Development and validation of a genetic algorithm for flexible docking

Computer based screening of compound databases: 1. Preselection of benzamidine-based thrombin inhibitors

We present a computational protocol which uses the known three-dimensional structure of a target enzyme to identify possible ligands from databases of compounds with low molecular weight. This is accomplished by first mapping the essential interactions in the binding site with the program GRID. The resulting regions of favorable interaction between target and ligand are translated into a database query, and with UNITY a flexible 3D database search is performed. The feasibility of this approach is calibrated with thrombin as the target. Our results show that the resulting hit lists are enriched with thrombin inhibitors compared to the total database.

Structure-based library design: molecular modelling merges with combinatorial chemistry

Recent advances in both computational and experimental techniques now allow a very fruitful interplay of computational and combinatorial chemistry in the structure-based design of combinatorial libraries.

A method for including protein flexibility in protein-ligand docking: improving tools for database mining and virtual screening

Second-generation methods for docking ligands into their biological receptors, such as FLOG, provide for flexibility of the ligand but not of the receptor. Molecular dynamics based methods, such as free energy perturbation, account for flexibility, solvent effects, etc., but are very time consuming. We combined the use of statistical analysis of conformational samples from short-run protein molecular dynamics with grid-based docking protocols and demonstrated improved performance in two test cases. Our statistical analysis explores the importance of the average strength of a potential interaction with the biological target and optionally applies a weighting depending on the variability in the strength of the interaction seen during dynamics simulation. Using these methods, we improved the num-top-ranked 10% of a database of drug-like molecules, in searches based on the three-dimensional structure of the protein. These methods are able to match the ability of manual docking to assess likely inactivity on steric grounds and indeed to rank order ligands from a homologous series of cyclooxygenase-2 inhibitors with good correlation to their true activity. Furthermore, these methods reduce the need for human intervention in setting up molecular docking experiments.

Automated docking of ligands to antibodies: methods and applications

Many approaches to studying protein-ligand interactions by computational docking are currently available. Given the structures of a protein and a ligand, the ultimate goal of all docking methods is to predict the structure of the resulting complex. This requires a suitable representation of molecular structures and properties, search algorithms to efficiently scan the configuration space for favorable interaction geometries, and accurate scoring functions to evaluate and rank the generated orientations. For many of the available methods, tests on experimentally known antibody-antigen or antibody-hapten complexes have appeared in the literature. In addition, some of them have been used in predictive studies on antibody-ligand interactions to provide structural insights where adequate experimental information is missing. The AutoDock program is presented as example of a method for flexibly docking ligands to antibodies. Applying parameters of the second-generation AMBER force field, three antibody-hapten complexes (AN02, DB3, NC6.8) are used as new test cases to analyze the ability of the method to reproduce experimental findings. The X-ray structures could be reconstituted and the corresponding solutions were ranked with best energy score in all cases. Docking to the free instead of the complexed NC6.8 structure indicated the limits of the rigid protein treatment, although fairly good guesses about the location of the binding site and the contact residues could still be obtained if conformational flexibility was allowed at least in the ligand.

New approach to molecular docking and its application to virtual screening of chemical databases

This paper describes the validation of a molecular docking method and its application to virtual database screening. The code flexibly docks ligand molecules into rigid receptor structures using a tabu search methodology driven by an empirically derived function for estimating the binding affinity of a protein-ligand complex. The docking method has been tested on 70 ligand-receptor complexes for which the experimental binding affinity and binding geometry are known. The lowest energy geometry produced by the docking protocol is within 2.0 A root mean square of the experimental binding mode for 79% of the complexes. The method has been applied to the problem of virtual database screening to identify known ligands for thrombin, factor Xa, and the estrogen receptor. A database of 10,000 randomly chosen "druglike" molecules has been docked into the three receptor structures. In each case known receptor ligands were included in the study. The results showed good separation between the predicted binding affinities of the known ligand set and the database subset.

Novel treatment of conformational flexibility using interval analysis

A revolutionary new flexible conformational search technique is presented together with its application to geometrical docking. The algorithm is guaranteed to find all (even an infinite number of) solutions in a continuous manner. Examples are given using 2-(4'-amidinophenyl)pyruvate (APPA) docked to trypsin. Other potential applications are briefly discussed.

