Systems Biology	1
	Contents	7
	Preface	13
	Guide to Different Topics of the Book	15
	About the Authors	17
	Part One: Introduction to Systems Biology	19
	1: Introduction	21
	1.1 Biology in Time and Space	21
	1.2 Models and Modeling	22
	1.2.1 What Is a Model?	22
	1.2.2 Purpose and Adequateness of Models	23
	1.2.3 Advantages of Computational Modeling	23
	1.3 Basic Notions for Computational Models	24
	1.3.1 Model Scope	24
	1.3.2 Model Statements	24
	1.3.3 System State	24
	1.3.4 Variables, Parameters, and Constants	24
	1.3.5 Model Behavior	25
	1.3.6 Model Classification	25
	1.3.7 Steady States	25
	1.3.8 Model Assignment Is Not Unique	25
	1.4 Networks	26
	1.5 Data Integration	26
	1.6 Standards	27
	1.7 Model Organisms	27
	1.7.1 Escherichia coli	27
	1.7.2 Saccharomyces cerevisiae	29
	1.7.3 Caenorhabditis elegans	29
	1.7.4 Drosophila melanogaster	29
	1.7.5 Mus musculus	30
	References	30
	Further Reading	32
	2: Modeling of Biochemical Systems	33
	2.1 Overview of Common Modeling Approaches for Biochemical Systems	33
	2.2 ODE Systems for Biochemical Networks	35
	2.2.1 Basic Components of ODE Models	36
	2.2.2 Illustrative Examples of ODE Models	36
	2.2.2.1 Metabolic Example	36
	2.2.2.2 Regulatory Network Example	37
	References	39
	Further Reading	39
	3: Structural Modeling and Analysis of Biochemical Networks	41
	3.1 Structural Analysis of Biochemical Systems	42
	3.1.1 System Equations	42
	3.1.2 Information Encoded in the Stoichiometric Matrix N	43
	3.1.3 The Flux Cone	45
	3.1.4 Elementary Flux Modes and Extreme Pathways	45
	3.1.5 Conservation Relations - Null Space of N	47
	3.2 Constraint-Based Flux Optimization	48
	3.2.1 Flux Balance Analysis	49
	3.2.2 Geometric Interpretation of Flux Balance Analysis	49
	3.2.3 Thermodynamic Constraints	49
	3.2.4 Applications and Tests of the Flux Optimization Paradigm	50
	3.2.5 Extensions of Flux Balance Analysis	51
	3.2.5.1 Minimization of Metabolic Adjustments	51
	3.2.5.2 Flux Variability Analysis	52
	3.2.5.3 Dynamic FBA	52
	3.2.5.4 Regulatory FBA	52
	Exercises	53
	References	54
	Further Reading	55
	4: Kinetic Models of Biochemical Networks: Introduction	57
	4.1 Reaction Kinetics and Thermodynamics	57
	4.1.1 Kinetic Modeling of Enzymatic Reactions	57
	4.1.2 The Law of Mass Action	58
	4.1.3 Reaction Thermodynamics	58
	4.1.4 Michaelis-Menten Kinetics	60
	4.1.4.1 How to Derive a Rate Equation	61
	4.1.4.2 Parameter Estimation and Linearization of the Michaelis-Menten Equation	62
	4.1.4.3 The Michaelis-Menten Equation for Reversible Reactions	62
	4.1.5 Regulation of Enzyme Activity by Effectors	62
	4.1.5.1 Substrate Inhibition	64
	4.1.5.2 Binding of Ligands to Proteins	64
	4.1.5.3 Positive Homotropic Cooperativity and the Hill Equation	65
	4.1.5.4 The Monod-Wyman-Changeux Model for Sigmoid Kinetics	66
	4.1.6 Generalized Mass Action Kinetics	66
	4.1.7 Approximate Kinetic Formats	66
	4.1.8 Convenience Kinetics and Modular Rate Laws	67
	4.2 Metabolic Control Analysis	68
	4.2.1 The Coefficients of Control Analysis	69
	4.2.1.1 The Elasticity Coefficients	69
	4.2.1.2 Control Coefficients	70
	4.2.1.3 Response Coefficients	71
	4.2.1.4 Matrix Representation of the Coefficients	71
