Prediction of the interaction of metallic moieties with proteins: An update for protein‐ligand docking techniques

In this article, we present a new approach to expand the range of application of protein‐ligand docking methods in the prediction of the interaction of coordination complexes (i.e., metallodrugs, natural and artificial cofactors, etc.) with proteins. To do so, we assume that, from a pure computational point of view, hydrogen bond functions could be an adequate model for the coordination bonds as both share directionality and polarity aspects. In this model, docking of metalloligands can be performed without using any geometrical constraints or energy restraints. The hard work consists in generating the convenient atom types and scoring functions. To test this approach, we applied our model to 39 high‐quality X‐ray structures with transition and main group metal complexes bound via a unique coordination bond to a protein. This concept was implemented in the protein‐ligand docking program GOLD. The results are in very good agreement with the experimental structures: the percentage for which the RMSD of the simulated pose is smaller than the X‐ray spectra resolution is 92.3% and the mean value of RMSD is < 1.0 Å. Such results also show the viability of the method to predict metal complexes–proteins interactions when the X‐ray structure is not available. This work could be the first step for novel applicability of docking techniques in medicinal and bioinorganic chemistry and appears generalizable enough to be implemented in most protein‐ligand docking programs nowadays available. © 2017 Wiley Periodicals, Inc.     

Protein‐protein docking by shape‐complementarity and property matching

We present a computational approach to protein‐protein docking based on surface shape complementarity (“ProBinder”). Within this docking approach, we implemented a new surface decomposition method that considers local shape features on the protein surface. This new surface shape decomposition results in a deterministic representation of curvature features on the protein surface, such as “knobs,” “holes,” and “flats” together with their point normals. For the actual docking procedure, we used geometric hashing, which allows for the rapid, translation‐, and rotation‐free comparison of point coordinates. Candidate solutions were scored based on knowledge‐based potentials and steric criteria. The potentials included electrostatic complementarity, desolvation energy, amino acid contact preferences, and a van‐der‐Waals potential. We applied ProBinder to a diverse test set of 68 bound and 30 unbound test cases compiled from the Dockground database. Sixty‐four percent of the protein‐protein test complexes were ranked with an root mean square deviation (RMSD) < 5 Å to the target solution among the top 10 predictions for the bound data set. In 82% of the unbound samples, docking poses were ranked within the top ten solutions with an RMSD < 10 Å to the target solution. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Evaluation of a knowledge‐based potential of mean force for scoring docked protein–ligand complexes

The Biomolecular Ligand Energy Evaluation Protocol (BLEEP) is a knowledge‐based potential derived from high‐resolution X‐ray structures of protein–ligand complexes. The performance of this potential in ranking the hypothetical structures resulting from a docking study has been evaluated using fifteen protein–ligand complexes from the Protein Data Bank. In the majority of complexes BLEEP was successful in identifying the native (experimental) binding mode or an alternative of low rms deviation (from the native) as the lowest in energy. Overall BLEEP is slightly better than the DOCK energy function in discriminating native‐like modes. Even when alternative binding modes rank lower than the native structure, a reasonable energy is assigned to the latter. Breaking down the BLEEP scores into the atom–atom contributions reveals that this type of potential is grossly dominated by longer range interactions (>5 Å), which makes it relatively insensitive to small local variations in the binding site. However, despite this limitation, the lack, at present, of accurate protein–ligand potentials means that BLEEP is a promising approach to improve the filtering of structures resulting from docking programs. Moreover, BLEEP should improve with the continuously increasing number of complexes available in the PDB. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 673–688, 2001     

A pose prediction approach based on ligand 3D shape similarity

Molecular docking predicts the best pose of a ligand in the target protein binding site by sampling and scoring numerous conformations and orientations of the ligand. Failures in pose prediction are often due to either insufficient sampling or scoring function errors. To improve the accuracy of pose prediction by tackling the sampling problem, we have developed a method of pose prediction using shape similarity. It first places a ligand conformation of the highest 3D shape similarity with known crystal structure ligands into protein binding site and then refines the pose by repacking the side-chains and performing energy minimization with a Monte Carlo algorithm. We have assessed our method utilizing CSARdock 2012 and 2014 benchmark exercise datasets consisting of co-crystal structures from eight proteins. Our results revealed that ligand 3D shape similarity could substitute conformational and orientational sampling if at least one suitable co-crystal structure is available. Our method identified poses within 2 Å RMSD as the top-ranking pose for 85.7 % of the test cases. The median RMSD for our pose prediction method was found to be 0.81 Å and was better than methods performing extensive conformational and orientational sampling within target protein binding sites. Furthermore, our method was better than similar methods utilizing ligand 3D shape similarity for pose prediction.     

