Role of binding entropy in the refinement of protein-ligand docking predictions: analysis based on the use of 11 scoring functions

Binding Affinity Determination in Drug Design: Insights from Lock and Key, Induced Fit, Conformational Selection, and Inhibitor Trapping Models

Binding affinity is a fundamental parameter in drug design, describing the strength of the interaction between a molecule and its target protein. Accurately predicting binding affinity is crucial for the rapid development of novel therapeutics, the prioritization of promising candidates, and the optimization of their properties through rational design strategies. Binding affinity is determined by the mechanism of recognition between proteins and ligands. Various models, including the lock and key, induced fit, and conformational selection, have been proposed to explain this recognition process. However, current computational strategies to predict binding affinity, which are based on these models, have yet to produce satisfactory results. This article explores the connection between binding affinity and these protein-ligand interaction models, highlighting that they offer an incomplete picture of the mechanism governing binding affinity. Specifically, current models primarily center on the binding of the ligand and do not address its dissociation. In this context, the concept of ligand trapping is introduced, which models the mechanisms of dissociation. When combined with the current models, this concept can provide a unified theoretical framework that may allow for the accurate determination of the ligands' binding affinity.

Strengths and Weaknesses of Docking Simulations in the SARS-CoV-2 Era: the Main Protease (Mpro) Case Study

The scientific community is working against the clock to arrive at therapeutic interventions to treat patients with COVID-19. Among the strategies for drug discovery, virtual screening approaches have the capacity to search potential hits within millions of chemical structures in days, with the appropriate computing infrastructure. In this article, we first analyzed the published research targeting the inhibition of the main protease (Mpro), one of the most studied targets of SARS-CoV-2, by docking-based methods. An alarming finding was the lack of an adequate validation of the docking protocols (i.e., pose prediction and virtual screening accuracy) before applying them in virtual screening campaigns. The performance of the docking protocols was tested at some level in 57.7% of the 168 investigations analyzed. However, we found only three examples of a complete retrospective analysis of the scoring functions to quantify the virtual screening accuracy of the methods. Moreover, only two publications reported some experimental evaluation of the proposed hits until preparing this manuscript. All of these findings led us to carry out a retrospective performance validation of three different docking protocols, through the analysis of their pose prediction and screening accuracy. Surprisingly, we found that even though all tested docking protocols have a good pose prediction, their screening accuracy is quite limited as they fail to correctly rank a test set of compounds. These results highlight the importance of conducting an adequate validation of the docking protocols before carrying out virtual screening campaigns, and to experimentally confirm the predictions made by the models before drawing bold conclusions. Finally, successful structure-based drug discovery investigations published during the redaction of this manuscript allow us to propose the inclusion of target flexibility and consensus scoring as alternatives to improve the accuracy of the methods.

ALADDIN: Docking Approach Augmented by Machine Learning for Protein Structure Selection Yields Superior Virtual Screening Performance

Protein flexibility and solvation pose major challenges to docking algorithms and scoring functions. One established strategy for addressing these challenges is to use multiple protein conformations for docking (all-against-all ensemble docking). Recent studies have shown that the performance of ensemble docking can be improved by selecting the most relevant protein structures for docking. In search for a robust approach to protein structure selection, we have come up with an integrated mAchine Learning AnD DockINg approach (ALADDIN). ALADDIN employs a battery of random forest classifiers to select, individually for each compound of interest, from an ensemble of protein structures, the single most suitable protein structure for docking. ALADDIN outperformed the best single-structure docking runs, ensemble docking and a similarity-based docking approach on three out of four investigated targets, with up to 0.15, 0.11 and 0.16 higher area under the receiver operating characteristic curve (AUC) values, respectively. Only in the case of cytochrome P450 3A4, ALADDIN, like any of the other tested approaches, failed to obtain decent performance. ALADDIN can be particularly useful for structure-based virtual screening of malleable proteins, including kinases, some viral enzymes and anti-targets.

Practices in Molecular Docking and Structure-Based Virtual Screening

Drug discovery has evolved significantly over the past two decades. Progress in key areas such as molecular and structural biology has contributed to the elucidation of the three-dimensional structure and function of a wide range of biological molecules of therapeutic interest. In this context, the integration of experimental techniques, such as X-ray crystallography, and computational methods, such as molecular docking, has promoted the emergence of several areas in drug discovery, such as structure-based drug design (SBDD). SBDD strategies have been broadly used to identify, predict and optimize the activity of small molecules toward a molecular target and have contributed to major scientific breakthroughs in pharmaceutical R&D. This chapter outlines molecular docking and structure-based virtual screening (SBVS) protocols used to predict the interaction of small molecules with the phosphatidylinositol-bisphosphate-kinase PI3Kδ, which is a molecular target for hematological diseases. A detailed description of the molecular docking and SBVS procedures and an evaluation of the results are provided.

