Discrete and Topological Models in Molecular Biology

1. Front Matter

   Pages i-xiii

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2. Discrete and Graph-Theoretic Models for Data Analysis

   1. Front Matter

      Pages 1-1

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   2. Perspectives in Computational Genome Analysis

      • Giuditta Franco

      Pages 3-22

   3. The Sequence Reconstruction Problem

      • Angela Angeleska, Sabrina Kleessen, Zoran Nikoloski

      Pages 23-43

   4. Extracting Coevolving Characters from a Tree of Species

      • Alessandra Carbone

      Pages 45-65

   5. When and How the Perfect Phylogeny Model Explains Evolution

      • Paola Bonizzoni, Anna Paola Carrieri, Gianluca Della Vedova, Riccardo Dondi, Teresa M. Przytycka

      Pages 67-83

   6. An Invitation to the Study of Brain Networks, with Some Statistical Analysis of Thresholding Techniques

      • Mark Daley

      Pages 85-107

   7. Simplicial Models and Topological Inference in Biological Systems

      • Vidit Nanda, Radmila Sazdanović

      Pages 109-141

3. Molecular Arrangements and Structures

   1. Front Matter

      Pages 143-143

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   2. Combinatorial Insights into RNA Secondary Structure

      • Christine Heitsch, Svetlana Poznanović

      Pages 145-166

   3. Redundant and Critical Noncovalent Interactions in Protein Rigid Cluster Analysis

      • Naomi Fox, Ileana Streinu

      Pages 167-196

   4. Modeling Autonomous Supramolecular Assembly

      • Meera Sitharam

      Pages 197-216

   5. The Role of Symmetry in Conformational Changes of Viral Capsids: A Mathematical Approach

      • Paolo Cermelli, Giuliana Indelicato, Reidun Twarock

      Pages 217-240

   6. Minimal Tile and Bond-Edge Types for Self-Assembling DNA Graphs

      • Joanna Ellis-Monaghan, Greta Pangborn, Laura Beaudin, David Miller, Nick Bruno, Akie Hashimoto

      Pages 241-270

4. Gene Rearrangements

   1. Front Matter

      Pages 271-271

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   2. Programmed Genome Processing in Ciliates

      • Aaron David Goldman, Elizabeth M. Stein, John R. Bracht, Laura F. Landweber

      Pages 273-287

   3. The Algebra of Gene Assembly in Ciliates

      • Robert Brijder, Hendrik Jan Hoogeboom

      Pages 289-307

   4. Invariants of Graphs Modeling Nucleotide Rearrangements

      • Egor Dolzhenko, Karin Valencia

      Pages 309-323

5. Topological Models and Spatial DNA Embeddings

   1. Front Matter

      Pages 325-325

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   2. Introduction to DNA Topology

      • Isabel K. Darcy, Stephen D. Levene, Robert G. Scharein

      Pages 327-345

Theoretical tools and insights from discrete mathematics, theoretical computer science, and topology now play essential roles in our understanding of vital biomolecular processes. The related methods are now employed in various fields of mathematical biology as instruments to "zoom in" on processes at a molecular level. This book contains expository chapters on how contemporary models from discrete mathematics – in domains such as algebra, combinatorics, and graph and knot theories – can provide perspective on biomolecular problems ranging from data analysis, molecular and gene arrangements and structures, and knotted DNA embeddings via spatial graph models to the dynamics and kinetics of molecular interactions. The contributing authors are among the leading scientists in this field and the book is a reference for researchers in mathematics and theoretical computer science who are engaged with modeling molecular and biological phenomena using discrete methods. It may also serve as aguide and supplement for graduate courses in mathematical biology or bioinformatics, introducing nontraditional aspects of mathematical biology.

• Cell biology
• DNA
• Evolutionary biology
• Gene assembly
• Genome analysis
• Genome processing
• RNA
• Recombination
• Self-assembly
• Systems biology

• Dept. Mathematics & Statistics, University of South Florida, Tampa, USA

  Nataša Jonoska, Masahico Saito

Prof. Nataša Jonoska is a professor in the Dept. of Mathematics and Statistics of the University of South Florida, Tampa, USA. She received her PhD from the Dept. of Mathematical Sciences, SUNY Binghamton in 1993. Her research is driven by the issue of how biology computes, in particular using formal models such as cellular or other finite types of automata, formal language theory symbolic dynamics, and topological graph theory to describe molecular computation. She is a board member of related prestigious journals such as Theoretical Computer Science, the Int. J. of Foundations of Computer Science, Computability, and Natural Computing. She has edited a number of books, among them the Springer book Nanotechnology: Science and Computation. Dr. Masahico Saito is a researcher in the Dept. of Mathematics and Statistics, University of South Florida, Tampa, USA. He is a member of the Discrete and Topological Methods for DNA Assembly team, and his research interests include knots and quandles.

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