Scaffold hopping using clique detection applied to reduced graphs

Similarity-based methods for virtual screening are widely used. However, conventional searching using 2D chemical fingerprints or 2D graphs may retrieve only compounds which are structurally very similar to the original target molecule. Of particular current interest then is scaffold hopping, that is, the ability to identify molecules that belong to different chemical series but which could form the same interactions with a receptor. Reduced graphs provide summary representations of chemical structures and, therefore, offer the potential to retrieve compounds that are similar in terms of their gross features rather than at the atom-bond level. Using only a fingerprint representation of such graphs, we have previously shown that actives retrieved were more diverse than those found using Daylight fingerprints. Maximum common substructures give an intuitively reasonable view of the similarity between two molecules. However, their calculation using graph-matching techniques is too time-consuming for use in practical similarity searching in larger data sets. In this work, we exploit the low cardinality of the reduced graph in graph-based similarity searching. We reinterpret the reduced graph as a fully connected graph using the bond-distance information of the original graph. We describe searches, using both the maximum common induced subgraph and maximum common edge subgraph formulations, on the fully connected reduced graphs and compare the results with those obtained using both conventional chemical and reduced graph fingerprints. We show that graph matching using fully connected reduced graphs is an effective retrieval method and that the actives retrieved are likely to be topologically different from those retrieved using conventional 2D methods.     

Pharmacophore alignment search tool: influence of the third dimension on text-based similarity searching

Previously (Hähnke et al., J Comput Chem 2010, 31, 2810) we introduced the concept of nonlinear dimensionality reduction for canonization of two‐dimensional layouts of molecular graphs as foundation for text‐based similarity searching using our Pharmacophore Alignment Search Tool (PhAST), a ligand‐based virtual screening method. Here we apply these methods to three‐dimensional molecular conformations and investigate the impact of these additional degrees of freedom on virtual screening performance and assess differences in ranking behavior. Best‐performing variants of PhAST are compared with 16 state‐of‐the‐art screening methods with respect to significance estimates for differences in screening performance. We show that PhAST sorts new chemotypes on early ranks without sacrificing overall screening performance. We succeeded in combining PhAST with other virtual screening techniques by rank‐based data fusion, significantly improving screening capabilities. We also present a parameterization of double dynamic programming for the problem of small molecule comparison, which allows for the calculation of structural similarity between compounds based on one‐dimensional representations, opening the door to a holistic approach to molecule comparison based on textual representations. © 2011 Wiley Periodicals, Inc. J Comput Chem , 2011.     

Heuristics for similarity searching of chemical graphs using a maximum common edge subgraph algorithm

Recently a method (RASCAL) for determining graph similarity using a maximum common edge subgraph algorithm has been proposed which has proven to be very efficient when used to calculate the relative similarity of chemical structures represented as graphs. This paper describes heuristics which simplify a RASCAL similarity calculation by taking advantage of certain properties specific to chemical graph representations of molecular structure. These heuristics are shown experimentally to increase the efficiency of the algorithm, especially at more distant values of chemical graph similarity.     

SPOT‐Ligand: Fast and effective structure‐based virtual screening by binding homology search according to ligand and receptor similarity

Structure‐based virtual screening usually involves docking of a library of chemical compounds onto the functional pocket of the target receptor so as to discover novel classes of ligands. However, the overall success rate remains low and screening a large library is computationally intensive. An alternative to this “ab initio” approach is virtual screening by binding homology search. In this approach, potential ligands are predicted based on similar interaction pairs (similarity in receptors and ligands). SPOT‐Ligand is an approach that integrates ligand similarity by Tanimoto coefficient and receptor similarity by protein structure alignment program SPalign. The method was found to yield a consistent performance in DUD and DUD‐E docking benchmarks even if model structures were employed. It improves over docking methods (DOCK6 and AUTODOCK Vina) and has a performance comparable to or better than other binding‐homology methods (FINDsite and PoLi) with higher computational efficiency. The server is available at http://sparks-lab.org . © 2016 Wiley Periodicals, Inc.     

A knowledge-based weighting approach to ligand-based virtual screening

On the basis of the recently introduced reduced graph concept of ErG (extending reduced graphs), a straightforward weighting approach to include additional (e.g., structural or SAR) knowledge into similarity searching procedures for virtual screening (wErG) is proposed. This simple procedure is exemplified with three data sets, for which interaction patterns available from X-ray structures of native or peptidomimetic ligands with their target protein are used to significantly improve retrieval rates of known actives from the MDL Drug Report database. The results are compared to those of other virtual screening techniques such as Daylight fingerprints, FTrees, UNITY, and various FlexX docking protocols. Here, it is shown that wErG exhibits a very good and stable performance independent of the target structure. On the basis of this (and the fact that ErG retrieves structurally more dissimilar compounds due to its potential to perform scaffold-hopping), the combination of wErG and FlexX is successfully explored. Overall, wErG is not only an easily applicable weighting procedure that efficiently identifies actives in large data sets but it is also straightforward to understand for both medicinal and computational chemists and can, therefore, be driven by several aspects of project-related knowledge (e.g., X-ray, NMR, SAR, and site-directed mutagenesis) in a very early stage of the hit identification process.     