Performance of multiple docking and refinement methods in the pose prediction D3R prospective Grand Challenge 2016

We describe the performance of multiple pose prediction methods for the D3R 2016 Grand Challenge. The pose prediction challenge includes 36 ligands, which represent 4 chemotypes and some miscellaneous structures against the FXR ligand binding domain. In this study we use a mix of fully automated methods as well as human-guided methods with considerations of both the challenge data and publicly available data. The methods include ensemble docking, colony entropy pose prediction, target selection by molecular similarity, molecular dynamics guided pose refinement, and pose selection by visual inspection. We evaluated the success of our predictions by method, chemotype, and relevance of publicly available data. For the overall data set, ensemble docking, visual inspection, and molecular dynamics guided pose prediction performed the best with overall mean RMSDs of 2.4, 2.2, and 2.2 Å respectively. For several individual challenge molecules, the best performing method is evaluated in light of that particular ligand. We also describe the protein, ligand, and public information data preparations that are typical of our binding mode prediction workflow.

Comparing pairwise-additive and many-body generalized Born models for acid/base calculations and protein design

Generalized Born (GB) solvent models are common in acid/base calculations and protein design. With GB, the interaction between a pair of solute atoms depends on the shape of the protein/solvent boundary and, therefore, the positions of all solute atoms, so that GB is a many-body potential. For compute-intensive applications, the model is often simplified further, by introducing a mean, native-like protein/solvent boundary, which removes the many-body property. We investigate a method for both acid/base calculations and protein design that uses Monte Carlo simulations in which side chains can explore rotamers, bind/release protons, or mutate. The fluctuating protein/solvent dielectric boundary is treated in a way that is numerically exact (within the GB framework), in contrast to a mean boundary. Its originality is that it captures the many-body character while retaining the residue-pairwise complexity given by a fixed boundary. The method is implemented in the Proteus protein design software. It yields a slight but systematic improvement for acid/base constants in nine proteins and a significant improvement for the computational design of three PDZ domains. It eliminates a source of model uncertainty, which will facilitate the analysis of other model limitations. © 2017 Wiley Periodicals, Inc.

Molecular Docking: From Lock and Key to Combination Lock

Accurate modeling of protein ligand binding is an important step in structure-based drug design, is a useful starting point for finding new lead compounds or drug candidates. The 'Lock and Key' concept of protein-ligand binding has dominated descriptions of these interactions, and has been effectively translated to computational molecular docking approaches. In turn, molecular docking can reveal key elements in protein-ligand interactions-thereby enabling design of potent small molecule inhibitors directed against specific targets. However, accurate predictions of binding pose and energetic remain challenging problems. The last decade has witnessed more sophisticated molecular docking approaches to modeling protein-ligand binding and energetics. However, the complexities that confront accurate modeling of binding phenomena remain formidable. Subtle recognition and discrimination patterns governed by three-dimensional features and microenvironments of the active site play vital roles in consolidating the key intermolecular interactions that mediates ligand binding. Herein, we briefly review contemporary approaches and suggest that future approaches treat protein-ligand docking problems in the context of a 'combination lock' system.

Scoring Functions of Protein-Ligand Interactions

Scoring function of protein-ligand interactions is used to recognize the “native” binding pose of a ligand on the protein and to predict the binding affinity, so that the active small molecules can be discriminated from the non-active ones. Scoring function is widely used in computationally molecular docking and structure-based drug discovery. The development and improvement of scoring functions have broad implications in pharmaceutical industry and academic research. During the past three decades, much progress have been made in methodology and accuracy for scoring functions, and many successful cases have be witnessed in virtual database screening. In this chapter, the authors introduced the basic types of scoring functions and their derivations, the commonly-used evaluation methods and benchmarks, as well as the underlying challenges and current solutions. Finally, the authors discussed the promising directions to improve and develop scoring functions for future molecular docking-based drug discovery.

Leveraging Data Fusion Strategies in Multireceptor Lead Optimization MM/GBSA End-Point Methods

Accurate and efficient affinity calculations are critical to enhancing the contribution of in silico modeling during the lead optimization phase of a drug discovery campaign. Here, we present a large-scale study of the efficacy of data fusion strategies to leverage results from end-point MM/GBSA calculations in multiple receptors to identify potent inhibitors among an ensemble of congeneric ligands. The retrospective analysis of 13 congeneric ligand series curated from publicly available data across seven biological targets demonstrates that in 90% of the individual receptor structures MM/GBSA scores successfully identify subsets of inhibitors that are more potent than a random selection, and data fusion strategies that combine MM/GBSA scores from each of the receptors significantly increase the robustness of the predictions. Among nine different data fusion metrics based on consensus scores or receptor rankings, the SumZScore (i.e., converting MM/GBSA scores into standardized Z-Scores within a receptor and computing the sum of the Z-Scores for a given ligand across the ensemble of receptors) is found to be a robust and physically meaningful metric for combining results across multiple receptors. Perhaps most surprisingly, even with relatively low to modest overall correlations between SumZScore and experimental binding affinities, SumZScore tends to reliably prioritize subsets of inhibitors that are at least as potent as those that are prioritized from a "best" single receptor identified from known compounds within the congeneric series.

