Systems Biology: A Textbook

Edda Klipp

Wolfram Liebermeister

Christoph Wierling

Axel Kowald

Systems Biology

Edda Klipp

Wolfram Liebermeister

Christoph Wierling

Axel Kowald

Systems Biology

A Textbook

Second, Completely Revised

and Enlarged Edition

Authors

Prof. Dr. h.c. Edda Klipp

Theoretical Biophysics

Humboldt-Universität zu Berlin

Invalidenstr. 42

10115 Berlin

Germany

Dr. Wolfram Liebermeister

Institute of Biochemistry

Charité - Universitätsmedizin Berlin

Charitéplatz 1

10117 Berlin

Germany

Dr. Christoph Wierling

Alacris Theranostics GmbH

Fabeckstr. 60-62

14195 Berlin

Germany

and

Max Planck Institute for Molecular Genetics

Ihnestr. 63-73

14195 Berlin

Germany

Dr. Axel Kowald

Theoretical Biophysics

Humboldt University Berlin

Invalidenstr. 42

10115 Berlin

Germany

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Contents

Preface xi

Guide to Different Topics of the Book xiii

About the Authors xv

Part One Introduction to Systems Biology 1

1 Introduction 3

1.1 Biology in Time and Space 3

1.2 Models and Modeling 4

1.2.1 What Is a Model? 4

1.2.2 Purpose and Adequateness of Models 5

1.2.3 Advantages of Computational Modeling 5

1.3 Basic Notions for Computational Models 6

1.3.1 Model Scope 6

1.3.2 Model Statements 6

1.3.3 System State 6

1.3.4 Variables, Parameters, and Constants 6

1.3.5 Model Behavior 7

1.3.6 Model Classification 7

1.3.7 Steady States 7

1.3.8 Model Assignment Is Not Unique 7

1.4 Networks 8

1.5 Data Integration 8

1.6 Standards 9

1.7 Model Organisms 9

1.7.1 Escherichia coli 9

1.7.2 Saccharomyces cerevisiae 11

1.7.3 Caenorhabditis elegans 11

1.7.4 Drosophila melanogaster 11

1.7.5 Mus musculus 12

References 12

Further Reading 14

2 Modeling of Biochemical Systems 15

2.1 Overview of Common Modeling Approaches

for Biochemical Systems 15

2.2 ODE Systems for Biochemical Networks 17

2.2.1 Basic Components of ODE Models 18

2.2.2 Illustrative Examples of ODE Models 18

References 21

Further Reading 21

3 Structural Modeling and Analysis of

Biochemical Networks 23

3.1 Structural Analysis of Biochemical Systems 24

3.1.1 System Equations 24

3.1.2 Information Encoded in the Stoichiometric

Matrix N 25

3.1.3 The Flux Cone 27

3.1.4 Elementary Flux Modes and Extreme

Pathways 27

3.1.5 Conservation Relations – Null Space of NT 29

3.2 Constraint-Based Flux Optimization 30

3.2.1 Flux Balance Analysis 31

3.2.2 Geometric Interpretation of Flux Balance

Analysis 31

3.2.3 Thermodynamic Constraints 31

3.2.4 Applications and Tests of the Flux Optimization

Paradigm 32

3.2.5 Extensions of Flux Balance Analysis 33

Exercises 35

References 36

Further Reading 37

4 Kinetic Models of Biochemical Networks:

Introduction 39

4.1 Reaction Kinetics and Thermodynamics 39

4.1.1 Kinetic Modeling of Enzymatic Reactions 39

4.1.2 The Law of Mass Action 40

4.1.3 Reaction Thermodynamics 40

4.1.4 Michaelis–Menten Kinetics 42

4.1.5 Regulation of Enzyme Activity by Effectors 44

4.1.6 Generalized Mass Action Kinetics 48

4.1.7 Approximate Kinetic Formats 48

4.1.8 Convenience Kinetics and Modular Rate Laws 49

4.2 Metabolic Control Analysis 50

4.2.1 The Coefficients of Control Analysis 51

vi Contents

4.2.2 The Theorems of Metabolic Control Theory 53

