Preface
Contents
Mitotic Cycle Regulation. I. Oscillations and Bistability
Introduction
Physiology
Molecular Mechanisms
Mathematical Model, Results, Predictions and Confirmations
Limit-Cycle Oscillations
Bistability
Experimental Confirmation of Hysteresis
Experimental Confirmation of Limit-Cycle Oscillations
Discussion
Additional Reading
References
Mitotic Cycle Regulation. II. Traveling Waves
Introduction
FitzHugh-Nagumo (FHN) Model of Nerve Impulse Propagation
Novak-Tyson Model of MPF Waves in Frog-Egg Extracts
Discussion
Additional Reading
References
Cell Cycle Regulation. Bifurcation Theory
Introduction
The Growth-Controlled Fission-Yeast Cell Cycle
What Is Bifurcation Theory?
Historical Background
One-Parameter Bifurcation Diagrams and Signal-Response Curves
How Many Types of Generic Bifurcations Are Exhibited by Dynamical Systems?
A Model Illustrating the Bifurcation Diagram in Fig. 1
Discussion
Additional Reading
References
Glycolytic Oscillations
Introduction
Physiology and Molecular Mechanism
Mathematical Model
Results
Discussion
Additional Reading
References
NF-ΞΊB Spiky Oscillations
Introduction
Physiology and Molecular Mechanism
Mathematical Model
Results
Discussion
References
Tick, Tock, Circadian Clocks
Introduction
Physiology and Molecular Mechanisms
Mathematical Model
Results
Discussion
References
Spruce Budworm and the Forest
Introduction
Ecological Mechanisms
Mathematical Model
Spruce Budworm Model
Spruce Budworm and Forest Model
Results
Spruce Budworm Model
Spruce Budworm and Forest Model
Discussion
References
Selected Additional Reading Resources
Modeling cAMP Oscillations in Budding Yeast
Introduction
Molecular Mechanisms and Physiology
The cAMP/PKA Pathway
Experimental Observations of the cAMP/PKA Pathway Response
Model of cAMP/PKA Pathway
Results
Examining the Reduced Two-Variable System
Exploring Oscillatory Regimes of cAMP
Discussion
Part A: Model Definition-Two Variable
Part B: Model Definition-Four Variable
Part C: Stress Parameter A Induces Oscillations in Intermediate Regime
Part D: Bifurcation Analysis
Additional Material
References
Synchronization of Oscillatory Gene Networks
Introduction
Molecular Mechanism
Mathematical Models
Synchronization of Oscillators
Discussion
Additional Reading
References
The lac Operon
Introduction
Physiology
Molecular Mechanism
Mathematical Model
Results
Discussion
Additional Reading
References
Fate Decisions of CD4+ T Cells
Introduction
Physiology and Molecular Mechanisms
Mathematical Models and Results
Master Regulator Cross-Repression with TCR Signal
Master Regulator Cross-Repression and Autoactivation with TCR Signal and Polarizing Cytokines
Discussion
References
Stochastic Gene Expression
Introduction
Molecular Mechanism
Mathematical Model and Simulation Method
Revisit the Deterministic Model
Deterministic Model Implies Property of Stochastic Dynamics
Derive the Chemical Master Equation for Stochastic Dynamics of mRNA
Chemical Master Equations for Stochastic Dynamics of mRNA and Protein
Chemical Master Equations for General Reaction Networks
GillespieΒ΄s Stochastic Simulation Algorithm
Results
Steady State Equations for Stochastic Model
Steady State Probability Distribution of mRNA Number
Steady State Probability Distribution of Protein Number
Simulated Stochastic Dynamics
Discussion
Appendix A: Sampling for Continuous Random Variables
Appendix B: Probability Distribution for the Waiting Time of Next Reaction
Appendix C: Probability Distribution for the Index of Next Reaction
Appendix D: MATLAB Code for Gillespie Simulation of Stochastic mRNA and Protein Dynamics
Appendix E: MATLAB Code for Statistical Analysis of Results from Stochastic Simulation
References
Collective Molecular Motor Transport
Introduction
Model
Gillespie Algorithm
Model 1: Transport by a Team
Model 2: Tug-of-War
Results
Discussion and Exercises
References
Principle of Cooperativity in Olfactory Receptor Selection
Introduction
Physiology and Molecular Mechanisms
Physiology Background
Summary of Known Experimental Information
Formulation of the Problem
Mathematical Model
Epigenetic Dynamics
Enhancer Binding Dynamics
Transcriptional Dynamics
Results
Discussion
References
Applying Quantitative Systems Pharmacology (QSP) Modeling to Understand the Treatment of Pneumocystis
Introduction
Physiology and Molecular Mechanisms
Mathematical Model
Step One: Construction of the PK module
Step Two: Construction of the PD module
Step Three: Integration of the PK Module and the PD Modules into QSP Models
Results
The Constructed PK and PD Modules Are Consistent to Multiple Experimental Data
Quantitative Systems Pharmacology Model Construction and Validation
Discussion
References
Virus Dynamics
Introduction
Mathematical Model
Per Capita Rates and Average Lifespans
Results
Mathematical Models of Immune Responses
Mathematical Models of Drug Therapy
Finding the Basic Reproduction Number
Biphasic Decay
Reflections on Data Fitting and Model Selection
Discussion
Methods
References
Identifying Virus-Like Regions in Microbial Genomes Using Hidden Markov Models
Background
The Role of Viruses in Genome Evolution
Overview of Current Methods
Detection of EVEs
Homology Searches and Hidden Markov Models: Practical Considerations
ViralRecall: A Simple Approach for Identifying EVEs and Other Virus-Like Regions in Genomic Data
Conclusions
References
Computational Software
XPPAUT
XPP Graphical User Interface Description
Solving Equations and Displaying Solution
AUTO Program
Partial Differential Equations
MATLAB and Octave
Python
References
Index