Molecular docking and structure-based drug design strategies

Pharmaceutical research has successfully incorporated a wealth of molecular modeling methods, within a variety of drug discovery programs, to study complex biological and chemical systems. The integration of computational and experimental strategies has been of great value in the identification and development of novel promising compounds. Broadly used in modern drug design, molecular docking methods explore the ligand conformations adopted within the binding sites of macromolecular targets. This approach also estimates the ligand-receptor binding free energy by evaluating critical phenomena involved in the intermolecular recognition process. Today, as a variety of docking algorithms are available, an understanding of the advantages and limitations of each method is of fundamental importance in the development of effective strategies and the generation of relevant results. The purpose of this review is to examine current molecular docking strategies used in drug discovery and medicinal chemistry, exploring the advances in the field and the role played by the integration of structure- and ligand-based methods.

Challenges, applications, and recent advances of protein-ligand docking in structure-based drug design

The docking methods used in structure-based virtual database screening offer the ability to quickly and cheaply estimate the affinity and binding mode of a ligand for the protein receptor of interest, such as a drug target. These methods can be used to enrich a database of compounds, so that more compounds that are subsequently experimentally tested are found to be pharmaceutically interesting. In addition, like all virtual screening methods used for drug design, structure-based virtual screening can focus on curated libraries of synthesizable compounds, helping to reduce the expense of subsequent experimental verification. In this review, we introduce the protein-ligand docking methods used for structure-based drug design and other biological applications. We discuss the fundamental challenges facing these methods and some of the current methodological topics of interest. We also discuss the main approaches for applying protein-ligand docking methods. We end with a discussion of the challenging aspects of evaluating or benchmarking the accuracy of docking methods for their improvement, and discuss future directions.

Computation of binding energies including their enthalpy and entropy components for protein-ligand complexes using support vector machines

Computing binding energies of protein-ligand complexes including their enthalpy and entropy terms by means of computational methods is an appealing approach for selecting initial hits and for further optimization in early stages of drug discovery. Despite the importance, computational predictions of thermodynamic components have evaded attention and reasonable solutions. In this study, support vector machines are used for developing scoring functions to compute binding energies and their enthalpy and entropy components of protein-ligand complexes. The binding energies computed from our newly derived scoring functions have better Pearson's correlation coefficients with experimental data than previously reported scoring functions in benchmarks for protein-ligand complexes from the PDBBind database. The protein-ligand complexes with binding energies dominated by enthalpy or entropy term could be qualitatively classified by the newly derived scoring functions with high accuracy. Furthermore, it is found that the inclusion of comprehensive descriptors based on ligand properties in the scoring functions improved the accuracy of classification as well as the prediction of binding energies including their thermodynamic components. The prediction of binding energies including the enthalpy and entropy components using the support vector machine based scoring functions should be of value in the drug discovery process.

A neurosteroid analogue photolabeling reagent labels the colchicine-binding site on tubulin: a mass spectrometric analysis

Previous studies have shown that the neurosteroid analogue, 6-Azi-pregnanolone (6-AziP), photolabels voltage-dependent anion channels and proteins of approximately 55 kDa in rat brain membranes. The present study used two-dimensional electrophoresis and nanoelectrospray ionization ion-trap mass spectrometry (nano-ESI-MS) to identify the 55 kDa proteins (isoelectric point 4.8) as isoforms of β-tubulin. This identification was confirmed by immunoblot and immunoprecipitation of photolabeled protein with anti-β-tubulin antibody and by the demonstration that 6-AziP photolabels purified bovine brain tubulin in a concentration-dependent pattern. To identify the photolabeling sites, purified bovine brain tubulin was photolabeled with 6-AziP, digested with trypsin, and analyzed by matrix-assisted laser desorption/ionization MS (MALDI). A 6-AziP adduct of TAVCDIPPR(m/z = 1287.77), a β-tubulin specific peptide, was detected by MALDI. High-resolution liquid chromatography-MS/MS analysis identified that 6-AziP was covalently bound to cysteine 354 (Cys-354), previously identified as a colchicine-binding site. 6-AziP photolabeling was inhibited by 2-methoxyestradiol, an endogenous derivative of estradiol thought to bind to the colchicine site. Structural modeling predicted that neurosteroids could dock in this colchicine site at the interface between α- and β-tubulin with the photolabeling group of 6-AziP positioned proximate to Cys-354.