4.2.3 Matrix Expressions for Control Coefficients 55

4.2.4 Upper Glycolysis as Realistic Model Example 58

4.2.5 Time-Dependent Response Coefficients 59

Exercises 61

References 61

Further Reading 62

5 Data Formats, Simulation Techniques, and

Modeling Tools 63

5.1 Simulation Techniques and Tools 63

5.1.1 Differential Equations 63

5.1.2 Stochastic Simulations 64

5.1.3 Simulation Tools 65

5.2 Standards and Formats for Systems

Biology 72

5.2.1 Systems Biology Markup Language 72

5.2.2 BioPAX 74

5.2.3 Systems Biology Graphical Notation 74

5.3 Data Resources for Modeling of Cellular

Reaction Systems 75

5.3.1 General-Purpose Databases 75

5.3.2 Pathway Databases 76

5.3.3 Model Databases 77

5.4 Sustainable Modeling and Model

Semantics 78

5.4.1 Standards for Systems Biology Models 78

5.4.2 Model Semantics and Model Comparison 78

5.4.3 Model Combination 80

5.4.4 Model Validity 82

References 83

Further Reading 85

6 Model Fitting, Reduction, and Coupling 87

6.1 Parameter Estimation 88

6.1.1 Regression, Estimators, and Maximal

Likelihood 88

6.1.2 Parameter Identifiability 90

6.1.3 Bootstrapping 91

6.1.4 Bayesian Parameter Estimation 92

6.1.5 Probability Distributions for Rate

Constants 94

6.1.6 Optimization Methods 97

6.2 Model Selection 99

6.2.1 What Is a Good Model? 99

6.2.2 The Problem of Model Selection 100

6.2.3 Likelihood Ratio Test 102

6.2.4 Selection Criteria 102

6.2.5 Bayesian Model Selection 103

6.3 Model Reduction 104

6.3.1 Model Simplification 104

6.3.2 Reduction of Fast Processes 105

6.3.3 Quasi-Equilibrium and Quasi-Steady State 107

6.3.4 Global Model Reduction 108

6.4

6.4.1

6.4.2

6.4.3

6.4.4

6.4.5

7

7.1

7.1.1

7.1.2

7.2

7.2.1

7.2.2

7.2.3

7.2.4

7.2.5

7.2.6

7.3

7.3.1

7.3.2

7.3.3

7.3.4

7.3.5

7.3.6

8

8.1

8.1.1

8.1.2

8.1.3

8.1.4

8.1.5

8.2

8.2.1

8.2.2

8.2.3

8.2.4

8.2.5

Coupled Systems and Emergent

Behavior 110

Modeling of Coupled Systems 111

Combining Rate Laws into Models 113

Modular Response Analysis 113

Emergent Behavior in Coupled Systems 114

Causal Interactions and Global Behavior 115

Exercises 116

References 117

Further Reading 119

Discrete, Stochastic, and Spatial Models 121

Discrete Models 122

Boolean Networks 122

Petri Nets 124

Stochastic Modeling of Biochemical

Reactions 127

Chance in Biochemical Reaction Systems 127

The Chemical Master Equation 129

Stochastic Simulation 129

Chemical Langevin Equation and Chemical

Noise 130

Dynamic Fluctuations 132

From Stochastic to Deterministic

Modeling 133

Spatial Models 133

Types of Spatial Models 134

Compartment Models 135

Reaction–Diffusion Systems 136

Robust Pattern Formation in Embryonic

Development 138

Spontaneous Pattern Formation 139

Linear Stability Analysis of the Activator–

Inhibitor Model 140

Exercises 142

References 143

Further Reading 144

Network Structure, Dynamics, and

Function 145

Structure of Biochemical Networks 146

Random Graphs 147

Scale-Free Networks 148

Connectivity and Node Distances 149

Network Motifs and Significance Tests 150

Explanations for Network Structures 151

Regulation Networks and Network

Motifs 152

Structure of Transcription Networks 153

Regulation Edges and Their Steady-State

Response 156

Negative Feedback 156

Adaptation Motif 157

