Advances in Mathematical Chemistry and Applications: Volume 1

1st Edition - January 18, 2016
Editors: Subhash C. Basak, Guillermo Restrepo, Jose L. Villaveces
Language: English
Paperback ISBN:
9 7 8 - 1 - 6 8 1 0 8 - 1 9 8 - 4
eBook ISBN:
9 7 8 - 1 - 6 8 1 0 8 - 1 9 7 - 7

Advances in Mathematical Chemistry and Applications highlights the recent progress in the emerging discipline of discrete mathematical chemistry. Editors Subhash C. Basak, Gu… Read more

Advances in Mathematical Chemistry and Applications: Volume 1

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Advances in Mathematical Chemistry and Applications highlights the recent progress in the emerging discipline of discrete mathematical chemistry. Editors Subhash C. Basak, Guillermo Restrepo, and Jose Luis Villaveces have brought together 27 chapters written by 68 internationally renowned experts in these two volumes.

Each volume comprises a wise integration of mathematical and chemical concepts and covers numerous applications in the field of drug discovery, bioinformatics, chemoinformatics, computational biology, mathematical proteomics, and ecotoxicology.

Volume 1 includes chapters on mathematical structural descriptors of molecules and biomolecules, applications of partially ordered sets (posets) in chemistry, optimal characterization of molecular complexity using graph theory, different connectivity matrices and their polynomials, use of 2D fingerprints in similarity-based virtual screening, mathematical approaches to molecular structure generation, comparability graphs, applications of molecular topology in drug design, density functional theory of chemical reactivity, application of mathematical descriptors in the quantification of drug-likeness, utility of pharmacophores in drug design, and much more.

Foreword
Preface
Acknowledgements
- Reviewers of Ebook Chapters
Chapter 1: Mathematical Structural Descriptors of Molecules and Biomolecules: Background and Applications
- Abstract
- Introduction
- Molecular Structure
- Statistical Methods for Qsar Model Development
- Differential Qsar to Characterize Molecular Basis of Drug Resistance
- Similarity: Birds (And Chemicals!) of a Feather Flock Together
- Mathematical Descriptors of Nucleic Acid Sequences
- Descriptors from Mathematical Proteomics
- Combined use of Chemodescriptors and Biodescriptors for Bioactivity Prediction
- Conclusion
- Guest Editorial
- Acknowledgements
- Conflict of Interest
Chapter 2: Ordering Thinking in Chemistry
- Abstract
- Introduction
- Mathematical Way of Thinking
- Order Theory in the Mathematical Way of Thinking in Chemistry
- Concluding Remarks
- Acknowledgements
- Conflict of Interest
Chapter 3: On the Concept for Overall Topological Representation of Molecular Structure
- Abstract
- Introduction
- From Simple Graph-Invariants to a more General Representation of Molecular Topology
- Topological Complexity as a Guide in the Search for a Generalized Topological Characterization of Molecular Structure
- The Concept for Overall Topological Descriptors of Molecular Structure
- Formulas for the Overall Topological Indices of some Classes of Graphs
- Overall Topological Indices Capture the Patterns of Increasing Molecular Complexity
- Overall Topological Indices (OI) Provide a Basis for High Structure-Property and Structure-Activity Correlations
- Alternative Approaches to a More Complete Topological Representation of Molecular Structure
- Acknowledgements
- Conflict of Interest
Chapter 4: The Four Connectivity Matrices, Their Indices, Polynomials and Spectra
- Abstract
- Introduction
- Product-Connectivity Matrices
- Sum-Connectivity Matrices
- Comparisons Between the Connectivity Indices
- Connectivity Polynomials
- Concluding Remarks
- Acknowledgements
- Conflict of Interest
- Abbreviations
Chapter 5: The Use of Weighted 2D Fingerprints in Similarity-Based Virtual Screening
- Abstract
- Introduction
- Previous Studies
- Methods
- Inverse Frequency Weighting
- Frequency Weighting
- Conclusion
- Appendix
- Acknowledgements
- Conflict of Interest
- Abbreviations
Chapter 6: MOLGEN 5.0, A Molecular Structure Generator
- Abstract
- Introduction
- Applications
- Acknowledgements
- Conflict of Interest
Chapter 7: On Comparability Graphs: Theory and Applications
- Abstract
- Introduction
- Comparability Graphs
- Applications
- Summary and Conclusion
- Acknowledgements
- Conflict of Interest
- Abbreviations and Notations
Chapter 8: Basic Concepts and Applications of Molecular Topology to Drug Design
- Abstract
- Introduction
- Methodology and Applications
- Conclusion
- Acknowledgements
- Conflict of Interest
- Abbreviations
Chapter 9: Conceptual Density Functional Theory of Chemical Reactivity
- Abstract
- Introduction
- Conclusions
- Acknowledgements
- Conflict of Interest
- Abbreviations and Symbols of Some Important Quantities
Chapter 10: Mathematical (Structural) Descriptors in QSAR: Applications in Drug Design and Environmental Toxicology
- Abstract
- Introduction
- Structural Descriptors
- QSAR in Drug Discovery
- QSAR in Environmental Toxicology
- Caesar Models
- Concluding Remarks
- Acknowledgements
- Conflict of Interest
Chapter 11: Current Landscape of Hierarchical QSAR Modeling and its Applications: Some Comments on the Importance of Mathematical Descriptors as well as Rigorous Statistical Methods of Model Building and Validation
- Abstract
- 1 Introduction
- 2 The Tortuous History of QSAR: From 1868 to the Present Time
- 3 Calculation of Molecular Descriptors for QSAR
- 4 Hierarchical QSAR Development and Validation
- Discussion and Conclusion
- Acknowledgements
- Conflict of Interest
Chapter 12: Recent Advances in the Assessment of Druglikeness Using 2D-Structural Descriptors
- Abstract
- Introduction
- Development of Drug-Like Filters (DLFS) from Structural Descriptors
- Druglike Index (DLI) From Structural Descriptors
- Structural Descriptors for the Analysis of Druglikeness: Atom Type Diversity
- Atomic Level Assessment of Druglikeness
- Future Direction
- Acknowledgements
- Conflict of Interest
- Abbreviations
Chapter 13: Role of In Silico Stereoelectronic Properties and Pharmacophores in Aid of Discovery of Novel Antimalarials, Antileishmanials, and Insect Repellents
- Abstract
- Introduction
- Results and Discussions
- Concluding Remarks
- Acknowledgements
- Conflict of Interest
- Abbreviations
Chapter 14: Molecular Taxonomy
- Abstract
- Introduction
- Strings and their Periodicities
- Quarks and their Periodicities
- Hadron Periodicities
- Nuclear Periodicity
- Atomic Periodicities
- Molecular Periodicities
- Summary
- Acknowledgements
- Conflict of Interest
Subject Index

