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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.

Due to their widespread use in bactericides, insecticides, herbicides, andfungicides, chlorophenols represent an important source of soil contaminants. Theenvironmental fate of these chemicals depends on their physico-chemical properties. In theabsence of experimental values for these physico-chemical properties, one can use predictedvalues computed with quantitative structure-property relationships (QSPR). As analternative to correlations to molecular structure we have studied the super-structure of areaction network, thereby developing three new QSSPR models (poset-average, cluster-expansion, and splinoid poset) that can be applied to chemical compounds which can behierarchically ordered into a reaction network. In the present work we illustrate these posetQSSPR models for the correlation of the octanol/water partition coefficient (log Kow) and thesoil sorption coefficient (log KOC) of chlorophenols. Excellent results are obtained for allQSSPR poset models to yield: log Kow, r = 0.991, s = 0.107, with the cluster-expansionQSSPR; and log KOC, r = 0.938, s = 0.259, with the spline QSSPR. Thus, the poset QSSPRmodels predict environmentally important properties of chlorophenols.

During bioconcentration, chemical pollutants from water are absorbed by aquatic animals via the skin or a respiratory surface, while the entry routes of chemicals during bioaccumulation are both directly from the environment (skin or a respiratory surface) and indirectly from food. The bioconcentration factor (BCF) and the bioaccumulation factor (BAF) for a particular chemical compound are defined as the ratio of the concentration of a chemical inside an organism to the concentration in the surrounding environment. Because the experimental determination of BAF and BCF is time-consuming and expensive, it is efficacious to develop models to provide reliable activity predictions for a large number of chemical compounds. Polychlorinated biphenyls (PCBs) released from industrial activities are persistent pollutants of the environment that produce widespread contamination of water and soil. PCBs can bioaccumulate in the food chain, constituting a potential source of exposure for the general population. To predict the bioconcentration and bioaccumulation factors for PCBs we make use of the biphenyl substitution-reaction network for the sequential substitution of H-atoms by Cl-atoms. Each PCB structure then occurs as a node of this reaction network, which is some sort of super-structure, turning out mathematically to be a partially ordered set (poset). Rather than dealing with the molecular structure via ordinary QSAR we use only this poset, making different quantitative super-structure/activity relationships (QSSAR). Thence we developed cluster expansion and splinoid QSSARs for PCB bioconcentration and bioaccumulation factors. The predictive ability of the BAF and BCF models generated for 20 data sets (representing different conditions and fish species) was evaluated with the leave-one-out cross-validation, which shows that the splinoid QSSAR (r between 0.903 and 0.935) are better than models computed with the cluster expansion (r between 0.745 and 0.887). The splinoid QSSAR models for BAF and BCF yield predictions for the missing PCBs in the investigated data sets.

Substitution-reaction networks frequently arise in chemistry and are naturally identifiable as “partially ordered sets” (or posets). The direction of the reaction identifies the partial ordering of the set of the member molecular species, for which various properties may be developed in light of the partial ordering. Here some general characteristics of such posets are noted, and a chemically appealing posetic cluster-expansion analysis of molecular properties is described and illustrated for methyl substitutions on cyclobutane. The results for computed energies and a few further selected properties are compared to alternative posetic approaches.

Molecular graph descriptors are used, together with a large diversity of geometric, electrostatic, and quantum indices, to model physical, chemical, or biological properties with quantitative structure–property relationships and quantitative structure–activity relationships. The interest of developing new graph descriptors for organic compounds was stimulated in recent years by their use in virtual screening of combinatorial libraries, database mining, similarity and diversity assessment. Recently, we have extended topological indices by defining a series of molecular graph operators, providing an effective systematization and generalization of these structural descriptors. A graph operator uses a mathematical equation to compute a family of related molecular graph descriptors with different molecular matrices and various sets of parameters for atoms and bonds. In this paper we use structural descriptors computed with molecular graph operators to develop quantitative structure–activity relationships (QSAR) models for the dihydrofolate reductase inhibition with diaminopyrimidines. The molecular descriptors are derived from five molecular matrices, namely adjacency A , distance D , reciprocal distance RD , distance-path D p , and reciprocal distance-path RD p . The QSAR models are obtained by selecting descriptors with a genetic algorithm, and the best models are validated with the leave-one-out cross-validation method. The QSAR models with the highest prediction power are comparable with those obtained with substituent constants and neural networks, but they use a much lower number of parameters.