Feed-Forward Loops 158

8.3 Modularity and Gene Functions 160

8.3.1 Cell Functions Are Reflected in Structure,

Dynamics, Regulation, and Genetics 160

8.3.2 Metabolics Pathways and Elementary

Modes 162

8.3.3 Epistasis Can Indicate Functional Modules 163

8.3.4 Evolution of Function and Modules 163

8.3.5 Independent Systems as a Tacit Model

Assumption 165

8.3.6 Modularity and Biological Function Are

Conceptual Abstractions 165

Exercises 166

References 167

Further Reading 169

9 Gene Expression Models 171

9.1 Mechanisms of Gene Expression

Regulation 171

9.1.1 Transcription Factor-Initiated Gene

Regulation 171

9.1.2 General Promoter Structure 173

9.1.3 Prediction and Analysis of Promoter

Elements 174

9.1.4 Posttranscriptional Regulation through

microRNAs 176

9.2 Dynamic Models of Gene Regulation 180

9.2.1 A Basic Model of Gene Expression and

Regulation 180

9.2.2 Natural and Synthetic Gene Regulatory

Networks 183

9.2.3 Gene Expression Modeling with Stochastic

Equations 186

9.3 Gene Regulation Functions 187

9.3.1 The Lac Operon in E. coli 187

9.3.2 Gene Regulation Functions Derived from

Equilibrium Binding 188

9.3.3 Thermodynamic Models of Promoter

Occupancy 189

9.3.4 Gene Regulation Function of the Lac

Promoter 191

9.3.5 Inferring Transcription Factor Activities from

Transcription Data 192

9.3.6 Network Component Analysis 194

9.3.7 Correspondences between mRNA and Protein

Levels 196

9.4 Fluctuations in Gene Expression 196

9.4.1 Stochastic Model of Transcription and

Translation 197

9.4.2 Intrinsic and Extrinsic Variability 200

9.4.3 Temporal Fluctuations in Gene

Cascades 202

Exercises 203

References 205

Further Reading 207

Contents vii

10 Variability, Robustness, and Information 209

10.1 Variability and Biochemical Models 210

10.1.1 Variability and Uncertainty Analysis 210

10.1.2 Flux Sampling 212

10.1.3 Elasticity Sampling 213

10.1.4 Propagation of Parameter Variability in Kinetic

Models 214

10.1.5 Models with Parameter Fluctuations 216

10.2 Robustness Mechanisms and Scaling

Laws 217

10.2.1 Robustness in Biochemical Systems 218

10.2.2 Robustness by Backup Elements 219

10.2.3 Feedback Control 219

10.2.4 Perfect Robustness by Structure 222

10.2.5 Scaling Laws 224

10.2.6 Time Scaling, Summation Laws, and

Robustness 227

10.2.7 The Role of Robustness in Evolution and

Modeling 228

10.3 Adaptation and Exploration Strategies 229

10.3.1 Information Transmission in Signaling

Pathways 230

10.3.2 Adaptation and Fold-Change Detection 230

10.3.3 Two Adaptation Mechanisms: Sensing and

Random Switching 231

10.3.4 Shannon Information and the Value of

Information 232

10.3.5 Metabolic Shifts and Anticipation 233

10.3.6 Exploration Strategies 234

Exercises 236

References 237

Further Reading 239

11 Optimality and Evolution 241

11.1 Optimality in Systems Biology Models 243

11.1.1 Mathematical Concepts for Optimality and

Compromise 245

11.1.2 Metabolism Is Shaped by Optimality 248

11.1.3 Optimality Approaches in Metabolic

Modeling 250

11.1.4 Metabolic Strategies 252

11.1.5 Optimal Metabolic Adaptation 253

11.2 Optimal Enzyme Concentrations 255

11.2.1 Optimization of Catalytic Properties of Single

Enzymes 255

11.2.2 Optimal Distribution of Enzyme Concentrations

