Energetic analysis of fragment docking and application to structure-based pharmacophore hypothesis generation

We have developed a method that uses energetic analysis of structure-based fragment docking to elucidate key features for molecular recognition. This hybrid ligand- and structure-based methodology uses an atomic breakdown of the energy terms from the Glide XP scoring function to locate key pharmacophoric features from the docked fragments. First, we show that Glide accurately docks fragments, producing a root mean squared deviation (RMSD) of <1.0 Å for the top scoring pose to the native crystal structure. We then describe fragment-specific docking settings developed to generate poses that explore every pocket of a binding site while maintaining the docking accuracy of the top scoring pose. Next, we describe how the energy terms from the Glide XP scoring function are mapped onto pharmacophore sites from the docked fragments in order to rank their importance for binding. Using this energetic analysis we show that the most energetically favorable pharmacophore sites are consistent with features from known tight binding compounds. Finally, we describe a method to use the energetically selected sites from fragment docking to develop a pharmacophore hypothesis that can be used in virtual database screening to retrieve diverse compounds. We find that this method produces viable hypotheses that are consistent with known active compounds. In addition to retrieving diverse compounds that are not biased by the co-crystallized ligand, the method is able to recover known active compounds from a database screen, with an average enrichment of 8.1 in the top 1% of the database.     

Random Computer Generation of 3D Molecular Structures: Theoretical and Statistical Analysis

Summary: A computer program has been developed to generate three‐dimensional molecular structures randomly from a given collection of elementary chemical functional groups: the so‐called fragment database. The gradual assembly of the various fragments present in the database is performed according to a “self‐generation algorithm” (SGA). The latter is based on the covalent binding, step by step, between the unoccupied electronic valencies associated with the fragments of the database, and those of the growing molecular structure. When the number of electronic valencies of the molecular structure is zero, the growth process for this particular molecule is completed. It is shown that SGA is able to reproduce the asymmetric mass distributions of some natural colloids, like humic substances. In this article, particular attention is given to the analysis of the relationship existing between the fragment composition of the database and that of the collection of molecules generated. Mathematical expressions are derived and discussed, to understand the relationship between the proportions of the different types of fragments and the final composition of the generated molecular ensembles. For that purpose, a “pathway” formalism is proposed to describe exhaustively the whole set of generated molecules by specifying the distribution function of all of the fragments therein integrated. A statistical analysis that satisfactorily reproduces the predictions of the pathway model is extensively discussed.

Example of a three‐dimensional structure obtained with the “self‐generation algorithm” (SGA).     

The atom assignment problem in automated de novo drug design. 3. Algorithms for optimization of fragment placement onto 3D molecular graphs

Summary Atom assignment onto 3D molecular graphs is a combinatoric problem in discrete space. If atoms are to be placed efficiently on molecular graphs produced in drug binding sites, the assignment must be optimized. An algorithm, based on simulated annealing, is presented for efficient optimization of fragment placement. Extensive tests of the method have been performed on five ligands taken from the Protein Data Bank. The algorithm is presented with the ligand graph and the electrostatic potential as input. Self placement of molecular fragments was monitored as an objective test. A hydrogen-bond option was also included, to enable the user to highlight specific needs. The algorithm performed well in the optimization, with successful replications. In some cases, a modification was necessary to reduce the tendency to give multiple halogenated structures. This optimization procedure should prove useful for automated de novo drug design.     

The atom assignment problem in automated de novo drug design. 1. Transferability of molecular fragment properties

Summary This paper is the first of a series which examines the problems of atom assignment in automated de novo drug design. In subsequent papers, a combinatoric optimization method for fragment placement onto 3D molecular graphs is provided. Molecules are built from molecular graphs by placing fragments onto the graph. Here we examine the transferability of atomic residual charge, by fragment placement, with respect to the electrostatic potential. This transferability has been tested on 478 molecular structures extracted from the Cambridge Structural Database. The correlation found between the electrostatic potential computed from composite fragments and that computed for the whole molecule was encouraging, except for extended conjugated systems.     