New 1,4-dihydropyridine derivatives with C4 heterocyclic substituents

4-(2-Pyrrolyl)-2,6-dimethyl-1,4-dihydropyridine-3,5-bis(methoxycarbonyl), 4-(3-furyl)-2,6-dimethyl-1,4-di-hydropyridine-3,5-bis(methoxycarbonyl) and 4-(3-bromo-2-furyl)-2,6-dimethyl-1,4-dihydropyridine-3,5-bis(methoxy-carbonyl) are potential antiarrhythmic pharmaceuticals with Ca2+ antagonistic activity in L type voltage gated channels. Conformation of the 3 and 5 substituted carbonyl groups appears influenced by hydrogen bonding with ap orientation observed for carbonyl groups serving as H-bonding acceptor groups in the solid. This behavior appears to mimic in vivo conformational preferences.

Morphological similarity: a 3D molecular similarity method correlated with protein-ligand recognition

Recognition of small molecules by proteins depends on three-dimensional molecular surface complementarity. However, the dominant techniques for analyzing the similarity of small molecules are based on two-dimensional chemical structure, with such techniques often outperforming three-dimensional techniques in side-by-side comparisons of correlation to biological activity. This paper introduces a new molecular similarity method, termed morphological similarity (MS), that addresses the apparent paradox. Two sets of molecule pairs are identified from a set of ligands whose protein-bound states are known crystallographically. Pairs that bind the same protein sites form the first set, and pairs that bind different sites from the second. MS is shown to separate the two sets significantly better than a benchmark 2D similarity technique. Further, MS agrees with crystallographic observation of bound ligand states, independent of information about bound states. MS is efficient to compute and can be practically applied to large libraries of compounds.

De novo design of peptides targeted to the EF hands of calmodulin

This report describes the use of the concept of inversion of hydropathy patterns to the de novo design of peptides targeted to a predetermined site on a protein. Eight- and 12-residue peptides were constructed with the EF hands or Ca(2+)-coordinating sites of calmodulin as their anticipated points of interaction. These peptides, but not unrelated peptides nor those with the same amino acid composition but a scrambled sequence, interacted with the two carboxyl-terminal Ca(2+)-binding sites of calmodulin as well as the EF hands of troponin C. The interactions resulted in a conformational change whereby the 8-mer peptide-calmodulin complex could activate phosphodiesterase in the absence of Ca(2+). In contrast, the 12-mer peptide-calmodulin complex did not activate phosphodiesterase but rather inhibited activation by Ca(2+). This inhibition could be overcome by high levels of Ca(2+). Thus, it would appear that the aforementioned concept can be used to make peptide agonists and antagonists that are targeted to predetermined sites on proteins such as calmodulin.

Knowledge-based scoring function to predict protein-ligand interactions

The development and validation of a new knowledge-based scoring function (DrugScore) to describe the binding geometry of ligands in proteins is presented. It discriminates efficiently between well-docked ligand binding modes (root-mean-square deviation <2.0 A with respect to a crystallographically determined reference complex) and those largely deviating from the native structure, e.g. generated by computer docking programs. Structural information is extracted from crystallographically determined protein-ligand complexes using ReLiBase and converted into distance-dependent pair-preferences and solvent-accessible surface (SAS) dependent singlet preferences for protein and ligand atoms. Definition of an appropriate reference state and accounting for inaccuracies inherently present in experimental data is required to achieve good predictive power. The sum of the pair preferences and the singlet preferences is calculated based on the 3D structure of protein-ligand binding modes generated by docking tools. For two test sets of 91 and 68 protein-ligand complexes, taken from the Protein Data Bank (PDB), the calculated score recognizes poses generated by FlexX deviating <2 A from the crystal structure on rank 1 in three quarters of all possible cases. Compared to FlexX, this is a substantial improvement. For ligand geometries generated by DOCK, DrugScore is superior to the "chemical scoring" implemented into this tool, while comparable results are obtained using the "energy scoring" in DOCK. None of the presently known scoring functions achieves comparable power to extract binding modes in agreement with experiment. It is fast to compute, regards implicitly solvation and entropy contributions and produces correctly the geometry of directional interactions. Small deviations in the 3D structure are tolerated and, since only contacts to non-hydrogen atoms are regarded, it is independent from assumptions of protonation states.