in a Metabolic Pathway 257

11.2.3 Temporal Transcription Programs 259

11.3 Evolution and Self-Organization 261

11.3.1 Introduction 261

11.3.2 Selection Equations for Biological

Macromolecules 263

11.3.3 The Quasispecies Model: Self-Replication with

Mutations 265

viii Contents

11.3.4 The Hypercycle 267

11.3.5 Other Mathematical Models of Evolution: Spin

Glass Model 269

11.3.6 The Neutral Theory of Molecular

Evolution 270

11.4 Evolutionary Game Theory 271

11.4.1 Social Interactions 272

11.4.2 Game Theory 273

11.4.3 Evolutionary Game Theory 274

11.4.4 Replicator Equation for Population Dynamics 274

11.4.5 Evolutionarily Stable Strategies 275

11.4.6 Dynamical Behavior in the Rock–Scissors–Paper

Game 276

11.4.7 Evolution of Cooperative Behavior 276

11.4.8 Compromises between Metabolic Yield and

Efficiency 278

Exercises 279

References 280

Further Reading 283

12 Models of Biochemical Systems 285

12.1 Metabolic Systems 285

12.1.1 Basic Elements of Metabolic Modeling 286

12.1.2 Toy Model of Upper Glycolysis 286

12.1.3 Threonine Synthesis Pathway Model 289

12.2 Signaling Pathways 291

12.2.1 Function and Structure of Intra- and Intercellular

Communication 292

12.2.2 Receptor–Ligand Interactions 293

12.2.3 Structural Components of Signaling

Pathways 295

12.2.4 Analysis of Dynamic and Regulatory Features

of Signaling Pathways 304

12.3 The Cell Cycle 307

12.3.1 Steps in the Cycle 309

12.3.2 Minimal Cascade Model of a Mitotic

Oscillator 310

12.3.3 Models of Budding Yeast Cell Cycle 311

12.4 The Aging Process 314

12.4.1 Evolution of the Aging Process 316

12.4.2 Using Stochastic Simulations to Study

Mitochondrial Damage 318

12.4.3 Using Delay Differential Equations to Study

Mitochondrial Damage 323

Exercises 327

References 327

Part Two Reference Section 331

13 Cell Biology 333

13.1 The Origin of Life 334

13.2 Molecular Biology of the Cell 336

13.2.1 Chemical Bonds and Forces Important in

Biological Molecules 336

13.2.2 Functional Groups in Biological Molecules 338

13.2.3 Major Classes of Biological Molecules 338

13.3 Structural Cell Biology 345

13.3.1 Structure and Function of Biological

Membranes 347

13.3.2 Nucleus 349

13.3.3 Cytosol 349

13.3.4 Mitochondria 350

13.3.5 Endoplasmic Reticulum and Golgi

Complex 350

13.3.6 Other Organelles 351

13.4 Expression of Genes 351

13.4.1 Transcription 351

13.4.2 Processing of the mRNA 353

13.4.3 Translation 353

13.4.4 Protein Sorting and Posttranslational

Modifications 355

13.4.5 Regulation of Gene Expression 355

Exercises 356

References 356

Further Reading 356

14 Experimental Techniques 357

14.1 Restriction Enzymes and Gel

Electrophoresis 358

14.2 Cloning Vectors and DNA Libraries 359

14.3 1D and 2D Protein Gels 361

14.4 Hybridization and Blotting Techniques 362

14.4.1 Southern Blotting 363

14.4.2 Northern Blotting 363

14.4.3 Western Blotting 363

14.4.4 In Situ Hybridization 364

14.5 Further Protein Separation Techniques 364

14.5.1 Centrifugation 364

14.5.2 Column Chromatography 364

14.6 Polymerase Chain Reaction 365

14.7 Next-Generation Sequencing 366

14.8 DNA and Protein Chips 367

14.8.1 DNA Chips 367

14.8.2 Protein Chips 367

14.9 RNA-Seq 368

14.10 Yeast Two-Hybrid System 368

14.11 Mass Spectrometry 369

