Detailed analysis of grid-based molecular docking: A case study of CDOCKER-A CHARMm-based MD docking algorithm

The influence of various factors on the accuracy of protein-ligand docking is examined. The factors investigated include the role of a grid representation of protein-ligand interactions, the initial ligand conformation and orientation, the sampling rate of the energy hyper-surface, and the final minimization. A representative docking method is used to study these factors, namely, CDOCKER, a molecular dynamics (MD) simulated-annealing-based algorithm. A major emphasis in these studies is to compare the relative performance and accuracy of various grid-based approximations to explicit all-atom force field calculations. In these docking studies, the protein is kept rigid while the ligands are treated as fully flexible and a final minimization step is used to refine the docked poses. A docking success rate of 74% is observed when an explicit all-atom representation of the protein (full force field) is used, while a lower accuracy of 66-76% is observed for grid-based methods. All docking experiments considered a 41-member protein-ligand validation set. A significant improvement in accuracy (76 vs. 66%) for the grid-based docking is achieved if the explicit all-atom force field is used in a final minimization step to refine the docking poses. Statistical analysis shows that even lower-accuracy grid-based energy representations can be effectively used when followed with full force field minimization. The results of these grid-based protocols are statistically indistinguishable from the detailed atomic dockings and provide up to a sixfold reduction in computation time. For the test case examined here, improving the docking accuracy did not necessarily enhance the ability to estimate binding affinities using the docked structures.     

Conformational Transitions and Convergence of Absolute Binding Free Energy Calculations

The Binding Energy Distribution Analysis Method (BEDAM) is employed to compute the standard binding free energies of a series of ligands to a FK506 binding protein (FKBP12) with implicit solvation. Binding free energy estimates are in reasonably good agreement with experimental affinities. The conformations of the complexes identified by the simulations are in good agreement with crystallographic data, which was not used to restrain ligand orientations. The BEDAM method is based on λ -hopping Hamiltonian parallel Replica Exchange (HREM) molecular dynamics conformational sampling, the OPLS-AA/AGBNP2 effective potential, and multi-state free energy estimators (MBAR). Achieving converged and accurate results depends on all of these elements of the calculation. Convergence of the binding free energy is tied to the level of convergence of binding energy distributions at critical intermediate states where bound and unbound states are at equilibrium, and where the rate of binding/unbinding conformational transitions is maximal. This finding mirrors similar observations in the context of order/disorder transitions as for example in protein folding. Insights concerning the physical mechanism of ligand binding and unbinding are obtained. Convergence for the largest FK506 ligand is achieved only after imposing strict conformational restraints, which however require accurate prior structural knowledge of the structure of the complex. The analytical AGBNP2 model is found to underestimate the magnitude of the hydrophobic driving force towards binding in these systems characterized by loosely packed protein-ligand binding interfaces. Rescoring of the binding energies using a numerical surface area model corrects this deficiency. This study illustrates the complex interplay between energy models, exploration of conformational space, and free energy estimators needed to obtain robust estimates from binding free energy calculations.     

Development and evaluation of a generic evolutionary method for protein-ligand docking

We have developed a generic evolutionary method with an empirical scoring function for the protein-ligand docking, which is a problem of paramount importance in structure-based drug design. This approach, referred to as the GEMDOCK (Generic Evolutionary Method for molecular DOCKing), combines both continuous and discrete search mechanisms. We tested our approach on seven protein-ligand complexes, and the docked lowest energy structures have root-mean-square derivations ranging from 0.32 to 0.99 A with respect to the corresponding crystal ligand structures. In addition, we evaluated GEMDOCK on crossdocking experiments, in which some complexes with an identical protein used for docking all crystallized ligands of these complexes. GEMDOCK yielded 98% docked structures with RMSD below 2.0 A when the ligands were docked into foreign protein structures. We have reported the validation and analysis of our approach on various search spaces and scoring functions. Experimental results show that our approach is robust, and the empirical scoring function is simple and fast to recognize compounds. We found that if GEMDOCK used the RMSD scoring function, then the prediction accuracy was 100% and the docked structures had RMSD below 0.1 A for each test system. These results suggest that GEMDOCK is a useful tool, and may systematically improve the forms and parameters of a scoring function, which is one of major bottlenecks for molecular recognition.     

