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1 Introduction to Quantitative Biology 1
B. Munsky, W. S. Hlavacek, L. S. Tsimring
1.1 History and Overview of the q-bio Summer School 1
1.2 Origin and Organization of this Textbook 2
1.3 How to Use this Book 4
1.4 Acknowledgments 6

2 Fostering Collaborations between Experimentalists and Modelers 9
K. Tkach Tuzman
2.1 Education 10
2.2 Presentation 10
2.3 Practice 11
2.4 Attitude 11

I DEFINING AND SIMULATING MODELS
Introduction to the Simulation of Models 15

3 Modeling with Ordinary Differential Equations 19
D. Fey, M. Dobrzy?ski, B. N. Kholodenko
3.1 Introduction 19
3.2 A Primer to Ordinary Differential Equations 20
3.3 From Biochemical Reactions Networks to ODEs 21
3.4 Solving ODEs 27
3.5 Complex Dynamic Behavior: Different Types of Solutions 33
3.6 Detailed Balance: Thermodynamic Constraints 36
3.7 Model Simplifications and Level of Abstraction 38
3.8 Some Advanced Modeling Concepts 42
3.9 Overview of Relevant Software Tools 45
3.10 Exercises 46

4 Modeling with Partial Differential Equations 49
S. D. Olson, J. Huang
4.1 Introduction to Partial Differential Equations 49
4.2 PDE Theory 56
4.3 Analytical Solutions 57
4.4 Numerical Solutions 63
4.5 Summary and Discussion 66
4.6 Exercises 66

5 Stochasticity or Noise in Biochemical Reactions 71
Z. Fox, B. Munsky
5.1 Introduction 71
5.2 The Chemical Master Equation 73
5.3 Analyzing Population Statistics with FSP Approaches 77
5.4 Comparing CME Models to Single-Cell Data 83
5.5 Examples 85
5.6 Summary 91
5.7 Exercises 92

6 The Linear-Noise Approximation and Moment Closure Approximations
for Stochastic Chemical Kinetics 95
A. Singh, R. Grima
6.1 Introduction 95
6.2 Stochastic Models of Biochemical Systems 96
6.3 Time Evolution of Statistical Moments 98
6.4 Moment Closure Methods 101
6.5 The Linear-Noise Approximation 105
6.6 Conclusion 111
6.7 Exercises 112

7 Kinetic Monte Carlo Analyses of Discrete Biomolecular Events 113
R. Bertolusso, M. Kimmel
7.1 Introduction to Stochastic Simulations 113
7.2 Example 127
7.3 Model Specification Using Petri Nets 128
7.4 BIOPN 131
7.5 Exercises 135
Contents ix

8 The Extra Reaction Algorithm for Stochastic Simulation of Biochemical
Reaction Systems in Fluctuating Environments 137
M. Voliotis, P. Thomas, C. G. Bowsher, R. Grima
8.1 Introduction 137
8.2 The Extrande Method 138
8.3 Gene Expression with Time-Varying Transcription 142
8.4 Discussion 145

9 Spatial-Stochastic Simulation of Reaction-Diffusion Systems 149
T. R. Sokolowski, P. R. ten Wolde
9.1 Why Spatiality Matters 150
9.2 Brownian Dynamics Simulations with Reactions 152
9.3 Event-Driven Schemes 161
9.4 Recent Developments: Hybrid Schemes and Parallelization 172
9.5 Further Reading 173
9.6 Online Resources 173
9.7 Summary 174
9.8 Exercises 174

10 Introduction to Molecular Simulation 179
P. ?ulc, J. P. K. Doye, A. A. Louis
10.1 Introduction 179
10.2 Molecular Dynamics 180
10.3 Monte Carlo Sampling 185
10.4 Practical Aspects of Numerical Simulations 187
10.5 Acceleration of Equilibration and Simulating Rare Events 195
10.6 Simulation Tools 199
10.7 Summary 202
10.8 Exercises 203

II MODEL DEVELOPMENT AND ANALYSIS TOOLS
Introduction to Model Development and Analysis 209

11 Reverse-Engineering Biological Networks from Large Data Sets 213
J. L. Natale, D. Hofmann, D. G. Hern?ndez, I. Nemenman
11.1 Lay of the Land 213
11.2 Roles for Reverse-Engineering in Systems Biology Research 220
11.3 Two Different Meanings of Phenomenological “Reconstruction” 228
11.4 Discussion 241
11.5 Try on Your Own: Become a Reverse Engineer 244
11.6 Exercises 245