Chemical structures of organic compounds are characterized numerically by a variety of structural descriptors, one of the earliest and most widely used being the Wiener index W, derived from the interatomic distances in a molecular graph. Extensive use of distance-based structural descriptors or topological indices has been made in QSPR and QSAR models, drug design, toxicology, virtual screening of combinatorial libraries, similarity and diversity assessment. Novel topological indices are introduced representing a partitioning of the Wiener polynomial based on counts of even and odd molecular graph distances. During the QSAR/QSPR modeling process the variables of the even and odd power functions are optimized in order to offer an improved mapping of the investigated property. These novel topological indices are tested in QSPR models for the boiling temperature, molar heat capacity, standard Gibbs energy of formation, vaporization enthalpy, refractive index, and density of alkanes. In many cases, the even/odd Wiener polynomial indices proposed here give notably improved correlations or suggest simpler QSPR models.

Quantitative structure-retention relationships (QSRR) represent statistical models that quantify the connection between the molecular structure and the chromatographic retention indices of organic compounds, allowing the prediction of retention indices of novel, not yet synthesized compounds, solely from their structural descriptors. Using multiple linear regression, QSRR models for the gas chromatographic Kováts retention indices of 129 alkylbenzenes are generated using molecular graph descriptors. The correlational ability of structural descriptors computed from 10 molecular matrices is investigated, showing that the novel reciprocal matrices give numerical indices with improved correlational ability. A QSRR equation with 5 graph descriptors gives the best calibration and prediction results, demonstrating the usefulness of the molecular graph descriptors in modeling chromatographic retention parameters. The sequential orthogonalization of descriptors suggests simpler QSRR models by eliminating redundant structural information.

Organic compounds containing heteroatoms or multiple bonds can be conveniently represented as vertex- and edge-weighted molecular graphs. These atom and bond parameters can be computed for any organic compound with two parameter sets that we have recently defined, namely, the relative electronegativity X and the relative covalent radius Y weighting schemes. Structural descriptors computed with these two weighting schemes and the previously defined atomic number Z parameter set are used to develop quantitative structure-retention relationship (QSRR) models for alkylphenols in gas-liquid chromatography. The QSRR models are generated with structural descriptors computed with several newly introduced graph operators, namely, the Wiener, hyper-Wiener, minimum eigenvalue, maximum eigenvalue, Ivanciuc-Balaban, and information on distance operators. These molecular graph operators were applied to the distance D and the reciprocal distance RD matrixes.

In the pharmaceutical industry, the virtual screening of combinatorial libraries is used to rationally select compounds for biological testing from databases of hundreds of thousands of compounds. In addition to structural descriptors, such as fingerprints and pharmacophores, the application of relatively simple structural descriptors traditionally used in quantitative structure-activity studies offers speed and efficiency for rapidly measuring the molecular diversity of such collections. We explore new topological indices computed from the molecular graph as potential structural descriptors for the characterization of molecular diversity. A database of 2000 compounds randomly selected from the National Cancer Institute AIDS database was used to measure the intercorrelation of the descriptors. The initial collection of 240 structural descriptors was reduced to several quasi-orthogonal sets of up to 9 descriptors, using different thresholds for the maximum intercorrelation coefficient.

MolNet, a new type of multi-layer feedforward neural network, is presented together with its application to the computation of alkane enthalpies. The MolNet neural network changes its topology (the number of neurons in the input and hidden layers, together with the number and type of connections) according to the molecular structure of the chemical compound presented to the network. The structure of each molecule is encoded in the corresponding molecular graph that is used to set the MolNet topology. Each atom from the molecular graph has a corresponding neuron in the input and hidden layers, respectively. Three structural descriptors derived from the molecular graph are used as input data for the first layer of neurons, namely the degree, the distance sum, and the reciprocal distance sum.

