Algebraic and Discrete Mathematical Methods for Modern Biology - 1st Edition - ISBN: 9780128012130, 9780128012710

Algebraic and Discrete Mathematical Methods for Modern Biology

1st Edition

Editors: Raina Robeva
eBook ISBN: 9780128012710
Hardcover ISBN: 9780128012130
Imprint: Academic Press
Published Date: 25th March 2015
Page Count: 382
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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.

Key Features

  • Examines significant questions in modern biology and their mathematical treatments
  • Presents important mathematical concepts and tools in the context of essential biology
  • Features material of interest to students in both mathematics and biology
  • Presents chapters in modular format so coverage need not follow the Table of Contents
  • Introduces projects appropriate for undergraduate research
  • Utilizes freely accessible software for visualization, simulation, and analysis in modern biology
  • Requires no calculus as a prerequisite
  • Provides a complete Solutions Manual
  • Features a companion website with supplementary resources


Students and researchers in biomathematics, mathematics, and biology.

Table of Contents

  • Preface
  • Companion Website
  • Chapter 1: Graph Theory for Systems Biology: Interval Graphs, Motifs, and Pattern Recognition
    • Abstract
    • 1.1 Introduction
    • 1.2 Revisualizing, Recognizing, and Reasoning About Relationships
    • 1.3 Example I—Differentiation: Gene Expression
    • Projects
    • 1.4 Example II—Disease Etiology
    • 1.5 Conclusion
    • Acknowledgments
  • Chapter 2: Food Webs and Graphs
    • Abstract
    • 2.1 Introduction
    • 2.2 Modeling Predator-Prey Relationships with Food Webs
    • 2.3 Trophic Levels and Trophic Status
    • Research Questions
    • 2.4 Competition Graphs and Habitat Dimension
    • Research Questions
    • 2.5 Connectance, Competition Number, and Projection Graphs
    • Research Questions
    • Research Questions
    • 2.6 Conclusions
    • Further Research Questions
  • Chapter 3: Adaptation and Fitness Graphs
    • Abstract
    • 3.1 Introduction
    • 3.2 Fitness Landscapes and Fitness Graphs
    • 3.3 Fitness Graphs and Recombination
    • 3.4 Fitness Graphs and Drug Cycling
  • Chapter 4: Signaling Networks: Asynchronous Boolean Models
    • Abstract
    • 4.1 Introduction to Signaling Networks
    • 4.2 A Brief Summary of Graph-Theoretic Analysis of Signaling Networks
    • 4.3 Dynamic Modeling of Signaling Networks
    • 4.4 The Representation of Node Regulation in Boolean Models
    • 4.5 The Dynamics of Boolean Models
    • 4.6 Attractor Analysis for Stochastic Asynchronous Update
    • 4.7 Boolean Models Capture Characteristic Dynamic Behavior
    • 4.8 How to Deal with Incomplete Information when Constructing the Model
    • 4.9 Generate Novel Predictions with the Model
    • 4.10 Boolean Rule-Based Structural Analysis of Cellular Networks
    • 4.11 Conclusions
  • Chapter 5: Dynamics of Complex Boolean Networks: Canalization, Stability, and Criticality
    • Abstract
    • Acknowledgments
    • 5.1 Introduction
    • 5.2 Boolean Network Models
    • 5.3 Canalization
    • 5.4 Dynamics Over Complex Networks
  • Chapter 6: Steady State Analysis of Boolean Models: A Dimension Reduction Approach
    • Abstract
    • 6.1 Introduction
    • 6.2 An Example: Toy Model of the lac Operon
    • 6.3 General Reduction
    • 6.4 Implementing the Reduction Algorithm Using Boolean Algebra
    • 6.5 Implementing the Reduction Algorithm Using Polynomial Algebra
    • 6.6 Applications
    • 6.7 AND Boolean Models
    • 6.8 Conclusion
  • Chapter 7: BioModel Engineering with Petri Nets
    • Abstract
    • Acknowledgments
    • 7.1 Introduction
    • 7.2 Running Case Study
    • 7.3 Petri Nets (PN)
    • 7.4 Stochastic Petri Nets (SPN)
    • 7.5 Continuous Petri Nets (CPN)
    • 7.6 Hybrid Petri Nets (HPN)
    • 7.7 Colored Petri Nets
    • 7.8 Conclusions
  • 7.9 Supplementary Materials
  • Chapter 8: Transmission of Infectious Diseases: Data, Models, and Simulations
    • Abstract
    • 8.1 Introduction: Why Do We Want to Model Infectious Diseases?
    • 8.2 Mathematical Models of Disease Transmission
    • 8.3 How Does the Computer Run Simulations?
  • Chapter 9: Disease Transmission Dynamics on Networks: Network Structure Versus Disease Dynamics
    • Abstract
    • 9.1 Introduction
    • 9.2 Models Based on the Uniform Mixing Assumption
    • 9.3 Network-Based Models
    • 9.4 Suggestions for Further Study
    • Acknowledgments
  • Chapter 10: Predicting Correlated Responses in Quantitative Traits Under Selection: A Linear Algebra Approach
    • Abstract
    • 10.1 Introduction
    • 10.2 Quantifying Selection on Quantitative Traits
    • 10.3 Covariance Among Traits Under Selection
  • Chapter 11: Metabolic Analysis: Algebraic and Geometric Methods
    • Abstract
    • 11.1 Introduction
    • 11.2 Encoding the Reactions: Linear Algebraic Modeling
    • 11.3 Adding Reaction Kinetics: Algebraic Formulation of Mass-Action Kinetics
    • 11.4 Directions for Further Reading and Research: Metabolic Pathways
    • 11.5 NMR and Linear Algebraic Methods
    • 11.6 NMR Spectroscopy and Applications to the Study of Metabolism
    • 11.7 NMR for Metabolic Analysis and Mathematical Methods: Directions of Further Research
    • 11.8 Supplementary Materials
  • Chapter 12: Reconstructing the Phylogeny: Computational Methods
    • Abstract
    • 12.1 Introduction
    • 12.2 Quantifying Evolutionary Change
    • 12.3 Reconstructing the Tree
    • 12.4 Model Selection
    • 12.5 Statistical Methods to Test Congruency Between Trees
  • Chapter 13: RNA Secondary Structures: Combinatorial Models and Folding Algorithms
    • Abstract
    • Acknowledgments
    • 13.1 Introduction
    • 13.2 Combinatorial Models of Noncrossing RNA Structures
    • 13.3 Energy-Based Folding Algorithms for Secondary Structure Prediction
    • 13.4 Stochastic Folding Algorithms via Language Theory
    • 13.5 Pseudoknots
  • Chapter 14: RNA Secondary Structures: An Approach Through Pseudoknots and Fatgraphs
    • Abstract
    • Acknowledgments
    • 14.1 Introduction
    • 14.2 Fatgraphs and Shapes
    • 14.3 Genus Recursion
    • 14.4 Shapes of Fixed Topological Genus
  • Index