14.12 Transgenic Animals 370

14.12.1 Microinjection and ES Cells 370

14.12.2 Genome Editing Using ZFN, TALENs, and

CRISPR 370

14.13 RNA Interference 371

14.14 ChIP-on-Chip and ChIP-PET 372

14.15 Green Fluorescent Protein 374

14.16 Single-Cell Experiments 375

Contents ix

14.17 Surface Plasmon Resonance 376

Exercises 377

References 377

15 Mathematical and Physical Concepts 381

15.1 Linear Algebra 381

15.1.1 Linear Equations 381

15.1.2 Matrices 384

15.2 Dynamic Systems 386

15.2.1 Describing Dynamics with Ordinary Differential

Equations 386

15.2.2 Linearization of Autonomous Systems 388

15.2.3 Solution of Linear ODE Systems 388

15.2.4 Stability of Steady States 388

15.2.5 Global Stability of Steady States 390

15.2.6 Limit Cycles 390

15.3 Statistics 391

15.3.1 Basic Concepts of Probability Theory 391

15.3.2 Descriptive Statistics 396

15.3.3 Testing Statistical Hypotheses 399

15.3.4 Linear Models 401

15.3.5 Principal Component Analysis 404

15.4 Stochastic Processes 405

15.4.1 Chance in Physical Theories 405

15.4.2 Mathematical Random Processes 406

15.4.3 Brownian Motion as a Random Process 407

15.4.4 Markov Processes 409

15.4.5 Markov Chains 410

15.4.6 Jump Processes in Continuous Time 410

15.4.7 Continuous Random Processes 411

15.4.8 Moment-Generating Functions 412

15.5 Control of Linear Dynamical Systems 412

15.5.1 Linear Dynamical Systems 413

15.5.2 System Response and Linear Filters 414

15.5.3 Random Fluctuations and Spectral Density 415

15.5.4 The Gramian Matrices 415

15.5.5 Model Reduction 416

15.5.6 Optimal Control 416

15.6 Biological Thermodynamics 417

15.6.1 Microstate and Statistical Ensemble 417

15.6.2 Boltzmann Distribution and Free Energy 418

15.6.3 Entropy 419

15.6.4 Equilibrium Constant and Energies 421

15.6.5 Chemical Reaction Systems 422

15.6.6 Nonequilibrium Reactions 424

15.6.7 The Role of Thermodynamics in Systems

Biology 425

15.7 Multivariate Statistics 426

15.7.1 Planning and Designing Experiments for

Case-Control Studies 426

15.7.5 Clustering Algorithms 430

15.7.6 Cluster Validation 435

15.7.7 Overrepresentation and Enrichment

Analyses 436

15.7.8 Classification Methods 438

Exercises 441

References 443

16 Databases 445

16.1 General-Purpose Data Resources 445

16.1.1 PathGuide 445

16.1.2 BioNumbers 446

16.2 Nucleotide Sequence Databases 446

16.2.1 Data Repositories of the National

Center for Biotechnology

Information 446

16.2.2 GenBank/RefSeq/UniGene 446

16.2.3 Entrez 447

16.2.4 EMBL Nucleotide Sequence Database 447

16.2.5 European Nucleotide Archive 447

16.2.6 Ensembl 447

16.3 Protein Databases 448

16.3.1 UniProt/Swiss-Prot/TrEMBL 448

16.3.2 Protein Data Bank 448

16.3.3 PANTHER 448

16.3.4 InterPro 448

16.3.5 iHOP 449

16.4 Ontology Databases 449

16.4.1 Gene Ontology 449

16.5 Pathway Databases 449

16.5.1 KEGG 450

16.5.2 Reactome 450

16.5.3 ConsensusPathDB 451

16.5.4 WikiPathways 451

16.6 Enzyme Reaction Kinetics

Databases 451

16.6.1 BRENDA 451

16.6.2 SABIO-RK 452

16.7 Model Collections 452

16.7.1 BioModels 452

16.7.2 JWS Online 452

16.8 Compound and Drug Databases 452

16.8.1 ChEBI 453

16.8.2 Guide to PHARMACOLOGY 453

16.9 Transcription Factor Databases 453

16.9.1 JASPAR 453

16.9.2 TRED 453

16.9.3 Transcription Factor Encyclopedia 454

