Advances in Mathematical Chemistry and Applications

Volume 2

by

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

DOI: 10.2174/97816810805291150201
eISBN: 978-1-68108-052-9, 2015
ISBN: 978-1-68108-053-6
ISSN: 2352-7668 (Print)



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Advances in Mathematical Chemistry and Applications highlights the emerging discipline of mathematical chemistry, or, more precisely, ...[view complete introduction]

Table of Contents

Foreword

- Pp. i

Lemont B. Kier

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Preface

- Pp. iii-v (3)

Subhash C. Basak, Guillermo Restrepo and José L. Villaveces

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List of Contributors

- Pp. vii-ix (3)

Subhash C. Basak, Guillermo Restrepo and José L. Villaveces

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Acknowledgements

- Pp. xi

Subhash C. Basak, Guillermo Restrepo and José L. Villaveces

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Topological Efficiency Approach to Fullerene Stability - Case Study with C<sub>50</sub>

- Pp. 3-23 (21)

Ante Graovac, Ali Reza Ashrafi and Ottorino Ori

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Similarity in Chemical Reaction Networks: Categories, Concepts and Closures

- Pp. 24-54 (31)

Andrés Bernal, Eugenio Llanos, Wilmer Leal and Guillermo Restrepo

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Discrimination of Small Molecules Using Topological Molecular Descriptors

- Pp. 55-73 (19)

Chandan Raychaudhury and Debnath Pal

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The Periodicity of Molecules

- Pp. 74-95 (22)

Fanao Kong, Weiqiang Wu, Na Ji and C. L. Calson

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The GRANCH Techniques for Analysis of DNA, RNA and Protein Sequences

- Pp. 96-124 (29)

Ashesh Nandy

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Linear Regression, Model Averaging, and Bayesian Techniques for Predicting Chemical Activities from Structure

- Pp. 125-147 (23)

Jarad B. Niemi and Gerald J. Niemi

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Marine Algal Toxicity Models with Dunaliella tertiolecta: In Vivo and In Silico

- Pp. 148-178 (31)

Melek T. Saçan, Marjana Novic, M. Doğa Ertürk and Nikola Minovski

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Anti-Tubercular Drug Designing Using Structural Descriptors

- Pp. 179-190 (12)

Manish C. Bagchi and Payel Ghosh

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Integrating Bioinformatics and Systems Biology for Exploring Novel Lipid Pathways in Infectious Diseases

- Pp. 191-220 (30)

Sonali Shinde, Vineetha Mandlik and Shailza Singh

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Applications of Molecular Docking and Molecular Dynamics on the Inhibition of Quorum Sensing Systems

- Pp. 221-242 (22)

Santiago Medina, Susana Casas, Mariana Restrepo, Alejandro Alvarez, Adriana J. Bernal and Andrés Fernando González Barrios

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Designing Models for Metalloenzymes

- Pp. 243-264 (22)

James F. Weston

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The Multi-Factor Coupled Protein Folding: Insights from Molecular Dynamics Simulations

- Pp. 265-299 (35)

Xiaomin Wu, Gang Yang and Lijun Zhou

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Generalized Topologies: Hypergraphs, Chemical Reactions, and Biological Evolution

- Pp. 300-328 (29)

Christoph Flamm, Bärbel M. R. Stadler and Peter F. Stadler

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Subject Index

- Pp. 329-334 (6)

Subhash C. Basak, Guillermo Restrepo and José L. Villaveces

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Foreword

In the middle 1960’s, there arose a significant number of approaches to the quantitation of molecular attributes influencing their behavior and function. These approaches took the form of some physical properties and various approaches to quantitate molecular structure. Since molecular structure is an attribute most directly correlateable with function, this approach prospered and led to a number of useful methods at that time. These included molecular orbital theory, graph theory, information theory and some spatial quantitative methods. As we begin the second half of this century of study, we have on hand a plethora of methods to achieve these goals. The extent of this burgeoning has given rise to a descriptive categorical term, Mathematical Chemistry.

This volume appears on the scene to celebrate the emergence of Mathematical Chemistry in its second half century. It brings to the molecular scientist several new approaches plus the introduction of variations on existing ideas. The editors of this text have wisely and thoroughly gathered together a broad representation of contributions. About a half of the book contains contributions of scientists active in the life sciences. These chapters focus primarily on methods of creating models of drug function relative to molecular structure. This realm of applications of mathematical chemistry has contributed significantly over the years to the process of drug design. We would still be in the empirical realm of trial and error to find a new drug, without the role of structure-activity models using many good methods.