A scalable and accurate method for classifying protein-ligand binding geometries using a MapReduce approach

We present a scalable and accurate method for classifying protein-ligand binding geometries in molecular docking. Our method is a three-step process: the first step encodes the geometry of a three-dimensional (3D) ligand conformation into a single 3D point in the space; the second step builds an octree by assigning an octant identifier to every single point in the space under consideration; and the third step performs an octree-based clustering on the reduced conformation space and identifies the most dense octant. We adapt our method for MapReduce and implement it in Hadoop. The load-balancing, fault-tolerance, and scalability in MapReduce allow screening of very large conformation spaces not approachable with traditional clustering methods. We analyze results for docking trials for 23 protein-ligand complexes for HIV protease, 21 protein-ligand complexes for Trypsin, and 12 protein-ligand complexes for P38alpha kinase. We also analyze cross docking trials for 24 ligands, each docking into 24 protein conformations of the HIV protease, and receptor ensemble docking trials for 24 ligands, each docking in a pool of HIV protease receptors. Our method demonstrates significant improvement over energy-only scoring for the accurate identification of native ligand geometries in all these docking assessments. The advantages of our clustering approach make it attractive for complex applications in real-world drug design efforts. We demonstrate that our method is particularly useful for clustering docking results using a minimal ensemble of representative protein conformational states (receptor ensemble docking), which is now a common strategy to address protein flexibility in molecular docking.

Docking and scoring with ICM: the benchmarking results and strategies for improvement

Flexible docking and scoring using the internal coordinate mechanics software (ICM) was benchmarked for ligand binding mode prediction against the 85 co-crystal structures in the modified Astex data set. The ICM virtual ligand screening was tested against the 40 DUD target benchmarks and 11-target WOMBAT sets. The self-docking accuracy was evaluated for the top 1 and top 3 scoring poses at each ligand binding site with near native conformations below 2 Å RMSD found in 91 and 95% of the predictions, respectively. The virtual ligand screening using single rigid pocket conformations provided the median area under the ROC curves equal to 69.4 with 22.0% true positives recovered at 2% false positive rate. Significant improvements up to ROC AUC = 82.2 and ROC((2%)) = 45.2 were achieved following our best practices for flexible pocket refinement and out-of-pocket binding rescore. The virtual screening can be further improved by considering multiple conformations of the target.

PHOENIX: a scoring function for affinity prediction derived using high-resolution crystal structures and calorimetry measurements

Binding affinity prediction is one of the most critical components to computer-aided structure-based drug design. Despite advances in first-principle methods for predicting binding affinity, empirical scoring functions that are fast and only relatively accurate are still widely used in structure-based drug design. With the increasing availability of X-ray crystallographic structures in the Protein Data Bank and continuing application of biophysical methods such as isothermal titration calorimetry to measure thermodynamic parameters contributing to binding free energy, sufficient experimental data exists that scoring functions can now be derived by separating enthalpic (ΔH) and entropic (TΔS) contributions to binding free energy (ΔG). PHOENIX, a scoring function to predict binding affinities of protein-ligand complexes, utilizes the increasing availability of experimental data to improve binding affinity predictions by the following: model training and testing using high-resolution crystallographic data to minimize structural noise, independent models of enthalpic and entropic contributions fitted to thermodynamic parameters assumed to be thermodynamically biased to calculate binding free energy, use of shape and volume descriptors to better capture entropic contributions. A set of 42 descriptors and 112 protein-ligand complexes were used to derive functions using partial least-squares for change of enthalpy (ΔH) and change of entropy (TΔS) to calculate change of binding free energy (ΔG), resulting in a predictive r2 (r(pred)2) of 0.55 and a standard error (SE) of 1.34 kcal/mol. External validation using the 2009 version of the PDBbind "refined set" (n = 1612) resulted in a Pearson correlation coefficient (R(p)) of 0.575 and a mean error (ME) of 1.41 pK(d). Enthalpy and entropy predictions were of limited accuracy individually. However, their difference resulted in a relatively accurate binding free energy. While the development of an accurate and applicable scoring function was an objective of this study, the main focus was evaluation of the use of high-resolution X-ray crystal structures with high-quality thermodynamic parameters from isothermal titration calorimetry for scoring function development. With the increasing application of structure-based methods in molecular design, this study suggests that using high-resolution crystal structures, separating enthalpy and entropy contributions to binding free energy, and including descriptors to better capture entropic contributions may prove to be effective strategies toward rapid and accurate calculation of binding affinity.

TSCC: Two-Stage Combinatorial Clustering for virtual screening using protein-ligand interactions and physicochemical features

BACKGROUND

The increasing numbers of 3D compounds and protein complexes stored in databases contribute greatly to current advances in biotechnology, being employed in several pharmaceutical and industrial applications. However, screening and retrieving appropriate candidates as well as handling false positives presents a challenge for all post-screening analysis methods employed in retrieving therapeutic and industrial targets.

RESULTS

Using the TSCC method, virtually screened compounds were clustered based on their protein-ligand interactions, followed by structure clustering employing physicochemical features, to retrieve the final compounds. Based on the protein-ligand interaction profile (first stage), docked compounds can be clustered into groups with distinct binding interactions. Structure clustering (second stage) grouped similar compounds obtained from the first stage into clusters of similar structures; the lowest energy compound from each cluster being selected as a final candidate.