	4.2.2 The Theorems of Metabolic Control Theory	71
	4.2.2.1 The Summation Theorems	72
	4.2.2.2 The Connectivity Theorems	72
	4.2.3 Matrix Expressions for Control Coefficients	73
	4.2.4 Upper Glycolysis as Realistic Model Example	76
	4.2.5 Time-Dependent Response Coefficients	77
	Exercises	79
	References	79
	Further Reading	80
	5: Data Formats, Simulation Techniques, and Modeling Tools	81
	5.1 Simulation Techniques and Tools	81
	5.1.1 Differential Equations	81
	5.1.2 Stochastic Simulations	82
	5.1.2.1 Stochastic and Macroscopic Rate Constants	83
	First-Order Reaction	83
	Second-Order Reaction	83
	5.1.3 Simulation Tools	83
	5.1.3.1 CellDesigner	84
	5.1.3.2 COPASI	85
	5.1.3.3 Virtual Cell	88
	5.2 Standards and Formats for Systems Biology	90
	5.2.1 Systems Biology Markup Language	90
	5.2.2 BioPAX	92
	5.2.3 Systems Biology Graphical Notation	92
	5.3 Data Resources for Modeling of Cellular Reaction Systems	93
	5.3.1 General-Purpose Databases	93
	5.3.1.1 PathGuide	93
	5.3.1.2 BioNumbers	94
	5.3.2 Pathway Databases	94
	5.3.2.1 KEGG	94
	5.3.2.2 Reactome	95
	5.3.2.3 WikiPathways	95
	5.3.2.4 ConsensusPathDB	95
	5.3.3 Model Databases	95
	5.3.3.1 BioModels	95
	5.3.3.2 JWS Online	96
	5.4 Sustainable Modeling and Model Semantics	96
	5.4.1 Standards for Systems Biology Models	96
	5.4.2 Model Semantics and Model Comparison	96
	5.4.2.1 Semantics Annotations in SBML	97
	5.4.2.2 Element Similarities	97
	5.4.2.3 Model Alignment and Model Similarities	97
	5.4.3 Model Combination	98
	5.4.4 Model Validity	100
	References	101
	Further Reading	103
	6: Model Fitting, Reduction, and Coupling	105
	Introduction	105
	6.1 Parameter Estimation	106
	6.1.1 Regression, Estimators, and Maximal Likelihood	106
	6.1.1.1 Regression	106
	6.1.1.2 Estimators and Maximal Likelihood	107
	6.1.1.3 Method of Least Squares	107
	6.1.2 Parameter Identifiability	108
	6.1.2.1 Structural Nonidentifiability	108
	6.1.2.2 Practical Nonidentifiability	108
	6.1.3 Bootstrapping	109
	6.1.3.1 Cross-Validation	109
	6.1.4 Bayesian Parameter Estimation	110
	6.1.4.1 Bayesian Networks	111
	6.1.5 Probability Distributions for Rate Constants	112
	6.1.5.1 Distributions of Enzymatic Rate Constants	112
	6.1.5.2 Thermodynamic Constraints on Rate Constants	112
	6.1.5.3 Dependence Scheme for Model Parameters	113
	6.1.5.4 Parameter Balancing	114
	6.1.6 Optimization Methods	115
	6.1.6.1 Local Optimization	115
	6.1.6.2 Global Optimization	115
	6.1.6.3 Sampling Methods	116
	6.1.6.4 Genetic Algorithms	116
	6.2 Model Selection	117
	6.2.1 What Is a Good Model?	117
	6.2.2 The Problem of Model Selection	118
	6.2.2.1 Likelihood and Overfitting	118
	6.2.2.2 Methods for Model Selection	119
	6.2.3 Likelihood Ratio Test	120
	6.2.4 Selection Criteria	120
	6.2.5 Bayesian Model Selection	121
	6.3 Model Reduction	122
	6.3.1 Model Simplification	122
	6.3.2 Reduction of Fast Processes	123
	6.3.2.1 Time Scale Separation	123
	6.3.2.2 Relaxation Time and Other Characteristic Time Scales	124
	6.3.3 Quasi-Equilibrium and Quasi-Steady State	125
	6.3.4 Global Model Reduction	126
	6.3.4.1 Linearization of Biochemical Models	126
	6.3.4.2 Linear Relaxation Modes	127
	6.3.4.3 Model Reduction	127