Docking flexible ligands in proteins with a solvent exposure- and distance-dependent dielectric function

Physics-based force fields for ligand–protein docking usually determine electrostatic energy with distance-dependent dielectric (DDD) functions, which do not fully account for the dielectric permittivity variance between ~2 in the protein core and ~80 in bulk water. Here we propose an atom–atom solvent exposure- and distance-dependent dielectric (SEDDD) function, which accounts for both electrostatic and dehydration energy components. Docking was performed using the ZMM program, the AMBER force field, and precomputed libraries of ligand conformers. At the seeding stage, hundreds of thousands of positions and orientations of conformers from the libraries were sampled within the rigid protein. At the refinement stage, the ten lowest-energy structures from the seeding stage were Monte Carlo-minimized with the flexible ligand and flexible protein. A search was considered a success if the root mean square deviation (RMSD) of the ligand atoms in the apparent global minimum from the x-ray structure was <2 Å. Calculations on an examining set of 60 ligand–protein complexes with different DDD functions and solvent-exclusion energy revealed outliers in most of which the ligand-binding site was located at the protein surface. Using a training set of 16 ligand–protein complexes, which did not overlap with the examining set, we parameterized the SEDDD function to minimize the RMSD of the apparent global minima from the x-ray structures. Recalculation of the examining set with the SEDDD function demonstrated a 20% increase in the success rate versus the best-performing DDD function.     

New and fast statistical-thermodynamic method for computation of protein-ligand binding entropy substantially improves docking accuracy

We present a novel method to estimate the contributions of translational and rotational entropy to protein-ligand binding affinity. The method is based on estimates of the configurational integral through the sizes of clusters obtained from multiple docking positions. Cluster sizes are defined as the intervals of variation of center of ligand mass and Euler angles in the cluster. Then we suggest a method to consider the entropy of torsional motions. We validate the suggested methods on a set of 135 PDB protein-ligand complexes by comparing the averaged root-mean square deviations (RMSD) of the top-scored ligand docked positions, accounting and not accounting for entropy contributions, relative to the experimentally determined positions. We demonstrate that the method increases docking accuracy by 10-21% when used in conjunction with the AutoDock docking program, thus reducing the percent of incorrectly docked ligands by 1.4-fold to four-fold, so that in some cases the percent of ligands correctly docked to within an RMSD of 2 A is above 90%. We show that the suggested method to account for entropy of relative motions is identical to the method based on the Monte Carlo integration over intervals of variation of center of ligand mass and Euler angles in the cluster.     

Docking small ligands in flexible binding sites

A novel procedure for docking ligands in a flexible binding site is presented. It relies on conjugate gradient minimization, during which nonbonded interactions are gradually switched on. Short Monte Carlo minimization runs are performed on the most promising candidates. Solvation is implicitly taken into account in the evaluation of structures with a continuum model. It is shown that the method is very accurate and can model induced fit in the ligand and the binding site. The docking procedure has been successfully applied to three systems. The first two are the binding of progesterone and 5β-androstane-3,17-dione to the antigen binding fragment of a steroid binding antibody. A comparison of the crystal structures of the free and the two complexed forms reveals that any attempt to model binding must take protein rearrangements into account. Furthermore, the two ligands bind in two different orientations, posing an additional challenge. The third test case is the docking of N^α-(2-naphthyl-sulfonyl-glycyl)-D -para-amidino-phenyl-alanyl-piperidine (NAPAP) to human α-thrombin. In contrast to steroids, NAPAP is a very flexible ligand, and no information of its conformation in the binding site is used. All docking calculations are started from X-ray conformations of proteins with the uncomplexed binding site. For all three systems the best minima in terms of free energy have a root mean square deviation from the X-ray structure smaller than 1.5 Å for the ligand atoms. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 21–37, 1998     

LEAP: Highly accurate prediction of protein loop conformations by integrating coarse‐grained sampling and optimized energy scores with all‐atom refinement of backbone and side chains