CONCLUSION

By representing interactions at the atomic-level and including measures of interaction strength, better descriptions of protein-ligand interactions and a more specific analysis of virtual screening was achieved. The two-stage clustering approach enhanced our post-screening analysis resulting in accurate performances in clustering, mining and visualizing compound candidates, thus, improving virtual screening enrichment.

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.

Inclusion of solvation and entropy in the knowledge-based scoring function for protein-ligand interactions

The effects of solvation and entropy play a critical role in determining the binding free energy in protein-ligand interactions. Despite the good balance between speed and accuracy, no current knowledge-based scoring functions account for the effects of solvation and configurational entropy explicitly due to the difficulty in deriving the corresponding pair potentials and the resulting double counting problem. In the present work, we have included the solvation effect and configurational entropy in the knowledge-based scoring function by an iterative method. The newly developed scoring function has yielded a success rate of 91% in identifying near-native binding modes with Wang et al.'s benchmark of 100 diverse protein-ligand complexes. The results have been compared with the results of 15 other scoring functions for validation purpose. In binding affinity prediction, our scoring function has yielded a correlation of R(2) = 0.76 between the predicted binding scores and the experimentally measured binding affinities on the PMF validation sets of 77 diverse complexes. The results have been compared with R(2) of four other well-known knowledge-based scoring functions. Finally, our scoring function was also validated on the large PDBbind database of 1299 protein-ligand complexes and yielded a correlation coefficient of 0.474. The present computational model can be applied to other scoring functions to account for solvation and entropic effects.

Dockres: a computer program that analyzes the output of virtual screening of small molecules

Background

This paper describes a computer program named Dockres that is designed to analyze and summarize results of virtual screening of small molecules. The program is supplemented with utilities that support the screening process. Foremost among these utilities are scripts that run the virtual screening of a chemical library on a large number of processors in parallel.

Methods

Dockres and some of its supporting utilities are written Fortran-77; other utilities are written as C-shell scripts. They support the parallel execution of the screening. The current implementation of the program handles virtual screening with Autodock-3 and Autodock-4, but can be extended to work with the output of other programs.

Results

Analysis of virtual screening by Dockres led to both active and selective lead compounds.

Conclusions

Analysis of virtual screening was facilitated and enhanced by Dockres in both the authors' laboratories as well as laboratories elsewhere.

Automated site preparation in physics-based rescoring of receptor ligand complexes

Hydrogen atoms are not typically observable in X-ray crystal structures, but inferring their locations is often important in structure-based drug design. In addition, protonation states of the protein can change in response to ligand binding, as can the orientations of OH groups, a subtle form of "induced fit." We implement and evaluate an automated procedure for optimizing polar hydrogens in protein-binding sites in complex with ligands. Specifically, we apply the previously described Independent Cluster Decomposition Algorithm (ICDA) algorithm (Li et al., Proteins 2007;66:824-837), which assigns the ionization states of titratable residues, the amide orientations of Asn/Gln side chains, the imidazole ring orientation in His, and the orientations of OH/SH groups, in a unified algorithm. We test the utility of this method for identifying nativelike ligand poses using 247 protein-ligand complexes from an established database of docked decoys. Pose selection is performed with a physics-based scoring function based on a molecular mechanics energy function and a Generalized Born implicit solvent model. The use of the ICDA receptor preparation protocol, implemented with no knowledge of the native ligand pose, increases the accuracy of pose selection significantly, with the average RMSD over all complexes decreasing from 2.7 to 1.5 A when applying ICDA. Large improvements are seen for specific classes of binding sites with titratable groups, such as aspartyl proteases.

Structure-activity relationship and comparative docking studies for cycloguanil analogs as PfDHFR-TS inhibitors

Drug resistance acquired by Plasmodium falciparum (Pf) is a major problem in the treatment and control of malaria. One of the major examples of drug resistance is that caused by mutations in the active site of dihydrofolate reductase (DHFR) of Pf (PfDHFR-TS). A double mutation, A16V+S108T, is specific for resistance to the marketed drug cycloguanil. In this study, we used 58 cycloguanil (2,4-diamino-1,6-dihydro-1,3,5-triazine) derivatives to explore the relationship between various physicochemical properties and reported binding affinity data on wild-type and mutant-type A16V+S108T. Using the Hansch 2D-quantitative structure-activity relationship method, we obtained a parabolic relationship of hydrophobicity of substituents at the N1-phenyl ring with the wild-type binding affinity data. Hydrophobicity being a key property for wild-type binding affinity data, we found steric factors to be crucial for A16V+S108T mutant resistance. We investigated FlexX, GOLD, Glide and Molegro virtual docking programs and 13 different scoring functions on 10 of the cycloguanil derivatives to evaluate which program was best for reproducing the experimental binding mode and correlating the docking scores with the reported binding affinity data. We identified GOLD, using its GoldScore fitness function, as the most accurate docking program for predicting binding affinity data of cycloguanil derivatives to DHFR and Molegro virtual docker, with its template docking algorithm and MolDock [GRID] scoring function, as most accurate for reproducing the experimental binding mode of a reference ligand that is structurally similar to the cycloguanil derivatives studied. We also report an interaction index which best describes the structure-activity relationships exhibited by these analogs in terms of PfDHFR-TS active site interactions.