Consensus scoring: A method for obtaining improved hit rates from docking databases of three-dimensional structures into proteins

We present the results of an extensive computational study in which we show that combining scoring functions in an intersection-based consensus approach results in an enhancement in the ability to discriminate between active and inactive enzyme inhibitors. This is illustrated in the context of docking collections of three-dimensional structures into three different enzymes of pharmaceutical interest: p38 MAP kinase, inosine monophosphate dehydrogenase, and HIV protease. An analysis of two different docking methods and thirteen scoring functions provides insights into which functions perform well, both singly and in combination. Our data shows that consensus scoring further provides a dramatic reduction in the number of false positives identified by individual scoring functions, thus leading to a significant enhancement in hit-rates.

Exploring the conformational diversity of loops on conserved frameworks

Loops are structurally variable regions, but the secondary structural elements bracing loops are often conserved. Motifs with similar secondary structures exist in the same and different protein families. In this study, we made an all-PDB-based analysis and produced 495 motif families accessible from the Internet. Every motif family contains some variable loops spanning a common framework (a pair of secondary structures). The diversity of loops and the convergence of frameworks were examined. In addition, we also identified 119 loops with conformational changes in different PDB files. These materials can give some directions for functional loop design and flexible docking.

Efficacy and selectivity in flexible database docking

Flexible database docking with DOCK 4.0 has been evaluated for its ability to retrieve biologically active molecules from a database of approximately 1,000 compounds with known activities against thrombin and the progesterone receptor. The retrieval of known actives and chemically similar but inactive molecules was monitored as a function of conformational and orientational sampling. The largest enrichment of actives among the 10% highest ranking molecules is obtained when only five conformations are used to seed the next round of ligand reconstruction and limited sampling is applied to place the base fragment in the binding site. The performance of energy and chemical scoring, as implemented in DOCK 4.0, was found to depend on the protein used for docking. For the progesterone receptor, energy scoring yields the largest enrichments (64%) in terms of actives retrieved among the 10% top scoring molecules, while chemical scoring performs best for thrombin (94%). With the exception of the application of energy scoring to the progesterone receptor, both energy-based scoring schemes applied in this study do not discriminate well between true actives and chemically similar but inactive compounds. In conclusion, flexible docking is able to effectively prioritize high-throughput screening databases, using less conformational sampling than normally required for appropriate reconstruction of protein-ligand complexes. The more subtle discrimination between chemically similar classes of active and inactive compounds remains, however, problematic.

Evaluation of the FLEXX incremental construction algorithm for protein-ligand docking

We report on a test of FLEXX, a fully automatic docking tool for flexible ligands, on a highly diverse data set of 200 protein-ligand complexes from the Protein Data Bank. In total 46.5% of the complexes of the data set can be reproduced by a FLEXX docking solution at rank 1 with an rms deviation (RMSD) from the observed structure of less than 2 A. This rate rises to 70% if one looks at the entire generated solution set. FLEXX produces reliable results for ligands with up to 15 components which can be docked in 80% of the cases with acceptable accuracy. Ligands with more than 15 components tend to generate wrong solutions more often. The average runtime of FLEXX on this test set is 93 seconds per complex on a SUN Ultra-30 workstation. In addition, we report on "cross-docking" experiments, in which several receptor structures of complexes with identical proteins have been used for docking all cocrystallized ligands of these complexes. In most cases, these experiments show that FLEXX can acceptably dock a ligand into a foreign receptor structure. Finally we report on screening runs of ligands out of a library with 556 entries against ten different proteins. In eight cases FLEXX is able to find the original inhibitor within the top 7% of the total library.