Comparison of stochastic optimization methods for all-atom folding of the Trp-Cage protein.

The performances of three different stochastic optimization methods for all-atom protein structure prediction are investigated and compared. We use the recently developed all-atom free-energy force field (PFF01), which was demonstrated to correctly predict the native conformation of several proteins as the global optimum of the free energy surface. The trp-cage protein (PDB-code 1L2Y) is folded with the stochastic tunneling method, a modified parallel tempering method, and the basin-hopping technique. All the methods correctly identify the native conformation, and their relative efficiency is discussed.     

A scoring function for docking ligands to low-resolution protein structures

We present a docking method that uses a scoring function for protein-ligand docking that is designed to maximize the docking success rate for low-resolution protein structures. We find that the resulting scoring function parameters are very different depending on whether they were optimized for high- or low-resolution protein structures. We show that this docking method can be successfully applied to predict the ligand-binding site of low-resolution structures. For a set of 25 protein-ligand complexes, in 76% of the cases, more than 50% of ligand-contacting residues are correctly predicted (using receptor crystal structures where the binding site is unspecified). Using decoys of the receptor structures having a 4 A RMSD from the native structure, for the same set of complexes, in 72% of the cases, we obtain at least one correctly predicted ligand-contacting residue. Furthermore, using an 81-protein-ligand set described by Jain, in 76 (93.8%) cases, the algorithm correctly predicts more than 50% of the ligand-contacting residues when native protein structures are used. Using 3 A RMSD from native decoys, in all but two cases (97.5%), the algorithm predicts at least one ligand-binding residue correctly. Finally, compared to the previously published Dolores method, for 298 protein-ligand pairs, the number of cases in which at least half of the specific contacts are correctly predicted is more than four times greater.     

Continuum solvation models in the linear interaction energy method

The linear interaction energy (LIE) method in combination with two different continuum solvent models has been applied to calculate protein-ligand binding free energies for a set of inhibitors against the malarial aspartic protease plasmepsin II. Ligand-water interaction energies are calculated from both Poisson-Boltzmann (PB) and Generalized Born (GB) continuum models using snapshots from explicit solvent simulations of the ligand and protein-ligand complex. These are compared to explicit solvent calculations, and we find close agreement between the explicit water and PB solvation models. The GB model overestimates the change in solvation energy, and this is caused by consistent underestimation of the effective Born radii in the protein-ligand complex. The explicit solvent LIE calculations and LIE-PB, with our standard parametrization, reproduce absolute experimental binding free energies with an average unsigned error of 0.5 and 0.7 kcal/mol, respectively. The LIE-GB method, however, requires a constant offset to approach the same level of accuracy.     

Calculation of Host-Guest Binding Affinities Using a Quantum-Mechanical Energy Model

The prediction of protein-ligand binding affinities is of central interest in computer-aided drug discovery, but it is still difficult to achieve a high degree of accuracy. Recent studies suggesting that available force fields may be a key source of error motivate the present study, which reports the first mining minima (M2) binding affinity calculations based on a quantum mechanical energy model, rather than an empirical force field. We apply a semi-empirical quantum-mechanical energy function, PM6-DH+, coupled with the COSMO solvation model, to 29 host-guest systems with a wide range of measured binding affinities. After correction for a systematic error, which appears to derive from the treatment of polar solvation, the computed absolute binding affinities agree well with experimental measurements, with a mean error 1.6 kcal/mol and a correlation coefficient of 0.91. These calculations also delineate the contributions of various energy components, including solute energy, configurational entropy, and solvation free energy, to the binding free energies of these host-guest complexes. Comparison with our previous calculations, which used empirical force fields, point to significant differences in both the energetic and entropic components of the binding free energy. The present study demonstrates successful combination of a quantum mechanical Hamiltonian with the M2 affinity method.     

