hydrogen bond. For the test set of 28 protein complexes, the calculated energies have a correlation coefficient of 0.75 compared with experimental binding free energies. The performance of the method in ranking the binding energies of different protein-protein complexes shows that the energy estimation can be applied to value binding free energies for protein-protein associations.     

Probing carbohydrate product expulsion from a processive cellulase with multiple absolute binding free energy methods

Understanding the enzymatic mechanism that cellulases employ to degrade cellulose is critical to efforts to efficiently utilize plant biomass as a sustainable energy resource. A key component of cellulase action on cellulose is product inhibition from monosaccharide and disaccharides in the product site of cellulase tunnel. The absolute binding free energy of cellobiose and glucose to the product site of the catalytic tunnel of the Family 7 cellobiohydrolase (Cel7A) of Trichoderma reesei (Hypocrea jecorina) was calculated using two different approaches: steered molecular dynamics (SMD) simulations and alchemical free energy perturbation molecular dynamics (FEP/MD) simulations. For the SMD approach, three methods based on Jarzynski's equality were used to construct the potential of mean force from multiple pulling trajectories. The calculated binding free energies, -14.4 kcal/mol using SMD and -11.2 kcal/mol using FEP/MD, are in good qualitative agreement. Analysis of the SMD pulling trajectories suggests that several protein residues (Arg-251, Asp-259, Asp-262, Trp-376, and Tyr-381) play key roles in cellobiose and glucose binding to the catalytic tunnel. Five mutations (R251A, D259A, D262A, W376A, and Y381A) were made computationally to measure the changes in free energy during the product expulsion process. The absolute binding free energies of cellobiose to the catalytic tunnel of these five mutants are -13.1, -6.0, -11.5, -7.5, and -8.8 kcal/mol, respectively. The results demonstrated that all of the mutants tested can lower the binding free energy of cellobiose, which provides potential applications in engineering the enzyme to accelerate the product expulsion process and improve the efficiency of biomass conversion.     

Understanding microscopic binding of macrophage migration inhibitory factor with phenolic hydrazones by molecular docking, molecular dynamics simulations and free energy calculations

Macrophage migration inhibitory factor (MIF), an immunoregulatory protein, is a potential target for a number of inflammatory diseases. In the current work, the interactions between MIF and a series of phenolic hydrazones were studied by molecular docking, molecular dynamics (MD) simulations, binding free energy calculations, and binding energy decomposition analysis to determine the structural requirement for achieving favorable biological activity of phenolic hydrazones. First, molecular docking was used to predict the binding modes of inhibitors in the binding site of MIF. The good correlation between the predicted docking scores and the experimental activities shows that the binding conformations of the inhibitors in the active site of MIF are well predicted. Moreover, our results suggest that the flexibility of MIF is essential in ligand binding process. Then, MD simulations and MM/GBSA free energy calculations were employed to determine the dynamic binding process and compare the binding modes of the inhibitors with different activities. The predicted binding free energies given by MM/GBSA are not well correlated with the experimental activities for the two subsets of the inhibitors; however, for each subset, a good correlation between the predicted binding free energies and the experimental activities is achieved. The MM/GBSA free energy decomposition analysis highlights the importance of hydrophobic residues for the MIF binding of the studied inhibitors. Based on the essential factors for MIF-inhibitor interactions derived from the theoretical predictions, some derivatives were designed and the higher inhibitory activities of several candidates were confirmed by molecular docking studies. The structural insights obtained from our study are useful for designing potent inhibitors of MIF.     