	6.4 Coupled Systems and Emergent Behavior	128
	6.4.1 Modeling of Coupled Systems	129
	6.4.1.1 Modeling the System Boundary	129
	6.4.1.2 Coupling of Submodels	129
	6.4.1.3 Supply-Demand Analysis	130
	6.4.1.4 Hierarchical Regulation Analysis	130
	6.4.2 Combining Rate Laws into Models	131
	6.4.3 Modular Response Analysis	131
	6.4.4 Emergent Behavior in Coupled Systems	132
	6.4.5 Causal Interactions and Global Behavior	133
	Exercises	134
	References	135
	Further Reading	137
	7: Discrete, Stochastic, and Spatial Models	139
	7.1 Discrete Models	140
	7.1.1 Boolean Networks	140
	7.1.1.1 Basic Principles of Boolean Networks	140
	7.1.1.2 Advanced Types of Boolean Networks	141
	7.1.2 Petri Nets	142
	7.2 Stochastic Modeling of Biochemical Reactions	145
	7.2.1 Chance in Biochemical Reaction Systems	145
	7.2.2 The Chemical Master Equation	147
	7.2.3 Stochastic Simulation	147
	7.2.3.1 Direct Method	147
	7.2.3.2 Explicit ?-Leaping Method	148
	7.2.3.3 Stochastic Simulation and Spatial Models	148
	7.2.4 Chemical Langevin Equation and Chemical Noise	148
	7.2.5 Dynamic Fluctuations	150
	7.2.6 From Stochastic to Deterministic Modeling	151
	7.3 Spatial Models	151
	7.3.1 Types of Spatial Models	152
	7.3.2 Compartment Models	153
	7.3.3 Reaction-Diffusion Systems	154
	7.3.3.1 Diffusion Equation	154
	7.3.3.2 Solutions of the Diffusion Equation	155
	7.3.3.3 Reaction-Diffusion Equation	155
	7.3.4 Robust Pattern Formation in Embryonic Development	156
	7.3.4.1 Bicoid Gradient in the Fly Embryo	156
	7.3.5 Spontaneous Pattern Formation	157
	7.3.6 Linear Stability Analysis of the Activator-Inhibitor Model	158
	Exercises	160
	References	161
	Further Reading	162
	8: Network Structure, Dynamics, and Function	163
	8.1 Structure of Biochemical Networks	164
	8.1.1 Random Graphs	165
	8.1.1.1 Mathematical Graphs	165
	8.1.1.2 Random Graphs	165
	8.1.1.3 Erdös-Rényi Random Graphs	165
	8.1.1.4 Geometric Random Graphs	166
	8.1.1.5 Random Graphs with Predefined Degree Sequence	166
	8.1.2 Scale-Free Networks	166
	8.1.2.1 Preferential Attachment Model	167
	8.1.3 Connectivity and Node Distances	167
	8.1.3.1 Clustering Coefficient	167
	8.1.3.2 Small-World Networks	167
	8.1.4 Network Motifs and Significance Tests	168
	8.1.4.1 Network Motifs	168
	8.1.4.2 Null Hypotheses for Detecting Network Structures	169
	8.1.5 Explanations for Network Structures	169
	8.1.5.1 The Network Picture Revisited	170
	8.2 Regulation Networks and Network Motifs	170
	8.2.1 Structure of Transcription Networks	171
	8.2.2 Regulation Edges and Their Steady-State Response	174
	8.2.3 Negative Feedback	174
	8.2.4 Adaptation Motif	175
	8.2.5 Feed-Forward Loops	176
	8.3 Modularity and Gene Functions	178
	8.3.1 Cell Functions Are Reflected in Structure, Dynamics, Regulation, and Genetics	178
	8.3.2 Metabolic Pathways and Elementary Modes	180
	8.3.3 Epistasis Can Indicate Functional Modules	181
	8.3.4 Evolution of Function and Modules	181
	8.3.5 Independent Systems as a Tacit Model Assumption	183
	8.3.6 Modularity and Biological Function Are Conceptual Abstractions	183
	Exercises	184
	References	185
	Further Reading	187
	9: Gene Expression Models	189
	9.1 Mechanisms of Gene Expression Regulation	189