The sensitivity of the results of molecular docking to induced fit effects: application to thrombin, thermolysin and neuraminidase

This paper describes the application of PRO_LEADS to the flexible docking of ligands into crystallographically derived enzyme structures that are assumed to be rigid. PRO_LEADS uses a Tabu search methodology to perform the flexible search and an empirically derived estimate of the binding affinity to drive the docking process. The paper tests the extent to which the assumption of a rigid enzyme compromises the accuracy of the results. All-pairs docking experiments are performed for three enzymes (thrombin, thermolysin and influenza virus neuraminidase) based on six or more ligand-enzyme crystal structures for each enzyme. In 76% of the cases, PRO_LEADS can successfully identify the correct ligand conformation as the lowest energy configuration when the enzyme structure is derived from that ligand's crystal structure, but the methodology only docks 49% of the cases successfully when the ligand is docked against enzyme crystal structures derived from other ligands. Small movements in the enzyme structure lead to an under-prediction in the energy of the correct binding mode by up to 14 kJ/mol and in some cases this under-prediction can lead to the native mode not being recognised as the lowest energy solution. The type of movements responsible for mis-docking are: the movement of sidechains as a result of changes in C alpha position; the movement of sidechains without changes in C alpha position; the movement of flexible portions of main chains to facilitate the formation of hydrogen bonds; and the movement of metal atoms bound to the enzyme active site. The work illustrates that the assumption of a rigid active site can lead to errors in identification of the correct binding mode and the assessment of binding affinity, even for enzymes which show relatively small shift in atomic positions from one ligand to the next. A good docking code, such as PRO_LEADS, can usually dock successfully if there is induced fit in relatively rigid enzymes but there remains the need to develop improved strategies for dealing with enzyme flexibility. The work implies that treatments of enzyme flexibility which focus only on sidechain rotations will not deal with the critical shifts responsible for mis-docking of ligands in thrombin, thermolysin and neuraminidase. The paper demonstrates the utility of all pairs docking experiments as a method of assessing the effectiveness of docking methodologies in dealing with enzyme flexibility.

Towards understanding the mechanisms of molecular recognition by computer simulations of ligand-protein interactions

The thermodynamic and kinetic aspects of molecular recognition for the methotrexate (MTX)-dihydrofolate reductase (DHFR) ligand-protein system are investigated by the binding energy landscape approach. The impact of 'hot' and 'cold' errors in ligand mutations on the thermodynamic stability of the native MTX-DHFR complex is analyzed, and relationships between the molecular recognition mechanism and the degree of ligand optimization are discussed. The nature and relative stability of intermediates and thermodynamic phases on the ligand-protein association pathway are studied, providing new insights into connections between protein folding and molecular recognition mechanisms, and cooperativity of ligand-protein binding. The results of kinetic docking simulations are rationalized based on the thermodynamic properties determined from equilibrium simulations and the shape of the underlying binding energy landscape. We show how evolutionary ligand selection for a receptor active site can produce well-optimized ligand-protein systems such as MTX-DHFR complex with the thermodynamically stable native structure and a direct transition mechanism of binding from unbound conformations to the unique native structure.

"RKKH" peptides from the snake venom metalloproteinase of Bothrops jararaca bind near the metal ion-dependent adhesion site of the human integrin alpha(2) I-domain

Integrin alpha(1)beta(1) and alpha(2)beta(1) are the major cellular receptors for collagen, and collagens bind to these integrins at the inserted I-domain in their alpha subunit. We have previously shown that a cyclic peptide derived from the metalloproteinase domain of the snake venom protein jararhagin blocks the collagen-binding function of the alpha(2) I-domain. Here, we have optimized the structure of the peptide and identified the site where the peptide binds to the alpha(2) I-domain. The peptide sequence Arg-Lys-Lys-His is critical for recognition by the I-domain, and five negatively charged residues surrounding the "metal ion-dependent adhesion site" (MIDAS) of the I-domain, when mutated, show significantly impaired binding of the peptide. Removal of helix alphaC, located along one side of the MIDAS and suggested to be involved in collagen-binding in these I-domains, does not affect peptide binding. This study supports the notion that the metalloproteinase initially binds to the alpha(2) I-domain at a location distant from the active site of the protease, thus blocking collagen binding to the adhesion molecule in the vicinity of the MIDAS, while at the same time leaving the active site free to degrade nearby proteins, the closest being the beta(1) subunit of the alpha(2)beta(1) cell-surface integrin itself.

Two-stage method for protein-ligand docking

A two-stage method for the computational prediction of the structure of protein-ligand complexes is proposed. Given an experimentally determined structure of the protein, in the first stage a large number of plausible ligand conformations is generated using the fast docking algorithm FlexX. In the second stage these conformations are minimized and reranked using a method based on a classical force field. The two-stage method is tested for 10 different protein-ligand complexes. For 9 of them experimentally determined structures are known. It turns out that the two-stage method strongly improves the predictive power as compared to that of the fast docking stage alone. The tenth case is a bona fide prediction of a complex of thrombin with a new inhibitor for which no experimentally determined structure is available so far.