The other half of the chapters describes current work, new applications, and new approaches to quantitation of the essential aspects of molecular structure. The imaginative ideas flowing through these chapters are quite impressive. It creates a text that should be on the shelf of every scientist working quantitatively at the molecular level. There is a stimulation arising from the book that will excite the creativity in many readers. Such a book is essential in every field of science where periodic overview and exposure to new ideas is essential.

Congratulations to the authors who have contributed to the book and congratulations to the editors who have selected the mix of articles and authors.

Lemont B. Kier
Emeritus Professor
Dept. of Medicinal Chemistry
Virginia Commonwealth University
USA


Preface

I would like to emphasize strongly my belief that the era of computing chemists, when hundreds if not thousands of chemists will go to the computing machine instead of the laboratory for increasingly many facets of chemical information, is already at hand. There is only one obstacle, namely that someone must pay for the computing time.

Robert Sanderson Mulliken

In the first quarter of the nineteenth century the experimental proof for the interdependence of the composition and properties of chemical compounds resulted in the theory that they are mutually related, so that like composition governs like properties, and conversely.

Wilhelm Ostwald

We are glad to introduce our readers to volume 2 of the eBook Advances in Mathematical Chemistry and Applications. This volume, like volume 1, has thirteen chapters written by well-known experts from around the world. As shown in the two figures of the preface of volume 1, chapters of volume 1 and 2 of this eBook deal with several mathematical approaches to chemistry, e.g. topology, graph theory, information theory, to name but a few. Readers interested in a particular mathematical area, say topology, are directed to those figures to know which other chapters report novel topological approaches in chemistry.

In the first chapter entitled “Topological Efficiency Approach to Fullerene Stability - Case Study with C50”, by Ante Graovac, Ali Reza Ashrafi, and Ottorino Ori, the authors use topological approaches for classifying fullerene isomers, a group of structures important both from the mathematical and chemical points of view. In this approach two shape descriptors: topological compactness and topological sphericality turn out to be of key importance for the ordering.

Andrés Bernal, Eugenio Llanos, Wilmer Leal, and Guillermo Restrepo, authors of the second chapter, entitled “Similarity in Chemical Reaction Networks: Categories, Concepts and Closures”, claim that chemical identity is the result of chemical reactivity and analyze chemical entities by studying reaction networks. In such formalism the identity of a substance is given by those related to it, which gives place to an interpretation in the framework of Category Theory. The similarity between substances is studied through topological spaces, with closures as key concepts for similarity.

The third chapter, “Discrimination of Small Molecules Using Topological Molecular Descriptors”, by Chandan Raychaudhury and Debnath Pal, reviews the use of numerical topological graph invariants to differentiate molecular structures of small size, a subject of utter importance in chemo and bioinformatics.

“The Periodicity of Molecules” is the title of the fourth chapter, by Fanao Kong, Weiqiang Wu, Na Ji, and C. L. Calson, where the authors review their work on periodic tables for di, tri, and tetra-atomic molecules. These tables are further used to estimate properties of molecules, such as bond length, binding energy, ionization potential, among others.

The fifth chapter, “The GRANCH Techniques for Analysis of DNA, RNA and Protein Sequences”, by Ashesh Nandy, reviews two classes of methods, viz., graphical methods and graph invariant techniques, for the characterization of sequences of DNA, RNA, and proteins, which constitute the GRANCH (graphical representation and numerical characterization) methods. The author shows how these characterizations can be used in the study of viral proteins as an example of application.

Jarad B. Niemi and Gerald J. Niemi are the authors of the sixth chapter, entitled “Linear Regression, Model Averaging, and Bayesian Techniques for Predicting Chemical Activities from Structure”. The chapter reviews several statistical approaches to deal with situations where there are more chemical structure measurements or available molecular descriptors/ properties than the number of chemicals with measured property values, which are commonly found in many current Quantitative Structure-Activity Relationship (QSAR) and Quantitative Structure-Property Relationship (QSPR) studies.

“Marine Algal Toxicity Models with Dunaliella Tertiolecta: In Vivo and In Silico”, by Melek T. Saçan, Marjana Novic, M. Doğa Ertürk, and Nikola Minovski, is the seventh chapter of this volume. In their chapter, authors model toxicity of phenolic compounds to Dunaliella Tertiolecta using counter-propagation artificial neural networks and point out to the importance of D. tertiolecta, a marine alga, for toxicity determination of chemical substances.

In the eighth chapter of this volume, “Anti-Tubercular Drug Designing Using Structural Descriptors”, Manish C. Bagchi and Payel Ghosh discuss the use of molecular descriptors, including graph invariants, and robust statistical methods like ridge regression in the formulation of models for the discovery of drugs active against tuberculosis, a contemporary problem to human health worldwide.