	9.1.1 Transcription Factor-Initiated Gene Regulation	189
	9.1.2 General Promoter Structure	191
	9.1.3 Prediction and Analysis of Promoter Elements	192
	9.1.3.1 Sequence-Based Analysis	192
	9.1.3.2 Approaches that Incorporate Additional Information	193
	9.1.4 Posttranscriptional Regulation through microRNAs	194
	9.1.4.1 Identification of microRNAs in the Genome Sequence	194
	9.1.4.2 MicroRNA Target Prediction	196
	9.1.4.3 Experimental Implications: RNA Interference	196
	9.2 Dynamic Models of Gene Regulation	198
	9.2.1 A Basic Model of Gene Expression and Regulation	198
	9.2.2 Natural and Synthetic Gene Regulatory Networks	201
	9.2.3 Gene Expression Modeling with Stochastic Equations	204
	9.3 Gene Regulation Functions	205
	9.3.1 The Lac Operon in E. coli	205
	9.3.2 Gene Regulation Functions Derived from Equilibrium Binding	206
	9.3.3 Thermodynamic Models of Promoter Occupancy	207
	9.3.4 Gene Regulation Function of the Lac Promoter	209
	9.3.5 Inferring Transcription Factor Activities from Transcription Data	210
	9.3.5.1 Global Regulation by Transcription Resources	211
	9.3.6 Network Component Analysis	212
	9.3.7 Correspondences between mRNA and Protein Levels	214
	9.4 Fluctuations in Gene Expression	214
	9.4.1 Stochastic Model of Transcription and Translation	215
	9.4.1.1 Macroscopic Kinetic Model	215
	9.4.1.2 Microscopic Stochastic Model	216
	9.4.1.3 Fluctuations in a Genetic Network	217
	9.4.2 Intrinsic and Extrinsic Variability	218
	9.4.2.1 Measurement of Intrinsic and Extrinsic Variability	218
	9.4.2.2 Calculation of Intrinsic and Extrinsic Variability	218
	9.4.3 Temporal Fluctuations in Gene Cascades	220
	9.4.3.1 Linear Model with Two Genes	220
	9.4.3.2 Measuring the Time Correlations in Protein Levels	221
	Exercises	221
	References	223
	Further Reading	225
	10: Variability, Robustness, and Information	227
	10.1 Variability and Biochemical Models	228
	10.1.1 Variability and Uncertainty Analysis	228
	10.1.1.1 Uncertainty Analysis and the Principle of Minimal Information	229
	10.1.1.2 Variability Analysis and Model Ensembles	229
	10.1.2 Flux Sampling	230
	10.1.3 Elasticity Sampling	231
	10.1.3.1 Elasticity Sampling	231
	10.1.3.2 Elasticity Sampling under Thermodynamic Constraints	231
	10.1.4 Propagation of Parameter Variability in Kinetic Models	232
	10.1.4.1 Propagation of Variability	232
	10.1.4.2 Variability Can Shift Mean Values	233
	10.1.4.3 The Value of Robustness	234
	10.1.5 Models with Parameter Fluctuations	234
	10.1.5.1 Biochemical Systems under Periodic Perturbations	234
	10.1.5.2 Biochemical Systems under Random Fluctuations	235
	10.2 Robustness Mechanisms and Scaling Laws	235
	10.2.1 Robustness in Biochemical Systems	236
	10.2.1.1 Biological Robustness Properties	236
	10.2.1.2 Mathematical Robustness Criteria	236
	10.2.2 Robustness by Backup Elements	237
	10.2.2.1 Backup Genes and Gene Loss	237
	10.2.2.2 Backup Pathways	237
	10.2.3 Feedback Control	237
	10.2.3.1 Feedback Regulation Changes the System Dynamics	237
	10.2.3.2 Allosteric and Transcriptional Feedback	238
	10.2.3.3 Integral Feedback	239
	10.2.4 Perfect Robustness by Structure	240
	10.2.4.1 The Two-component System	240
