Mathematical Modeling in Systems Biology
An Introduction
by Ingalls, Ingalls
ISBN: 9780262315647  Copyright 2013
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Systems techniques are integral to current research in molecular cell biology, and systemlevel investigations are often accompanied by mathematical models. These models serve as working hypotheses: they help us to understand and predict the behavior of complex systems. This book offers an introduction to mathematical concepts and techniques needed for the construction and interpretation of models in molecular systems biology. It is accessible to upperlevel undergraduate or graduate students in life science or engineering who have some familiarity with calculus, and will be a useful reference for researchers at all levels.
The first four chapters cover the basics of mathematical modeling in molecular systems biology. The last four chapters address specific biological domains, treating modeling of metabolic networks, of signal transduction pathways, 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 penandpaper calculations, appear throughout the text to encourage interaction with the mathematical techniques. More involved endofchapter problem sets require computational software. Appendixes provide a review of basic concepts of molecular biology, additional mathematical background material, and tutorials for two computational software packages (XPPAUT and MATLAB) that can be used for model simulation and analysis.
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Contents (pg. v)  
Preface (pg. xi)  
1 Introduction (pg. 1)  
1.1 Systems Biology and Synthetic Biology (pg. 1)  
1.2 What Is a Dynamic Mathematical Model? (pg. 3)  
1.3 Why Are Dynamic Mathematical Models Needed? (pg. 5)  
1.4 How Are Dynamic Mathematical Models Used? (pg. 6)  
1.5 Basic Features of Dynamic Mathematical Models (pg. 7)  
1.6 Dynamic Mathematical Models in Molecular Cell Biology (pg. 10)  
1.7 Suggestions for Further Reading (pg. 18)  
2 Modeling of Chemical Reaction Networks (pg. 21)  
2.1 Chemical Reaction Networks (pg. 22)  
2.2 Separation of Timescales and Model Reduction (pg. 39)  
2.3 Suggestions for Further Reading (pg. 48)  
2.4 Problem Set (pg. 48)  
3 Biochemical Kinetics (pg. 55)  
3.1 Enzyme Kinetics (pg. 55)  
3.2 Regulation of Enzyme Activity (pg. 64)  
3.3 Cooperativity (pg. 68)  
3.4 Compartmental Modeling and Transport (pg. 74)  
3.5* Generalized Mass Action and SSystem Modeling (pg. 77)  
3.6 Suggestions for Further Reading (pg. 80)  
3.7 Problem Set (pg. 81)  
4 Analysis of Dynamic Mathematical Models (pg. 89)  
4.1 Phase Plane Analysis (pg. 89)  
4.2 Stability (pg. 95)  
4.3 LimitCycle Oscillations (pg. 108)  
4.4 Bifurcation Analysis (pg. 112)  
4.5 Sensitivity Analysis (pg. 115)  
4.6* Parameter Fitting (pg. 119)  
4.7 Suggestions for Further Reading (pg. 122)  
4.8 Problem Set (pg. 122)  
5 Metabolic Networks (pg. 131)  
5.1 Modeling of Metabolism (pg. 132)  
5.2 Metabolic Pathways (pg. 136)  
5.3 Modeling of Metabolic Networks (pg. 143)  
5.4* Stoichiometric Network Analysis (pg. 150)  
5.5 Suggestions for Further Reading (pg. 166)  
5.6 Problem Set (pg. 166)  
6 Signal Transduction Pathways (pg. 175)  
6.1 Signal Amplification (pg. 177)  
6.2 Ultrasensitivity (pg. 182)  
6.3 Adaptation (pg. 188)  
6.4 Memory and Irreversible DecisionMaking (pg. 193)  
6.5 Frequency Encoding (pg. 196)  
6.6* Frequency Response Analysis (pg. 200)  