Prediction of protein loop conformations without any prior knowledge (ab initio prediction) is an unsolved problem. Its solution will significantly impact protein homology and template‐based modeling as well as ab initio protein‐structure prediction. Here, we developed a coarse‐grained, optimized scoring function for initial sampling and ranking of loop decoys. The resulting decoys are then further optimized in backbone and side‐chain conformations and ranked by all‐atom energy scoring functions. The final integrated technique called loop prediction by energy‐assisted protocol achieved a median value of 2.1 Å root mean square deviation (RMSD) for 325 12‐residue test loops and 2.0 Å RMSD for 45 12‐residue loops from critical assessment of structure‐prediction techniques (CASP) 10 target proteins with native core structures (backbone and side chains). If all side‐chain conformations in protein cores were predicted in the absence of the target loop, loop‐prediction accuracy only reduces slightly (0.2 Å difference in RMSD for 12‐residue loops in the CASP target proteins). The accuracy obtained is about 1 Å RMSD or more improvement over other methods we tested. The executable file for a Linux system is freely available for academic users at http://sparks‐lab.org . © 2013 Wiley Periodicals, Inc.     

High–quality protein backbone reconstruction from alpha carbons using Gaussian mixture models

Coarse‐grained protein structure models offer increased efficiency in structural modeling, but these must be coupled with fast and accurate methods to revert to a full‐atom structure. Here, we present a novel algorithm to reconstruct mainchain models from C traces. This has been parameterized by fitting Gaussian mixture models (GMMs) to short backbone fragments centered on idealized peptide bonds. The method we have developed is statistically significantly more accurate than several competing methods, both in terms of RMSD values and dihedral angle differences. The method produced Ramachandran dihedral angle distributions that are closer to that observed in real proteins and better Phaser molecular replacement log‐likelihood gains. Amino acid residue sidechain reconstruction accuracy using SCWRL4 was found to be statistically significantly correlated to backbone reconstruction accuracy. Finally, the PD2 method was found to produce significantly lower energy full‐atom models using Rosetta which has implications for multiscale protein modeling using coarse‐grained models. A webserver and C++ source code is freely available for noncommercial use from: http://www.sbg.bio.ic.ac.uk/phyre2/PD2_ca2main/ . © 2013 Wiley Periodicals, Inc.     

Power transformations improve interpolation of grids for molecular mechanics interaction energies

A common strategy for speeding up molecular docking calculations is to precompute nonbonded interaction energies between a receptor molecule and a set of three‐dimensional grids. The grids are then interpolated to compute energies for ligand atoms in many different binding poses. Here, I evaluate a smoothing strategy of taking a power transformation of grid point energies and inverse transformation of the result from trilinear interpolation. For molecular docking poses from 85 protein‐ligand complexes, this smoothing procedure leads to significant accuracy improvements, including an approximately twofold reduction in the root mean square error at a grid spacing of 0.4 Å and retaining the ability to rank docking poses even at a grid spacing of 0.7 Å. © 2018 Wiley Periodicals, Inc.     

LigDockCSA: protein-ligand docking using conformational space annealing

Protein–ligand docking techniques are one of the essential tools for structure‐based drug design. Two major components of a successful docking program are an efficient search method and an accurate scoring function. In this work, a new docking method called LigDockCSA is developed by using a powerful global optimization technique, conformational space annealing (CSA), and a scoring function that combines the AutoDock energy and the piecewise linear potential (PLP) torsion energy. It is shown that the CSA search method can find lower energy binding poses than the Lamarckian genetic algorithm of AutoDock. However, lower‐energy solutions CSA produced with the AutoDock energy were often less native‐like. The loophole in the AutoDock energy was fixed by adding a torsional energy term, and the CSA search on the refined energy function is shown to improve the docking performance. The performance of LigDockCSA was tested on the Astex diverse set which consists of 85 protein–ligand complexes. LigDockCSA finds the best scoring poses within 2 Å root‐mean‐square deviation (RMSD) from the native structures for 84.7% of the test cases, compared to 81.7% for AutoDock and 80.5% for GOLD. The results improve further to 89.4% by incorporating the conformational entropy. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Fast and accurate grid representations for atom‐based docking with partner flexibility

Macromolecular docking methods can broadly be divided into geometric and atom‐based methods. Geometric methods use fast algorithms that operate on simplified, grid‐like molecular representations, while atom‐based methods are more realistic and flexible, but far less efficient. Here, a hybrid approach of grid‐based and atom‐based docking is presented, combining precalculated grid potentials with neighbor lists for fast and accurate calculation of atom‐based intermolecular energies and forces. The grid representation is compatible with simultaneous multibody docking and can tolerate considerable protein flexibility. When implemented in our docking method ATTRACT, grid‐based docking was found to be ∼35x faster. With the OPLSX forcefield instead of the ATTRACT coarse‐grained forcefield, the average speed improvement was >100x. Grid‐based representations may allow atom‐based docking methods to explore large conformational spaces with many degrees of freedom, such as multiple macromolecules including flexibility. This increases the domain of biological problems to which docking methods can be applied. © 2017 Wiley Periodicals, Inc.     

