Modeling in Systems Biology (eBook)

Foreword 5
Preface 7
Who Should Read This Book? 7
How to Read This Book? 8
Official FTP Site 9
FTP Site for Supplementary Material 9
Acknowledgements 10
Contents 11
Contributors 18
Foundations 21
Introduction 22
Systems Biology 23
Models and Modeling 24
Analysis of Models 25
Model Development 27
Model Composition 28
Dynamic Behavior 28
Data Resources 29
Repositories of Gene Expression Data 30
Protein-Protein Interaction Databases 30
Pathway Databases 31
Visualization 32
Visualization Methods 32
Systems Biology Graphical Notation 33
Visualization Tools 34
Petri Nets in Biology 35
Motivation for Using Petri Nets 35
Petri Nets in Biology 35
Problems 36
Biochemical Fundamentals 38
Cell Biology 38
Cellular Organization 39
Mitochondria 40
Plastids 41
Metabolism 42
Metabolic Pathways and Networks 42
Metabolites 43
Enzymes 43
Enzyme Inhibition 44
Enzyme Kinetics and Activity 46
Central Metabolic Pathways 48
Glycolysis 48
The Citric Acid Cycle 48
The Oxidative Pentose Phosphate Pathway 49
Fatty Acid Synthesis 49
Metabolic Networks 49
Regulation of Metabolism 50
Gene Expression 51
Transcription 51
Translation 51
Gene Regulation 53
Gene Regulatory Networks 53
Signal Transduction 53
Hormones and Other Signaling Molecules 54
Receptors 55
Problems 55
Petri Nets 56
Introduction 56
An Introductory Example 57
Models of Substances 57
Models of Reactions 57
Sequentially Composed Reactions 58
Quantitative Aspects 60
Alternative Composition 60
Modeling the Interface 61
Putting it All Together 61
The Static Structure of Petri Nets 62
Places 62
Transitions 62
Arcs 63
Markings 63
Static Net Structures 63
Dynamic Behavior of Petri Nets 64
Enabled Transitions 64
Steps 64
Step Sequences and Reachable Markings 65
The Role of Infinity 65
Analysis Techniques for Petri Nets 66
Important Properties 66
The Linear Algebra of Steps 67
The Matrix of a Petri Net 67
Place Invariants 68
Transition Invariants 70
Traps 71
Syphons 71
The Marking Graph 71
Concurrent Runs 72
Petri Nets as a Modeling Technique for Systems Biology 72
Discrete Steps 73
Local Cause and Effect 73
Invariance of Substance 74
Other Models of Dynamic Systems 74
References and Tools 74
Problems 75
Modeling Techniques 76
Discrete Modeling 77
Modeling Concepts 77
Qualitative Analysis 80
P-invariants 81
T-invariants 82
Feasible T-invariants 83
MCT-sets 85
T-clusters 86
Mauritius Maps 87
Related Work 88
Software 89
Problems 89
Modeling Genetic Regulatory Networks 91
Introduction 91
Synchronous Models of GRNs 93
Constructing a Qualitative Petri Net Model 94
Phase One: Next State Decision 96
Phase Two: Synchronous State Update 97
Tool Support 98
Case Study: Nutritional Stress Response in E. coli 99
Constructing the Petri Net Model 99
Analyzing the Petri Net Model 101
Model Validation 102
Property Analysis 102
Mutant Analysis 103
Asynchronous Models of GRNs 104
Signal Transition Graphs and Speed-Independent Circuits 105
Refining Asynchronous Models of GRNs 109
Case Study: Lysis-Lysogeny Switch in Phage lambda 112
Model Construction 112
Model Analysis and Refinement 114
Related Work 116
Summary 117
Problems 117
Hybrid Functional Petri Net with Extension for Dynamic Pathway Modeling 119
Introduction 119
Pathway Modeling with Concept of Petri Net 121
Petri Net (PN) 121
Representation of Biological Pathway 121
Timed Petri Net (TPN) 122
Continuous Timed Petri Net (CTPN) 124
Hybrid Functional Petri Net with Extension 124
Modeling MicroRNAs Double-Negative Feedback Loop in Gustatory Neurons of C. elegans 132
Concluding Remarks 137
Problems 137
Stochastic Modeling 139
Introduction 139
Basic Concepts 141
The Theoretical Basis of Stochastic Molecular Dynamics 141
SPN Modeling of Stochastic Molecular Dynamics 143
Beyond Pure Mass-Action 148
Methods to Determine SPN Evolution 150
Analytical and Numerical Approaches 152
Transient Analysis 152
Steady-State Analysis 155
Simulation Approaches 158
Examples of Modeling and Evaluation 161
A Biochemical Oscillator 161
A Protein Synthesis Network 164
A Gene Regulatory Network 165
Related Work 166
Summary 168
Problems 168
Quantitative Analysis 170
Introduction 171
Mass Action 171
Zero-Order Reactions 172
First-Order Reactions or Unimolecular Reactions 172
Second-Order Reactions or Bimolecular Reactions 174
Reversible Mass Action or Equilibrium Reactions 175
Example: A Simple Predator Prey Model 176
Steady States 178
Stability Analysis 178
Spatial Instability 181
Michaelis-Menten Kinetics 182
Enzyme Kinetics with Inhibitors 184
Hill Kinetics 186
Neutral Binding 186
Cooperative Binding 189
Tool Support 190
