Current Computer - Aided Drug Design - Volume 9, Issue 2, 2013

Chemical and molecular graphs have fundamental applications in chemoinformatics, quantitative structureproperty relationships (QSPR), quantitative structure-activity relationships (QSAR), virtual screening of chemical libraries, and computational drug design. Chemoinformatics applications of graphs include chemical structure representation and coding, database search and retrieval, and physicochemical property prediction. QSPR, QSAR and virtual screening are based on the structure-property principle, which states that the physicochemical and biological properties of chemical compounds can be predicted from their chemical structure. Such structure-property correlations are usually developed from topological indices and fingerprints computed from the molecular graph and from molecular descriptors computed from the three-dimensional chemical structure. We present here a selection of the most important graph descriptors and topological indices, including molecular matrices, graph spectra, spectral moments, graph polynomials, and vertex topological indices. These graph descriptors are used to define several topological indices based on molecular connectivity, graph distance, reciprocal distance, distance-degree, distance-valency, spectra, polynomials, and information theory concepts. The molecular descriptors and topological indices can be developed with a more general approach, based on molecular graph operators, which define a family of graph indices related by a common formula. Graph descriptors and topological indices for molecules containing heteroatoms and multiple bonds are computed with weighting schemes based on atomic properties, such as the atomic number, covalent radius, or electronegativity. The correlation in QSPR and QSAR models can be improved by optimizing some parameters in the formula of topological indices, as demonstrated for structural descriptors based on atomic connectivity and graph distance.

A new mathematical approach is proposed in the definition of molecular descriptors (MDs) based on the application of information theory concepts. This approach stems from a new matrix representation of a molecular graph (G) which is derived from the generalization of an incidence matrix whose row entries correspond to connected subgraphs of a given G, and the calculation of the Shannon’s entropy, the negentropy and the standardized information content, plus for the first time, the mutual, conditional and joint entropy-based MDs associated with G. We also define strategies that generalize the definition of global or local invariants from atomic contributions (local vertex invariants, LOVIs), introducing related metrics (norms), means and statistical invariants. These invariants are applied to a vector whose components express the atomic information content calculated using the Shannon’s, mutual, conditional and joint entropybased atomic information indices. The novel information indices (IFIs) are implemented in the program TOMOCOMDCARDD. A principal component analysis reveals that the novel IFIs are capable of capturing structural information not codified by IFIs implemented in the software DRAGON. A comparative study of the different parameters (e.g. subgraph orders and/or types, invariants and class of MDs) used in the definition of these IFIs reveals several interesting results. The mutual entropy-based indices give the best correlation results in modeling of a physicochemical property, namely the partition coefficient of the 34 derivatives of 2-furylethylenes, among the classes of indices investigated in this study. In a comparison with classical MDs it is demonstrated that the new IFIs give good results for various QSPR models.

This review discusses structure-property modeling applications of a novel variant of the Randic connectivity index that is called the sum-connectivity index. We compare published one-descriptor quantitative structure-property relationship (QSPR) models obtained with the new sum-connectivity index and with the Randic connectivity index, called here the product-connectivity index. Additionally, the efficiency of both variants of connectivity indices in QSPR modeling is tested on five datasets of alkanes and two datasets of polycyclic hydrocarbons. Several physicochemical properties of alkanes (i.e. boiling and melting points, retention index, molar volume, molar refraction, heat of vaporization, standard Gibbs energy of formation, critical temperature, critical pressure, surface tension, density) and π- electronic energies of two sets of polycyclic hydrocarbons were correlated with the product- and sum-connectivity indices. A comparison of these QSPR models shows that both variants of connectivity indices are equivalent, and only slightly (but not significantly) better results are obtained with the sum-connectivity index. Inter-correlations between the product- and sum-connectivity indices are mostly linear with a slope very close to 1.0 for alkanes, and with a slope more different from 1.0 (0.88) for polycyclic compounds. The comparative analysis presented here supports the use of the sumconnectivity index in QSPR/QSAR studies together with the product-connectivity index. Further studies on larger and more heterogeneous datasets should test the sum-connectivity index in QSPR/QSAR models.