	10.2.4.2 Chemotaxis Signaling Pathway	241
	10.2.5 Scaling Laws	242
	10.2.5.1 Geometric Scaling	242
	10.2.5.2 Power Laws	242
	10.2.5.3 Scale Invariance	243
	10.2.5.4 Allometric Scaling	243
	10.2.5.5 Scaling Relations within Cells: Ribosome Content and Growth Rate	243
	10.2.6 Time Scaling, Summation Laws, and Robustness	245
	10.2.6.1 Time Scaling and Metabolic Control	245
	10.2.6.2 Robustness against Correlated Expression Changes	245
	10.2.6.3 Temperature Compensation	246
	10.2.6.4 Limits of Robustness	246
	10.2.7 The Role of Robustness in Evolution and Modeling	246
	10.2.7.1 Robustness and Evolution	246
	10.2.7.2 Robustness and Modeling	247
	10.3 Adaptation and Exploration Strategies	247
	10.3.1 Information Transmission in Signaling Pathways	248
	10.3.2 Adaptation and Fold-Change Detection	248
	10.3.3 Two Adaptation Mechanisms: Sensing and Random Switching	249
	10.3.3.1 Random Switching in Cell Populations	249
	10.3.3.2 Phenotypic or Responsive Switching	250
	10.3.4 Shannon Information and the Value of Information	250
	10.3.5 Metabolic Shifts and Anticipation	251
	10.3.5.1 Metabolic Shifts	251
	10.3.5.2 Management of a Transient State	251
	10.3.5.3 Adaptation Based on Indirect Cues	252
	10.3.6 Exploration Strategies	252
	10.3.6.1 Stress-Induced Mutagenesis	252
	10.3.6.2 Chemotaxis	252
	10.3.6.3 Infotaxis	253
	Exercises	254
	References	255
	Further Reading	257
	11: Optimality and Evolution	259
	11.1 Optimality in Systems Biology Models	261
	11.1.1 Mathematical Concepts for Optimality and Compromise	263
	11.1.2 Metabolism Is Shaped by Optimality	266
	11.1.3 Optimality Approaches in Metabolic Modeling	268
	11.1.4 Metabolic Strategies	270
	11.1.5 Optimal Metabolic Adaptation	271
	11.2 Optimal Enzyme Concentrations	273
	11.2.1 Optimization of Catalytic Properties of Single Enzymes	273
	11.2.2 Optimal Distribution of Enzyme Concentrations in a Metabolic Pathway	275
	11.2.3 Temporal Transcription Programs	277
	11.3 Evolution and Self-Organization	279
	11.3.1 Introduction	279
	11.3.2 Selection Equations for Biological Macromolecules	281
	11.3.2.1 Self-Replication without Interactions	282
	11.3.2.2 Selection at Constant Total Concentration of Self-Replicating Molecules	282
	11.3.3 The Quasispecies Model: Self-Replication with Mutations	283
	11.3.3.1 The Genetic Algorithm	284
	11.3.3.2 Assessment of Sequence Length for Stable Passing On of Sequence Information	284
	11.3.3.3 Coexistence of Self-Replicating Sequences: Complementary Replication of RNA	285
	11.3.4 The Hypercycle	285
	11.3.5 Other Mathematical Models of Evolution: Spin Glass Model	287
	11.3.6 The Neutral Theory of Molecular Evolution	288
	11.4 Evolutionary Game Theory	289
	11.4.1 Social Interactions	290
	11.4.2 Game Theory	291
	11.4.3 Evolutionary Game Theory	292
	11.4.4 Replicator Equation for Population Dynamics	292
	11.4.5 Evolutionarily Stable Strategies	293
	11.4.6 Dynamical Behavior in the Rock-Scissors-Paper Game	294
	11.4.7 Evolution of Cooperative Behavior	294
	11.4.8 Compromises between Metabolic Yield and Efficiency	296
	Exercises	297
	References	298
	Further Reading	301
	12: Models of Biochemical Systems	303
	12.1 Metabolic Systems	303
