About This Book
Written by experts in both mathematics and biology, Algebraic and Discrete Mathematical Methods for Modern Biology offers a bridge between math and biology, providing a framework for simulating, analyzing, predicting, and modulating the behavior of complex biological systems. Each chapter begins with a question from modern biology, followed by the description of certain mathematical methods and theory appropriate in the search of answers. Every topic provides a fast-track pathway through the problem by presenting the biological foundation, covering the relevant mathematical theory, and highlighting connections between them. Many of the projects and exercises embedded in each chapter utilize specialized software, providing students with much-needed familiarity and experience with computing applications, critical components of the “modern biology” skill set. This book is appropriate for mathematics courses such as finite mathematics, discrete structures, linear algebra, abstract/modern algebra, graph theory, probability, bioinformatics, statistics, biostatistics, and modeling, as well as for biology courses such as genetics, cell and molecular biology, biochemistry, ecology, and evolution.
Table of Contents
Preface
1. Graph Theory for Systems Biology: Interval Graphs, Motifs, and Pattern Recognition
John R. Jungck and Rama Viswanathan
2. Food Webs and Graphs
Margaret (Midge) Cozzens
3. Adaptation and Fitness Graphs
Kristina Crona and Emilie Wiesner
4. Signaling Networks: Asynchronous Boolean Models
Réka Albert and Raina Robeva
5. Dynamics of Complex Boolean Networks: Canalization, Stability, and Criticality
Qijun He, Matthew Macauley and Robin Davies
6. Steady State Analysis of Boolean Models: A Dimension Reduction Approach
Alan Veliz-Cuba and David Murrugarra
7. BioModel Engineering with Petri Nets
Mary Ann Blätke, Monika Heiner and Wolfgang Marwan
8. Transmission of Infectious Diseases: Data, Models, and Simulations
Winfried Just, Hannah Callender, M. Drew LaMar and Natalia Toporikova
9. Disease Transmission Dynamics on Networks: Network Structure Versus Disease Dynamics
Winfried Just, Hannah Callender and M. Drew LaMar
10. Predicting Correlated Responses in Quantitative Traits Under Selection: A Linear Algebra Approach
Janet Steven and Bessie Kirkwood
11. Metabolic Analysis: Algebraic and Geometric Methods
Terrell L. Hodge, Blair R. Szymczyna and Todd J. Barkman
12. Reconstructing the Phylogeny: Computational Methods
Grady Weyenberg and Ruriko Yoshida
13. RNA Secondary Structures: Combinatorial Models and Folding Algorithms
Qijun He, Matthew Macauley and Robin Davies
14. RNA Secondary Structures: An Approach Through Pseudoknots and Fatgraphs
Christian M. Reidys