Entropic cost of protein-ligand binding and its dependence on the entropy in solution

Two theoretical formulations are proposed and compared for the loss of translational and rotational entropy upon protein-ligand binding in water. The two theories share the same approach to evaluate the translational and rotational entropy of the ligand when bound. The potential of the bound ligand is modeled by six harmonic oscillators that are parametrized from the force and torque magnitudes measured in a molecular dynamics simulation, yielding vibrational and librational entropies. In the aqueous phase, the theories differ because there is no unique way to assign the total entropy to molecules in solution. In one approach, the ligand is allowed unrestricted access to the full solution volume at the standard concentration and is assigned the same translational and rotational entropy as if it were an ideal gas. We term this a "molecule-frame" (MF) theory because it considers configurational space in the reference frame of the molecule of interest. The entropy of the solvent is penalized because it is excluded from the molecule's volume. In the second theory, all molecules including the solvent are confined by their neighbors in mean-field configurational volumes. This we term a "system-frame" (SF) theory because the configurational space available to all molecules is considered in the reference frame of the whole system. Molecules have vibrational and librational entropy in the same way as they do when bound. In addition, the discrete size of the solvent molecules quantizes the configurational space into an effective number of minima according to the solute molecule's standard concentration and the mean volume of a solvent molecule. This leads to the cratic entropy expressed in terms of the solute molecule's mole fraction. The equivalent number of minima in rotational space depends on both the solute molecule's volume and the solvent molecule's volume. This leads to an equation for the orientational entropy based on the proposed concept of "angle fraction". The MF and SF theories are applied to calculate the translational and rotational entropy losses involved in the formation of six different protein-ligand complexes, in two of which the ligand is water. The MF entropy losses range from -80 to -142 J K(-1) mol(-1) for ligands at the 1 M standard-state concentration and from -52 to -63 J K(-1) mol(-1) for water at the 55.6 M standard-state concentration. They depend logarithmically on both the number and strength of interactions between the ligand and protein through the forces and torques. This is observed to lead to moderate dependencies on the ligands' moments of inertia and masses. The SF entropy losses are smaller and range from -50 to -75 J K(-1) mol(-1) for ligands at the 1 M standard-state concentration and from 0 to -12 J K(-1) mol(-1) for water. They depend logarithmically on the ligand solvent's molecular volume and weakly on the relative strengths of the ligand's interactions with the protein and water. The cratic entropy loss in water at the standard concentration is constant and is also demonstrated to be implicit in MF theories. Entropy losses from the two approaches are also compared with those from other computational approaches and with experiment. The use of the force and torque magnitudes leads to smaller bound volumes than are obtained from ligand-displacement approaches. The general agreement of the SF entropy losses with those from experiment suggests that the SF theory is more consistent with the assumptions made in experimental measurements than the MF solvation theories, which would require a compensating entropy gain in the solvent in order to agree.

Comparative assessment of scoring functions on a diverse test set

Scoring functions are widely applied to the evaluation of protein-ligand binding in structure-based drug design. We have conducted a comparative assessment of 16 popular scoring functions implemented in main-stream commercial software or released by academic research groups. A set of 195 diverse protein-ligand complexes with high-resolution crystal structures and reliable binding constants were selected through a systematic nonredundant sampling of the PDBbind database and used as the primary test set in our study. All scoring functions were evaluated in three aspects, that is, "docking power", "ranking power", and "scoring power", and all evaluations were independent from the context of molecular docking or virtual screening. As for "docking power", six scoring functions, including GOLD::ASP, DS::PLP1, DrugScore(PDB), GlideScore-SP, DS::LigScore, and GOLD::ChemScore, achieved success rates over 70% when the acceptance cutoff was root-mean-square deviation < 2.0 A. Combining these scoring functions into consensus scoring schemes improved the success rates to 80% or even higher. As for "ranking power" and "scoring power", the top four scoring functions on the primary test set were X-Score, DrugScore(CSD), DS::PLP, and SYBYL::ChemScore. They were able to correctly rank the protein-ligand complexes containing the same type of protein with success rates around 50%. Correlation coefficients between the experimental binding constants and the binding scores computed by these scoring functions ranged from 0.545 to 0.644. Besides the primary test set, each scoring function was also tested on four additional test sets, each consisting of a certain number of protein-ligand complexes containing one particular type of protein. Our study serves as an updated benchmark for evaluating the general performance of today's scoring functions. Our results indicate that no single scoring function consistently outperforms others in all three aspects. Thus, it is important in practice to choose the appropriate scoring functions for different purposes.

