Mathematical Structural Descriptors of Molecules and Biomolecules: Background and Applications

Subhash C. Basak

doi:10.1016/B978-1-68108-198-4.50001-1

Mathematical Structural Descriptors of Molecules and Biomolecules: Background and Applications

Subhash C. Basak

Natural Resources Research Institute

Research output: Chapter in Book/Report/Conference proceeding › Chapter

9 Scopus citations

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)
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	https://doi.org/10.1016/B978-1-68108-198-4.50001-1
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

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10.1016/B978-1-68108-198-4.50001-1

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author = "Basak, {Subhash C.}",

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: {\textcopyright} 2015 Bentham Science Publishers Ltd Published by Elsevier Inc. All rights reserved.",

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N2 - 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.

AB - 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.

KW - 2-D gel electrophoresis

KW - Adjacency matrix

KW - Analog selection

KW - Balaban index

KW - Biodescriptor

KW - Clustering

KW - Combinatorial chemistry

KW - Connectivity indices

KW - DNA sequence descriptor

KW - Differential QSAR (DiffQSAR)

KW - Distance matrix

KW - E-state indices

KW - Environmental protection

KW - Graph invariant

KW - Graph theoretic matrices

KW - Graph theory

KW - Hierarchical quantitative structure-activity relationship (HiQSAR)

KW - Hosoya index

KW - Information theoretic indices

KW - Information theoretic proteomics descriptors

KW - Leave one out (LOO) method

KW - Mathematical chemodescriptor

KW - Mathematical proteomics

KW - Mode of action (MOA)

KW - Molecular graphs

KW - Mutagenicity

KW - Naïve q

KW - Networks

KW - New drug discovery

KW - Partial least square (PLS)

KW - Prediction of property/bioactivity

KW - Predictive toxicology

KW - Principal components regression (PCR)

KW - Proper cross validation

KW - Quantitative molecular similarity analysis (QMSA)

KW - Quantum chemical descriptors

KW - Ridge regression (RR)

KW - Spectrum like descriptors

KW - Tailored similarity

KW - Topological indices

KW - True q

KW - Valence connectivity indices

KW - Weighted pseudograph

KW - Wiener index

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SN - 9781681081984

VL - 1

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EP - 23

BT - Advances in Mathematical Chemistry and Applications

PB - Elsevier Inc.

ER -

Mathematical Structural Descriptors of Molecules and Biomolecules: Background and Applications

Abstract

Bibliographical note

Keywords

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