MCDOCK: a Monte Carlo simulation approach to the molecular docking problem

Prediction of the binding mode of a ligand (a drug molecule) to its macromolecular receptor, or molecular docking, is an important problem in rational drug design. We have developed a new docking method in which a non-conventional Monte Carlo (MC) simulation technique is employed. A computer program, MCDOCK, was developed to carry out the molecular docking operation automatically. The current version of the MCDOCK program (version 1.0) allows for the full flexibility of ligands in the docking calculations. The scoring function used in MCDOCK is the sum of the interaction energy between the ligand and its receptor, and the conformational energy of the ligand. To validate the MCDOCK method, 19 small ligands, the binding modes of which had been determined experimentally using X-ray diffraction, were docked into their receptor binding sites. To produce statistically significant results, 20 MCDOCK runs were performed for each protein-ligand complex. It was found that a significant percentage of these MCDOCK runs converge to the experimentally observed binding mode. The root-mean-square (rms) of all non-hydrogen atoms of the ligand between the predicted and experimental binding modes ranges from 0.25 to 1.84 A for these 19 cases. The computational time for each run on an SGI Indigo2/R10000 varies from less than 1 min to 15 min, depending upon the size and the flexibility of the ligands. Thus MCDOCK may be used to predict the precise binding mode of ligands in lead optimization and to discover novel lead compounds through structure-based database searching.

4-hydroxy-5,6-dihydro-2H-pyran-2-ones.3. Bicyclic and hetero-aromatic ring systems as 3-position scaffolds to bind to S1' and S2' of the HIV-1 protease enzyme

5,6-Dihydro-2H-pyran-2-ones are potent inhibitors of HIV-1 protease, which bind to the S1, S2, S1', and S2' pockets and have a unique binding mode with the catalytic aspartyl groups and the flap region of the enzyme. Efforts to explore 3-position heterocyclic scaffolds that bind to the S1' and S2' pockets have provided a number of selected analogs that display high HIV-1 protease inhibitory activity. reserved.

Evaluation of PMF scoring in docking weak ligands to the FK506 binding protein

A new knowledge-based scoring function (PMF-score), implemented into the DOCK4 program, was used to screen a database of 3247 small molecules for binding to the FK506 binding protein (FKBP). The computational ranking of these compounds was compared to the binding affinities measured by NMR. It was demonstrated that small, weakly binding molecules have, on average, higher computational scores than nonbinders and are enriched in the upper ranks of the computational scoring lists. In addition, the results obtained with the PMF scoring function were superior (by 30-120% larger enrichment factors) to those obtained with the standard force field score of DOCK4. The reliable ranking of small, weakly binding molecules offers new ways of designing building blocks in combinatorial libraries as well as SAR by NMR libraries with the increased chance of identifying suitable lead compounds for drug design.

SuperStar: a knowledge-based approach for identifying interaction sites in proteins

An empirical method for identifying interaction sites in proteins is described and validated. The method is based entirely on experimental information about non-bonded interactions occurring in small-molecule crystal structures. These data are used in the form of scatterplots that show the experimentally observed distribution of one functional group (the "contact group" or "probe") around another. A template molecule (e.g. a protein binding site) is broken down into structure fragments and the scatterplots, showing the distribution of a chosen probe around these structure fragments, are superimposed on the corresponding parts of the template. The scatterplots are then translated into a three-dimensional map that shows the propensity of the probe at different positions around the template molecule. The method is illustrated for l -arabinose-binding protein, complexed with l -arabinose and with d -fucose, and for dihydrofolate reductase complexed with methotrexate. The method is validated on 122 X-ray structures of protein-ligand complexes. For all the binding sites of these proteins, propensity maps are generated for four different probes: a charged NH+3nitrogen, a carbonyl oxygen, a hydroxyl oxygen and a methyl carbon atom. Next, the maps are compared with the experimentally observed positions of ligand atoms of these types. For 74% of these ligand atoms (84% of the solvent-inaccessible ones) the calculated propensity of the matching probe at the experimental positions is higher than expected by chance. For 68% of the atoms (82% of the solvent-inaccessible ones) the propensity of the matching probe is higher than that of the other three probes. These results indicate that the approach generally gives good predictions for protein-ligand interactions. The potential applications of the propensity maps range from an aid in manual docking and structure-based drug design to their use in pharmacophore development.