VoteDock: Consensus docking method for prediction of protein–ligand interactions

Molecular recognition plays a fundamental role in all biological processes, and that is why great efforts have been made to understand and predict protein–ligand interactions. Finding a molecule that can potentially bind to a target protein is particularly essential in drug discovery and still remains an expensive and time‐consuming task. In silico, tools are frequently used to screen molecular libraries to identify new lead compounds, and if protein structure is known, various protein–ligand docking programs can be used. The aim of docking procedure is to predict correct poses of ligand in the binding site of the protein as well as to score them according to the strength of interaction in a reasonable time frame. The purpose of our studies was to present the novel consensus approach to predict both protein–ligand complex structure and its corresponding binding affinity. Our method used as the input the results from seven docking programs (Surflex, LigandFit, Glide, GOLD, FlexX, eHiTS, and AutoDock) that are widely used for docking of ligands. We evaluated it on the extensive benchmark dataset of 1300 protein–ligands pairs from refined PDBbind database for which the structural and affinity data was available. We compared independently its ability of proper scoring and posing to the previously proposed methods. In most cases, our method is able to dock properly approximately 20% of pairs more than docking methods on average, and over 10% of pairs more than the best single program. The RMSD value of the predicted complex conformation versus its native one is reduced by a factor of 0.5 Å. Finally, we were able to increase the Pearson correlation of the predicted binding affinity in comparison with the experimental value up to 0.5. © 2010 Wiley Periodicals, Inc. J Comput Chem 32: 568–581, 2011     

FIPSDock: A new molecular docking technique driven by fully informed swarm optimization algorithm

The accurate prediction of protein–ligand binding is of great importance for rational drug design. We present herein a novel docking algorithm called as FIPSDock, which implements a variant of the Fully Informed Particle Swarm (FIPS) optimization method and adopts the newly developed energy function of AutoDock 4.20 suite for solving flexible protein–ligand docking problems. The search ability and docking accuracy of FIPSDock were first evaluated by multiple cognate docking experiments. In a benchmarking test for 77 protein/ligand complex structures derived from GOLD benchmark set, FIPSDock has obtained a successful predicting rate of 93.5% and outperformed a few docking programs including particle swarm optimization (PSO)@AutoDock, SODOCK, AutoDock, DOCK, Glide, GOLD, FlexX, Surflex, and MolDock. More importantly, FIPSDock was evaluated against PSO@AutoDock, SODOCK, and AutoDock 4.20 suite by cross‐docking experiments of 74 protein–ligand complexes among eight protein targets (CDK2, ESR1, F2, MAPK14, MMP8, MMP13, PDE4B, and PDE5A) derived from Sutherland‐crossdock‐set. Remarkably, FIPSDock is superior to PSO@AutoDock, SODOCK, and AutoDock in seven out of eight cross‐docking experiments. The results reveal that FIPS algorithm might be more suitable than the conventional genetic algorithm‐based algorithms in dealing with highly flexible docking problems. © 2012 Wiley Periodicals, Inc.     

Blind docking method combining search of low‐resolution binding sites with ligand pose refinement by molecular dynamics‐based global optimization

This study describes the development of a new blind hierarchical docking method, bhDock, its implementation, and accuracy assessment. The bhDock method uses two‐step algorithm. First, a comprehensive set of low‐resolution binding sites is determined by analyzing entire protein surface and ranked by a simple score function. Second, ligand position is determined via a molecular dynamics‐based method of global optimization starting from a small set of high ranked low‐resolution binding sites. The refinement of the ligand binding pose starts from uniformly distributed multiple initial ligand orientations and uses simulated annealing molecular dynamics coupled with guided force‐field deformation of protein–ligand interactions to find the global minimum. Assessment of the bhDock method on the set of 37 protein–ligand complexes has shown the success rate of predictions of 78%, which is better than the rate reported for the most cited docking methods, such as AutoDock, DOCK, GOLD, and FlexX, on the same set of complexes. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

A QXP-based multistep docking procedure for accurate prediction of protein-ligand complexes