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About the Editor

Raina Robeva

Raina Robeva

Raina Robeva was born in Sofia, Bulgaria. She has a PhD in Mathematics from the University of Virginia and has led multiple NSF-funded curriculum development projects at the interface of mathematics and biology. She is the lead author of the textbook An Invitation to Biomathematics (2008) and the lead editor of the volume Mathematical Concepts and Methods in Modern Biology: Using Modern Discrete Models (2013), both published by Academic Press. Robeva is the founding Chief Editor of the research journal Frontiers in Systems Biology. She is a professor of Mathematical Sciences at Sweet Briar College and lives in Charlottesville, Virginia.

Affiliations and Expertise

Professor of Mathematical Sciences, Sweet Briar College, Sweet Briar, VA, USA


"...makes an important contribution to mathematical biology education. It brings to the reader important biological problems and novel mathematical approaches that are mostly not discussed in other undergraduate texts on the subject." --Society for Industrial and Applied Mathematics

"The book will serve as an excellent resource for instructors in the overlap between biology, mathematics, and computing who are looking for interesting and well-worked-out examples that apply algebra to modern biological questions." --The Quarterly Review of Biology

"This is an excellent book which would be suitable as a textbook...I therefore strongly recommend it, over other classic texts, for use in teaching Discrete Mathematics."