Predicting Ligand Binding Affinity with Alchemical Free Energy Methods in a Polar Model Binding Site

We present a combined experimental and modeling study of organic ligand molecules binding to a slightly polar engineered cavity site in T4 lysozyme (L99A/M102Q). For modeling, we computed alchemical absolute binding free energies. These were blind tests performed prospectively on 13 diverse, previously untested candidate ligand molecules. We predicted that eight compounds would bind to the cavity and five would not; 11 of 13 predictions were correct at this level. The RMS error to the measurable absolute binding energies was 1.8 kcal/mol. In addition, we computed “relative” binding free energies for six phenol derivatives starting from two known ligands: phenol and catechol. The average RMS error in the relative free energy prediction was 2.5 kcal/mol (phenol) and 1.1 kcal/mol (catechol). To understand these results at atomic resolution, we obtained x-ray co-complex structures for nine of the diverse ligands and for all six phenol analogs. The average RMSD of the predicted pose to the experiment was 2.0 Å (diverse set), 1.8 Å (phenol-derived predictions), and 1.2 Å (catechol-derived predictions). We found that predicting accurate affinities and rank-orderings required near-native starting orientations of the ligand in the binding site. Unanticipated binding modes, multiple ligand binding, and protein conformational change all proved challenging for the free energy methods. We believe that these results can help guide future improvements in physics-based absolute binding free energy methods.     

Mechanisms of protein folding

The strong correlation between protein folding rates and the contact order suggests that folding rates are largely determined by the topology of the native structure. However, for a given topology, there may be several possible low free energy paths to the native state and the path that is chosen (the lowest free energy path) may depend on differences in interaction energies and local free energies of ordering in different parts of the structure. For larger proteins whose folding is assisted by chaperones, such as the Escherichia coli chaperonin GroEL, advances have been made in understanding both the aspects of an unfolded protein that GroEL recognizes and the mode of binding to the chaperonin. The possibility that GroEL can remove non-native proteins from kinetic traps by unfolding them either during polypeptide binding to the chaperonin or during the subsequent ATP-dependent formation of folding-active complexes with the co-chaperonin GroES has also been explored.     

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.     

Binding free energy calculations of adenosine deaminase inhibitors

The interactions between four inhibitors and adenosine deaminase (ADA) were examined by calculating their binding free energies after molecular dynamics simulations. A bonded model was used to represent the electrostatic potentials of the zinc coordination site. The charge distribution of the model was derived by using a two-stage electrostatic potential fitting calculations. The calculated binding free energies are in good agreement with the experimental data and the ranking of binding affinities is well reproduced. Notably, our findings suggest that non-polar contributions play an important role for ADA-inhibitor interactions.     

Energetic analysis of binding of progesterone and 5 beta-androstane-3,17-dione to anti-progesterone antibody DB3 using molecular dynamics and free energy calculations.

Molecular dynamics simulations and molecular mechanics-Poisson-Boltzmann surface area (MM-PBSA) free energy calculations were used to study the energetics of the binding of progesterone (PRG) and 5 beta-androstane-3,17-dione (5AD) to anti-PRG antibody DB3. Although the two steroids bind to DB3 in different orientations, their binding affinities are of the same magnitude, 1 nM for PRG and 8 nM for 5AD. The calculated relative binding free energy of the steroids, 8.8 kJ/mol, is in fair agreement with the experimental energy, 5.4 kJ/mol. In addition, computational alanine scanning was applied to study the role of selected amino acid residues of the ligand-binding site on the steroid cross-reactivity. The electrostatic and van der Waals components of the total binding free energies were found to favour more the binding of PRG, whereas solvation energies were more favourable for the binding of 5AD. The differences in the free energy components are due to the binding of the A rings of the steroids to different binding pockets: PRG is bound to a pocket in which electrostatic antibody-steroid interactions are dominating, whereas 5AD is bound to a pocket in which van der Waals and hydrophobic interactions dominate.     

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.     

Docking study and binding free energy calculation of poly (ADP-ribose) polymerase inhibitors

Recently, the massively parallel computation of absolute binding free energy with a well-equilibrated system (MP-CAFEE) has been developed. The present study aimed to determine whether the MP-CAFEE method is useful for drug discovery research. In the drug discovery process, it is important for computational chemists to predict the binding affinity accurately without detailed structural information for protein / ligand complex. We investigated the absolute binding free energies for Poly (ADP-ribose) polymerase-1 (PARP-1) / inhibitor complexes, using the MP-CAFEE method. Although each docking model was used as an input structure, it was found that the absolute binding free energies calculated by MP-CAFEE are well consistent with the experimental ones. The accuracy of this method is much higher than that using molecular mechanics Poisson-Boltzmann / surface area (MM / PBSA). Although the simulation time is quite extensive, the reliable predictor of binding free energies would be a useful tool for drug discovery projects.     