Improving accuracy and efficiency of blind protein-ligand docking by focusing on predicted binding sites

The use of predicted binding sites (binding sites calculated from the protein structure alone) is evaluated here as a tool to focus the docking of small molecule ligands into protein structures, simulating cases where the real binding sites are unknown. The resulting approach consists of a few independent docking runs carried out on small boxes, centered on the predicted binding sites, as opposed to one larger blind docking run that covers the complete protein structure. The focused and blind approaches were compared using a set of 77 known protein-ligand complexes and 19 ligand-free structures. The focused approach is shown to: (1) identify the correct binding site more frequently than blind docking; (2) produce more accurate docking poses for the ligand; (3) require less computational time. Additionally, the results show that very few real binding sites are missed in spite of focusing on only three predicted binding sites per target protein. Overall the results indicate that, by improving the sampling in regions that are likely to correspond to binding sites, the focused docking approach increases accuracy and efficiency of protein ligand docking for those cases where the ligand-binding site is unknown. This is especially relevant in applications such as reverse virtual screening and structure-based functional annotation of proteins.

Computational evaluation of protein-small molecule binding

Determining protein-small molecule binding affinity is a key component of present-day rational drug discovery. To circumvent the time, labor, and materials costs associated with experimental protein-small molecule binding assays, a variety of structure-based computational methods have been developed for determining protein-small molecule binding affinities. These methods can be placed in one of two classes: accurate but slow (Class 1), and fast but approximate (Class 2). Class 1 methods, which explicitly take into account protein flexibility and include an atomic-level description of solvation, are capable of quantitatively reproducing experimental protein-small molecule absolute binding free energies. However, Class 1 computational requirements make screening thousands to millions of small molecules against a protein, as required for rational drug design, infeasible for the foreseeable future. Class 2 methods, on the contrary, are sufficiently fast to perform such inhibitor screening, yet they suffer from limited descriptions of protein flexibility and solvation, which in turn limit their ability to select and rank-order small molecules by computed binding affinities. This review presents an overview of Class 1 and Class 2 methods, and avenues of research in Class 2 methods aimed at bringing them closer to Class 1 accuracy.

Computation of the contribution from the cavity effect to protein-ligand binding free energy

We present results of the investigation of the cavity creation/annihilation effect in view of formation of the protein-ligand (PL) complexes. The protein and ligand were considered as rigid structures. The change of the cavity creation/annihilation free energy DeltaG(cav) was calculated for three PL complexes using the thermodynamic integration procedure with the original algorithm for growing the interaction potential between the cavity and the water molecules. The thermodynamic cycle consists of two stages, annihilation of the cavity of the ligand for the unbound state and its creation at the active site of the protein (bound state). It was revealed that for all complexes under investigation, the values of DeltaG(cav) are negative and favorable for binding. The main contribution to DeltaG(cav) appears due to the annihilation of the cavity of the ligand. All computations were made using the parallel version of CAVE code, elaborated in our preceding work.

An improved relaxed complex scheme for receptor flexibility in computer-aided drug design

The interactions among associating (macro)molecules are dynamic, which adds to the complexity of molecular recognition. While ligand flexibility is well accounted for in computational drug design, the effective inclusion of receptor flexibility remains an important challenge. The relaxed complex scheme (RCS) is a promising computational methodology that combines the advantages of docking algorithms with dynamic structural information provided by molecular dynamics (MD) simulations, therefore explicitly accounting for the flexibility of both the receptor and the docked ligands. Here, we briefly review the RCS and discuss new extensions and improvements of this methodology in the context of ligand binding to two example targets: kinetoplastid RNA editing ligase 1 and the W191G cavity mutant of cytochrome c peroxidase. The RCS improvements include its extension to virtual screening, more rigorous characterization of local and global binding effects, and methods to improve its computational efficiency by reducing the receptor ensemble to a representative set of configurations. The choice of receptor ensemble, its influence on the predictive power of RCS, and the current limitations for an accurate treatment of the solvent contributions are also briefly discussed. Finally, we outline potential methodological improvements that we anticipate will assist future development.

Empirical entropic contributions in computational docking: evaluation in APS reductase complexes

The results from reiterated docking experiments may be used to evaluate an empirical vibrational entropy of binding in ligand-protein complexes. We have tested several methods for evaluating the vibrational contribution to binding of 22 nucleotide analogues to the enzyme APS reductase. These include two cluster size methods that measure the probability of finding a particular conformation, a method that estimates the extent of the local energetic well by looking at the scatter of conformations within clustered results, and an RMSD-based method that uses the overall scatter and clustering of all conformations. We have also directly characterized the local energy landscape by randomly sampling around docked conformations. The simple cluster size method shows the best performance, improving the identification of correct conformations in multiple docking experiments.