The two great challenges of the docking process are the prediction of ligand poses in a protein binding site and the scoring of the docked poses. Ligands that are composed of extended chains in their molecular structure display the most difficulties, predominantly because of the torsional flexibility. On the basis of the molecular docking program QXP-Flo+0802, we have developed a procedure particularly for ligands with a high degree of rotational freedom that allows the accurate prediction of the orientation and conformation of ligands in protein binding sites. Starting from an initial full Monte Carlo docking experiment, this was achieved by performing a series of successive multistep docking runs using a local Monte Carlo search with a restricted rotational angle, by which the conformational search space is limited. The method was established by using a highly flexible acetylcholinesterase inhibitor and has been applied to a number of challenging protein-ligand complexes known from the literature.     

Fast and accurate predictions of binding free energies using MM‐PBSA and MM‐GBSA

In the drug discovery process, accurate methods of computing the affinity of small molecules with a biological target are strongly needed. This is particularly true for molecular docking and virtual screening methods, which use approximated scoring functions and struggle in estimating binding energies in correlation with experimental values. Among the various methods, MM‐PBSA and MM‐GBSA are emerging as useful and effective approaches. Although these methods are typically applied to large collections of equilibrated structures of protein‐ligand complexes sampled during molecular dynamics in water, the possibility to reliably estimate ligand affinity using a single energy‐minimized structure and implicit solvation models has not been explored in sufficient detail. Herein, we thoroughly investigate this hypothesis by comparing different methods for the generation of protein‐ligand complexes and diverse methods for free energy prediction for their ability to correlate with experimental values. The methods were tested on a series of structurally diverse inhibitors of Plasmodium falciparum DHFR with known binding mode and measured affinities. The results showed that correlations between MM‐PBSA or MM‐GBSA binding free energies with experimental affinities were in most cases excellent. Importantly, we found that correlations obtained with the use of a single protein‐ligand minimized structure and with implicit solvation models were similar to those obtained after averaging over multiple MD snapshots with explicit water molecules, with consequent save of computing time without loss of accuracy. When applied to a virtual screening experiment, such an approach proved to discriminate between true binders and decoy molecules and yielded significantly better enrichment curves. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Computer simulations of ligand–protein binding with ensembles of protein conformations: A Monte Carlo study of HIV‐1 protease binding energy landscapes

We present the results of molecular docking simulations with HIV‐1 protease for the sb203386 and skf107457 inhibitors by Monte Carlo simulated annealing. A simplified piecewise linear energy function, the standard AMBER force field, and the AMBER force field with solvation and a soft‐core smoothing component are employed in simulations with a single‐protein conformation to determine the relationship between docking simulations with a simple energy function and more realistic force fields. The temperature‐dependent binding free energy profiles of the inhibitors interacting with a single protein conformation provide a detailed picture of relative thermodynamic stability and a distribution of ligand binding modes in agreement with experimental crystallographic data. Using the simplified piecewise linear energy function, we also performed Monte Carlo docking simulations with an ensemble of protein conformations employing preferential biased sampling of low‐energy protein conformations, and the results are analyzed in connection with the free energy profiles. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 73–84, 1999     

Flexible docking simulations: Scaled collective variable Monte Carlo minimization approach using Bezier splines,and comparison with a standard Monte Carlo algorithm

An algorithm for docking a flexible ligand onto a flexible or rigid receptor, using the scaled‐collective‐variables Monte Carlo with energy minimization approach, is presented. Energy minimization is shown to be one of the best techniques for distinguishing between native‐ and nonnative‐generated conformations. Incorporation of this technique into a Monte Carlo procedure enables one to distinguish the native conformation directly during the conformational search. It avoids the generation of a large number of ligand conformers for which more sophisticated energy evaluation tools would have had to be applied to identify the nativelike conformations. The efficiency of the Monte Carlo minimization was greatly improved by incorporating a new grid‐based energy evaluation technique using Bezier splines for which the energy function, as well as all of its derivatives, can be deduced from the values at the grid points. Comparison between our ECEPP/3‐based algorithm and the Monte Carlo algorithm presented elsewhere (Hart, T. N.; Read, R. J. Prot Struct Funct Genet 1992, 13, 206–222) has been made for docking NH₂ D Phe Pro Arg COOH, the noncovalent analog of NH₂ D Phe Pro Arg chloromethylketone (PPACK), onto the active site of human α‐thrombin. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 244–252, 1999