Binding free energy contributions of interfacial waters in HIV-1 protease/inhibitor complexes

Water molecules are commonly observed in crystal structures of protein-ligand complexes where they mediate protein-ligand binding. It is of considerable theoretical and practical importance to determine quantitatively the individual free energy contributions of these interfacial water molecules to protein-ligand binding and to elucidate factors that influence them. The double-decoupling free energy molecular dynamics simulation method has been used to calculate the binding free energy contribution for each of the four interfacial water molecules observed in the crystal structure of HIV-1 protease complexed with KNI-272, a potent inhibitor. While two of these water molecules contribute significantly to the binding free energy, the other two have close to zero contribution. It was further observed that the protonation states of two catalytic aspartate residues, Asp25 and Asp125, strongly influence the free energy contribution of a conserved water molecule Wat301 and that different inhibitors significantly influence the free energy contribution of Wat301. Our results have important implications on our understanding of the role of interfacial water molecules in protein-ligand binding and to structure-based drug design aimed at incorporating these interfacial water molecules into ligands.     

A displaced-solvent functional analysis of model hydrophobic enclosures

Calculation of protein-ligand binding affinities continues to be a hotbed of research. Although many techniques for computing protein-ligand binding affinities have been introduced--ranging from computationally very expensive approaches, such as free energy perturbation (FEP) theory; to more approximate techniques, such as empirically derived scoring functions, which, although computationally efficient, lack a clear theoretical basis--there remains pressing need for more robust approaches. A recently introduced technique, the displaced-solvent functional (DSF) method, was developed to bridge the gap between the high accuracy of FEP and the computational efficiency of empirically derived scoring functions. In order to develop a set of reference data to test the DSF theory for calculating absolute protein-ligand binding affinities, we have pursued FEP theory calculations of the binding free energies of a methane ligand with 13 different model hydrophobic enclosures of varying hydrophobicity. The binding free energies of the methane ligand with the various hydrophobic enclosures were then recomputed by DSF theory and compared with the FEP reference data. We find that the DSF theory, which relies on no empirically tuned parameters, shows excellent quantitative agreement with the FEP. We also explored the ability of buried solvent accessible surface area and buried molecular surface area models to describe the relevant physics, and find the buried molecular surface area model to offer superior performance over this dataset.     

Steric and allosteric effects of fatty acids on the binding of warfarin to human serum albumin revealed by molecular dynamics and free energy calculations

Human serum albumin (HSA) binds with drugs and fatty acids (FAs). This study was initiated to elucidate the relationship between the warfarin binding affinity of HSA and the positions of bound FA molecules. Molecular dynamics simulations of 11 HSA-warfarin-myristate complexes were performed. HSA-warfarin binding free energy was then calculated for each of the complexes by the molecular mechanics-Poisson-Boltzmann surface area (MM-PBSA) method. The results indicated that the magnitude of the binding free energy was smaller in HSA-warfarin complexes that had 4 or more myristate molecules than in complexes with no myristate molecules. The unfavorable effect on the HSA-warfarin binding affinity was caused sterically by the binding of a myristate molecule to the FA binding site closest to the warfarin binding site. On the other hand, the magnitude of HSA-warfarin binding free energy was largest when 3 myristate molecules were bound to the high-affinity sites. The strongest HSA-warfarin binding was attributable to favorable entropic contribution related to larger atomic fluctuations of the amino acid residues at the warfarin binding site. In the binding of 2 myristate molecules to the sites with the highest and second-highest affinities, allosteric modulation that enhanced electrostatic interactions between warfarin and some of the amino acid residues around the warfarin binding site was observed. This study clarified the structural and energetic properties of steric/allosteric effects of FAs on the HSA-warfarin binding affinity and illustrated the approach to analyze protein-ligand interactions in situations such that multiple ligands bind to the other sites of the protein.     