Prediction of trypsin/molecular fragment binding affinities by free energy decomposition and empirical scores

Two families of binding affinity estimation methodologies are described which were utilized in the SAMPL3 trypsin/fragment binding affinity challenge. The first is a free energy decomposition scheme based on a thermodynamic cycle, which included separate contributions from enthalpy and entropy of binding as well as a solvent contribution. Enthalpic contributions were estimated with PM6-DH2 semiempirical quantum mechanical interaction energies, which were modified with a statistical error correction procedure. Entropic contributions were estimated with the rigid-rotor harmonic approximation, and solvent contributions to the free energy were estimated with several different methods. The second general methodology is the empirical score LISA, which contains several physics-based terms trained with the large PDBBind database of protein/ligand complexes. Here we also introduce LISA+, an updated version of LISA which, prior to scoring, classifies systems into one of four classes based on a ligand's hydrophobicity and molecular weight. Each version of the two methodologies (a total of 11 methods) was trained against a compiled set of known trypsin binders available in the Protein Data Bank to yield scaling parameters for linear regression models. Both raw and scaled scores were submitted to SAMPL3. Variants of LISA showed relatively low absolute errors but also low correlation with experiment, while the free energy decomposition methods had modest success when scaling factors were included. Nonetheless, re-scaled LISA yielded the best predictions in the challenge in terms of RMS error, and six of these models placed in the top ten best predictions by RMS error. This work highlights some of the difficulties of predicting binding affinities of small molecular fragments to protein receptors as well as the benefit of using training data.     

Multiple ligand simultaneous docking: Orchestrated dancing of ligands in binding sites of protein

Present docking methodologies simulate only one single ligand at a time during docking process. In reality, the molecular recognition process always involves multiple molecular species. Typical protein–ligand interactions are, for example, substrate and cofactor in catalytic cycle; metal ion coordination together with ligand(s); and ligand binding with water molecules. To simulate the real molecular binding processes, we propose a novel multiple ligand simultaneous docking (MLSD) strategy, which can deal with all the above processes, vastly improving docking sampling and binding free energy scoring. The work also compares two search strategies: Lamarckian genetic algorithm and particle swarm optimization, which have respective advantages depending on the specific systems. The methodology proves robust through systematic testing against several diverse model systems: E. coli purine nucleoside phosphorylase (PNP) complex with two substrates, SHP2NSH2 complex with two peptides and Bcl‐xL complex with ABT‐737 fragments. In all cases, the final correct docking poses and relative binding free energies were obtained. In PNP case, the simulations also capture the binding intermediates and reveal the binding dynamics during the recognition processes, which are consistent with the proposed enzymatic mechanism. In the other two cases, conventional single‐ligand docking fails due to energetic and dynamic coupling among ligands, whereas MLSD results in the correct binding modes. These three cases also represent potential applications in the areas of exploring enzymatic mechanism, interpreting noisy X‐ray crystallographic maps, and aiding fragment‐based drug design, respectively. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Time-efficient flexible superposition of medium-sized molecules

We present an efficient algorithm for the structural alignment of medium-sized organic molecules. The algorithm has been developed for applications in 3D QSAR and in receptor modeling. The method assumes one of the molecules, the reference ligand, to be presented in the conformation that it adopts inside the receptor pocket. The second molecule, the test ligand, is considered to be flexible, and is assumed to be given in an arbitrary low-energy conformation. Ligand flexibility is modeled by decomposing the test ligand into molecular fragments, such that ring systems are completely contained in a single fragment. Conformations of fragments and torsional angles of single bonds are taken from a small finite set, which depends on the fragment and bond, respectively. The algorithm superimposes a distinguished base fragment of the test ligand onto a suitable region of the reference ligand and then attaches the remaining fragments of the test ligand in a step-by-step fashion. During this process, a scoring function is optimized that encompasses bonding terms and terms accounting for steric overlap as well as for similarity of chemical properties of both ligands. The algorithm has been implemented in the FLEXS system. To validate the quality of the produced results, we have selected a number of examples for which the mutual superposition of two ligands is experimentally given by the comparison of the binding geometries known from the crystal structures of their corresponding protein–ligand complexes. On more than two-thirds of the test examples the algorithm produces rms deviations of the predicted versus the observed conformation of the test ligand below 1.5 Å. The run time of the algorithm on a single problem instance is a few minutes on a common-day workstation. The overall goal of this research is to drastically reduce run times, while limiting the inaccuracies of the model and the computation to a tolerable level.     