A number of recently graph matrices encoding in various ways the topological information is presented. Four graph operators are used to compute 19 topological indices for a set of 306 alkanes. The intercorrelation coefficients of the 19 topological indices are computed and used to identify highly intercorrelated indices.

In this paper we present a Prolog program which generates a molecular code that identifies the topological and geometrical equivalence classes of atoms in molecules. The initial partitioning of atoms is based on the list of successive extended connectivity and on the chromatism of the molecular graph. The definitive topological classes are obtained by matching all canonical labeled mapping trees exhaustively generated during the construction of a unique one-to-one topological code. Further, the geometric classes of atoms are identified on the basis of the lists of successive interatomic Euclidean distances generated following the molecular topology. The resulting topo-geometrical equivalence classes of atoms allow the construction of a molecular canonical code which maintains the distinction between the topology and the geometry. Thus stereoisomers and conformers share the same topological part of the canonical code but differ by their geometrical parts. The method developed in this work has a wide range ...

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 general molecular coding Prolog program is used in theoretical studies of the properties of fullerene isomers and derivatives to identify the topological equivalence classes of atoms and bonds in C 20-C60 fullerenes. The symmetry perception algorithm is based on an exhaustive search of a minimal code. During this search all canonical labeled mapping trees are generated, allowing construction of equivalence classes of atoms and bonds. Although the present algorithm makes a complete search of canonical labelings in the molecular graph, computational time is maintained within reasonable limits even for large regular graphs such as fullerenes. In the case of fullerenes, topological equivalence classes of atoms allow an easy generation of heterofullerene isomers, while the bond classes allow for the generation of addition or cycloaddition isomers. Also, the number of atom classes and the number of atoms in each class gives important information on the number of 13 C NMR signals and intensity patterns in fullerenes.

Recently, four new types of vertex invariants, namelyu, v, x, andy, were defined on the basis of information on graph distances. They were combined to give four highly selective topological indices:U, V, X, andY. The degeneracy, i.e. equal values for nonisomorphic graphs, of the four topological indices is investigated. A structural condition and a graphical method which gives pairs of molecular graphs with identicalU, V, X, andY topological indices are introduced. The smallest pair of 4-trees representing alkanes having degeneratedU, V, X, andY values consists of trees with eighteen vertices.

A new molecular graph matrix, the reciprocal distance (RD) matrix, is defined. Its nondiagonal elements are equal to the reciprocals of the topological distances between the corresponding vertices, while the diagonal elements are all equal to zero. Based on the RD matrix, a real-number local vertex invariant, RDS was proposed, and three topological indices, namely RDSUM, RDSQ, and RDCHI, were defined. Their degeneracy was investigated and proved to be lower than that of the topological index W based on the distance matrix. The correlational ability of the new molecular descriptors was tested against van der Waals molecular surfaces and boiling points of alkanes, showing a satisfactory monoparametric dependence.

The sequence of all paths pi of lengths i = 1 to the maximum possible length in a hydrogen-depleted molecular graph (which sequence is also called the molecular path code) contains significant information on the molecular topology, and as such it is a reasonable choice to be selected as the basis of topological indices (TIs). Four new (or five partly new) TIs with progressively improved performance (judged by correctly reflecting branching, centricity, and cyclicity of graphs, ordering of alkanes, and low degeneracy) have been explored. (i) By summing the squares of all numbers in the sequence one obtains Sigmaipi(2), and by dividing this sum by one plus the cyclomatic number, a Quadratic TI is obtained: Q = Sigmaipi(2)/(mu+1). (ii) On summing the Square roots of all numbers in the sequence one obtains Sigmaipi(1/2), and by dividing this sum by one plus the cyclomatic number, the TI denoted by S is obtained: S = Sigmaipi(1/2)/(mu+1). (iii) On dividing terms in this sum by the corresponding topological distances, one obtains the Distance-reduced index D = Sigmai{pi(1/2)/[i(mu+1)]}. Two similar formulas define the next two indices, the first one with no square roots: (iv) distance-Attenuated index: A = Sigmai{pi/[i(mu + 1)]}; and (v) the last TI with two square roots: Path-count index: P = Sigmai{pi(1/2)/[i(1/2)(mu + 1)]}. These five TIs are compared for their degeneracy, ordering of alkanes, and performance in QSPR (for all alkanes with 3-12 carbon atoms and for all possible chemical cyclic or acyclic graphs with 4-6 carbon atoms) in correlations with six physical properties and one chemical property.