	12.1.1 Basic Elements of Metabolic Modeling	304
	12.1.2 Toy Model of Upper Glycolysis	304
	12.1.3 Threonine Synthesis Pathway Model	307
	12.2 Signaling Pathways	309
	12.2.1 Function and Structure of Intra- and Intercellular Communication	310
	12.2.2 Receptor-Ligand Interactions	311
	12.2.3 Structural Components of Signaling Pathways	313
	12.2.3.1 G Proteins	314
	12.2.3.2 Small G Proteins	315
	12.2.3.3 Phosphorelay Systems	315
	12.2.3.4 MAP Kinase Cascades	316
	12.2.3.5 The Wnt/?-Catenin Signaling Pathway	319
	12.2.4 Analysis of Dynamic and Regulatory Features of Signaling Pathways	322
	12.2.4.1 Detecting Feedback Loops in Dynamical Systems	322
	12.2.4.2 Quantitative Measures for Properties of Signaling Pathways	323
	12.2.4.3 Crosstalk in Signaling Pathways	324
	12.3 The Cell Cycle	325
	12.3.1 Steps in the Cycle	327
	12.3.2 Minimal Cascade Model of a Mitotic Oscillator	328
	12.3.3 Models of Budding Yeast Cell Cycle	329
	12.4 The Aging Process	332
	12.4.1 Evolution of the Aging Process	334
	12.4.2 Using Stochastic Simulations to Study Mitochondrial Damage	336
	12.4.3 Using Delay Differential Equations to Study Mitochondrial Damage	341
	Exercises	345
	References	345
	Part Two: Reference Section	349
	13: Cell Biology	351
	13.1 The Origin of Life	352
	13.2 Molecular Biology of the Cell	354
	13.2.1 Chemical Bonds and Forces Important in Biological Molecules	354
	13.2.2 Functional Groups in Biological Molecules	356
	13.2.3 Major Classes of Biological Molecules	356
	13.3 Structural Cell Biology	363
	13.3.1 Structure and Function of Biological Membranes	365
	13.3.2 Nucleus	367
	13.3.3 Cytosol	367
	13.3.4 Mitochondria	368
	13.3.5 Endoplasmic Reticulum and Golgi Complex	368
	13.3.6 Other Organelles	369
	13.4 Expression of Genes	369
	13.4.1 Transcription	369
	13.4.2 Processing of the mRNA	371
	13.4.3 Translation	371
	13.4.4 Protein Sorting and Posttranslational Modifications	373
	13.4.5 Regulation of Gene Expression	373
	Exercises	374
	References	374
	Further Reading	374
	14: Experimental Techniques	375
	14.1 Restriction Enzymes and Gel Electrophoresis	376
	14.2 Cloning Vectors and DNA Libraries	377
	14.3 1D and 2D Protein Gels	379
	14.4 Hybridization and Blotting Techniques	380
	14.4.1 Southern Blotting	381
	14.4.2 Northern Blotting	381
	14.4.3 Western Blotting	381
	14.4.4 In Situ Hybridization	382
	14.5 Further Protein Separation Techniques	382
	14.5.1 Centrifugation	382
	14.5.2 Column Chromatography	382
	14.6 Polymerase Chain Reaction	383
	14.7 Next-Generation Sequencing	384
	14.8 DNA and Protein Chips	385
	14.8.1 DNA Chips	385
	14.8.2 Protein Chips	385
	14.9 RNA-Seq	386
	14.10 Yeast Two-Hybrid System	386
	14.11 Mass Spectrometry	387
	14.12 Transgenic Animals	388
	14.12.1 Microinjection and ES Cells	388
	14.12.2 Genome Editing Using ZFN, TALENs, and CRISPR	388
	14.13 RNA Interference	389
	14.14 ChIP-on-Chip and ChIP-PET	390
	14.15 Green Fluorescent Protein	392
	14.16 Single-Cell Experiments	393
	14.17 Surface Plasmon Resonance	394
	Exercises	395
	References	395
	15: Mathematical and Physical Concepts	399
	15.1 Linear Algebra	399
	15.1.1 Linear Equations	399
	15.1.1.1 The Gaussian Elimination Algorithm	401
