Representation of the molecular topology of cyclical structures by means of cycle graphs. 2. Application to clustering of chemical databases

The great size of chemical databases and the high computational cost required in the atom-atom comparison of molecular structures for the calculation of the similarity between two chemical compounds necessitate the proposal of new clustering models with the aim of reducing the time of recovery of a set of molecules from a database that satisfies a range of similarities with regard to a given molecule pattern. In this paper we make use of the information corresponding to the cycles existing in the structure of molecules as an approach for the classification of chemical databases. The clustering method here proposed is based on the representation of the topological structure of molecules stored in chemical databases through its corresponding cycle graph. This method presents a more appropriate behavior for others described in the bibliography in which the information corresponding to the cyclicity of the molecules is also used.     

From Wiener index to molecules

In this paper we present an algorithm for the generation of molecular graphs with a given value of the Wiener index. The high number of graphs for a given value of the Wiener index is reduced thanks to the application of a set of heuristics taking into account the structural characteristics of the molecules. The selection of parameters as the interval of values for the Wiener index, the diversity and occurrence of atoms and bonds, the size and number of cycles, and the presence of structural patterns guide the processing of the heuristics generating molecular graphs with a considerable saving in computational cost. The modularity in the design of the algorithm allows it to be used as a pattern for the development of other algorithms based on different topological invariants, which allow for its use in areas of interest, say as involving combinatorial databases and screening in chemical databases.     

Clustering chemical databases using adaptable projection cells and MCS similarity values

In this paper we propose a new method based on measurements of the structural similarity for the clustering of chemical databases. The proposed method allows the dynamic adjustment of the size and number of cells or clusters in which the database is classified. Classification is carried out using measurements of structural similarity obtained from the matching of molecular graphs. The classification process is open to the use of different similarity indexes and different measurements of matching. This process consists of the projection of the obtained measures of similarity among the elements of the database in a new space of similarity. The possibility of the dynamic readjustment of the dimension and characteristic of the projection space to adapt to the most favorable conditions of the problem under study and the simplicity and computational efficiency make the proposed method appropriate for its use with medium and large databases. The clustering method increases the performance of the screening processes in chemical databases, facilitating the recovery of chemical compounds that share all or subsets of common substructures to a given pattern. For the realization of the work a database of 498 natural compounds with wide molecular diversity extracted from SPECS and BIOSPECS B.V. free database has been used.     

Algorithm for naming molecular equivalence classes represented by labeled pseudographs

The emergence of large chemical databases imposes a need for organizing the compounds in these databases. Mapping the chemical graph in particular, and a molecular equivalence class represented by a labeled pseudograph in general, to a unique number or string facilitates high-throughput browsing, grouping, and searching of the chemical database. Computing this number using a naming adaptation of the Morgan algorithm, we observed a large classification noise in which nonisomorphic graphs were mapped to the same number. Our extensions to that algorithm greatly reduced the classification noise.     

The scaffold tree--visualization of the scaffold universe by hierarchical scaffold classification

A hierarchical classification of chemical scaffolds (molecular framework, which is obtained by pruning all terminal side chains) has been introduced. The molecular frameworks form the leaf nodes in the hierarchy trees. By an iterative removal of rings, scaffolds forming the higher levels in the hierarchy tree are obtained. Prioritization rules ensure that less characteristic, peripheral rings are removed first. All scaffolds in the hierarchy tree are well-defined chemical entities making the classification chemically intuitive. The classification is deterministic, data-set-independent, and scales linearly with the number of compounds included in the data set. The application of the classification is demonstrated on two data sets extracted from the PubChem database, namely, pyruvate kinase binders and a collection of pesticides. The examples shown demonstrate that the classification procedure handles robustly synthetic structures and natural products.     

Scaffold topologies. 1. Exhaustive enumeration up to eight rings

Mapping the chemical space of small organic molecules is approached from a theoretical graph theory viewpoint, in an effort to begin the systematic exploration of molecular topologies. We present an algorithm for exhaustive generation of scaffold topologies with up to eight rings and an efficient comparison method for graphs within this class. This method uses the return index, a topological invariant derived from the adjacency matrix of the graph. Furthermore, we describe an algorithm that verifies the adequacy of the comparison method. Applications of this method for chemical space exploration in the context of drug discovery are discussed. The key result is a unique characterization of scaffold topologies, which may lead to more efficient ways to query large chemical databases.     

On the classification of polyhexes

An improved classification of polyhexes, a family of important chemical graphs, is proposed. This classification follows the hierarchy of criteria related to the graph-theoretical properties of polyhexes.The final version of this work was prepared whilst the author was in an air-raid shelter when the old part of air-raid defenceless Zagreb, the capital of Croatia, was bombed by Serbian fascists.     