As a result of the widespread industrial use of polychlorinated hydrocarbons, they have accumulated in nearly all types of environmental compartments, especially in aquatic systems. Particularly, chloroaromatics are among the most undesirable industrial effluents because of their persistence and toxicity. To predict chlorobenzene (CB) toxicities, we make use of a novel scheme that looks beyond simple molecular structure to the manner in which such a structure embeds in an overall reaction network. Thence, a resultant modeling gives a quantitative superstructure/activity relationship (QSSAR) with the (chloro-substitution) reaction network viewed mathematically as a partially ordered set (or poset). Different numerical fittings to the overall poset lead to different QSSAR models, of which we investigate three: average poset, cluster expansion, and splinoid poset QSSAR models for the CBs' toxicities against various species (Poecilia reticulata,Pimephales promelas, Daphnia magna, Rana japonica, etc). Excellent results are obtained for all QSSAR toxicity models. On the basis of the poset reaction diagram, all three of these QSSAR models reflect, in distinct ways, the topology of the network that describes the interconversion of chemical species. Although in the majority of investigated datasets all poset QSSAR models give very good predictions, in some cases, they complement each other. These differences show that more reliable predictions can be obtained by using a consensus prediction that combines data from the three posetic models.

The reaction of 1,2-diphenylethanedione (benzil) with cyclopentadiene in the presence of sodium methoxide unexpectedly afforded the novel fully conjugated 2,3,7-triphenyl derivative of cyclopenta[c]pyran, a pyranic pseudoazulene. The structure was proved by physical methods (IR, UV/VIS; 'H-NMR, 1 3 C-NMR; MS), and confirmed by X-ray crystallography. Protonation affords a pyrylium salt with a structure that agrees with the results of semiempirical and ab-initio methods, which also agree fairly well with experimentally-determined bond lengths.

Chemical structures of organic compounds are characterized numerically by a variety of structural descriptors, one of the earliest and most widely used being the Wiener index W, derived from the interatomic distances in a molecular graph. Extensive use of such structural descriptors or topological indices has been made in drug design, screening of chemical databases, and similarity and diversity assessment. A new set of topological indices is introduced representing a partitioning of the Wiener index based on counts of even and odd molecular graph distances. These new indices are further generalized by weighting exponents which can be optimized during the quantitative structure-activity/-property relationship (QSAR/QSPR) modeling process. These novel topological indices are tested in QSPR models for the boiling temperature, molar heat capacity, standard Gibbs energy of formation, vaporization enthalpy, refractive index, and density of alkanes. In many cases, the even/odd distance indices proposed here give notably improved correlations.

Quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies use statistical models to compute physical, chemical, or biological properties of a chemical substance from its molecular structure, encoded in a numerical form with the aid of various descriptors. Structural indices derived from molecular graph matrices represent an important group of descriptors used in QSPR and QSAR models; recently, their utilization was extended to molecular similarity and diversity, in database mining and virtual screening of combinatorial libraries. Initially defined from the distance matrix, the Wiener index W was the source of novel graph descriptors derived from recently proposed molecular matrices and of the Wiener graph operator. In this work we present a comparative study of several Wiener-type descriptors computed for vertex- and edge-weighted molecular graphs, corresponding to organic compounds with heteroatoms and multiple bonds. The acute toxicities toward Tetrahymena pyriformis of 47 nitrobenzenes are modeled with multilinear regression equations, using as structural descriptors the hydrophobicity (corrected for ionization) and various Wiener-type indices, with better results than a comparative molecular field analysis model.