Localization of molecular orbitals on fragments

A non‐iterative algorithm for the localization of molecular orbitals (MOs) from complete active space self consistent field (CASSCF) and for single‐determinantal wave functions on predefined moieties is given. The localized fragment orbitals can be used to analyze chemical reactions between fragments and also the binding of fragments in the product molecule with a fragments‐in‐molecules approach by using a valence bond expansion of the CASSCF wave function. The algorithm is an example of the orthogonal Procrustes problem, which is a matrix optimization problem using the singular value decomposition. It is based on the similarity of the set of MOs for the moieties to the localized MOs of the molecule; the similarity is expressed by overlap matrices between the original fragment MOs and the localized MOs. For CASSCF wave functions, localization is done independently in the space of occupied orbitals and active orbitals, whereas, the space of virtual orbitals is mostly uninteresting. Localization of Hartree–Fock or Kohn–Sham density functional theory orbitals is not straightforward; rather, it needs careful consideration, because in this case some virtual orbitals are needed but the space of virtual orbitals depends on the basis sets used and causes considerable problems due to the diffuse character of most virtual orbitals. © 2012 Wiley Periodicals, Inc.     

Further development of reduced graphs for identifying bioactive compounds

Reduced graphs provide summary representations of chemical structures. Here, a variety of different types of reduced graphs are compared in similarity searches. The reduced graphs are found to give comparable performance to Daylight fingerprints in terms of the number of active compounds retrieved. However, no one type of reduced graph is found to be consistently superior across a variety of different data sets. Consequently, a representative set of reduced graphs was chosen and used together with Daylight fingerprints in data fusion experiments. The results show improved performance in 10 out of 11 data sets compared to using Daylight fingerprints alone. Finally, the potential of using reduced graphs to build SAR models is demonstrated using recursive partitioning. An SAR model consistent with a published model is found following just two splits in the decision tree.     

Domain‐Averaged Exchange‐Correlation Energies as a Physical Underpinning for Chemical Graphs

A novel solution to the problem of assigning a molecular graph to a collection of nuclei (i.e. how to draw a molecular structure) is presented. Molecules are universally understood as a set of nuclei linked by bonds, but establishing which nuclei are bonded and which are not is still an empirical matter. Our approach borrows techniques from quantum chemical topology, which showed for the first time the construction of chemical graphs from wave functions, shifting the focus on energetics. This new focus resolves issues surrounding previous topological analyses, in which domain‐averaged exchange‐correlation energies (V_xc), quantities defined in real space between each possible atom pair, hold the key. Exponential decay of V_xc in non‐metallic systems as the intercenter distance increases guarantees a well‐defined hierarchy for all possible V_xc values in a molecule. Herein, we show that extracting the set of atom pairs that display the largest V_xc values in the hierarchy is equivalent to retrieving the molecular graph itself. Notably, domain‐averaged exchange‐correlation energies are transferable, and they can be used to calculate bond strengths. Fine‐grained details resulted to be related to simple stereoelectronic effects. These ideas are demonstrated in a set of simple pilot molecules.     

Critical point representations of electron density maps for the comparison of benzodiazepine-type ligands

A procedure for the comparison of three-dimensional electron density distributions is proposed for similarity searches between pharmacological ligands at various levels of crystallographic resolution. First, a graph representation of molecular electron density distributions is generated using a critical point analysis approach. Pairwise as well as multiple comparisons between the obtained graphs of critical points are then carried out using a Monte Carlo/simulated annealing technique, and results are compared with genetic algorithm solutions.     

Targeting programmed cell death 4 (PDCD4) with biogenic compounds in ARDS by Gaussian process‐based QSAR virtual screening

