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Information theory was used in defining several measures of the topological properties of molecules, namely, information for adjacency, incidence, polynomial coefficients of the adjacency matrix, and for distances of molecular graphs. The latter was found to have a greater ability for discrimination between structural isomers than all known topological indices and to be a very appropriate measure of branching. All the quantities related to the distance matrix (two information measures, the Weiner number and the largest eigenvalue of the characteristic polynomial) were found to reflect in the same way the main features of molecular branching. On this basis, as well as on the basis of general expressions for information content and Wiener number derived for tree graphs, the essence of molecular branching was expressed in a number of rules. It was shown that these theoretical rules on branching are in agreement with the intuitive understanding of branching and are reflected in a large number of molecular properties.

A clear perception of gene essentiality in bacterial pathogens is pivotal for identifying drug targets to combat emergence of new pathogens and antibiotic-resistant bacteria, for synthetic biology, and for understanding the origins of life. We have constructed a comprehensive set of deletion mutants and systematically identified a clearly defined set of essential genes for Streptococcus sanguinis. Our results were confirmed by growing S. sanguinis in minimal medium and by double-knockout of paralogous or isozyme genes. Careful examination revealed that these essential genes were associated with only three basic categories of biological functions: maintenance of the cell envelope, energy production, and processing of genetic information. Our finding was subsequently validated in two other pathogenic streptococcal species, Streptococcus pneumoniae and Streptococcus mutans and in two other gram-positive pathogens, Bacillus subtilis and Staphylococcus aureus. Our analysis has thus led to a simplified model that permits reliable prediction of gene essentiality.

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Software for network motifs and modules is briefly reviewed, along with programs for network comparison. The three major software packages for network analysis, CYTOSCAPE, INGENUITY and PATHWAY STUDIO, and their associated databases, are compared in detail. A comparative test evaluated how these software packages perform the search for key terms and the creation of network from those terms and from experimental expression data.

Several series of novel chirality descriptors of chemical organic molecules have been introduced. The descriptors have been developed on the basis of conventional topological descriptors of molecular graphs. They include modified molecular connectivity indices, Zagreb group indices, extended connectivity, overall connectivity, and topological charge indices. These modified descriptors make use of an additional term called chirality correction, which is added to the vertex degrees of asymmetric atoms in a molecular graph. Chirality descriptors can be real or complex numbers. Advantages and drawbacks of different series of chirality descriptors are discussed. These descriptors circumvent the inability of conventional topological indices to distinguish chiral or enantiomeric isomers, which so far has been the major drawback of 2D descriptors as compared to true 3D descriptors (e.g., shape, molecular fields) of molecular structure. These novel chirality descriptors have been implemented in a quantitative structure-activity releationship (QSAR) study of a set of ecdysteroids with a high content of chiral and enantiomeric compounds using the k nearest neighbor QSAR method (kNN) recently developed in this laboratory. We show that the results of this study compare favorably with those obtained with the comparative molecular field analysis (CoMFA) applied to the same dataset. The novel chirality descriptors of molecular structure should find their applications in QSAR studies and related investigations of molecular sdatasets.

A comparative analysis of ten topological indices is made. No index is found to discriminate isomers uniquely. A combined topological index, named the superindex, consisting of a number of topological indices is proposed. Information theory is applied to express all components of the superindex on a common quantitative scale. The superindex is tested on the sample of 427 graphs consisting of all acyclic, monocyclic, and bicyclic graphs with 4–8 vertices.