Systems biology - dynamic pathway modeling

1 Preface......Page 6
2 Modelling Natural Systems......Page 11
2.0.1 Differential Equations......Page 13
2.0.2 Dynamic Systems Theory......Page 16
2.0.3 Dealing with Uncertainty......Page 20
2.0.4 The Systems Biology Approach......Page 24
2.1 Cell Chemistry......Page 27
2.2 Cell Signalling......Page 29
2.3.2 Blotting......Page 33
2.3.3 Scanning and Laser Densitometry of Western Blots......Page 34
2.3.4 Quantification of Western blots - General Considerations......Page 35
2.4 The Dynamic Proteome......Page 37
2.5 Zooming In......Page 39
2.6 Outlook......Page 46
3.1 The ODE Approach......Page 49
3.1.1 Differential vs. Difference Equations......Page 52
3.1.2 Numerical Simulation......Page 53
3.3 Fundamental quantities and definitions......Page 54
3.4 Basic Principles and Assumptions......Page 56
3.5 Elementary Reactions......Page 57
3.5.1 Monomolecular reactions......Page 58
3.5.2 Bimolecular Reactions......Page 59
3.5.3 Bimolecular reaction of identical species......Page 61
3.5.4 Trimolecular reactions......Page 62
3.5.5 Higher and rational reaction orders......Page 64
3.6 Complex Reactions......Page 65
3.6.1 Reversible Reactions......Page 66
3.7 Parallel Reactions......Page 69
3.7.1 Consecutive Reactions......Page 72
3.8 Autocatalytic Reactions......Page 78
4.1 Common Roots: To be and not to be (the same)!......Page 81
4.2 A matter of life and death......Page 84
4.3 Mass action models the average of the CME?......Page 89
4.4 Review: Mass action models and CMEs......Page 91
4.5 Stochastic Simulation......Page 93
4.5.1 Gillespie modelling......Page 95
4.5.2 Stochastic rate constant versus rate constant......Page 97
4.5.3 So are they, or are they not?......Page 101
4.5.4 The Gillespie Algorithm......Page 102
4.5.5 Examples......Page 105
4.5.6 Molecules as individuals......Page 110
4.6 An ODE to Differential Equations......Page 111
4.7 A never ending story......Page 118
4.7.1 Steady-state solution for the master equation......Page 120
4.7.2 Temporal evolution of average and variance......Page 126
4.7.3 Solution of the mass action model......Page 128
4.7.4 Generating functions......Page 130
4.7.5 Summary: The master-equation approach......Page 140
5 Cell Communication......Page 141
6.1 Pathways as Dynamic Systems......Page 142
6.2 The Role of Feedback......Page 143
6.3 Tutorial Examples......Page 146
6.4 Discussion......Page 150
6.5 Phase-Plane Analysis......Page 151
6.6 Nonlinear Dynamics......Page 159
7 Receptor Modelling......Page 166
8 Dynamic Modelling of Biochemical Networks......Page 175
8.1 Simulation example......Page 178
8.2 Michaelis-Menten modelling......Page 179
8.3 Multinomial Systems......Page 182
8.4 S-Systems......Page 184
8.5 The Heinrich Model......Page 185
8.6 The MAP Kinase (MAPK) Pathway......Page 187
8.7 The Ras/Raf/MEK/ERK Pathway......Page 189
8.8 Feedback and Oscillations in Signalling Pathways......Page 193
9.1 Linear Module......Page 203
9.2 Hyperbolic Module......Page 206
9.3 Sigmoidal Module......Page 208
9.4 Robust or Adaptive Module......Page 210
9.5 Feedback Systems......Page 212
9.5.1 Positive Feedback/Feedforward - Switches......Page 213
9.5.2 Negative Feedback - Oscillations......Page 223
9.5.3 Mixed Control Mechanisms......Page 229
A Glossary......Page 236
B Notation......Page 243