The aim of the present paper is to present the methodology of the molecular descriptors family (MDF) as an integrative tool in molecular modeling and its abilities as a multivariate QSAR/QSPR modeling tool. An algorithm for extracting useful information from the topological and geometrical representation of chemical compounds was developed and integrated to calculate MDF members. The MDF methodology was implemented and the software is available online (http://l.academicdirect.org/Chemistry/SARs/MDF_SARs/). This integrative tool was developed in order to maximize performance, functionality, efficiency and portability. The MDF methodology is able to provide reliable and valid multiple linear regression models. Furthermore, in many cases, the MDF models were better than the published results in the literature in terms of correlation coefficients (statistically significant Steiger’s Z test at a significance level of 5%) and/or in terms of values of information criteria and Kubinyi function. The MDF methodology developed and implemented as a platform for investigating and characterizing quantitative relationships between the chemical structure and the activity/property of active compounds was used on more than 50 study cases. In almost all cases, the methodology allowed obtaining of QSAR/QSPR models improved in explanatory power of structure-activity and structure-property relationships. The algorithms applied in the computation of geometric and topological descriptors (useful in modeling physicochemical or biological properties of molecules) and those used in searching for reliable and valid multiple linear regression models certain enrich the pool of low-cost low-time drug design tools.

The successful high throughput screening of molecule libraries for a specific biological property is one of the main improvements in drug discovery. The virtual molecular filtering and screening relies greatly on quantitative structure-activity relationship (QSAR) analysis, a mathematical model that correlates the activity of a molecule with molecular descriptors. QSAR models have the potential to reduce the costly failure of drug candidates in advanced (clinical) stages by filtering combinatorial libraries, eliminating candidates with a predicted toxic effect and poor pharmacokinetic profiles, and reducing the number of experiments. To obtain a predictive and reliable QSAR model, scientists use methods from various fields such as molecular modeling, pattern recognition, machine learning or artificial intelligence. QSAR modeling relies on three main steps: molecular structure codification into molecular descriptors, selection of relevant variables in the context of the analyzed activity, and search of the optimal mathematical model that correlates the molecular descriptors with a specific activity. Since a variety of techniques from statistics and artificial intelligence can aid variable selection and model building steps, this review focuses on the evolutionary computation methods supporting these tasks. Thus, this review explains the basic of the genetic algorithms and genetic programming as evolutionary computation approaches, the selection methods for high-dimensional data in QSAR, the methods to build QSAR models, the current evolutionary feature selection methods and applications in QSAR and the future trend on the joint or multi-task feature selection methods.

The aim of this review is description of the logic and evolution of optimal descriptors OCWLGI calculated with the molecular graph and the demonstration of their ability as tools for the modeling of biological and physicochemical parameters of chemical compounds. The ability of optimal descriptors calculated with hydrogen suppressed graph (HSG), hydrogen filled graph (HFG) and graph of atomic orbitals (GAO) is demonstrated as a collection of quantitative structure-property relationships (QSPR) and quantitative structure-activity relationships (QSAR) for properties and endpoints available from the literature. The Monte Carlo method optimization of the correlation weights of local and global invariants (OCWLGI) of molecular graphs is used as the principle for building up descriptors which are discussed in this article. The statistical quality of the QSPR and QSAR models for physicochemical and biological properties which were obtained with the optimal descriptors are reasonably high.

Usual quantitative structure-activity relationship (QSAR) models are computed from unstructured input data, by using a vector of molecular descriptors for each chemical in the dataset. Another alternative is to consider the structural relationships between the chemical structures, such as molecular similarity, presence of certain substructures, or chemical transformations between compounds. We defined a class of network-QSAR models based on molecular networks induced by a sequence of substitution reactions on a chemical structure that generates a partially ordered set (or poset) oriented graph that may be used to predict various molecular properties with quantitative superstructure-activity relationships (QSSAR). The network-QSAR interpolation models defined on poset graphs, namely average poset, cluster expansion, and spline poset, were tested with success for the prediction of several physicochemical properties for diverse chemicals. We introduce the flow network QSAR, a new poset regression model in which the dataset of chemicals, represented as a reaction poset, is transformed into an oriented network of electrical resistances in which the current flow results in a potential at each node. The molecular property considered in the QSSAR model is represented as the electrical potential, and the value of this potential at a particular node is determined by the electrical resistances assigned to each edge and by a system of batteries. Each node with a known value for the molecular property is attached to a battery that sets the potential on that node to the value of the respective molecular property, and no external battery is attached to nodes from the prediction set, representing chemicals for which the values of the molecular property are not known or are intended to be predicted. The flow network QSAR algorithm determines the values of the molecular property for the prediction set of molecules by applying Ohm’s law and Kirchhoff's current law to the poset network of electrical resistances. Several applications of the flow network QSAR are demonstrated.