16.10 Microarray and Sequencing

Databases 454

15.7.2 Tests for Differential Expression 427 16.10.1 Gene Expression Omnibus 454

15.7.3 Multiple Testing 428 16.10.2 ArrayExpress 454

15.7.4 ROC Curve Analysis 429 References 455

x Contents

17 Software Tools for Modeling 457 17.31

17.1 13C-Flux2 458 17.32

17.2 Antimony 458 17.33

17.3 Berkeley Madonna 459 17.34

17.4 BIOCHAM 459 17.35

17.5 BioNetGen 459 17.36

17.6 Biopython 459 17.37

17.7 BioTapestry 460 17.38

17.8 BioUML 460 17.39

17.9 CellDesigner 460 17.40

17.10 CellNetAnalyzer 460 17.41

17.11 Copasi 461 17.42

17.12 CPN Tools 461 17.43

17.13 Cytoscape 461 17.44

17.14 E-Cell 461 17.45

17.15 EvA2 461 17.46

17.16 FEniCS Project 462 17.47

17.17 Genetic Network Analyzer (GNA) 462 17.48

17.18 Jarnac 462 17.49

17.19 JDesigner 463 17.50

17.20 JSim 463 17.51

17.21 KNIME 463 17.52

17.22 libSBML 464 17.53

17.23 MASON 464 17.54

17.24 Mathematica 464 17.55

17.25 MathSBML 465 17.56

17.26 Matlab 465 17.57

17.27 MesoRD 465

17.28 Octave 465

17.29 Omix Visualization 466

17.30 OpenCOR 466

Oscill8 466

PhysioDesigner 466

PottersWheel 467

PyBioS 467

PySCeS 467

R 468

SAAM II 468

SBMLeditor 468

SemanticSBML 468

SBML-PET-MPI 469

SBMLsimulator 469

SBMLsqueezer 469

SBML Toolbox 470

SBtoolbox2 470

SBML Validator 470

SensA 470

SmartCell 471

STELLA 471

STEPS 471

StochKit2 471

SystemModeler 472

Systems Biology Workbench 472

Taverna 472

VANTED 473

Virtual Cell (VCell) 473

xCellerator 473

XPPAUT 473

Exercises 474

References 474

Index 475

Preface

Systems biology is the scientific discipline that studies

the systemic properties and dynamic interactions in a

biological object, be it a cell, an organism, a virus, or an

infected host, in a qualitative and quantitative manner

and by combining experimental studies with mathemati￾cal modeling. Scientists can describe the inner processes

of stars a thousand light years away with great accuracy.

But how a tiny cell under our microscope grows and

divides remains puzzling in many ways. We see kids

growing, people aging, plants blooming, and microbes

degrading their remains. We use yeast for brewery and

bakery, and doctors prescribe drugs to cure diseases. But

do we understand how processes of life work?

Starting in the nineteenth century, such processes

have no longer been explained by referring to special

“life forces,” but by laws of physics and chemistry. By

studying the structure and dynamics of living systems in

finer and finer details, researchers from different disci￾plines have revealed how life processes arise from the

structure and functional organization of cells, how tens

of thousands of biochemical components interact in

orchestrated ways, and how these systems are regulated

by genetic information and continuously adapted

through mutations and selection. With this conceptual

shift, new questions became central in biology: How

does an organism’s phenotype emerge from the geno￾type, as encoded in the organism’s DNA, and how is it

shaped by environmental factors? Initially, such ques￾tions were approached by statistics, for example, by

studying what mutations are associated with specific

inheritable diseases. But the task, now, is to understand

the mechanistic details.