PSI-DOCK: towards highly efficient and accurate flexible ligand docking

We have developed a new docking method, Pose-Sensitive Inclined (PSI)-DOCK, for flexible ligand docking. An improved SCORE function has been developed and used in PSI-DOCK for binding free energy evaluation. The improved SCORE function was able to reproduce the absolute binding free energies of a training set of 200 protein-ligand complexes with a correlation coefficient of 0.788 and a standard error of 8.13 kJ/mol. For ligand binding pose exploration, a unique searching strategy was designed in PSI-DOCK. In the first step, a tabu-enhanced genetic algorithm with a rapid shape-complementary scoring function is used to roughly explore and store potential binding poses of the ligand. Then, these predicted binding poses are optimized and compete against each other by using a genetic algorithm with the accurate SCORE function to determine the binding pose with the lowest docking energy. The PSI-DOCK 1.0 program is highly efficient in identifying the experimental binding pose. For a test dataset of 194 complexes, PSI-DOCK 1.0 achieved a 67% success rate (RMSD < 2.0 A) for only one run and a 74% success rate for 10 runs. PSI-DOCK can also predict the docking binding free energy with high accuracy. For a test set of 64 complexes, the correlation between the experimentally observed binding free energies and the docking binding free energies for 64 complexes is r = 0.777 with a standard deviation of 7.96 kJ/mol. Moreover, compared with other docking methods, PSI-DOCK 1.0 is extremely easy to use and requires minimum docking preparations. There is no requirement for the users to add hydrogen atoms to proteins because all protein hydrogen atoms and the flexibility of the terminal protein atoms are intrinsically taken into account in PSI-DOCK. There is also no requirement for the users to calculate partial atomic charges because PSI-DOCK does not calculate an electrostatic energy term. These features are not only convenient for the users but also help to avoid the influence of different preparation methods.     

Specificity in the interaction of non intercalative groove binding ligands with nucleic acids

This paper presents results of theoretical computations on the interaction energies and geometries for the binding to nucleic acids of a number of representative groove binding non intercalating drugs: netropsin, distamycin A, SN 18071, etc. The computations account for the specificity of binding in all cases and demonstrate that the formation of hydrogen bonds is not necessary neither for binding nor for the preference for the minor groove of AT sequences of B-DNA. It appears that if a relatively good steric fit can be obtained in the minor groove, the interaction will be preferentially stabilized there by the favorable electrostatic potential generated in this groove by the AT sequences. The computation of the interaction energies in free space does not reproduce, however, the order of affinities of the ligands studied and yields too great values of the binding energies. The introduction of the solvent effect, through the computation of the hydration and cavitation effects, confirms the specificity, improves the ordering and brings the values of the energies close to the experimental ones. The theoretical account of the “surprising” effect of netrospin binding to the major groove of theTψC stem of tRNA^Phe confirms the decisive significance of the distribution of the molecular electrostatic potential for the selection of the binding site. The inclusion in the computations of the flexibility of DNA enables to predict correctly the main features of the macromolecular deformation upon the binding of the ligand.     

Protein chemistry at membrane interfaces: non-additivity of electrostatic and hydrophobic interactions