On the nonpolar hydration free energy of proteins: surface area and continuum solvent models for the solute-solvent interaction energy

Implicit solvent hydration free energy models are an important component of most modern computational methods aimed at protein structure prediction, binding affinity prediction, and modeling of conformational equilibria. The nonpolar component of the hydration free energy, consisting of a repulsive cavity term and an attractive van der Waals solute-solvent interaction term, is often modeled using estimators based on the solvent exposed solute surface area. In this paper, we analyze the accuracy of linear surface area models for predicting the van der Waals solute-solvent interaction energies of native and non-native protein conformations, peptides and small molecules, and the desolvation penalty of protein-protein and protein-ligand binding complexes. The target values are obtained from explicit solvent simulations and from a continuum solvent van der Waals interaction energy model. The results indicate that the standard surface area model, while useful on a coarse-grained scale, may not be accurate or transferable enough for high resolution modeling studies of protein folding and binding. The continuum model constructed in the course of this study provides one path for the development of a computationally efficient implicit solvent nonpolar hydration free energy estimator suitable for high-resolution structural and thermodynamic modeling of biological macromolecules.     

Solvated interaction energy (SIE) for scoring protein-ligand binding affinities. 1. Exploring the parameter space

We present a binding free energy function that consists of force field terms supplemented by solvation terms. We used this function to calibrate the solvation model along with the binding interaction terms in a self-consistent manner. The motivation for this approach was that the solute dielectric-constant dependence of calculated hydration gas-to-water transfer free energies is markedly different from that of binding free energies (J. Comput. Chem. 2003, 24, 954). Hence, we sought to calibrate directly the solvation terms in the context of a binding calculation. The five parameters of the model were systematically scanned to best reproduce the absolute binding free energies for a set of 99 protein-ligand complexes. We obtained a mean unsigned error of 1.29 kcal/mol for the predicted absolute binding affinity in a parameter space that was fairly shallow near the optimum. The lowest errors were obtained with solute dielectric values of Din = 20 or higher and scaling of the intermolecular van der Waals interaction energy by factors ranging from 0.03 to 0.15. The high apparent Din and strong van der Waals scaling may reflect the anticorrelation of the change in solvated potential energy and configurational entropy, that is, enthalpy-entropy compensation in ligand binding (Biophys. J. 2004, 87, 3035-3049). Five variations of preparing the protein-ligand data set were explored in order to examine the effect of energy refinement and the presence of bound water on the calculated results. We find that retaining water in the final protein structure used for calculating the binding free energy is not necessary to obtain good results; that is the continuum solvation model is sufficient. Virtual screening enrichment studies on estrogen receptor and thymidine kinase showed a good ability of the binding free energy function to recover true hits in a collection of decoys.     

Binding-affinity predictions of HSP90 in the D3R Grand Challenge 2015 with docking,MM/GBSA,QM/MM,and free-energy simulations

We have estimated the binding affinity of three sets of ligands of the heat-shock protein 90 in the D3R grand challenge blind test competition. We have employed four different methods, based on five different crystal structures: first, we docked the ligands to the proteins with induced-fit docking with the Glide software and calculated binding affinities with three energy functions. Second, the docked structures were minimised in a continuum solvent and binding affinities were calculated with the MM/GBSA method (molecular mechanics combined with generalised Born and solvent-accessible surface area solvation). Third, the docked structures were re-optimised by combined quantum mechanics and molecular mechanics (QM/MM) calculations. Then, interaction energies were calculated with quantum mechanical calculations employing 970–1160 atoms in a continuum solvent, combined with energy corrections for dispersion, zero-point energy and entropy, ligand distortion, ligand solvation, and an increase of the basis set to quadruple-zeta quality. Fourth, relative binding affinities were estimated by free-energy simulations, using the multi-state Bennett acceptance-ratio approach. Unfortunately, the results were varying and rather poor, with only one calculation giving a correlation to the experimental affinities larger than 0.7, and with no consistent difference in the quality of the predictions from the various methods. For one set of ligands, the results could be strongly improved (after experimental data were revealed) if it was recognised that one of the ligands displaced one or two water molecules. For the other two sets, the problem is probably that the ligands bind in different modes than in the crystal structures employed or that the conformation of the ligand-binding site or the whole protein changes.     