	15.1.1.2 Systematic Solution of Linear Systems	401
	15.1.2 Matrices	402
	15.1.2.1 Basic Notions	402
	15.1.2.2 Linear Dependency	402
	15.1.2.3 Basic Matrix Operations	402
	15.1.2.4 Dimension and Rank	403
	15.1.2.5 Eigenvalues and Eigenvectors of a Square Matrix	404
	15.2 Dynamic Systems	404
	15.2.1 Describing Dynamics with Ordinary Differential Equations	404
	15.2.1.1 Notations	404
	15.2.2 Linearization of Autonomous Systems	406
	15.2.3 Solution of Linear ODE Systems	406
	15.2.4 Stability of Steady States	406
	15.2.5 Global Stability of Steady States	408
	15.2.6 Limit Cycles	408
	15.3 Statistics	409
	15.3.1 Basic Concepts of Probability Theory	409
	15.3.1.1 Probability Spaces	409
	15.3.1.2 Random Variables, Densities, and Distribution Functions	411
	15.3.1.3 Transforming Probability Densities	413
	15.3.1.4 Product Experiments and Independence	413
	15.3.1.5 Limit Theorems	413
	15.3.2 Descriptive Statistics	414
	15.3.2.1 Statistics for Sample Location	414
	15.3.2.2 Statistics for Sample Variability	415
	15.3.2.3 Density Estimation	415
	15.3.2.4 Correlation of Samples	416
	15.3.3 Testing Statistical Hypotheses	417
	15.3.3.1 Statistical Framework	418
	15.3.3.2 Two Sample Location Tests	418
	15.3.4 Linear Models	419
	15.3.4.1 ANOVA	420
	15.3.4.2 Multiple Linear Regression	421
	15.3.5 Principal Component Analysis	422
	15.4 Stochastic Processes	423
	15.4.1 Chance in Physical Theories	423
	15.4.2 Mathematical Random Processes	424
	15.4.2.1 Reduced and Conditional Distributions	425
	15.4.3 Brownian Motion as a Random Process	425
	15.4.4 Markov Processes	427
	15.4.5 Markov Chains	428
	15.4.6 Jump Processes in Continuous Time	428
	15.4.6.1 Deriving the Master Equation	428
	15.4.7 Continuous Random Processes	429
	15.4.7.1 Langevin Equations	429
	15.4.7.2 The Fokker-Planck Equation	429
	15.4.8 Moment-Generating Functions	430
	15.5 Control of Linear Dynamical Systems	430
	15.5.1 Linear Dynamical Systems	431
	15.5.2 System Response and Linear Filters	432
	15.5.2.1 Impulse Input	432
	15.5.2.2 Oscillatory Input	432
	15.5.3 Random Fluctuations and Spectral Density	433
	15.5.4 The Gramian Matrices	433
	15.5.5 Model Reduction	434
	15.5.6 Optimal Control	434
	15.6 Biological Thermodynamics	435
	15.6.1 Microstate and Statistical Ensemble	435
	15.6.1.1 Thermodynamic Equilibrium and Detailed Balance	436
	15.6.2 Boltzmann Distribution and Free Energy	436
	15.6.2.1 Boltzmann Distribution	436
	15.6.2.2 Free Energy	437
	15.6.3 Entropy	437
	15.6.3.1 The Second Law of Thermodynamics	437
	15.6.3.2 Statistical Entropy	438
	15.6.3.3 Principle of Maximal Entropy	439
	15.6.4 Equilibrium Constant and Energies	439
	15.6.5 Chemical Reaction Systems	440
	15.6.5.1 Temperature and Pressure as Free Variables	440
	15.6.5.2 Gibbs Energy and Chemical Potentials	440
	15.6.5.3 Reaction Gibbs Energy	441
	15.6.5.4 Wegscheider Conditions and Haldane Relationships	441
	15.6.5.5 Data for Thermodynamic Calculations	442
	15.6.6 Nonequilibrium Reactions	442
	15.6.6.1 Variational Principle for Flux States	442
	15.6.6.2 Consequences of the Flux-Force Relation	443
	15.6.6.3 Reaction Energetics and Flux Control	443
	15.6.7 The Role of Thermodynamics in Systems Biology	443
