## Abstract

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.

Original language | English (US) |
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Title of host publication | Advances in Mathematical Chemistry and Applications |

Subtitle of host publication | Revised Edition |

Publisher | Elsevier Inc. |

Pages | 3-23 |

Number of pages | 21 |

Volume | 1 |

ISBN (Electronic) | 9781681081977 |

ISBN (Print) | 9781681081984 |

DOIs | |

State | Published - 2015 |

### Bibliographical note

Funding Information:I am thankful to US Environmental Protection Agency, National Institute of Neurological Disorders and Stroke (NINDS/NIH), Minnesota Technology Inc, Air Force Office of Scientific Research (AFOSR, US Air Force), Center for Disease Control and Prevention (CDC), and US Department of Agriculture (USDA) for sustained support of my research program at UMD-NRRI for over three decades.

Publisher Copyright:

© 2015 Bentham Science Publishers Ltd Published by Elsevier Inc. All rights reserved.

## Keywords

- 2-D gel electrophoresis
- Adjacency matrix
- Analog selection
- Balaban index
- Biodescriptor
- Clustering
- Combinatorial chemistry
- Connectivity indices
- DNA sequence descriptor
- Differential QSAR (DiffQSAR)
- Distance matrix
- E-state indices
- Environmental protection
- Graph invariant
- Graph theoretic matrices
- Graph theory
- Hierarchical quantitative structure-activity relationship (HiQSAR)
- Hosoya index
- Information theoretic indices
- Information theoretic proteomics descriptors
- Leave one out (LOO) method
- Mathematical chemodescriptor
- Mathematical proteomics
- Mode of action (MOA)
- Molecular graphs
- Mutagenicity
- Naïve q
- Networks
- New drug discovery
- Partial least square (PLS)
- Prediction of property/bioactivity
- Predictive toxicology
- Principal components regression (PCR)
- Proper cross validation
- Quantitative molecular similarity analysis (QMSA)
- Quantum chemical descriptors
- Ridge regression (RR)
- Spectrum like descriptors
- Tailored similarity
- Topological indices
- True q
- Valence connectivity indices
- Weighted pseudograph
- Wiener index