12 Mathematically Controlled Comparisons for Elucidation of Biological
Design Principles 247
H. Lee, J. G. Lomnitz, M. A. Savageau
12.1 Introduction 248
12.2 End-Product Inhibition: Steady-State Behavior 251
12.3 Transcriptional Autorepression: Dynamic Behavior 259
12.4 Discussion 265
12.5 Summary 268
12.6 Exercises 269

13 Parameter Estimation, Sloppiness, and Model Identifiability 271
B. C. Daniels, M. Dobrzy?ski, D. Fey
13.1 Introduction 272
13.2 Formulating the Parameter Estimation Problem 273
13.3 Solving the Inverse Problem: Nonlinear Optimization 277
13.4 Model Identifiability: Parameters Cannot Always Be Estimated 279
13.5 Precision of Parameter Estimates Using Sensitivity Analysis 283
13.6 Parameter Estimation in the Wild: Practicalities 289
13.7 Summary 290
13.8 Exercises 290

14 Sensitivity Analysis 293
K. Nienałtowski, T. Jetka, M. Komorowski
14.1 Introduction 293
14.2 Theoretical Concepts 294
14.3 Applications of the Sensitivity Analysis 305
14.4 Summary 315
14.5 Exercises 316

15 Experimental Design 321
T. Jetka, K. Nienałtowski, M. Komorowski
15.1 Introduction 321
15.2 General Framework 322
15.3 Frequentist Approach 323
15.4 Bayesian Approach 326
15.5 Asymptotic Equivalency 327
15.6 Applications of Experiment Design 328
15.7 Discussion 334
15.8 Exercises 335

16 Bayesian Parameter Estimation and Markov Chain Monte Carlo 339
B. J. Daigle, Jr.
16.1 Introduction 339
16.2 Likelihood-Based Inference 340
16.3 Bayesian Inference 343
16.4 Markov Chain Monte Carlo for Bayesian Inference 345
16.5 Likelihood-Free Methods for Bayesian Inference 350
16.6 Exercises 355

17 Uses of Bifurcation Analysis in Understanding Cellular
Decision-Making 357
D. Jia, M. K. Jolly, H. Levine
17.1 Introduction 357
17.2 Basic Concepts in Bifurcation Analysis 360
17.3 Bifurcations in One Dimension 363
17.4 Using Bifurcation Theory to Understand Cellular
Decision-Making 365
17.5 Bifurcation Theory in Parameter Sensitivity Analyses 375
17.6 Bifurcation Theory and Experimental Testing with Flow
Cytometry 377
17.7 Conclusions 377
17.8 Exercises 378

18 Performance Measures for Stochastic Processes and the
Matrix-Analytic Approach 379
M. L?pez-Garc?a, M. Nowicka, G. W. Fearnley, S. Ponnambalam,
G. Lythe, C. Molina-Par?s

18.1 Introduction 379
18.2 Analysis of the Stochastic Descriptors: An Application
to VEGFR2/VEGF-A Interaction and Signaling 382
18.3 Numerical Results 392
18.4 Discussion 394

III MODELING IN PRACTICE
Introduction to Computational Modeling Tools in
Quantitative Biology 403

19 Setting Up and Simulating ODE Models 405
H. M. Sauro
19.1 Introduction to TELLURIUM: A PYTHON-Based Platform 405
19.2 Building and Simulating a Model 406
19.3 ANTIMONY: Network Description Language 409
19.4 Running Simulations 411
19.5 Fitting Models to Data 413
19.6 Validation, Validation, and More Validation 416
19.7 Publishing a Reproducible Model 418
19.8 Illustrative Examples 420
19.9 Summary 421
19.10 Availability of Software 421
19.11 Exercises 421

20 Accelerating Stochastic Simulations Using Graphics Processing Units 423
P. Cazzaniga, M. S. Nobile, A. Tangherloni, D. Besozzi
20.1 Introduction 423
20.2 Methods 426
20.3 Example 437
20.4 Discussion 440

21 Rule-Based Modeling Using Virtual Cell (VCELL) 441
M. L. Blinov, D. Vasilescu, I. I. Moraru, J. C. Schaff
21.1 Introduction 441
21.2 Rule-Based Modeling in VCELL 444
21.3 Physiology 445
21.4 Rule-Based Modeling in VCELL: Applications and Simulations 451
21.5 Conclusions 453
21.6 Additional Information 454

