My Tortuous Pathway Through Mathematical Chemistry and QSAR Research With Memories of Some Personal Interactions and Collaborations With Professors Milan Randić and Mircea Diudea

This article describes my more than four decades of not so straightforward journey through mathematical chemistry and QSAR research with descriptions of some valuable personal interactions and collaborations with Professors Milan Randić and Mircea Diudea. This work is licensed under a Creative Commons Attribution 4.0 International License

Statistical theory of spectra: Statistical moments as descriptors in the theory of molecular similarity

Statistical moments of the intensity distributions are used as molecular descriptors. They are used as a basis for defining similarity distances between two model spectra. Parameters which carry the information derived from the comparison of shapes of the spectra and are related to the number of properties taken into account, are defined.Comment: Poster presented at the 3rd NEXT-Sigma-Phi Conference, Crete, Aug.2005, revtex, 13 pages including 6 figure

Use of Graph Invariants in Quantitative Structure-Activity Relationship Studies

This chapter reviews results of research carried out by Basak and collaborators during the past four decades or so in the development of novel mathematical chemodescriptors and their applications in quantitative structure-activity relationship (QSAR) studies related to the prediction of toxicities and bioactivities of chemicals. For chemodescriptors based QSAR studies, we have used graph theoretical, three dimensional (3-D), and quantum chemical indices. The graph theoretic chemodescriptors fall into two major categories: (a) Numerical invariants defined on simple molecular graphs representing only the adjacency and distance relationship of atoms and bonds; such invariants are called topostructural (TS) indices; (b) Topological indices derived from weighted molecular graphs, called topochemical (TC) indices. Collectively, the TS and TC descriptors are known as topological indices (TIs). The set of independent variables used for modeling also includes a group of three-dimensional (3-D) molecular descriptors. Semi-empirical and various levels of ab initio quantum chemical indices have also been used for hierarchical QSAR (HiQSAR) modeling. Results indicate that in many cases of property / activity / toxicity analyzed by us, a TS + TC combination explains most of the variance in the data. This work is licensed under a Creative Commons Attribution 4.0 International License

Applications of Multidimensional Space of Mathematical Molecular Descriptors in Large-Scale Bioactivity and Toxicity Prediction- Applications to Prediction of Mutagenicity and Blood-Brain Barrier Entry of Chemicals

In this chapter, we review our QSAR research in the prediction of toxicities, bioactivities and properties of chemicals using computed mathematical descriptors. Robust statistical methods have been used to develop high quality predictive quantitative structure-activity relationship (QSAR) models for the prediction of mutagenicity and BBB (blood-brain barrier) entry of two large and diverse sets chemicals. This work is licensed under a Creative Commons Attribution 4.0 International License

Mathematical Nanotoxicoproteomics: Quantitative Characterization of Effects of Multi-walled Carbon Nanotubes (MWCNT) and TiO2 Nanobelts (TiO2-NB) on Protein Expression Patterns in Human Intestinal Cells

Background: Various applications of nanosubstances in industrial and consumer goods sectors are growing rapidly because of their useful chemical and physical properties. Objectives: Assessment of hazard posed by exposure to nanosubstances is essential for the protection of human and ecological health. Methods: We analyzed the proteomics patterns of Caco-2/HT29-MTX cells in co-culture exposed for three and twenty four hours to two kinds of nanoparticles: multi-walled carbon nanotubes (MWCNT) and TiO2 nanobelts (TiO2-NB). For each nanosubstance cells were exposed to two concentrations of the material before carrying out proteomics analyses: 10 μg and 100 μg. In each case over 3000 proteins were identified. A mathematically based similarity index, which measures the changes in abundances of cellular proteins that are highly affected by exposure to the nanosubstances, was used to characterize toxic effects of the nanomaterials. Results: We identified 8 and 25 proteins, which are most highly affected by MWCNT and TiO2-NB, respectively. These proteins may be responsible for specific response of cells to the nanoparticles. Further 14 reported proteins are affected by either of the two nanoparticles and they are probably related to nonspecific toxic response of the cells. Conclusion: The similarity methods proposed in this paper may be useful in the management and visualization of the large amount of data generated by proteomics technologies

Characterization of Isospectral Graphs Using Graph Invariants and Derived Orthogonal Parameters

Numerical graph theoretic invariants or topological indices (TIs) and principal components (PCs) derived from TIs have been used in discriminating a set of isospectral graphs. Results show that lower order connectivity and information theoretic TIs suffer from a high degree of redundancy, whereas higher order indices can characterize the graphs reasonably well. On the other hand, PCs derived from the TIs had no redundancy for the set of isospectral graphs studied

Interrelationship of Major Topological Indices Evidenced by Clustering

This study examines the mutual relatedness of 318 major topological indices (TIs) for three sets of molecules: (i) a set of 139 hydrocarbons, (ii) a diverse set of 1029 compounds and (iii) a diverse set of 2887 compounds. The TIs included in this study are those that have been frequently used in the characterization of structure and QSAR/ QSPR studies. After variable reduction based on the elimination of TIs for which all values were zero and those that were completely correlated with another TI, a variable clustering technique was used to cluster the TIs which resulted in 16, 37 and 56 clusters, respectively, for the three data sets mentioned above. Analysis of the correspondence among the clusters derived from the three groups of chemicals has been carried out in an effort to understand the dimensionality of the structure spaces derived for the three different sets of chemicals and the structural aspects characterized by the various TIs

Estimation of the Normal Boiling Points of Haloalkanes Using Molecular Similarity

A molecular similarity measure has been used to estimate the normal boiling points of a set of 267 haloalkanes with 1-4 carbon atoms. Molecular similarity/dissimilarity was quantified in terms of Euclidean distances of molecules in the eight dimensional principal component space derived from fifty-nine topological indices. Correlation coefficients between the experimental and estimated boiling points ranged from 0.854 to 0.943 in the K-nearest neighbor estimation of boiling points using a different number of nearest neighbors (K = 1-10, 15, 20, 25)

Characterization of 2-D Proteome Maps Based on the Nearest Neighborhoods of Spots

A novel approach to the construction of invariants for characterization of 2-D maps, such as 2-D proteome maps, 2-D NMR spectral maps, etc., is put forward. The approach is based on consideration of the neighborhood of points (spots) of the map and it is sufficiently flexible to allow one to vary not only the number of nearest neighbor spots used in characterization of a map but also the density of information on the relative distance of the selected map points. The method is illustrated with a Coomassie brilliant blue stained 2-D gel electrophoresis pattern of the Fisher F344 rat liver proteome