Mathematical Modeling in Systems Biology An Introduction

ISBN-10: 0262018888
ISBN-13: 9780262018883
Edition: 2013
Authors: Brian P. Ingalls
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Description: Systems techniques are integral to current research in molecular cell biology, andsystem-level investigations are often accompanied by mathematical models. These models serve asworking hypotheses: they help us to understand and predict the behavior  More...

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Book details

Copyright year: 2013
Publisher: MIT Press
Publication date: 7/5/2013
Binding: Hardcover
Pages: 356
Size: 7.50" wide x 9.25" long x 1.00" tall
Weight: 2.046
Language: English

Systems techniques are integral to current research in molecular cell biology, andsystem-level investigations are often accompanied by mathematical models. These models serve asworking hypotheses: they help us to understand and predict the behavior of complex systems. Thisbook offers an introduction to mathematical concepts and techniques needed for the construction andinterpretation of models in molecular systems biology. It is accessible to upper-level undergraduateor graduate students in life science or engineering who have some familiarity with calculus, andwill be a useful reference for researchers at all levels.The first four chapterscover the basics of mathematical modeling in molecular systems biology. The last four chaptersaddress specific biological domains, treating modeling of metabolic networks, of signal transductionpathways, of gene regulatory networks, and of electrophysiology and neuronal action potentials.Chapters 3--8 end with optional sections that address more specialized modeling topics. Exercises,solvable with pen-and-paper calculations, appear throughout the text to encourage interaction withthe mathematical techniques. More involved end-of-chapter problem sets require computationalsoftware. Appendixes provide a review of basic concepts of molecular biology, additionalmathematical background material, and tutorials for two computational software packages (XPPAUT andMATLAB) that can be used for model simulation and analysis.

Brian P. Ingalls is Associate Professor in the Departments of Applied Mathematics, Biology, and Chemical Engineering at the University of Waterloo.

Preface
Introduction
Systems Biology and Synthetic Biology
What Is a Dynamic Mathematical Model?
Why Are Dynamic Mathematical Models Needed?
How Are Dynamic Mathematical Models Used?
Basic Features of Dynamic Mathematical Models
State Variables and Model Parameters
Steady-State Behavior and Transient Behavior
Linearity and Nonlinearity
Global and Local Behavior
Deterministic Models and Stochastic Models
Dynamic Mathematical Models in Molecular Cell Biology
Drug Target Prediction in Trypanosoma brucei Metabolism
Identifying the Source of Oscillatory Behavior in NF-�B Signaling
Model-Based Design of an Engineered Genetic Toggle Switch
Establishing the Mechanism for Neuronal Action Potential Generation
Suggestions for Further Reading
Modeling of Chemical Reaction Networks
Chemical Reaction Networks
Closed and Open Networks
Dynamic Behavior of Reaction Networks
Simple Network Examples
Numerical Simulation of Differential Equations
Separation of Timescales and Model Reduction
Separation of Timescales: The Rapid Equilibrium Assumption
Separation of Timescales: The Quasi-Steady-State Assumption
Suggestions for Further Reading
Problem Set
Biochemical Kinetics
Enzyme Kinetics
Michaelis-Menten Kinetics
Two-Substrate Reactions
Regulation of Enzyme Activity
Competitive Inhibition
Allosteric Regulation
Cooperativity
Compartmental Modeling and Transport
Diffusion
Facilitated Transport
Generalized Mass Action and S-System Modeling
Suggestions for Further Reading
Problem Set
Analysis of Dynamic Mathematical Models
Phase Plane Analysis
Direction Fields
Nullclines
Stability
Stable and Unstable Steady States
Linearized Stability Analysis
Limit-Cycle Oscillations
Bifurcation Analysis
Sensitivity Analysis
Local Sensitivity Analysis
Determination of Local Sensitivity Coefficients
Parameter Fitting
Suggestions for Further Reading
Problem Set
Metabolic Networks
Modeling of Metabolism
Example: A Pathway Model
Sensitivity Analysis of Metabolic Networks: Metabolic Control Analysis
Metabolic Pathways
Flux Control of Unbranched Pathways
Regulation of Unbranched Pathways
Branched Pathways
Modeling of Metabolic Networks
Model Construction
Case Study: Modeling the Regulation of the Methionine Cycle
Stoichiometric Network Analysis
Metabolic Pathway Analysis
Constraint-Based Modeling: Metabolic Flux Analysis
Suggestions for Further Reading
Problem Set
Signal Transduction Pathways
Signal Amplification
Bacterial Two-Component Signaling Pathways
G-Protein Signaling Pathways
Ultrasensitivity
Zero-Order Ultrasensitivity
Ultrasensitive Activation Cascades
Adaptation
Bacterial Chemotaxis
Memory and Irreversible Decision-Making
Apoptosis
Frequency Encoding
Calcium Oscillations
Frequency Response Analysis
Definition of the Frequency Response
Interpretation of the Frequency Response
Construction of the Frequency Response
Suggestions for Further Reading
Problem Set
Gene Regulatory Networks
Modeling of Gene Expression
Unregulated Gene Expression
Regulated Gene Expression
Gene Regulatory Networks
Genetic Switches
The lac Operon
The Phage Lambda Decision Switch
The Collins Toggle Switch
Oscillatory Gene Networks
The Goodwin Oscillator
Circadian Rhythms
Synthetic Oscillatory Gene Networks
Cell-to-Cell Communication
Bacterial Quorum Sensing
Engineered Cell-to-Cell Communication
Synchronization of Oscillating Cells
Computation by Gene Regulatory Networks
Promoters as Logic Gates
Digital Representations of Gene Circuits
Complex Gene Regulatory Networks
Stochastic Modeling of Biochemical and Genetic Networks
A Discrete Modeling Framework
The Chemical Master Equation
Gillespie's Stochastic Simulation Algorithm
Examples
Suggestions for Further Reading
Problem Set
Electrophysiology
Membrane Potential
The Nernst Potential
The Membrane Model
Excitable Membranes
Voltage-Gated Ion Channels
The Morris-Lecar Model
Intercellular Communication
Synaptic Transmission
Spatial Modeling
Propagation of Membrane Voltage
Passive Membrane
Excitable Membrane: Action Potential Propagation
Suggestions for Further Reading
Problem Set
Molecular Cell Biology
Cells
The Chemistry of Life
Macromolecules
Model Organisms
Mathematical Fundamentals
Differential Calculus
Linear Algebra
Probability
Computational Software
XPPAUT
MATLAB
Bibliography
Index

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