“Integrating Bioinformatics and Systems Biology for Exploring Novel Lipid Pathways in Infectious Diseases” is the title of the ninth chapter, written by Sonali Shinde, Vineetha Mandlik, and Shailza Singh. The authors develop mathematical models for delving into the complexity of biological interactions related to Schistosomiasis and Trypanosomiasis, two neglected tropical diseases affecting a large segment of world population. Their specific focus is on the lipid metabolism of the two parasites causing the diseases.

Santiago Medina, Susana Casas, Mariana Restrepo, Alejandro Alvarez, Adriana J. Bernal, and Andrés F. González are the authors of the tenth chapter, entitled “Applications of Molecular Docking and Molecular Dynamics on the Inhibition of Quorum Sensing Systems”. Given that bacteria communicate through chemical signals allowing the regulation of a variety of physiological functions and group behavior (quorum sensing), a key concept in medicinal chemistry is to inhibit such a communication through novel molecules. In this chapter the authors describe some computational approaches used to find such inhibitory molecules for several bacteria.

The eleventh chapter, entitled “Designing Models for Metalloenzymes”, by James F. Weston, discusses how quantum chemistry plays an important role in designing small organometallic catalysts. Weston particularly analyzes quantum mechanical approximations for the process of catalysis, showing the advantages and disadvantages of those approximations.

“The Multi-Factor Coupled Protein Folding: Insights from Molecular Dynamics Simulations” is the title of the twelfth chapter, where Xiaomin Wu, Gang Yang, and Lijun Zhou review factors that are important for protein folding, a process of paramount importance in understanding the physiological function of proteins. The factors analyzed are space limitation, where entropy constraints play a central role; solvent effects, where solvation models are discussed; physicochemical properties and their relationship with non-covalent interactions; and structural modifications, such as mutation and protonation.

Christoph Flamm, Bärbel M. R. Stadler, and Peter F. Stadler are the authors of the thirteenth chapter, entitled “Generalized Topologies: Hypergraphs, Chemical Reactions, and Biological Evolution”, where they discuss how the topological concepts of similarity, neighborhood, connectedness and continuity pervade chemical and biological situations such as chemical reaction networks and evolutionary processes. By finding, however, that those concepts are not laid down to the mathematical formalism of topology, they undertake the task of doing it by avoiding the topological concept of open set and instead taking advantage of the mathematical richness of closure operators.

We sincerely hope the second volume of the book, analogous to the first volume, will be highly appreciated by researchers and scholars worldwide.

Subhash C. Basak
International Society of Mathematical Chemistry
University of Minnesota
USA

Guillermo Restrepo
Universidad de Pamplona
Colombia

&

José L. Villaveces
Universidad de los Andes
Colombia

ACKNOWLEDGEMENTS

The editors of the eBook “Advances in Mathematical Chemistry and Applications” and Bentham Science Publishers would like to gratefully acknowledge the dedicated work of the following distinguished scientists who reviewed the chapters of this book and gave valuable suggestions as well as constructive criticisms to the authors and editors that substantially enhanced the quality of this volume.

List of Contributors

Editor(s):
Subhash C. Basak


Guillermo Restrepo


José L. Villaveces




Contributor(s):
Adriana J. Bernal
Mycology and Plant Disease Laboratory (LAMFU), Department of Biological Sciences
Universidad de los Andes
Bogotá
Colombia


Alejandro Alvarez
Grupo de Diseño de Productos y Procesos (GDPP), Department of Chemical Engineering, Universidad de los Andes, Bogotá, Colombia; Mycology and Plant Disease Laboratory (LAMFU)
Department of Biological Sciences, Universidad de los Andes
Bogotá
Colombia


Ali R. Ashrafi
Department of Pure Mathematics, Faculty of Mathematical Sciences
University of Kashan
Kashan
I. R., 87317 – 51167
Iran


Andrés Bernal
Grupo de Química Teórica
Universidad Nacional de Colombia
Bogotá
Colombia


Andrés F. González
Grupo de Diseño de Productos y Procesos (GDPP), Department of Chemical Engineering
Universidad de los Andes
Bogotá
Colombia


Ante Graovac
Faculty of Science
University of Split
Nikole Tesle 12, HR-21000
Split
Croatia


Ashesh Nandy
Centre for Interdisciplinary Research and Education
404B Jodhpur Park
Kolkata, 700068
India


Bärbel M.R. Stadler
Max Planck Institute for Mathematics in the Sciences
Inselstraße 22, D-04103 Leipzig
Germany


C. L. Calson
The Institute of Chemistry, Chinese Academy of Sciences
Beijing, 100190
China


Chandan Raychaudhury
Bioinformatics Centre, Indian Institute of Science
Bangalore, 560012
India


