Home Page Icon
Home Page
Table of Contents for
Cover image
Close
Cover image
by Terrell Hodge, Raina Robeva
Mathematical Concepts and Methods in Modern Biology
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
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
Search in book...
Toggle Font Controls
Playlists
Add To
Create new playlist
Name your new playlist
Playlist description (optional)
Cancel
Create playlist
Sign In
Email address
Password
Forgot Password?
Create account
Login
or
Continue with Facebook
Continue with Google
Sign Up
Full Name
Email address
Confirm Email Address
Password
Login
Create account
or
Continue with Facebook
Continue with Google
Next
Next Chapter
Title page
Add Highlight
No Comment
..................Content has been hidden....................
You can't read the all page of ebook, please click
here
login for view all page.
Day Mode
Cloud Mode
Night Mode
Reset