Electrostatics of ligand binding: parametrization of the generalized Born model and comparison with the Poisson-Boltzmann approach

An accurate and fast evaluation of the electrostatics in ligand-protein interactions is crucial for computer-aided drug design. The pairwise generalized Born (GB) model, a fast analytical method originally developed for studying the solvation of organic molecules, has been widely applied to macromolecular systems, including ligand-protein complexes. However, this model involves several empirical scaling parameters, which have been optimized for the solvation of organic molecules, peptides, and nucleic acids but not for energetics of ligand binding. Studies have shown that a good solvation energy does not guarantee a correct model of solvent-mediated interactions. Thus, in this study, we have used the Poisson-Boltzmann (PB) approach as a reference to optimize the GB model for studies of ligand-protein interactions. Specifically, we have employed the pairwise descreening approximation proposed by Hawkins et al.(1) for GB calculations and DelPhi for PB calculations. The AMBER all-atom force field parameters have been used in this work. Seventeen protein-ligand complexes have been used as a training database, and a set of atomic descreening parameters has been selected with which the pairwise GB model and the PB model yield comparable results on atomic Born radii, the electrostatic component of free energies of ligand binding, and desolvation energies of the ligands and proteins. The energetics of the 15 test complexes calculated with the GB model using this set of parameters also agrees well with the energetics calculated with the PB method. This is the first time that the GB model has been parametrized and thoroughly compared with the PB model for the electrostatics of ligand binding.     

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.     

Grand canonical Monte Carlo simulation of ligand-protein binding

A new application of the grand canonical thermodynamics ensemble to compute ligand-protein binding is described. The described method is sufficiently rapid that it is practical to compute ligand-protein binding free energies for a large number of poses over the entire protein surface, thus identifying multiple putative ligand binding sites. In addition, the method computes binding free energies for a large number of poses. The method is demonstrated by the simulation of two protein-ligand systems, thermolysin and T4 lysozyme, for which there is extensive thermodynamic and crystallographic data for the binding of small, rigid ligands. These low-molecular-weight ligands correspond to the molecular fragments used in computational fragment-based drug design. The simulations correctly identified the experimental binding poses and rank ordered the affinities of ligands in each of these systems.     

Q-Dock: Low-resolution flexible ligand docking with pocket-specific threading restraints

The rapidly growing number of theoretically predicted protein structures requires robust methods that can utilize low-quality receptor structures as targets for ligand docking. Typically, docking accuracy falls off dramatically when apo or modeled receptors are used in docking experiments. Low-resolution ligand docking techniques have been developed to deal with structural inaccuracies in predicted receptor models. In this spirit, we describe the development and optimization of a knowledge-based potential implemented in Q-Dock, a low-resolution flexible ligand docking approach. Self-docking experiments using crystal structures reveals satisfactory accuracy, comparable with all-atom docking. All-atom models reconstructed from Q-Dock's low-resolution models can be further refined by even a simple all-atom energy minimization. In decoy-docking against distorted receptor models with a root-mean-square deviation, RMSD, from native of approximately 3 A, Q-Dock recovers on average 15-20% more specific contacts and 25-35% more binding residues than all-atom methods. To further improve docking accuracy against low-quality protein models, we propose a pocket-specific protein-ligand interaction potential derived from weakly homologous threading holo-templates. The success rate of Q-Dock employing a pocket-specific potential is 6.3 times higher than that previously reported for the Dolores method, another low-resolution docking approach.     