DeepFrag: a deep convolutional neural network for fragment-based lead optimization

Machine learning has been increasingly applied to the field of computer-aided drug discovery in recent years, leading to notable advances in binding-affinity prediction, virtual screening, and QSAR. Surprisingly, it is less often applied to lead optimization, the process of identifying chemical fragments that might be added to a known ligand to improve its binding affinity. We here describe a deep convolutional neural network that predicts appropriate fragments given the structure of a receptor/ligand complex. In an independent benchmark of known ligands with missing (deleted) fragments, our DeepFrag model selected the known (correct) fragment from a set over 6500 about 58% of the time. Even when the known/correct fragment was not selected, the top fragment was often chemically similar and may well represent a valid substitution. We release our trained DeepFrag model and associated software under the terms of the Apache License, Version 2.0.

DeepFrag is a machine-learning model designed to assist with lead optimization. It recommends appropriate fragment additions given the 3D structures of a protein receptor and bound small-molecule ligand.     

A Monte Carlo method for finding important ligand fragments from receptor data

A simulated annealing method for finding important ligand fragments is described. At a given temperature, ligand fragments are randomly selected and randomly placed within the given receptor cavity, often replacing or forming bonds with existing ligand fragments. For each new ligand fragment combination, the bonded, nonbonded, polarization and solvation energies of the new ligand–receptor system are compared to the previous configuration. Acceptance or rejection of the new system is decided using the Boltzmann distribution , where E is the energy difference between the old and new systems, k is the Boltzmann constant and T is the temperature. Thus, energetically unfavorable fragment switches are sometimes accepted, sacrificing immediate energy gains in the interest of finding a system with minimum energy. By lowering the temperature, the rate of unfavorable switches decreases and energetically favorable combinations become more difficult to change. The process is terminated when the frequency of switches becomes too small. As a test, the method predicted positions and types of important ligand fragments for neuraminidase that were in accord with the known ligand, sialic acid.     

A fragment energy assembler method for Hartree-Fock calculations of large molecules

We present a fragment energy assembler approach for approximate Hartree-Fock (HF) calculations of macromolecules. In this method, a macromolecule is divided into small fragments with appropriate size, and then each fragment is capped by its neighboring fragments to form a subsystem. The total energy of the target system is evaluated as the sum of the fragment energies of all fragments, which are available from conventional HF calculations on all subsystems. By applying the method to a broad range of molecules, we demonstrate that the present approach could yield satisfactory HF energies for all studied systems.     

Mining a chemical database for fragment co-occurrence: discovery of "chemical clichés"

Nowadays millions of different compounds are known, their structures stored in electronic databases. Analysis of these data could yield valuable insights into the laws of chemistry and the habits of chemists. We have therefore explored the public database of the National Cancer Institute (>250,000 compounds) by pattern searching. We split the molecules of this database into fragments to find out which fragments exist, how frequent they are, and whether the occurrence of one fragment in a molecule is related to the occurrence of another, nonoverlapping fragment. It turns out that some fragments and combinations of fragments are so frequent that they can be called "chemical clichés". We believe that the fragment data can give insight into the chemical space explored so far by synthesis. The lists of fragments and their (co-)occurrences can help create novel chemical compounds by (i) systematically listing the most popular and therefore most easily used substituents and ring systems for synthesizing new compounds, (ii) being an easily accessible repository for rarer fragments suitable for lead compound optimization, and (iii) pointing out some of the yet unexplored parts of chemical space.     

