Advances in Mathematical Chemistry and Applications: Volume 2

Subhash C. Basak, Guillermo Restrepo, Jose L. Villaveces

• Publisher: Bentham Science Publishers
• Year: 2016
• Print ISBN:
  9781681080536
• eBook ISBN:
  9781681080529
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

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 2 explores deeper the topics introduced in Volume 1, with numerous additional topics such as topological approaches for classifying fullerene isomers; chemical reaction networks; discrimination of small molecules using topological molecular descriptors; GRANCH methods for the mathematical characterization of DNA, RNA and protein sequences; linear regression methods and Bayesian techniques; in silico toxicity prediction methods; drug design; integration of bioinformatics and systems biology, molecular docking, and molecular dynamics; metalloenzyme models; protein folding models; molecular periodicity; generalized topologies and their applications; and many 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 - 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

Chapter 1

Topological Efficiency Approach to Fullerene Stability - Case Study with C₅₀

Ante Graovac¹; Ali Reza Ashrafi²; Ottorino Ori^3,* ¹ Faculty of Science, University of Split, Nikole Tesle 12, HR-21000 Split, Croatia
² Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317 – 51167, I. R. Iran
³ Actinium Chemical Research, Via Casilina 1626/A, 00133 Rome, Italy
^* Actinium Chemical Research, Via Casilina 1626/A, 00133 Rome, Italy; Tel/Fax: + 39-06-2055084 [email protected]

Abstract:

An innovative theoretical mechanism leading to the classification of the stability of fullerene isomers is presented. This approach is based on the action of suitable topological potentials impacting on molecular stability, namely topological compactness and topological sphericality indexes, providing a fast and general ranking algorithm. Present results point out that electronic properties of sp² carbon systems are deeply rooted in the topology of their atomic network.

Keywords

C50 fullerene; chemical distance; chemical graph; DFT; energy ranking algorithm; fullerene stability; graph invariants; long-range connectivity effects; minimal vertices; schlegel graphs; sp2 carbon systems; topological compactness; topological efficiency index; topological modeling; topological potential; topological sphericality; wiener index; wiener-weights; π-electron energy

Introduction

The relevant role of topology in modeling chemical systems and their properties has been intensively demonstrated, graph theory representing nowadays one of the most established and effective tools in theoretical chemistry. Since the first collection of topology-based computational methods applied to chemistry, edited in 1976 by Balaban [1], an enormous amount of new topological graph invariants (topological indices) has been introduced and applied for Quantitative Structure-Activity Relationship (QSAR) and Quantitative Structure-Property Relationship (QSPR) studies focusing on structure-dependent chemical behavior of molecules. Predicting chemical properties of an untested compound from its molecular structure is in fact one of the main tasks fulfilled by QSAR methods, providing precious information about chemical hazards for example, while reducing cost, time and animal testing. Periodically, the atlas edited by Todeschini and Consonni [2] updates the international scientific community on the latest advances in this sector on both the practical and theoretical side. QSAR algorithms have been recently expanded by Putz [3] with innovative concepts, like the minimum spectral path principle and some new correlation factors to measure chemical–biological interactions, constituting the so-called SPECTRAL-SAR method. Successful SPECTRAL-SAR applications concern, for example, ecotoxicity hazard assessment of various chemicals.

It is worth noticing that topological methods are not confined to molecular finite systems being, ...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Cover Art
• Foreword
• Preface
• List of Contributors
• Acknowledgements
• Chapter 1: Topological Efficiency Approach to Fullerene Stability - Case Study with C50
• Chapter 2: Similarity in Chemical Reaction Networks: Categories, Concepts and Closures
• Chapter 3: Discrimination of Small Molecules Using Topological Molecular Descriptors
• Chapter 4: The Periodicity of Molecules
• Chapter 5: The GRANCH Techniques for Analysis of DNA, RNA and Protein Sequences
• Chapter 6: Linear Regression, Model Averaging, and Bayesian Techniques for Predicting Chemical Activities from Structure
• Chapter 7: Marine Algal Toxicity Models with Dunaliella tertiolecta: In Vivo and In Silico
• Chapter 8: Anti-Tubercular Drug Designing Using Structural Descriptors
• Chapter 9: Integrating Bioinformatics and Systems Biology for Exploring Novel Lipid Pathways in Infectious Diseases
• Chapter 10: Applications of Molecular Docking and Molecular Dynamics on the Inhibition of Quorum Sensing Systems
• Chapter 11: Designing Models for Metalloenzymes
• Chapter 12: The Multi-Factor Coupled Protein Folding: Insights from Molecular Dynamics Simulations
• Chapter 13: Generalized Topologies: Hypergraphs, Chemical Reactions, and Biological Evolution
• Subject Index