22 Spatial Modeling of Cellular Systems with VCELL 455
B. M. Slepchenko, J. C. Schaff, L. M. Loew
22.1 Introduction 455
22.2 Compartmental Models: Sizes of Cellular Compartments May
Matter even if Diffusion is Fast on the Time Scale of Reactions 456
22.3 Reaction-Diffusion in Explicit Geometries: Why Space should
be Explicitly Modeled 459
22.4 Numerical Approaches to Spatial Models Arising in Cell Biology 462
22.5 Conclusion 468

23 Stochastic Simulation of Well-Mixed and Spatially Inhomogeneous
Biochemical Systems 469
B. Drawert, K. R. Sanft, J. H. Abel, S. Hellander, A. Pourzanjani,
A. Hellander, L. R. Petzold
23.1 Introduction 469
23.2 Algorithms 471
23.3 Software for Stochastic Simulation of Biochemical Systems 474
23.4 Examples 477
23.5 Discussion 480
23.6 Summary 483
23.7 Exercises 483

24 Spatial Stochastic Modeling with MCELL and CELLBLENDER 485
S. Gupta, J. Czech, R. Kuczewski, T. M. Bartol, T. J. Sejnowski,
R. E. C. Lee, J. R. Faeder
24.1 Introduction: Why Stochastic Spatial Modeling? 485
24.2 A Brief Overview of MCELL 488
24.3 Getting Started with CELLBLENDER and MCELL 493
24.4 Simulating Free Molecular Diffusion 495
24.5 Restricting Diffusion by Defining Meshes 497
24.6 Simulating Bimolecular Reactions in a Volume 499
24.7 Simulating Molecules and Reactions on Surfaces 504
24.8 Extended Exercise: A Density-Dependent Switch 509
24.9 Concluding Remarks 511

IV EXAMPLE MODELS AND SPECIALIZED METHODS
Introduction to Examples in Quantitative Biology 515

25 The Use of Linear Analysis and Sensitivity Functions in Exploring
Trade-Offs in Biology: Applications to Glycolytic Oscillations 519
F. A. Chandra
25.1 Introduction 519
25.2 Analysis of the Minimal Model of Glycolysis 524
25.3 Discussion 528
xiv Contents

26 Models of Bacterial Chemotaxis 531
G. Lan
26.1 Introduction: The E. coli Chemotaxis Network 531
26.2 Ising-Type Description of the E. coli Chemotactic Process 536
26.3 Summary 544

27 Modeling Viral Dynamics 545
A. S. Perelson, R. M. Ribeiro
27.1 Introduction: Basic Biology of HIV Infection 546
27.2 A Simple Model of HIV Dynamics 547
27.3 Basic Principles of Viral Dynamics and Drug Treatment 549
27.4 Using Modeling to Gain Further Insight into HIV-1 Biology 551
27.5 Other Model Applications and Extensions 557
27.6 Further Reading 561
27.7 Exercises 561

28 Stochastic Modeling of Gene Expression, Protein Modification,
and Polymerization 563
A. Mugler, S. Fancher
28.1 Introduction 563
28.2 Gene Expression 564
28.3 Protein Modification 572
28.4 Polymerization 574
28.5 Interactions 577
28.6 More Complex Phenomena 579
28.7 Summary and Outlook 580
28.8 Exercises 580

29 Modeling Cell-Fate Decisions in Biological Systems: Bacteriophage,
Hematopoietic Stem Cells, Epithelial-to-Mesenchymal Transition,
and Beyond 583
M. K. Jolly, D. Jia, H. Levine
29.1 Introduction 583
29.2 Lysis/Lysogeny Decision in Lambda Phage 585
29.3 Cell-Fate Decisions in Hematopoietic Stem Cell System 588
29.4 Epithelial-to-Mesenchymal Transition 590
29.5 Notch-Delta-Jagged Signaling 594
29.6 Which Modeling Framework to Use and When? 597
29.7 Exercises 598

30 Tutorial on the Identification of Gene Regulation Models from
Single-Cell Data 599
L. Weber, W. Raymond, B. Munsky
30.1 Outline of Our Approach 599
30.2 Gene Regulation Model Description 600
30.3 Exercise Tasks 603
30.4 Exercise Results and GUI 614
30.5 Summary and Conclusions 616

References 617
Contributors 695
Index 701