The role of waters in docking strategies with incremental flexibility for carbohydrate derivatives: heat-labile enterotoxin, a multivalent test case

Molecular docking studies of carbohydrate derivatives in protein binding sites are often challenging because of water-mediated interactions and the inherent flexibility of the many terminal hydroxyl groups. Using the recognition process between heat-labile enterotoxin from Escherichia coli and ganglioside GM1 as a paradigm, we developed a modeling protocol that includes incremental conformational flexibility of the ligand and predicted water interactions. The strategy employs a modified version of the Monte Carlo docking program AUTODOCK and water affinity potentials calculated with GRID. After calibration of the protocol on the basis of the known binding modes of galactose and lactose to the toxin, blind predictions were made for the binding modes of four galactose derivatives: lactulose, melibionic acid, thiodigalactoside, and m-nitrophenyl-alpha-galactoside. Subsequent crystal structure determinations have demonstrated that our docking strategy can predict the correct binding modes of carbohydrate derivatives within 1.0 A from experiment. In addition, it is shown that repeating the docking simulations in each of the seemingly identical binding sites of the multivalent toxin increases the chance of finding the correct binding mode.

A general and fast scoring function for protein-ligand interactions: a simplified potential approach

A fast, simplified potential-based approach is presented that estimates the protein-ligand binding affinity based on the given 3D structure of a protein-ligand complex. This general, knowledge-based approach exploits structural information of known protein-ligand complexes extracted from the Brookhaven Protein Data Bank and converts it into distance-dependent Helmholtz free interaction energies of protein-ligand atom pairs (potentials of mean force, PMF). The definition of an appropriate reference state and the introduction of a correction term accounting for the volume taken by the ligand were found to be crucial for deriving the relevant interaction potentials that treat solvation and entropic contributions implicitly. A significant correlation between experimental binding affinities and computed score was found for sets of diverse protein-ligand complexes and for sets of different ligands bound to the same target. For 77 protein-ligand complexes taken from the Brookhaven Protein Data Bank, the calculated score showed a standard deviation from observed binding affinities of 1.8 log Ki units and an R2 value of 0.61. The best results were obtained for the subset of 16 serine protease complexes with a standard deviation of 1.0 log Ki unit and an R2 value of 0.86. A set of 33 inhibitors modeled into a crystal structure of HIV-1 protease yielded a standard deviation of 0.8 log Ki units from measured inhibition constants and an R2 value of 0.74. In contrast to empirical scoring functions that show similar or sometimes better correlation with observed binding affinities, our method does not involve deriving specific parameters that fit the observed binding affinities of protein-ligand complexes of a given training set. We compared the performance of the PMF score, Böhm's score (LUDI), and the SMOG score for eight different test sets of protein-ligand complexes. It was found that for the majority of test sets the PMF score performs best. The strength of the new approach presented here lies in its generality as no knowledge about measured binding affinities is needed to derive atomic interaction potentials. The use of the new scoring function in docking studies is outlined.

A method for biomolecular structural recognition and docking allowing conformational flexibility