Evaluation of several two-step scoring functions based on linear interaction energy, effective ligand size, and empirical pair potentials for prediction of protein-ligand binding geometry and free energy

The performances of several two-step scoring approaches for molecular docking were assessed for their ability to predict binding geometries and free energies. Two new scoring functions designed for "step 2 discrimination" were proposed and compared to our CHARMM implementation of the linear interaction energy (LIE) approach using the Generalized-Born with Molecular Volume (GBMV) implicit solvation model. A scoring function S1 was proposed by considering only "interacting" ligand atoms as the "effective size" of the ligand and extended to an empirical regression-based pair potential S2. The S1 and S2 scoring schemes were trained and 5-fold cross-validated on a diverse set of 259 protein-ligand complexes from the Ligand Protein Database (LPDB). The regression-based parameters for S1 and S2 also demonstrated reasonable transferability in the CSARdock 2010 benchmark using a new data set (NRC HiQ) of diverse protein-ligand complexes. The ability of the scoring functions to accurately predict ligand geometry was evaluated by calculating the discriminative power (DP) of the scoring functions to identify native poses. The parameters for the LIE scoring function with the optimal discriminative power (DP) for geometry (step 1 discrimination) were found to be very similar to the best-fit parameters for binding free energy over a large number of protein-ligand complexes (step 2 discrimination). Reasonable performance of the scoring functions in enrichment of active compounds in four different protein target classes established that the parameters for S1 and S2 provided reasonable accuracy and transferability. Additional analysis was performed to definitively separate scoring function performance from molecular weight effects. This analysis included the prediction of ligand binding efficiencies for a subset of the CSARdock NRC HiQ data set where the number of ligand heavy atoms ranged from 17 to 35. This range of ligand heavy atoms is where improved accuracy of predicted ligand efficiencies is most relevant to real-world drug design efforts.     

Information theory-based scoring function for the structure-based prediction of protein-ligand binding affinity

The development and validation of a new knowledge based scoring function (SIScoreJE) to predict binding energy between proteins and ligands is presented. SIScoreJE efficiently predicts the binding energy between a small molecule and its protein receptor. Protein-ligand atomic contact information was derived from a Non-Redundant Data set (NRD) of over 3000 X-ray crystal structures of protein-ligand complexes. This information was classified for individual "atom contact pairs" (ACP) which is used to calculate the atomic contact preferences. In addition to the two schemes generated in this study we have assessed a number of other common atom-type classification schemes. The preferences were calculated using an information theoretic relationship of joint entropy. Among 18 different atom-type classification schemes "ScoreJE Atom Type set2" (SATs2) was found to be the most suitable for our approach. To test the sensitivity of the method to the inclusion of solvent, Single-body Solvation Potentials (SSP) were also derived from the atomic contacts between the protein atom types and water molecules modeled using AQUARIUS2. Validation was carried out using an evaluation data set of 100 protein-ligand complexes with known binding energies to test the ability of the scoring functions to reproduce known binding affinities. In summary, it was found that a combined SSP/ScoreJE (SIScoreJE) performed significantly better than ScoreJE alone, and SIScoreJE and ScoreJE performed better than GOLD::GoldScore, GOLD::ChemScore, and XScore.     

Identification of ligand binding sites on proteins using a multi-scale approach

Identification of a ligand binding site on a protein is pivotal to drug discovery. To date, no reliable and computationally feasible general approach to this problem has been published. Here we present an automated efficient method for determining binding sites on proteins for potential ligands without any a priori knowledge. Our method is based upon the multiscale concept where we deal with a hierarchy of models generated using a k-means clustering algorithm for the potential ligand. This is done in a simple approach whereby a potential ligand is represented by a growing number of feature points. At each increasing level of detail, a pruning of potential binding site is performed. A nonbonding energy function is used to score the interactions between molecules at each step. The technique was successfully employed to seven protein-ligand complexes. In the current paper we show that the algorithm considerably reduces the computational effort required to solve this problem. This approach offers real opportunities for exploiting the large number of structures that will evolve from structural genomics.