Mathematical Structural Descriptors of Molecules and Biomolecules: Background and Applications

Mathematical chemistry or more accurately discrete mathematical chemistry had a tremendous growth spurt in the second half of the twentieth century and the same trend is continuing now. This growth was fueled primarily by two major factors: 1) Novel applications of discrete mathematical concepts to chemical and biological systems, and 2) Availability of high speed computers and associated software whereby hypothesis driven as well as discovery oriented research on large data sets could be carried out in a timely manner. This led to the development of not only a plethora of new concepts, but also to various useful applications to such important areas as drug discovery, protection of human as well as ecological health, and chemoinformatics. Following the completion of the Human Genome Project in 2003, discrete mathematical methods were applied to the “omics” data to develop descriptors relevant to bioinformatics, toxicoinformatics, and computational biology. This chapter will discuss the major milestones in the development of concepts of mathematical chemistry, mathematical proteomics as well as their important applications in chemobioinformatics with special reference to the contributions of Basak and coworkers.

Keywords: Graph theory, molecular graphs, networks, graph invariant, weighted pseudograph, graph theoretic matrices, adjacency matrix, distance matrix, topological indices, information theoretic indices, Wiener index, Hosoya index, Balaban index, connectivity indices, valence connectivity indices, E-state indices, mathematical chemodescriptor, quantum chemical descriptors, hierarchical quantitative structure-activity relationship (HiQSAR), differential QSAR (DiffQSAR), partial least square (PLS), principal components regression (PCR), ridge regression (RR), naïve q2, true q2, proper cross validation, leave one out (LOO) method, quantitative molecular similarity analysis (QMSA), tailored similarity, combinatorial chemistry, clustering, analog selection, mode of action (MOA), new drug discovery, environmental protection, prediction of property/bioactivity, predictive toxicology, mutagenicity, 2-D gel electrophoresis, biodescriptor, mathematical proteomics, spectrum like descriptors, information theoretic proteomics descriptors, DNA sequence descriptor.