Scaffold topologies. 2. Analysis of chemical databases

We have systematically enumerated graph representations of scaffold topologies for up to eight-ring molecules and four-valence atoms, thus providing coverage of the lower portion of the chemical space of small molecules (Pollock et al. J. Chem. Inf. Model., this issue). Here, we examine scaffold topology distributions for several databases: ChemNavigator and PubChem for commercially available chemicals, the Dictionary of Natural Products, a set of 2742 launched drugs, WOMBAT, a database of medicinal chemistry compounds, and two subsets of PubChem, "actives" and DSSTox comprising toxic substances. We also examined a virtual database of exhaustively enumerated small organic molecules, GDB (Fink et al. Angew. Chem., Int. Ed. 2005, 44, 1504-1508), and we contrast the scaffold topology distribution from these collections to the complete coverage of up to eight-ring molecules. For reasons related, perhaps, to synthetic accessibility and complexity, scaffolds exhibiting six rings or more are poorly represented. Among all collections examined, PubChem has the greatest scaffold topological diversity, whereas GDB is the most limited. More than 50% of all entries (13 000 000+ actual and 13 000 000+ virtual compounds) exhibit only eight distinct topologies, one of which is the nonscaffold topology that represents all treelike structures. However, most of the topologies are represented by a single or very small number of examples. Within topologies, we found that three-way scaffold connections (3-nodes) are much more frequent compared to four-way (4-node) connections. Fused rings have a slightly higher frequency in biologically oriented databases. Scaffold topologies can be the first step toward an efficient coarse-grained classification scheme of the molecules found in chemical databases.     

Quantum probability ranking principle for ligand-based virtual screening

Chemical libraries contain thousands of compounds that need screening, which increases the need for computational methods that can rank or prioritize compounds. The tools of virtual screening are widely exploited to enhance the cost effectiveness of lead drug discovery programs by ranking chemical compounds databases in decreasing probability of biological activity based upon probability ranking principle (PRP). In this paper, we developed a novel ranking approach for molecular compounds inspired by quantum mechanics, called quantum probability ranking principle (QPRP). The QPRP ranking criteria would make an attempt to draw an analogy between the physical experiment and molecular structure ranking process for 2D fingerprints in ligand based virtual screening (LBVS). The development of QPRP criteria in LBVS has employed the concepts of quantum at three different levels, firstly at representation level, this model makes an effort to develop a new framework of molecular representation by connecting the molecular compounds with mathematical quantum space. Secondly, estimate the similarity between chemical libraries and references based on quantum-based similarity searching method. Finally, rank the molecules using QPRP approach. Simulated virtual screening experiments with MDL drug data report (MDDR) data sets showed that QPRP outperformed the classical ranking principle (PRP) for molecular chemical compounds.     

In silico strategies for the selection of chelating compounds with potential application in metal-promoted neurodegenerative diseases

The development of new strategies to find commercial molecules with promising biochemical features is a main target in the field of biomedicine chemistry. In this work we present an in silico-based protocol that allows identifying commercial compounds with suitable metal coordinating and pharmacokinetic properties to act as metal-ion chelators in metal-promoted neurodegenerative diseases (MpND). Selection of the chelating ligands is done by combining quantum chemical calculations with the search of commercial compounds on different databases via virtual screening. Starting from different designed molecular frameworks, which mainly constitute the binding site, the virtual screening on databases facilitates the identification of different commercial molecules that enclose such scaffolds and, by imposing a set of chemical and pharmacokinetic filters, obey some drug-like requirements mandatory to deal with MpND. The quantum mechanical calculations are useful to gauge the chelating properties of the selected candidate molecules by determining the structure of metal complexes and evaluating their stability constants. With the proposed strategy, commercial compounds containing N and S donor atoms in the binding sites and capable to cross the BBB have been identified and their chelating properties analyzed.     

Application of the electronegativity indices of organic molecules to tasks of chemical informatics

An efficient structure filtration method for the operation with chemical databases containing information on the structures and properties of organic molecules was proposed. The technique involves the use of electronegativity indices for generation of identification keys and for isomorphism tests of the molecular graphs corresponding to the structural formulas. The test set for the method proposed included a total of 95,000,000 molecules containing up to sixty carbon atoms. Tests revealed a high discriminating capability of the electronegativity indices and high efficiency of the method for solving both general problems (recognition of chemical structures, chemical database management systems) and specific tasks (generation of molecular graphs, etc.) in chemical informatics. Dedicated to Academician N. S. Zefirov on the occasion of his 70th birthday. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 2166–2176, September, 2005.     

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.     

Graph theoretical classification and coding of chemical reactions with a linear mechanism

Linear mechanisms of catalytic and noncatalytic chemical reactions which are theoretically feasible have been classified and coded using a detailed procedure for the unique numbering of cycles, edges, and vertices in the kinetic graphs. The following classification criteria are used in a hierarchical order: number of cycles and vertices, mutual connectivity of the cycles, manner of linking any pair of cycles, number of elements linking two cycles, mutual position of two cycles joined to a third one, orientation of edges, and presence of pendant vertices. All the types and classes of mechanisms are presented for reactions having up to five and four routes, respectively.     

Effectiveness of graph-based and fingerprint-based similarity measures for virtual screening of 2D chemical structure databases

This paper reports an evaluation of both graph-based and fingerprint-based measures of structural similarity, when used for virtual screening of sets of 2D molecules drawn from the MDDR and ID Alert databases. The graph-based measures employ a new maximum common edge subgraph isomorphism algorithm, called RASCAL, with several similarity coefficients described previously for quantifying the similarity between pairs of graphs. The effectiveness of these graph-based searches is compared with that resulting from similarity searches using BCI, Daylight and Unity 2D fingerprints. Our results suggest that graph-based approaches provide an effective complement to existing fingerprint-based approaches to virtual screening.