	15.7 Multivariate Statistics	444
	15.7.1 Planning and Designing Experiments for Case-Control Studies	444
	15.7.2 Tests for Differential Expression	445
	15.7.2.1 DNA Arrays	445
	15.7.2.2 Next-Generation Sequencing	446
	15.7.3 Multiple Testing	446
	15.7.4 ROC Curve Analysis	447
	15.7.5 Clustering Algorithms	448
	15.7.5.1 Hierarchical Clustering	449
	15.7.5.2 Self-Organizing Maps (SOMs)	451
	15.7.5.3 K-Means	452
	15.7.6 Cluster Validation	453
	15.7.7 Overrepresentation and Enrichment Analyses	454
	15.7.8 Classification Methods	456
	15.7.8.1 Support Vector Machines	457
	15.7.8.2 Other Approaches	458
	Exercises	459
	References	461
	16: Databases	463
	16.1 General-Purpose Data Resources	463
	16.1.1 PathGuide	463
	16.1.2 BioNumbers	464
	16.2 Nucleotide Sequence Databases	464
	16.2.1 Data Repositories of the National Center for Biotechnology Information	464
	16.2.2 GenBank/RefSeq/UniGene	464
	16.2.3 Entrez	465
	16.2.4 EMBL Nucleotide Sequence Database	465
	16.2.5 European Nucleotide Archive	465
	16.2.6 Ensembl	465
	16.3 Protein Databases	466
	16.3.1 UniProt/Swiss-Prot/TrEMBL	466
	16.3.2 Protein Data Bank	466
	16.3.3 PANTHER	466
	16.3.4 InterPro	466
	16.3.5 iHOP	467
	16.4 Ontology Databases	467
	16.4.1 Gene Ontology	467
	16.5 Pathway Databases	467
	16.5.1 KEGG	468
	16.5.2 Reactome	468
	16.5.3 ConsensusPathDB	469
	16.5.4 WikiPathways	469
	16.6 Enzyme Reaction Kinetics Databases	469
	16.6.1 BRENDA	469
	16.6.2 SABIO-RK	470
	16.7 Model Collections	470
	16.7.1 BioModels	470
	16.7.2 JWS Online	470
	16.8 Compound and Drug Databases	470
	16.8.1 ChEBI	471
	16.8.2 Guide to PHARMACOLOGY	471
	16.9 Transcription Factor Databases	471
	16.9.1 JASPAR	471
	16.9.2 TRED	471
	16.9.3 Transcription Factor Encyclopedia	472
	16.10 Microarray and Sequencing Databases	472
	16.10.1 Gene Expression Omnibus	472
	16.10.2 ArrayExpress	472
	References	473
	17: Software Tools for Modeling	475
	17.1 13C-Flux2	476
	17.2 Antimony	476
	17.3 Berkeley Madonna	477
	17.4 BIOCHAM	477
	17.5 BioNetGen	477
	17.6 Biopython	477
	17.7 BioTapestry	478
	17.8 BioUML	478
	17.9 CellDesigner	478
	17.10 CellNetAnalyzer	478
	17.11 Copasi	479
	17.12 CPN Tools	479
	17.13 Cytoscape	479
	17.14 E-Cell	479
	17.15 EvA2	479
	17.16 FEniCS Project	480
	17.17 Genetic Network Analyzer (GNA)	480
	17.18 Jarnac	480
	17.19 JDesigner	481
	17.20 JSim	481
	17.21 KNIME	481
	17.22 libSBML	482
	17.23 MASON	482
	17.24 Mathematica	482
	17.25 MathSBML	483
	17.26 Matlab	483
	17.27 MesoRD	483
	17.28 Octave	483
	17.29 Omix Visualization	484
	17.30 OpenCOR	484
	17.31 Oscill8	484
	17.32 PhysioDesigner	484
	17.33 PottersWheel	485
	17.34 PyBioS	485
	17.35 PySCeS	485
	17.36 R	486
	17.37 SAAM II	486
	17.38 SBMLeditor	486
	17.39 SemanticSBML	486
	17.40 SBML-PET-MPI	487
	17.41 SBMLsimulator	487
	17.42 SBMLsqueezer	487
	17.43 SBML Toolbox	488
	17.44 SBtoolbox2	488
	17.45 SBML Validator	488
	17.46 SensA	488
	17.47 SmartCell	489
	17.48 STELLA	489
	17.49 STEPS	489
	17.50 StochKit2	489
	17.51 SystemModeler	490
	17.52 Systems Biology Workbench	490
	17.53 Taverna	490
	17.54 VANTED	491
	17.55 Virtual Cell (VCell)	491
	17.56 xCellerator	491
	17.57 XPPAUT	491
	Exercises	492
	References	492
	Index	493
	EULA	507