6.7 Suggestions for Further Reading (pg. 213)  
6.8 Problem Set (pg. 213)  
7 Gene Regulatory Networks (pg. 225)  
7.1 Modeling of Gene Expression (pg. 226)  
7.2 Genetic Switches (pg. 236)  
7.3 Oscillatory Gene Networks (pg. 253)  
7.4 CelltoCell Communication (pg. 263)  
7.5 Computation by Gene Regulatory Networks (pg. 272)  
7.6* Stochastic Modeling of Biochemical and Genetic Networks (pg. 280)  
7.7 Suggestions for Further Reading (pg. 295)  
7.8 Problem Set (pg. 296)  
8 Electrophysiology (pg. 315)  
8.1 Membrane Potential (pg. 316)  
8.2 Excitable Membranes (pg. 320)  
8.3 Intercellular Communication (pg. 326)  
8.4* Spatial Modeling (pg. 330)  
8.5 Suggestions for Further Reading (pg. 333)  
8.6 Problem Set (pg. 334)  
Appendix A: Molecular Cell Biology (pg. 343)  
Appendix B: Mathematical Fundamentals (pg. 357)  
Appendix C: Computational Software (pg. 371)  
Bibliography (pg. 395)  
Index (pg. 401)  
Contents (pg. v)  
Preface (pg. xi)  
1 Introduction (pg. 1)  
1.1 Systems Biology and Synthetic Biology (pg. 1)  
1.2 What Is a Dynamic Mathematical Model? (pg. 3)  
1.3 Why Are Dynamic Mathematical Models Needed? (pg. 5)  
1.4 How Are Dynamic Mathematical Models Used? (pg. 6)  
1.5 Basic Features of Dynamic Mathematical Models (pg. 7)  
1.6 Dynamic Mathematical Models in Molecular Cell Biology (pg. 10)  
1.7 Suggestions for Further Reading (pg. 18)  
2 Modeling of Chemical Reaction Networks (pg. 21)  
2.1 Chemical Reaction Networks (pg. 22)  
2.2 Separation of Timescales and Model Reduction (pg. 39)  
2.3 Suggestions for Further Reading (pg. 48)  
2.4 Problem Set (pg. 48)  
3 Biochemical Kinetics (pg. 55)  
3.1 Enzyme Kinetics (pg. 55)  
3.2 Regulation of Enzyme Activity (pg. 64)  
3.3 Cooperativity (pg. 68)  
3.4 Compartmental Modeling and Transport (pg. 74)  
3.5* Generalized Mass Action and SSystem Modeling (pg. 77)  
3.6 Suggestions for Further Reading (pg. 80)  
3.7 Problem Set (pg. 81)  
4 Analysis of Dynamic Mathematical Models (pg. 89)  
4.1 Phase Plane Analysis (pg. 89)  
4.2 Stability (pg. 95)  
4.3 LimitCycle Oscillations (pg. 108)  
4.4 Bifurcation Analysis (pg. 112)  
4.5 Sensitivity Analysis (pg. 115)  
4.6* Parameter Fitting (pg. 119)  
4.7 Suggestions for Further Reading (pg. 122)  
4.8 Problem Set (pg. 122)  
5 Metabolic Networks (pg. 131)  
5.1 Modeling of Metabolism (pg. 132)  
5.2 Metabolic Pathways (pg. 136)  
5.3 Modeling of Metabolic Networks (pg. 143)  
5.4* Stoichiometric Network Analysis (pg. 150)  
5.5 Suggestions for Further Reading (pg. 166)  
5.6 Problem Set (pg. 166)  
6 Signal Transduction Pathways (pg. 175)  
6.1 Signal Amplification (pg. 177)  
6.2 Ultrasensitivity (pg. 182)  
6.3 Adaptation (pg. 188)  
6.4 Memory and Irreversible DecisionMaking (pg. 193)  
6.5 Frequency Encoding (pg. 196)  
6.6* Frequency Response Analysis (pg. 200)  
6.7 Suggestions for Further Reading (pg. 213)  
6.8 Problem Set (pg. 213)  
7 Gene Regulatory Networks (pg. 225)  
7.1 Modeling of Gene Expression (pg. 226)  
7.2 Genetic Switches (pg. 236)  
7.3 Oscillatory Gene Networks (pg. 253)  
7.4 CelltoCell Communication (pg. 263)  
7.5 Computation by Gene Regulatory Networks (pg. 272)  
7.6* Stochastic Modeling of Biochemical and Genetic Networks (pg. 280)  
7.7 Suggestions for Further Reading (pg. 295)  
7.8 Problem Set (pg. 296)  
8 Electrophysiology (pg. 315)  
8.1 Membrane Potential (pg. 316)  
8.2 Excitable Membranes (pg. 320)  
8.3 Intercellular Communication (pg. 326)  