Christoph Flamm
Institute for Theoretical Chemistry
University of Vienna
Währingerstraße 17, A-1090
Vienna
Austria


Debnath Pal
Bioinformatics Centre
Indian Institute of Science
Bangalore, 560012
India


Eugenio Llanos
Corporación Colombiana del Saber Científico SCIO
Bogotá
Colombia


Fanao Kong
The Institute of Chemistry
Chinese Academy of Sciences
Beijing, 100190
China


Gang Yang
Resources and Environmental Department
Southwest University
Chongqing
P. R., 400715
China
/
Engineering Research Center of Forest Bio-preparation
Ministry of Education, Northeast Forestry University
Harbin
P. R., 150040
China


Gerald J. Niemi
Natural Resources Research Institute and Department of Biology
University of Minnesota, 5013 Miller Trunk Highway
Duluth
MN, 55811
USA


Guillermo Restrepo
Laboratorio de Química Teórica
Universidad de Pamplona
Pamplona
Colombia


James F. Weston
Departamento de Química
Universidad de los Andes
Carrera 1ª, N° 18 A 12, Bloque Q, 8°Piso
Bogotá, D.C.
Colombia, S. A.


Jarad B. Niemi
Department of Statistics
Iowa State University
Ames
IA, 50011
USA


Lijun Zhou
Resources and Environmental Department
Southwest University
Chongqing
P. R., 400715
China


M. Doğa Ertürk
Boğaziçi University, Institute of Environmental Sciences
34342, Hisar Campus, Bebek
Istanbul
Turkey


Manish C. Bagchi
School of Bioscience & Engineering, Jadavpur University
Kolkata, 700032
India


Mariana Restrepo
Mycology and Plant Disease Laboratory (LAMFU), Department of Biological Sciences
Universidad de los Andes
Bogotá
Colombia


Marjana Novic
National Institute of Chemistry
Hajdrihova 19, 1000 Ljubljana
Slovenia


Melek T. Saçan
Boğaziçi University
Institute of Environmental Sciences
34342, Hisar Campus, Bebek,
Istanbul
Turkey


Na Ji
The Institute of Chemistry
Chinese Academy of Sciences
Beijing, 100190
China


Nikola Minovski
National Institute of Chemistry
Hajdrihova 19
1000 Ljubljana
Slovenia


Ottorino Ori
Actinium Chemical Research
Via Casilina 1626/A
Rome, 00133
Italy


Payel Ghosh
Department of Biotechnology
University of Pune
Pune, 411007
India


Peter F. Stadler
Institute for Theoretical Chemistry
University of Vienna
Währingerstraße 17, A-1090
Vienna
Austria
/
Max Planck Institute for Mathematics in the Sciences
Inselstraße 22, D-04103
Leipzig
Germany
/
Bioinformatics Group, Department of Computer Science, and Interdisciplinary Center of Bioinformatics
University of Leipzig
Härtelstraße 16-18, D-04107
Leipzig
Germany
/
RNomics Group, Fraunhofer IZI
Perlickstraße 1, D-04103
Leipzig
Germany
/
Center for noncoding RNA in Technology and Health
Grønnegårdsvej 3, DK-1870
Frederiksberg
Denmark
/
The Santa Fe Institute
1399 Hyde Park Rd., Santa Fe
New Mexico
USA


Santiago Medina
Grupo de Diseño de Productos y Procesos (GDPP), Department of Chemical Engineering
Universidad de los Andes
Bogotá
Colombia


Shailza Singh
Computational and Systems Biology Laboratory
Lab 9, New Building, NCCS
Pune, 411007
India


Sonali Shinde
Computational and Systems Biology Laboratory
Lab 9, New Building, NCCS
Pune, 411007
India


Susana Casas
Grupo de Diseño de Productos y Procesos (GDPP), Department of Chemical Engineering
Universidad de los Andes
Bogotá
Colombia


Vineetha Mandlik
Computational and Systems Biology Laboratory
Lab 9, New Building, NCCS
Pune, 411007
India


Wilmer Leal
Laboratorio de Química Teórica
Universidad de Pamplona
Pamplona
Colombia
/
Universidad del Rosario
Bogotá
Colombia
/
Fundación Instituto de Inmunología de Colombia FIDIC
Bogotá
Colombia


Xiaomin Wu
Key Laboratory of Plant Resources and Biology
College of Life Sciences, Huaibei Normal University
Huaibei
P.R., 235000
China
/
Engineering Research Center of Forest Bio-preparation
Ministry of Education, Northeast Forestry University
Harbin
P.R., 150040
China




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