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Mathematical Concepts and Methods in Modern Biology
Using Modern Discrete Models
1st Edition - January 15, 2013
Editors: Raina Robeva, Terrell Hodge
Language: English
Hardback ISBN:9780124157804
9 7 8 - 0 - 1 2 - 4 1 5 7 8 0 - 4
eBook ISBN:9780124157934
9 7 8 - 0 - 1 2 - 4 1 5 7 9 3 - 4
Mathematical Concepts and Methods in Modern Biology offers a quantitative framework for analyzing, predicting, and modulating the behavior of complex biological systems. The book p…Read more
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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 project-based learning and problem-solving, 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, agent-based modeling and several algebraic approaches. Heavy computation in some of the examples is eased by the use of freely available open-source software.
Features self-contained 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
Researchers, educators, and students engaged in Biological Research and Mathematics
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
No. of pages: 372
Language: English
Edition: 1
Published: January 15, 2013
Imprint: Academic Press
Hardback ISBN: 9780124157804
eBook ISBN: 9780124157934
RR
Raina Robeva
Raina Robeva was born in Sofia, Bulgaria. She holds a PhD in Mathematics from the University of Virginia and has broad research interests spanning theoretical mathematics, applied probability, and systems biology. Robeva is the founding Chief Editor of the journal Frontiers in Systems Biology and the lead author/editor of the books An Invitation to Biomathematics (2008), Mathematical Concepts and Methods in Modern Biology: Using Modern Discrete Models (2013), and Algebraic and Discrete Mathematical Methods for Modern Biology (2015), all published by Academic Press. She is Professor of Mathematical Sciences and Director of the Center for Science and Technology in Society at Sweet Briar College.
Affiliations and expertise
Professor of Mathematical Sciences, Sweet Briar College, VA, USA
TH
Terrell Hodge
Affiliations and expertise
Western Michigan University, Kalamazoo, MI, USA
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