In this work, we present an algorithm developed to handle biomolecular structural recognition problems, as part of an interdisciplinary research endeavor of the Computer Vision and Molecular Biology fields. A key problem in rational drug design and in biomolecular structural recognition is the generation of binding modes between two molecules, also known as molecular docking. Geometrical fitness is a necessary condition for molecular interaction. Hence, docking a ligand (e.g., a drug molecule or a protein molecule), to a protein receptor (e.g., enzyme), involves recognition of molecular surfaces. Conformational transitions by "hinge-bending" involves rotational movements of relatively rigid parts with respect to each other. The generation of docked binding modes between two associating molecules depends on their three dimensional structures (3-D) and their conformational flexibility. In comparison to the particular case of rigid-body docking, the computational difficulty grows considerably when taking into account the additional degrees of freedom intrinsic to the flexible molecular docking problem. Previous docking techniques have enabled hinge movements only within small ligands. Partial flexibility in the receptor molecule is enabled by a few techniques. Hinge-bending motions of protein receptors domains are not addressed by these methods, although these types of transitions are significant, e.g., in enzymes activity. Our approach allows hinge induced motions to exist in either the receptor or the ligand molecules of diverse sizes. We allow domains/subdomains/group of atoms movements in either of the associating molecules. We achieve this by adapting a technique developed in Computer Vision and Robotics for the efficient recognition of partially occluded articulated objects. These types of objects consist of rigid parts which are connected by rotary joints (hinges). Our method is based on an extension and generalization of the Hough transform and the Geometric Hashing paradigms for rigid object recognition. We show experimental results obtained by the successful application of the algorithm to cases of bound and unbound molecular complexes, yielding fast matching times. While the "correct" molecular conformations of the known complexes are obtained with small RMS distances, additional, predictive good-fitting binding modes are generated as well. We conclude by discussing the algorithm's implications and extensions, as well as its application to investigations of protein structures in Molecular Biology and recognition problems in Computer Vision.

Comparison of two implementations of the incremental construction algorithm in flexible docking of thrombin inhibitors

A set of 32 known thrombin inhibitors representing different chemical classes has been used to evaluate the performance of two implementations of incremental construction algorithms for flexible molecular docking: DOCK 4.0 and FlexX 1.5. Both docking tools are able to dock 10-35% of our test set within 2 A of their known, bound conformations using default sampling and scoring parameters. Although flexible docking with DOCK or FlexX is not able to reconstruct all native complexes, it does offer a significant improvement over rigid body docking of single, rule-based conformations, which is still often used for docking of large databases. Docking of sets of multiple conformers of each inhibitor, obtained with a novel protocol for diverse conformer generation and selection, yielded results comparable to those obtained by flexible docking. Chemical scoring, which is an empirically modified force field scoring method implemented in DOCK 4.0, outperforms both interaction energy scoring by DOCK and the Böhm scoring function used by FlexX in rigid and flexible docking of thrombin inhibitors. Our results indicate that for reliable docking of flexible ligands the selection of anchor fragments, conformational sampling and currently available scoring methods still require improvement.

A hierarchical method for generating low-energy conformers of a protein-ligand complex

A novel dynamical protocol for finding the low-energy conformations of a protein-ligand complex is described. The energy functions examined consist of an empirical force field with four different dielectric screening models; the generalized Born/surface area model also is examined. Application of the method to three complexes of known crystal structure provides insights into the energy functions used for selecting low-energy docked conformations and into the structure of the binding-energy surface. Evidence is presented that the local energy minima of a ligand in a binding site are arranged in a hierarchical fashion. This observation motivates the construction of a hierarchical docking algorithm that substantially enriches the population of ligand conformations close to the crystal conformation. The algorithm is also adapted to permit docking into a flexible binding site and preliminary tests of this method are presented.

FLEXS: a method for fast flexible ligand superposition

If no structural information about a particular target protein is available, methods of rational drug design try to superimpose putative ligands with a given reference, e.g., an endogenous ligand. The goal of such structural alignments is, on the one hand, to approximate the binding geometry and, on the other hand, to provide a relative ranking of the ligands with respect to their similarity. An accurate superposition is the prerequisite of subsequent exploitation of ligand data by either 3D QSAR analyses, pharmacophore hypotheses, or receptor modeling. We present the automatic method FLEXS for structurally superimposing pairs of ligands, approximating their putative binding site geometry. One of the ligands is treated as flexible, while the other one, used as a reference, is kept rigid. FLEXS is an incremental construction procedure. The molecules to be superimposed are partitioned into fragments. Starting with placements of a selected anchor fragment, computed by two alternative approaches, the remaining fragments are added iteratively. At each step, flexibility is considered by allowing the respective added fragment to adopt a discrete set of conformations. The mean computing time per test case is about 1:30 min on a common-day workstation. FLEXS is fast enough to be used as a tool for virtual ligand screening. A database of typical drug molecules has been screened for potential fibrinogen receptor antagonists. FLEXS is capable of retrieving all ligands assigned to platelet aggregation properties among the first 20 hits. Furthermore, the program suggests additional interesting candidates, likely to be active at the same receptor. FLEXS proves to be superior to commonly used retrieval techniques based on 2D fingerprint similarities. The accuracy of computed superpositions determines the relevance of subsequently performed ligand analyses. In order to validate the quality of FLEXS alignments, we attempted to reproduce a set of 284 mutual superpositions derived from experimental data on 76 protein-ligand complexes of 14 proteins. The ligands considered cover the whole range of drug-size molecules from 18 to 158 atoms (PDB codes: 3ptb, 2er7). The performance of the algorithm critically depends on the sizes of the molecules to be superimposed. The limitations are clearly demonstrated with large peptidic inhibitors in the HIV and the endothiapepsin data set. Problems also occur in the presence of multiple binding modes (e.g., elastase and human rhinovirus). The most convincing results are achieved with small- and medium-sized molecules (as, e.g., the ligands of trypsin, thrombin, and dihydrofolate reductase). In more than half of the entire test set, we achieve rms deviations between computed and observed alignment of below 1.5 A. This underlines the reliability of FLEXS-generated alignments.

