Book Description
Mathematical Concepts and Methods in Modern Biology offers a quantitative framework for analyzing, predicting, and modulating the behavior of complex biological systems. The book presents important mathematical concepts, methods and tools in the context of essential questions raised in modern biology.
Designed around the principles of projectbased learning and problemsolving, the book considers biological topics such as neuronal networks, plant population growth, metabolic pathways, and phylogenetic tree reconstruction. The mathematical modeling tools brought to bear on these topics include Boolean and ordinary differential equations, projection matrices, agentbased modeling and several algebraic approaches. Heavy computation in some of the examples is eased by the use of freely available opensource software.
 Features selfcontained chapters with real biological research examples using freely available computational tools
 Spans several mathematical techniques at basic to advanced levels
 Offers broad perspective on the uses of algebraic geometry/polynomial algebra in molecular systems biology
Table of Contents
 Cover image
 Title page
 Table of Contents
 Front Matter
 Copyright
 Contributors
 Preface
 Chapter 1. Mechanisms of Gene Regulation: Boolean Network Models of the Lactose Operon in Escherichia coli

Chapter 2. Bistability in the Lactose Operon of Escherichia coli: A Comparison of Differential Equation and Boolean Network Models
 2.1 Introduction
 2.2 The Lactose Operon of Escherichia Coli
 2.3 Modeling Biochemical Reactions with Differential Equations
 2.4 The YildirimMackey Differential Equation Models for the Lactose Operon
 2.5 Boolean Modeling of Biochemical Interactions
 2.6 Boolean Approximations of the YildirimMackey Models
 2.7 Conclusions and Discussion
 Acknowledgment
 2.8 Supplementary Materials
 References
 Chapter 3. Inferring the Topology of Gene Regulatory Networks: An Algebraic Approach to Reverse Engineering
 Chapter 4. Global Dynamics Emerging from Local Interactions: AgentBased Modeling for the Life Sciences

Chapter 5. AgentBased Models and Optimal Control in Biology: A Discrete Approach
 5.1 Introduction
 5.2 A First Example
 5.3 Netlogo: An Introduction
 5.4 An Introduction to AgentBased Models
 5.5 Optimization and Optimal Control
 5.6 Scaling and Aggregation
 5.7 A Heuristic Approach
 5.8 Mathematical Framework for Representing AgentBased Models
 5.9 Translating AgentBased Models into Polynomial Dynamical Systems
 5.10 Summary
 5.11 Supplementary Materials
 References

Chapter 6. Neuronal Networks: A Discrete Model
 6.1 Introduction and Overview
 6.2 Neuroscience in a Nutshell
 6.3 The Discrete Model
 6.4 Exploring the Model for Some Simple Connectivities
 6.6.5 Exploring the Model for Some Random Connectivities
 6.6 Another Interpretation of the Model: Disease Dynamics
 6.7 More Neuroscience: Connection with ODE Models
 6.8 Directions of Further Research
 6.9 Supplementary Materials
 References

Chapter 7. Predicting Population Growth: Modeling with Projection Matrices
 7.1 Introduction
 7.2 Life Cycles and Population Growth
 7.3 Determining Stages in the Life Cycle
 7.4 Determining the Number of Individuals in a Stage at Time
 7.5 Constructing a Projection Matrix
 7.6 Predicting How a Population Changes after One Year
 7.7 The Stable Distribution of Individuals across Stages
 7.8 Theory Supporting the Calculation of Stable Distributions
 7.9 Determining Population Growth Rate and the Stable Distribution
 7.10 Further Applications of the Projection Matrix
 References
 Chapter 8. Metabolic Pathways Analysis: A Linear Algebraic Approach

Chapter 9. Identifying CpG Islands: Sliding Window and Hidden Markov Model Approaches
 9.1 Introduction
 9.2 Quantitative Characteristics of the CpG Island Regions and Sliding Windows Algorithms
 9.3 Definition and Basic Properties of Markov Chains and Hidden Markov Models
 9.4 Three Canonical Problems for HMMs with Applications to CGI Identification
 9.5 Conclusions and Discussion
 Acknowledgments
 9.6 Supplementary Materials
 References
 Chapter 10. Phylogenetic Tree Reconstruction: Geometric Approaches
 Index
Product Information
 Title: Mathematical Concepts and Methods in Modern Biology
 Author(s):
 Release date: February 2013
 Publisher(s): Academic Press
 ISBN: 9780124157804