We can easily understand the effects of gene disrup￾tions when gene products have simple, specific func￾tions. However, most gene mutations have only weak or

quantitative effects on physiology, and many genetic dis￾eases are multifactorial. Tracing the effects of multiple

mutations, of mutations affecting gene regulation, or of

drugs requires a deep, quantitative, and dynamical

understanding of cell physiology. In recent years, high￾throughput experiments, time series experiments, and

imaging techniques with high resolution have provided

us with a detailed picture of the cellular machinery. We

can observe how physical structures are built, main￾tained, and reproduced, how the metabolic state is

changing, and how signaling and regulation systems

allow cells to adapt to their environment. However, to

understand how all these systems act together – and

how cells can work as complex, robust systems – cata￾loging and understanding single-cell components is not

enough. Instead, we need to capture the global dynamics

between these components. This is where mathematical

models come into play.

Mathematical modeling has a long, though relatively

marginal, tradition in biology, and has influenced the

field in many ways. Models can be used to test hypothe￾ses and to yield quantitative predictions or reveal gaps

or inconsistencies in previous arguments, thus helping

us to improve our understanding of biochemical pro￾cesses. Inspired by the ideas of cybernetics in the sixties

and seventies, dynamical systems theory and control the￾ory have been increasingly applied to biochemical path￾ways. Thanks to powerful experimental techniques in

genomics and proteomics, a wealth of biological data

has accumulated and computational models of cells are

now within reach. Systems biology, the discipline

devoted to developing such models, uses biochemical

networks as a main concept. It studies biological systems

by investigating the network components and their

interactions with the help of experimental high-through￾put techniques and dedicated small-scale investigations

and by integrating these data into networks and dynami￾cal simulation models.

Like many new fields of research, systems biology

started out with great expectations. High-throughput

data and computational models were hoped to provide

xii Preface

answers to basic yet difficult biological questions: Why

do we age? What processes control cell proliferation,

and how? How do neurodegenerative disorders or dis￾eases such as cancer develop? How can we engineer

microbes more efficiently to produce valuable chemicals,

fuels, or specific drugs? Only few of these goals have

been achieved until now, and most of these questions

remain on our agenda. Nevertheless, systems biology has

greatly contributed to our understanding of cells and is

increasingly becoming a standard part of biological

research. It has fostered the formulation of new concepts

and methods, such as statistical network analysis, the

analysis of the robustness and fragility of dynamical sys￾tems, and the analysis of molecular noise. Even more

importantly, it has enabled experimental biologists to

realize that some scientific ideas cannot be easily

expressed by words only. Inspired by electrical engineer￾ing, biologists now communicate the structure of bio￾chemical systems by network graphics, which can then

be translated into dynamical models.

This book gives an overview of systems biology as a

rapidly developing field and provides readers with estab￾lished and emerging tools and methods. You will learn

how to formulate mathematical models of biological

processes, how to analyze them, how to use experimen￾tal data and other types of knowledge to make models

more precise, and how to interpret their simulation

results. Based on our own experiences in teaching

undergraduate and graduate students, the book is

designed as an introductory course for students of biol￾ogy, biophysics, and bioinformatics. It is as well useful

for senior scholars who approach systems biology for the

first time or seek more information about specific con￾cepts and techniques. In the first chapters, we introduce

stoichiometric and kinetic models, the main theoretical

frameworks for metabolism and signaling pathways. We

continue with methods for model construction (includ￾ing model fitting, data handling, and model reduction)

and related formalisms (spatial, discrete, and stochastic

models). Then, we move on to experimental high￾throughput techniques and to cellular networks. The

analysis of regulation networks leads us to more general

perspectives on cell physiology, including modularity,

robustness, and optimality. The main part of the book

ends with a chapter on case studies. Addressing readers

with different scientific backgrounds, we have added a

reference section summarizing some basic knowledge of

cell biology and mathematics, followed by a survey of pop￾ular biological databases and software tools. Further mate￾rial is available on an accompanying Web site (http://

www.wiley-vch.de/home/systemsbiology), which also con￾tains solutions to the exercises presented in the book.