Predicting structural effects in HIV-1 protease mutant complexes with flexible ligand docking and protein side-chain optimization

We present a computational approach for predicting structures of ligand-protein complexes and analyzing binding energy landscapes that combines Monte Carlo simulated annealing technique to determine the ligand bound conformation with the dead-end elimination algorithm for side-chain optimization of the protein active site residues. Flexible ligand docking and optimization of mobile protein side-chains have been performed to predict structural effects in the V32I/I47V/V82I HIV-1 protease mutant bound with the SB203386 ligand and in the V82A HIV-1 protease mutant bound with the A77003 ligand. The computational structure predictions are consistent with the crystal structures of these ligand-protein complexes. The emerging relationships between ligand docking and side-chain optimization of the active site residues are rationalized based on the analysis of the ligand-protein binding energy landscape.

RigFit: a new approach to superimposing ligand molecules

If structural knowledge of a receptor under consideration is lacking, drug design approaches focus on similarity or dissimilarity analysis of putative ligands. In this context the mutual ligand superposition is of utmost importance. Methods that are rapid enough to facilitate interactive usage, that allow to process sets of conformers and that enable database screening are of special interest here. The ability to superpose molecular fragments instead of entire molecules has proven to be helpful too. The RIGFIT approach meets these requirements and has several additional advantages. In three distinct test applications, we evaluated how closely we can approximate the observed relative orientation for a set of known crystal structures, we employed RIGFIT as a fragment placement procedure, and we performed a fragment-based database screening. The run time of RIGFIT can be traded off against its accuracy. To be competitive in accuracy with another state-of-the-art alignment tool, with which we compare our method explicitly, computing times of about 6 s per superposition on a common day workstation are required. If longer run times can be afforded the accuracy increases significantly. RIGFIT is part of the flexible superposition software FLEXS which can be accessed on the WWW [http:/(/)cartan.gmd.de/FlexS].

Reaching the global minimum in docking simulations: a Monte Carlo energy minimization approach using Bezier splines

The docking problem faces two major challenges: the global optimization of a multivariable function, such as the energy, and the ability to discriminate between true and false positive results, i.e., native from nonnative structures based on the input energy function. Among all energy evaluation tools, only a local energy-minimization method using an accurate enough potential function is able to discriminate between native and nonnative structures. To meet these requirements, a Monte Carlo with energy-minimization method has been incorporated into a new ECEPP/3 docking program. The efficiency of the simulation results from the use of an energy-grid technique based on Bezier splines and from a simplification of the receptor by switching on the energy of only important residues of the active site. Simulations of a thrombin-inhibitor complex show that the global minimum of the energy function was reached in every independent run within less than 3 min of time on an IBM RX 6000 computer. For comparison, 10 standard independent Monte Carlo simulations with 10(6) steps in each were carried out. Only three of them led to a conformation close to the x-ray structure. The latter simulations required an average of 24 min and about 10 hr with and without the grid, respectively. Another important result is that the Bezier spline technique not only speeds up the calculation by reducing the number of operations during the energy evaluation but also helps in reaching the global minimum by smoothing out the potential energy surface.