Fragment-based drug design: computational & experimental state of the art

Fragment-based screening is an emerging technology which is used as an alternative to high-throughput screening (HTS), and often in parallel. Fragment screening focuses on very small compounds. Because of their small size and simplicity, fragments exhibit a low to medium binding affinity (mM to μM) and must therefore be screened at high concentration in order to detect binding events. Since some issues are associated with high-concentration screening in biochemical assays, biophysical methods are generally employed in fragment screening campaigns. Moreover, these techniques are very sensitive and some of them can give precise information about the binding mode of fragments, which facilitates the mandatory hit-to-lead optimization. One of the main advantages of fragment-based screening is that fragment hits generally exhibit a strong binding with respect to their size, and their subsequent optimization should lead to compounds with better pharmacokinetic properties compared to molecules evolved from HTS hits. In other words, fragments are interesting starting points for drug discovery projects. Besides, the chemical space of low-complexity compounds is very limited in comparison to that of drug-like molecules, and thus easier to explore with a screening library of limited size. Furthermore, the "combinatorial explosion" effect ensures that the resulting combinations of interlinked binding fragments may cover a significant part of "drug-like" chemical space. In parallel to experimental screening, virtual screening techniques, dedicated to fragments or wider compounds, are gaining momentum in order to further reduce the number of compounds to test. This article is a review of the latest news in both experimental and in silico virtual screening in the fragment-based discovery field. Given the specificity of this journal, special attention will be given to fragment library design.     

Liquid water simulations with the density fragment interaction approach

We reformulate the density fragment interaction (DFI) approach [Fujimoto and Yang, J. Chem. Phys., 2008, 129, 054102.] to achieve linear-scaling quantum mechanical calculations for large molecular systems. Two key approximations are developed to improve the efficiency of the DFI approach and thus enable the calculations for large molecules: the electrostatic interactions between fragments are computed efficiently by means of polarizable electrostatic-potential-fitted atomic charges; and frozen fragment pseudopotentials, similar to the effective fragment potentials that can be fitted from interactions between small molecules, are employed to take into account the Pauli repulsion effect among fragments. Our reformulated and parallelized DFI method demonstrates excellent parallel performance based on the benchmarks for the system of 256 water molecules. Molecular dynamics simulations for the structural properties of liquid water also show a qualitatively good agreement with experimental measurements including the heat capacity, binding energy per water molecule, and the radial distribution functions of atomic pairs of O-O, O-H, and H-H. With this approach, large-scale quantum mechanical simulations for water and other liquids become feasible.     

Optimizing fragment and scaffold docking by use of molecular interaction fingerprints

Protein-ligand interaction fingerprints have been used to postprocess docking poses of three ligand data sets: a set of 40 low-molecular-weight compounds from the Protein Data Bank, a collection of 40 scaffolds from pharmaceutically relevant protein ligands, and a database of 19 scaffolds extracted from true cdk2 inhibitors seeded in 2230 scaffold decoys. Four popular docking tools (FlexX, Glide, Gold, and Surflex) were used to generate poses for ligands of the three data sets. In all cases, scoring by the similarity of interaction fingerprints to a given reference was statistically superior to conventional scoring functions in posing low-molecular-weight fragments, predicting protein-bound scaffold coordinates according to the known binding mode of related ligands, and screening a scaffold library to enrich a hit list in true cdk2-targeted scaffolds.     

Residue preference mapping of ligand fragments in the Protein Data Bank

The interaction between small molecules and proteins is one of the major concerns for structure-based drug design because the principles of protein-ligand interactions and molecular recognition are not thoroughly understood. Fortunately, the analysis of protein-ligand complexes in the Protein Data Bank (PDB) enables unprecedented possibilities for new insights. Herein, we applied molecule-fragmentation algorithms to split the ligands extracted from PDB crystal structures into small fragments. Subsequently, we have developed a ligand fragment and residue preference mapping (LigFrag-RPM) algorithm to map the profiles of the interactions between these fragments and the 20 proteinogenic amino acid residues. A total of 4032 fragments were generated from 71?798 PDB ligands by a ring cleavage (RC) algorithm. Among these ligand fragments, 315 unique fragments were characterized with the corresponding fragment-residue interaction profiles by counting residues close to these fragments. The interaction profiles revealed that these fragments have specific preferences for certain types of residues. The applications of these interaction profiles were also explored and evaluated in case studies, showing great potential for the study of protein-ligand interactions and drug design. Our studies demonstrated that the fragment-residue interaction profiles generated from the PDB ligand fragments can be used to detect whether these fragments are in their favorable or unfavorable environments. The algorithm for a ligand fragment and residue preference mapping (LigFrag-RPM) developed here also has the potential to guide lead chemistry modifications as well as binding residues predictions.     

