Table of Contents

Cover image

Title page

Front Matter

Copyright

Contributors

Preface

Chapter 1. Mechanisms of Gene Regulation: Boolean Network Models of the Lactose Operon in Escherichia coli

1.1 Introduction

1.2 E. Coli and the LAC Operon

1.3 Boolean Network Models of the LAC Operon

1.4 Determining the Fixed Points of Boolean Networks

1.5 Conclusions and Discussion

Acknowledgments

1.6 Supplementary Materials

References

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 Yildirim-Mackey Differential Equation Models for the Lactose Operon

2.5 Boolean Modeling of Biochemical Interactions

2.6 Boolean Approximations of the Yildirim-Mackey 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

3.1 Introduction

3.2 Polynomial Dynamical Systems (PDSs)

3.3 Computational Algebra Preliminaries

3.4 Construction of the Model Space: A Reverse Engineering Algorithm

3.5 Model Selection

3.6 Discretization

References

Chapter 4. Global Dynamics Emerging from Local Interactions: Agent-Based Modeling for the Life Sciences

4.1 Introduction

4.2 Axon Guidance

4.3 An Agent-Based Model for Cholera and the Importance of Replication

4.4 Use and Description of ABM in Research: Tick-Borne Disease Agent-Based Models

4.5 Comments for Instructors

Acknowledgments

4.6 Supplementary Materials

References

Chapter 5. Agent-Based 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 Agent-Based Models

5.5 Optimization and Optimal Control

5.6 Scaling and Aggregation

5.7 A Heuristic Approach

5.8 Mathematical Framework for Representing Agent-Based Models

5.9 Translating Agent-Based 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

8.1 Introduction

8.2 Biochemical Reaction Networks, Metabolic Pathways, and the Stoichiometry Matrix

8.3 Extreme Paths and Model Improvements

Acknowledgments

8.4 Supplementary Data

References

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

10.1 Introduction

10.2 Basics on Trees and Phylogenetic Trees

10.3 Tree Space

10.4 Neighbor-Joining and BME

10.5 Summary

References

Index