8.4* Spatial Modeling (pg. 330)  
8.5 Suggestions for Further Reading (pg. 333)  
8.6 Problem Set (pg. 334)  
Appendix A: Molecular Cell Biology (pg. 343)  
Appendix B: Mathematical Fundamentals (pg. 357)  
Appendix C: Computational Software (pg. 371)  
Bibliography (pg. 395)  
Index (pg. 401)  
Contents (pg. v)  
Preface (pg. xi)  
1 Introduction (pg. 1)  
1.1 Systems Biology and Synthetic Biology (pg. 1)  
1.2 What Is a Dynamic Mathematical Model? (pg. 3)  
1.3 Why Are Dynamic Mathematical Models Needed? (pg. 5)  
1.4 How Are Dynamic Mathematical Models Used? (pg. 6)  
1.5 Basic Features of Dynamic Mathematical Models (pg. 7)  
1.6 Dynamic Mathematical Models in Molecular Cell Biology (pg. 10)  
1.7 Suggestions for Further Reading (pg. 18)  
2 Modeling of Chemical Reaction Networks (pg. 21)  
2.1 Chemical Reaction Networks (pg. 22)  
2.2 Separation of Timescales and Model Reduction (pg. 39)  
2.3 Suggestions for Further Reading (pg. 48)  
2.4 Problem Set (pg. 48)  
3 Biochemical Kinetics (pg. 55)  
3.1 Enzyme Kinetics (pg. 55)  
3.2 Regulation of Enzyme Activity (pg. 64)  
3.3 Cooperativity (pg. 68)  
3.4 Compartmental Modeling and Transport (pg. 74)  
3.5* Generalized Mass Action and SSystem Modeling (pg. 77)  
3.6 Suggestions for Further Reading (pg. 80)  
3.7 Problem Set (pg. 81)  
4 Analysis of Dynamic Mathematical Models (pg. 89)  
4.1 Phase Plane Analysis (pg. 89)  
4.2 Stability (pg. 95)  
4.3 LimitCycle Oscillations (pg. 108)  
4.4 Bifurcation Analysis (pg. 112)  
4.5 Sensitivity Analysis (pg. 115)  
4.6* Parameter Fitting (pg. 119)  
4.7 Suggestions for Further Reading (pg. 122)  
4.8 Problem Set (pg. 122)  
5 Metabolic Networks (pg. 131)  
5.1 Modeling of Metabolism (pg. 132)  
5.2 Metabolic Pathways (pg. 136)  
5.3 Modeling of Metabolic Networks (pg. 143)  
5.4* Stoichiometric Network Analysis (pg. 150)  
5.5 Suggestions for Further Reading (pg. 166)  
5.6 Problem Set (pg. 166)  
6 Signal Transduction Pathways (pg. 175)  
6.1 Signal Amplification (pg. 177)  
6.2 Ultrasensitivity (pg. 182)  
6.3 Adaptation (pg. 188)  
6.4 Memory and Irreversible DecisionMaking (pg. 193)  
6.5 Frequency Encoding (pg. 196)  
6.6* Frequency Response Analysis (pg. 200)  
6.7 Suggestions for Further Reading (pg. 213)  
6.8 Problem Set (pg. 213)  
7 Gene Regulatory Networks (pg. 225)  
7.1 Modeling of Gene Expression (pg. 226)  
7.2 Genetic Switches (pg. 236)  
7.3 Oscillatory Gene Networks (pg. 253)  
7.4 CelltoCell Communication (pg. 263)  
7.5 Computation by Gene Regulatory Networks (pg. 272)  
7.6* Stochastic Modeling of Biochemical and Genetic Networks (pg. 280)  
7.7 Suggestions for Further Reading (pg. 295)  
7.8 Problem Set (pg. 296)  
8 Electrophysiology (pg. 315)  
8.1 Membrane Potential (pg. 316)  
8.2 Excitable Membranes (pg. 320)  
8.3 Intercellular Communication (pg. 326)  
8.4* Spatial Modeling (pg. 330)  
8.5 Suggestions for Further Reading (pg. 333)  
8.6 Problem Set (pg. 334)  
Appendix A: Molecular Cell Biology (pg. 343)  
Appendix B: Mathematical Fundamentals (pg. 357)  
Appendix C: Computational Software (pg. 371)  
Bibliography (pg. 395)  
Index (pg. 401) 
Brain P. Ingalls
Brian P. Ingalls is Associate Professor in the Departments of Applied Mathematics, Biology, and Chemical Engineering at the University of Waterloo, Canada. He is the coeditor of Control Theory and Systems Biology (MIT Press, 2010).
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