New fragment weighting scheme for the Bayesian inference network in ligand-based virtual screening

Many of the conventional similarity methods assume that molecular fragments that do not relate to biological activity carry the same weight as the important ones. One possible approach to this problem is to use the Bayesian inference network (BIN), which models molecules and reference structures as probabilistic inference networks. The relationships between molecules and reference structures in the Bayesian network are encoded using a set of conditional probability distributions, which can be estimated by the fragment weighting function, a function of the frequencies of the fragments in the molecule or the reference structure as well as throughout the collection. The weighting function combines one or more fragment weighting schemes. In this paper, we have investigated five different weighting functions and present a new fragment weighting scheme. Later on, these functions were modified to combine the new weighting scheme. Simulated virtual screening experiments with the MDL Drug Data Report (23) and maximum unbiased validation data sets show that the use of new weighting scheme can provide significantly more effective screening when compared with the use of current weighting schemes.     

The fragment molecular orbital and systematic molecular fragmentation methods applied to water clusters

Two electronic structure methods, the fragment molecular orbital (FMO) and systematic molecular fragmentation (SMF) methods, that are based on fragmenting a large molecular system into smaller, more computationally tractable components (fragments), are presented and compared with fully ab initio results for the predicted binding energies of water clusters. It is demonstrated that, even when explicit three-body effects are included (especially necessary for water clusters due to their complex hydrogen-bonded networks) both methods present viable, computationally efficient alternatives to fully ab initio quantum chemistry.     

Multiple ligand docking by Glide: implications for virtual second-site screening

Performance of Glide was evaluated in a sequential multiple ligand docking paradigm predicting the binding modes of 129 protein-ligand complexes crystallized with clusters of 2-6 cooperative ligands. Three sampling protocols (single precision-SP, extra precision-XP, and SP without scaling ligand atom radii-SP hard) combined with three different scoring functions (GlideScore, Emodel and Glide Energy) were tested. The effects of ligand number, docking order and druglikeness of ligands and closeness of the binding site were investigated. On average 36?% of all structures were reproduced with RMSDs lower than 2??. Correctly docked structures reached 50?% when docking druglike ligands into closed binding sites by the SP hard protocol. Cooperative binding to metabolic and transport proteins can dramatically alter pharmacokinetic parameters of drugs. Analyzing the cytochrome P450 subset the SP hard protocol with Emodel ranking reproduced two-thirds of the structures well. Multiple ligand binding is also exploited by the fragment linking approach in lead discovery settings. The HSP90 subset from real life fragment optimization programs revealed that Glide is able to reproduce the positions of multiple bound fragments if conserved water molecules are considered. These case studies assess the utility of Glide in sequential multiple docking applications.     

The atom assignment problem in automated de novo drug design. 2. A method for molecular graph and fragment perception

Summary If atom assignment onto 3D molecular graphs is to be optimized, an efficient scheme for placement must be developed. The strategy adopted in this paper is to analyze the molecular graphs in terms of cyclical and non-cyclical nodes; the latter are further divided into terminal and non-terminal nodes. Molecular fragments, from a fragments database, are described in a similar way. A canonical numbering scheme for the fragments and the local subgraph of the molecular graph enables fragments to be placed efficiently onto the molecular graph. Further optimization is achieved by placing similar fragments into bins using a hashing scheme based on the canonical numbering. The graph perception algorithm is illustrated in detail.