Advances in Mathematical Chemistry and Applications: Volume 1

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.

• Brings together both the theoretical and practical aspects of the fundamental concepts of mathematical chemistry
• Covers applications in diverse areas of physics, chemistry, drug discovery, predictive toxicology, systems biology, chemoinformatics, and bioinformatics
• Revised 2015 edition includes a new chapter on the current landscape of hierarchical QSAR modelling
• About half of the book focuses primarily on current work, new applications, and emerging approaches for the mathematical characterization of essential aspects of molecular structure, while the other half describes applications of structural approach to new drug discovery, virtual screening, protein folding, predictive toxicology, DNA structure, and systems biology

MSc and PhD students, academic personnel and researchers seeking updated and critically important information on the fundamental concepts of mathematical chemistry and their applications; Scientists working in new drug discovery and hazard assessment of chemicals

• 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