Docking to RNA via root-mean-square-deviation-driven energy minimization with flexible ligands and flexible targets

Structure-based drug design is now well-established for proteins as a key first step in the lengthy process of developing new drugs. In many ways, RNA may be a better target to treat disease than a protein because it is upstream in the translation pathway, so inhibiting a single mRNA molecule could prevent the production of thousands of protein gene products. Virtual screening is often the starting point for structure-based drug design. However, computational docking of a small molecule to RNA seems to be more challenging than that to protein due to the higher intrinsic flexibility and highly charged structure of RNA. Previous attempts at docking to RNA showed the need for a new approach. We present here a novel algorithm using molecular simulation techniques to account for both nucleic acid and ligand flexibility. In this approach, with both the ligand and the receptor permitted some flexibility, they can bind one another via an induced fit, as the flexible ligand probes the surface of the receptor. A possible ligand can explore a low-energy path at the surface of the receptor by carrying out energy minimization with root-mean-square-distance constraints. Our procedure was tested on 57 RNA complexes (33 crystal and 24 NMR structures); this is the largest data set to date to reproduce experimental RNA binding poses. With our procedure, the lowest-energy conformations reproduced the experimental binding poses within an atomic root-mean-square deviation of 2.5 A for 74% of tested complexes.

A statistical rescoring scheme for protein-ligand docking: Consideration of entropic effect

Computational prediction of protein-ligand binding modes provides useful information on the relationship between structure and activity needed for drug design. A statistical rescoring method that incorporates entropic effect is proposed to improve the accuracy of binding mode prediction. A probability function for two sampled conformations to belong to the same broad basin in the potential energy surface is introduced to estimate the contribution of the state represented by a sampled conformation to the configurational integral. The rescoring function is reduced to the colony energy introduced by Xiang et al. (Proc Natl Acad Sci USA 2002;99:7432-7437) when a particular functional form for the probability function is used. The scheme is applied to rescore protein-ligand complex conformations generated by AutoDock. It is demonstrated that this simple rescoring improves prediction accuracy substantially when tested on 163 protein-ligand complexes with known experimental structures. For example, the percentage of complexes for which predicted ligand conformations are within 1 A root-mean-square deviation from the native conformations is doubled from about 20% to more than 40%. Rescoring with 11 different scoring functions including AutoDock scoring functions were also tested using the ensemble of conformations generated by Wang et al. (J Med Chem 2003;46:2287-2303). Comparison with other methods that use clustering and estimation of conformational entropy is provided. Examination of the docked poses reveals that the rescoring corrects the predictions in which ligands are tightly fit into the binding pockets and have low energies, but have too little room for conformational freedom and thus have low entropy.

Interaction cutoff effect on ruggedness of protein-protein energy landscape

The concept of the energy landscape is important for better understanding of protein-protein interactions and for designing adequate docking procedures. The intermolecular landscape has a rugged terrain that impedes search procedures. Its inherent ruggedness is related to the conformational characteristics of the molecules and to the form of the potential function--more rugged for short-range potentials and less rugged for "soft," typically long-range potentials. Our study determined that the landscape ruggedness is further substantially exacerbated by truncation of the potentials. This additional ruggedness appears below certain critical interaction ranges that depend on the form of the potential. The theoretical model describing the cutoff effect on the landscape ruggedness is confirmed by the energy calculation on a dataset of protein-protein complexes. The negative effect of the potentials cutoff is well known. However, revealing its physical basis in terms of the energy landscape is important for better understanding of intermolecular interactions.

Towards the development of universal, fast and highly accurate docking/scoring methods: a long way to go

Accelerating the drug discovery process requires predictive computational protocols capable of reducing or simplifying the synthetic and/or combinatorial challenge. Docking-based virtual screening methods have been developed and successfully applied to a number of pharmaceutical targets. In this review, we first present the current status of docking and scoring methods, with exhaustive lists of these. We next discuss reported comparative studies, outlining criteria for their interpretation. In the final section, we describe some of the remaining developments that would potentially lead to a universally applicable docking/scoring method.

Calculations of protein-ligand binding entropy of relative and overall molecular motions

In the context of virtual database screening, calculations of protein-ligand binding entropy of relative and overall molecular motions are challenging, owing to the inherent structural complexity of the ligand binding well in the energy landscape of protein-ligand interactions and computing time limitations. We describe a fast statistical thermodynamic method for estimation the binding entropy to address the challenges. The method is based on the integration of the configurational integral over clusters obtained from multiple docked positions. We apply the method in conjunction with 11 popular scoring functions (AutoDock, ChemScore, DrugScore, D-Score, F-Score, G-Score, LigScore, LUDI, PLP, PMF, X-Score) to evaluate the binding entropy of 100 protein-ligand complexes. The averaged values of binding entropy contribution vary from 6.2 to 9.1 kcal/mol, showing good agreement with literature. We calculate positional sizes and the angular volume of the native ligand wells. The averaged geometric mean of positional sizes in principal directions varies from 0.8 to 1.4 A. The calculated range of angular volumes is 3.3-11.8 rad(2). Then we demonstrate that the averaged six-dimensional volume of the native well is larger than the volume of the most populated non-native well in energy landscapes described by all of 11 scoring functions.