In this review we present algorithms for classification and taxonomy based on information entropy, followed by structure-activity relationship (SAR) models for the inhibition of human prostate carcinoma cell line DU-145 by 26 derivatives of N-aryl-N-(3-aryl-1,2,4-oxadiazol-5-yl)amines (NNAs). The NNAs are classified using two characteristic chemical properties based on different regions of the molecules. A table of periodic properties of inhibitors of DU-145 human prostate carcinoma cell line is obtained based on structural features from the amine moiety and from the oxadiazole ring. Inhibitors in the same group and period of the periodic table are predicted to have highly similar properties, and those located only in the same group will present moderate similarity. The results of a virtual screening campaign are presented.

In this paper we study and analyze the behavior of different representational spaces for the clustering and building of QSAR models. Representational spaces based on fingerprint similarity, structural similarity using maximum common subgraphs (MCS) and all maximum common subgraphs (AMCS) approaches are compared against representational spaces based on structural fragments and non-isomorphic fragments (NIF), built using different molecular descriptors. Algorithms for extraction of MCS, AMCS and NIF are described and support vector machine is used for the classification of a dataset corresponding with 74 compounds of 1,4-benzoquinone derivatives. Molecular descriptors are tested in order to build QSAR models for the prediction of the antifungal activity of the dataset. Descriptors based on the consideration of graph connectivity and distances are the most appropriate for building QSAR models. Moreover, models based on approximate similarity improve the statistical of the equations thanks to combining structural similarity, nonisomorphic fragments and descriptors approaches for the creation of more robust and finer prediction equations.

We present several procedures to represent molecular electrostatic potential as a graph, based on the pattern of critical points and their neighborhood relations. This representation is used for the molecular electrostatic comparison, which is reduced to a comparison of tree-type graphs. Several methods to compare trees are also presented. The applications of this algorithm to compare and classify molecules through their electrostatic potential are illustrated.

Quinolones constitute a large class of antibacterial agents whose action is mediated through the formation of a ternary complex with DNA and either, DNA Gyrase or topoisomerase IV, resulting in the inhibition of DNA replication. In order to get a deeper insight into the features of the complex formation, we carried out docking studies of fifteen diverse quinolones to the cleaved topoisomerase IV-DNA complex. Docking studies were performed using the crystal structures of the cleaved complex with levofloxacin and moxifloxacin (pdb entries 3K9F and 2XKK, respectively) using the GOLD software. Ligands dock in positions similar to those of the crystal structures. Analysis of the results reveals that bound quinolones appear intercalated between the two nucleotides that are involved in the DNA cleavage and exhibit hydrogen bonds with Arg117 and, the latter mediated though a water molecule. Arg117 has not been described to be involved in resistance, since it is putatively involved in the enzymatic reaction and its mutation would be lethal for the organism. Mutants of Ser79 exhibit resistance to quinolones which can be explained by the loss of an important anchoring point. Interestingly, quinolone resistance observed in Asp83 mutants cannot be explained directly on the basis of the loss of a direct interaction, but could be explained on the basis of its involvement at the entrance of the ligands to their binding pocket since the residue is located at the mouth of the pocket. The results of the present study suggest that the 4-keto and 3-carboxyl groups of the fluoroquinolones bind a Mg2+ before binding to the cleaved topoisomarase IV-DNA complex and use Asp83 for entry into the binding pocket. Accordingly, mutations that do not conserve the binding capacity for the quinolone-Mg2+ complex will prevent the binding of this class of ligands. The results we present here are also compared with the structure of PD0305970 a 2,4-dione active against the Ser79 and Asp83 mutants.

Recent studies have demonstrated several biological activities of curcumin with therapeutic potential against Alzheimer’s disease, among them the inhibition of the enzyme acetylcholinesterase (AChE). Aiming at identifying the chemical features relevant for this activity, the inhibition of curcumin and a set of 7 derivatives against AChE of E. electricus was measured. These derivatives presented lower activity than curcumin, allowing for the identification of possible unfavorable enzyme-inhibitor interactions. Our computational approach was to dock the molecules to the active site of AChE, followed by an analysis of hydrogen bonds and close contacts to relevant aromatic amino acid residues. To account for inhibitory activity, we sought to define the common structural features between known acetylcholinesterase inhibitors and the tested derivatives. A pharmacophore model was generated, which consisted of two hydrophobic, one aromatic and one hydrogen bond acceptor features. We conclude that the presence of two aromatic rings and the distance between them, allows curcumin and its derivatives to favorably interact with both the quaternary and peripheral sites of AChE. Hydrogen bonds can be formed with the quaternary and acyl sites, which should further stabilize the complex. The acylation of the hydroxyl groups and the reduction of the conjugated double bonds lowered the inhibitory activity, pointing to the modification of the keto-enol moiety as the best alternative for the design of more potent curcumin derivatives as acetylcholinesterase inhibitors.