Subhash C. Basak

Dr. Basak is an adjunct professor in the department of chemistry and department of biochemistry & molecular biology at the University of Minnesota Duluth. He received his Ph.D. in Biochemistry from the University of Calcutta in 1980. He is a member of several academic societies, including International Society for Mathematical Chemistry, of which he is President, and is a US Chair in the organization of thirteen international mathematical chemistry workshops in USA, South America, and various universities/ research institutes in India. He was awarded ARA Journal Best Paper Award, American Romanian Academy of Arts and Sciences (2004) and Statistics in Chemistry Award, American Statistical Association (2004).

Affiliations and expertise

University of Minnesota Duluth, USA

Guillermo Restrepo

There are two main interests in the research carried out by Professor Guillermo Restrepo: mathematical chemistry and philosophy of chemistry. His mathematical approaches to chemistry have been through discrete mathematics, especially graph and order theory and point-set topology. This research has led him to estimate properties of substances, to assess environmental targets, and to find novel structures of chemical constructs such as the periodic system of chemical elements. His questions in philosophy of chemistry have to do with the mathematical way of thinking and its realization in chemistry. Professor Restrepo is Fellow of the Alexander von Humboldt Foundation/Stiftung, member of the International Academy of Mathematical Chemistry, and of the Executive Committee of the International Society for the Philosophy of Chemistry. He is also a member of the editorial board of MATCH Communications in Mathematical and in Computer Chemistry, and of Hyle -- International Journal for Philosophy of Chemistry.

Affiliations and expertise

Universidad de Pamplona, Colombia

Jose L. Villaveces

Theoretical chemistry, history, and philosophy of chemistry are some of the scientific interests of Professor José L. Villaveces. His approaches to theoretical chemistry range from quantum chemistry to mathematical chemistry, where topology plays a central role. Another interest is scientometrics, which is combined with his expertise in science administration and science policy. He is currently adviser to research of the Universidad de los Andes where he also teaches.

Affiliations and expertise

Universidad de los Andes, Colombia