Non-specific binding of proteins and peptides to charged membrane interfaces depends upon the combined contributions of hydrophobic (DeltaG(HPhi)) and electrostatic (DeltaG(ES)) free energies. If these are simply additive, then the observed free energy of binding (DeltaG(obs)) will be given by DeltaG(obs)=DeltaG(HPhi)+DeltaG(ES), where DeltaG(HPhi)=-sigma(NP)A(NP) and DeltaG(ES)=zFphi. In these expressions, A(NP) is the non-polar accessible area, sigma(NP) the non-polar solvation parameter, z the formal peptide valence, F the Faraday constant, and phi the membrane surface potential. But several lines of evidence suggest that hydrophobic and electrostatic binding free energies of proteins at membrane interfaces, such as those associated with cell signaling, are not simply additive. In order to explore this issue systematically, we have determined the interfacial partitioning free energies of variants of indolicidin, a cationic proline-rich antimicrobial peptide. The synthesized variants of the 13 residue peptide covered a wide range of hydrophobic free energies, which allowed us to examine the effect of hydrophobicity on electrostatic binding to membranes formed from mixtures of neutral and anionic lipids. Although DeltaG(obs) was always a linear function of DeltaG(HPhi), the slope depended upon anionic lipid content: the slope was 1.0 for pure, zwitterionic phosphocholine bilayers and 0.3 for pure phosphoglycerol membranes. DeltaG(obs) also varied linearly with surface potential, but the slope was smaller than the expected value, zF. As observed by others, this suggests an effective peptide valence z(eff) that is smaller than the formal valence z. Because of our systematic approach, we were able to establish a useful rule-of-thumb: z(eff) is reduced relative to z by about 20 % for each 3 kcal mol(-1) (1 kcal=4.184 kJ) favorable increase in DeltaG(HPhi). For neutral phosphocholine interfaces, we found that DeltaG(obs) could be predicted with remarkable accuracy using the Wimley-White experiment-based interfacial hydrophobicity scale.     

SCORE: A New Empirical Method for Estimating the Binding Affinity of a Protein-Ligand Complex

A new method is presented to estimate the binding affinity of a protein-ligand complex with known three-dimensional structure. The method, SCORE, uses an empirical scoring function to describe the binding free energy, which includes terms to account for van der Waals contact, metal-ligand bonding, hydrogen bonding, desolvation effect, and deformation penalty upon the binding process. The coefficients of each term are obtained by multivariate regressional analysis of a diverse training set of 170 protein-ligand complexes. The final scoring function reproduces the binding free energies of the whole training set with a cross-validated deviation of 6.3 kJ/mol. The predictive ability of the function is further tested by a set of 11 endothiapepsin complexes and the internal consistency of the function is demonstrated in a stepwise procedure named Evolutionary Test. A major innovation of this method is the introduction of an atomic binding score which allows the researcher to inspect and optimize the lead compound rationally in a structure-based drug design scheme.     

Quantum and molecular dynamics study for binding of macrocyclic inhibitors to human alpha-thrombin

Molecular dynamics simulations followed by quantum mechanical calculation and Molecular Mechanics Poisson-Boltzmann Surface Area (MM-PBSA) analysis have been carried out to study binding of proline- and pyrazinone-based macrocyclic inhibitors (L86 and T76) to human alpha-thrombin. Detailed binding interaction energies between these inhibitors and individual protein fragments are calculated using DFT method based on a new quantum mechanical approach for computing protein-ligand interaction energy. The analysis of detailed interaction energies provides insight on the protein-ligand binding mechanism. Study shows that T76 and L86 bind to thrombin in a very similar "inhibition mode" except that T76 has relatively weaker binding interaction with Glu(217). The analysis from quantum calculation of binding interaction is consistent with the MM-PBSA calculation of binding free energy, and the calculated free energies for L86/T76-thrombin binding agree well with the experimental data.     

Quantitative demonstration of the reciprocity of ligand effects in the ternary complex of chicken heart lactate dehydrogenase with nicotinamide adenine dinucleotide oxalate.

The reciprocity of effects of two ligands simultaneously bound to a protein as a ternary complex may be proven by measurements of four standard free energies of binding. Two of these are for the binding of each ligand in the absence of the other, and the other two for the binding of each ligand in the presence of saturating amounts of the other (conditional free energies). These four quantities have been measured for the complexes of oxalate and nicotinamide adenine dinucleotide with chick heart lactate dehydrogenase. The differences between conditional and unconditional free energies are: oxalate, -1.1 +/- 0.3 kcal; NADH,-1.3 +/- 0.2 kcal, thus proving the reciprocity within experimental error.