Problems 193
Continuous Versus Discrete Modeling 193
Stability Analysis of the Continuous Lotka-Volterra Model 194
Stability Analysis of the Discrete Lotka-Volterra Model 194
Michaelis-Menten Kinetics 195
Fuzzy Modeling 196
Introduction 196
Methods and Concepts 199
Ordinary Logic Reasoning 200
Modus Ponens 200
Ordinary Relations 200
Logic Implication 201
Fuzzy Sets 202
Operations on Fuzzy Sets 203
T-norms and T-conorms 203
Union, Intersection and Complement of Fuzzy Sets 203
Fuzzy Logic Reasoning 204
Generalized Modus Ponens 205
Fuzzy Relations and Implication 205
Implication 205
Fuzzy Logic Systems 207
Application to Petri Nets 209
Results 211
Design Principles 211
Semi-Discrete Modeling 212
Semi-Continuous Modeling 214
PNMA 214
Parameter Estimation 216
Application 217
Related Work 219
Common Network Motifs and Cell Cycle Model 219
Comparison of Fuzzy Logic to Multi-Class Discrete Logic 220
Classification of Gene Expression Data 220
Summary 221
Problems 221
Biochemical Applications 223
Topological Analysis of Metabolic and Regulatory Networks 224
Introduction 224
T-invariants 227
Modelling Steady States 227
Minimal T-invariants and Elementary Modes 228
Clustering of T-invariants 231
P-invariants 232
Definition and Biochemical Interpretation 232
Algorithms and Software Tools for Computing Minimal Invariants 234
Other Topological Properties 235
Related Work with Concrete Biological Examples 236
Conclusions 238
Problems 239
Analysis of Dynamical Models of Signaling Networks with Petri Nets and Dynamic Graphs 240
Introduction 240
Methods and Concepts 242
From Ordinary Differential Equations to a Petri Net Model 243
From a Petri Net Model to an Interaction Graph 245
Interaction Graphs and Conservative Components 245
Building the Interaction Graph of the Bhalla-Iyengar Model 246
From an Interaction Graph to an Influence Graph 247
Influence Graphs and Repetitive Components 247
Building the Influence Graph of the Bhalla-Iyengar Model 248
From an Influence Graph to Dynamic Graphs 251
Activation Ratio Using P-invariant to Display Activity of Signaling Components 252
Reaction Flow Ratio Using Maximum to Display Strength of Interaction Between Signaling Components 252
Tool Support 253
Results 253
Dynamic and Function of the Regulatory Motifs 257
Negative Feedback Loop 1: MAPK Inhibition of Upstream Activator cRaf is Inconsequential 257
Negative Feedback Loop 2: Phosphorylation of MKP1 and Increase of Its Expression by MAPK Are Both Needed to Halt MAPK Signaling 257
Nested Feedforward Motif 1: The Three Paths of the Motif Participates in a Cumulative Amplification of the Signal 259
Positive Feedback Loop 3: MAPK and PKC Form a Timed Bistable Switch 261
Lifetime of the Regulatory Motifs 262
Related Work 264
Summary 264
Problems 265
A Modular, Qualitative Modeling of Regulatory Networks Using Petri Nets 267
Introduction 268
Logical Modeling of Regulatory Networks 268
Logical Regulatory Graphs (LRGs) 269
Logical Functions Representation Based on Decision Diagrams 272
State Transition Graphs Associated to LRGs 274
P/T Petri Net Representation 275
Tools Support 278
Related Works 278
Modules, Their Composition and High-Level Petri Net Representation 278
Interconnecting Logical Regulatory Modules 279
High-Level Petri Net Representation 281
Implementation 283
Modeling Interconnected LRMs Using High-Level Petri Nets 284
Interconnecting Occurrences of the Toy LRM 284
The Drosophila Segment-Polarity Module 287
Conclusions 290
Problems 292
A Case Study of HFPN Simulation: Finding Essential Roles of Ror Gene in the Interaction of Feedback Loops in Mammalian Circadian Clock 294
Introduction 295
Modeling Molecular Circadian Oscillator in Mouse with Hybrid Functional Petri Net 297
Circadian Clock Oscillator with Five Genes 298
Construction of an HFPN Model 298
Effect of the Two Interlocked Loops in Circadian Gene Regulations in Mouse 301
A Problem of the Previous HFPN Model in an Oscillation Maintenance 301
Modification in Parameters for Constituting Interlocked Loops 301
Function of Ror in the Interlocked Model 307
Introduction of Ror 307
Inclusion of a Hypothetical Path: ROR Excites Bmal Only When PER/CRY Level Are Above the Threshold 312
Simulation for Rev-Erb Knockout Mice 315
Conclusions 316
Problems 317
Prediction of Network Structure 320
Introduction 320
Methods to Predict Network Structures 326
A General Combinatorial Reconstruction Approach 326
An Approach for the Case of Monotone Data 332
Results: A Reconstruction Algorithm 339
Related Work 345
Summary 347
Exercises and Solutions 348
Glossary 350
References 352
Index 370