The programmed cell death 4 (PDCD4) has recently been recognized as a new and attractive target of acute respiratory distress syndrome. Here, we attempted to discover new and potent PDCD4 mediator ligands from biogenic compounds using a synthetic strategy of statistical virtual screening and experimental affinity assay. In the procedure, a Gaussian process‐based quantitative structure‐activity relationship regression predictor was developed and validated statistically based on a curated panel of structure‐based protein‐ligand affinity data. The predictor was integrated with pharmacokinetics analysis, chemical redundancy reduction, and flexible molecular docking to perform high‐throughput virtual screening against a distinct library of chemically diverse, drug‐like biogenic compounds. Consequently, 6 hits with top scores were selected, and their binding affinities to the recumbent protein of human PDCD4 were identified, 3 out of which were determined to have high or moderate affinity with K_d at micromolar level. Structural analysis of protein‐ligand complexes revealed that hydrophobic interactions and van der Waals contacts are the primary chemical forces to stabilize the complex architecture of PDCD4 with these mediator ligands, while few hydrogen bonds, salt bridges, and/or π‐π stacking at the complex interfaces confer selectivity and specificity for the protein‐ligand recognition. It is suggested that the statistical Gaussian process‐based quantitative structure‐activity relationship screening strategy can be successfully applied to rational discovery of biologically active compounds. The newly identified molecular entities targeting PDCD4 are considered as promising lead scaffolds to develop novel chemical therapeutics for acute respiratory distress syndrome.     

Stalis: A Computational Method for Template-Based Ab Initio Ligand Design

Proteins interact with small molecules through specific molecular recognition, which is central to essential biological functions in living systems. Therefore, understanding such interactions is crucial for basic sciences and drug discovery. Here, we present S tructure t emplate-based a b initio li gand design s olution (Stalis), a knowledge-based approach that uses structure templates from the Protein Data Bank libraries of whole ligands and their fragments and generates a set of molecules (virtual ligands) whose structures represent the pocket shape and chemical features of a given target binding site. Our benchmark performance evaluation shows that ligand structure-based virtual screening using virtual ligands from Stalis outperforms a receptor structure-based virtual screening using AutoDock Vina, demonstrating reliable overall screening performance applicable to computational high-throughput screening. However, virtual ligands from Stalis are worse in recognizing active compounds at the small fraction of a rank-ordered list of screened library compounds than crystal ligands, due to the low resolution of the virtual ligand structures. In conclusion, Stalis can facilitate drug discovery research by designing virtual ligands that can be used for fast ligand structure-based virtual screening. Moreover, Stalis provides actual three-dimensional ligand structures that likely bind to a target protein, enabling to gain structural insight into potential ligands. Stalis can be an efficient computational platform for high-throughput ligand design for fundamental biological study and drug discovery research at the proteomic level. © 2019 Wiley Periodicals, Inc.     

Rapid determination of RMSDs corresponding to macromolecular rigid body motions

Finding the root mean sum of squared deviations (RMSDs) between two coordinate vectors that correspond to the rigid body motion of a macromolecule is an important problem in structural bioinformatics, computational chemistry, and molecular modeling. Standard algorithms compute the RMSD with time proportional to the number of atoms in the molecule. Here, we present RigidRMSD, a new algorithm that determines a set of RMSDs corresponding to a set of rigid body motions of a macromolecule in constant time with respect to the number of atoms in the molecule. Our algorithm is particularly useful for rigid body modeling applications, such as rigid body docking, and also for high‐throughput analysis of rigid body modeling and simulation results. We also introduce a constant‐time rotation RMSD as a similarity measure for rigid molecules. A C++ implementation of our algorithm is available at http://nano‐d.inrialpes.fr/software/RigidRMSD . © 2014 Wiley Periodicals, Inc.     

Optimization of TRPV6 Calcium Channel Inhibitors Using a 3D Ligand‐Based Virtual Screening Method

Herein, we report the discovery of the first potent and selective inhibitor of TRPV6, a calcium channel overexpressed in breast and prostate cancer, and its use to test the effect of blocking TRPV6‐mediated Ca²⁺‐influx on cell growth. The inhibitor was discovered through a computational method, xLOS, a 3D‐shape and pharmacophore similarity algorithm, a type of ligand‐based virtual screening (LBVS) method described briefly here. Starting with a single weakly active seed molecule, two successive rounds of LBVS followed by optimization by chemical synthesis led to a selective molecule with 0.3 μM inhibition of TRPV6. The ability of xLOS to identify different scaffolds early in LBVS was essential to success. The xLOS method may be generally useful to develop tool compounds for poorly characterized targets.     

Molecular graphs as topological objects in space

Stereochemistry deals primarily with distinctions based on rigid geometry, e.g., bond angles and lengths. But some chemical species have molecular graphs (such as knots, catenanes, and nonplanar graphs K₅ and K_3.3) that reside in space in a topologically nontrivial way. For such molecules there is hope of using topological methods to gain chemical information. Viewing a molecular graph as a topological object in space makes it unrealistically flexible; but if one proves that a certain graph is “topologically chiral” or that two graphs are “topological diastereomers,” then one has ruled out interconversion under any physical conditions for which the molecular graph still makes sense. In this paper, we consider several kinds of topological questions one might ask about graphs in space, methology and results available, and specific topological properties of various molecules.