For the second edition of this book, we have updated

and expanded the text to reflect advances in the field,

and have reorganized the chapters to improve readabil￾ity. Many of the changes reflect current developments in

systems biology. On the one hand, the development of

software tools is a very active area, where many new

tools are developed, while others drop into oblivion. In

the meantime, SBML has become an established

exchange format for computational models in systems

biology. We also notice that systems biology as a whole

has become a mainstream discipline: High-throughput

measurements have become an integral part of cell biol￾ogy, computational models are used in research and

teaching, and collaborations between experimentalists

and theoreticians are increasingly common. Today, sys￾tems biology is perceived as what it is: the endeavor to

understand complex processes in living organisms. Not

more, but also not less!

We thank our friends and colleagues who helped us

write this book. We are especially grateful to Mariapaola

Gritti, Bernd Binder, Andreas Hoppe, Dagmar Walte￾math, Elad Noor, Avi Flamholz, Terence Hwa, Ron

Milo, Jonathan Karr, Ulrich Liebermeister, David Jesing￾haus, Martina Fröhlich, and Severin Ehret for reading

and commenting on the text. We thank the Max Planck

Society for support and encouragement. We are grateful

to the European Commission for funding via different

European projects (UniCellSys, SysteMTb and FinSysB

to EK, HeCaToS 602156), the German Ministry for Edu￾cation and Research, BMBF (ViroSign, OncoPath, Sys￾ToxChip to EK), and the German Research Foundation

(GRK 1772 to EK, Ll 1676/2-1 to WL).

The book is dedicated to our teacher Prof. Dr. Rein￾hart Heinrich (1946–2006) whose work on metabolic

control theory in the 1970s paved the way to systems

biology and who greatly inspired our minds.

Preface xiii

Guide to Different Topics of the Book

Biological systems and processes

Metabolism (2, 3, 4, 11.1, 11.4, 12.1)

Gene regulatory network (7, 8.2, 9)

Gene expression regulation (2, 9)

Signaling systems (8.2, 12.2)

Cell cycle (12.3)

Development (7.3)

Aging (12.4)

Model types with different levels of abstraction

Statistical particle models (15.6)

Stochastic biochemical models (5.1.2, 7.2, 9.4, 15.4)

Kinetic models (4, 5.1.1, 11, 12, 16.7)

Constraint-based models (3.2)

Discrete models (7.1)

Spatial models (7.3)

Mathematical frameworks to describe cell states

Topological (network structures) (3.1, 8)

Structural stoichiometric models (3)

Dynamical systems (4, 12, 15.2)

Deterministic linear models (6.3)

Deterministic kinetic models (4, 9.1, 12)

Uncertain parameters (10.1)

Optimization and control theory (4.2, 11.1,11.2,15.5)

Experimental Techniques

Experimental techniques (14)

Concepts for biological function

Qualitative behavior (3, 7.1)

Parameter sensitivity and robustness (4.2, 10.2)

Modularity and functional subsystems (6.4, 8.3)

Robustness against failure (10.2)

Information (10.3, 15.6)

Population heterogeneity (10.3)

Optimality (3.2, 11.1, 11.2)

Evolution (11.3)

Population dynamics and game theory (11.4)

Modeling skills

Model building (2, 3, 4, 5.1, 7)

Model annotation (5.4)

Parameter estimation (6.1)

Model testing and selection (6.2)

Local sensitivity analysis/control theory (4.2, 10.1, 10.2)

Global sensitivity/uncertainty analysis (10.1)

Model reduction (6.3)

Model combination (5.4, 6.4)

Network theory (8)

Statistics (15.3, 15.7)

Optimization of model outputs and structure (11.1)

Optimal temporal control (11.2, 15.5)

Practical issues in modeling

Use of databases (5.3, 16)

Data formats (5.2, 5.4)

Data sources (5.3, 16)

Modeling software (5.1, 17)

Simulation techniques and tools (5.1)

Model visualization (5.1)

Data visualization (8.3)