Models of Cellular Regulation

Contents......Page 8
1.1 Goals......Page 12
1.2 Intracellular processes, cell states and cell fate: overview of the chapters......Page 13
1.3 On mathematical modelling of biological phenomena......Page 14
References......Page 16
2.1 Cell compartments and organelles......Page 17
2.2 The molecular machinery of gene expression......Page 20
2.3 Molecular pathways and networks......Page 23
2.4 The omics revolution......Page 26
References & further readings......Page 27
3.1 Chemical kinetics......Page 29
3.2.1 Theorems on uniqueness of solutions......Page 33
3.2.2 Vector fields, phase space, and trajectories......Page 34
3.2.3 Stability of steady states......Page 35
3.3 Phase portraits on the plane......Page 36
3.4 Bifurcations......Page 38
3.5 Bistability and hysteresis......Page 40
3.6 Hopf bifurcation......Page 41
3.7 Singular perturbations......Page 43
3.8.1 Reaction-diffusion equations......Page 44
3.8.2 Cauchy problem......Page 45
3.8.3 Dirichlet, Neumann and third-boundary-value problems......Page 46
3.9 Well posed and ill posed problems......Page 47
3.10.1 Conservation of mass equation......Page 48
3.10.2 Method of characteristics......Page 49
3.11 Stochastic simulations......Page 51
3.12 Computer software platforms for cell modelling......Page 52
Exercises......Page 53
4.1 Genome structure of Escherichia coli......Page 55
4.2 The Trp operon......Page 56
4.3 A model of the Trp operon......Page 58
4.4 Roles of the negative feedbacks in the Trp operon......Page 61
4.5 The lac operon......Page 63
4.6 Experimental evidence and modelling of bistable behavior of the lac operon......Page 65
4.7 A reduced model derived from the detailed lac operon network......Page 66
4.8 The challenge ahead: complexity of the global transcriptional network......Page 72
References......Page 73
Exercises......Page 74
5.1 The cell cycle of E. coli......Page 76
5.3 The oriC and the initiation of DNA replication......Page 78
5.4 The initiation-titration-activation model of replication initiation......Page 80
5.4.1 DnaA protein synthesis......Page 81
5.4.2 DnaA binding to boxes and initiation of replication......Page 82
5.4.3 Changing numbers of oriCs and dnaA boxes during chromosome replication......Page 84
5.5 Model dynamics......Page 85
5.6 Robustness of initiation control......Page 86
References......Page 88
Exercises......Page 89
6.1 Physiology of the eukaryotic cell cycle......Page 90
6.2 The biochemistry of the cell-cycle engine......Page 91
6.3 Embryonic cell cycles......Page 93
6.4 Control of MPF activity in embryonic cell cycles......Page 96
6.5 Essential elements of the basic eukaryotic cell-cycle engine......Page 98
6.6 Summary......Page 104
Exercises......Page 106
7.1 Cell-cycle checkpoints......Page 107
7.2 The restriction point......Page 108
7.3.1 The G1–S regulatory network......Page 109
7.3.2 A switching module......Page 111
7.4 The G2 DNA damage checkpoint......Page 112
7.5 The mitotic spindle checkpoint......Page 115
References......Page 117
Exercises......Page 118
8.1 Background on the biology of apoptosis......Page 119
8.2 Intrinsic and extrinsic caspase pathways......Page 120
8.3 A bistable model for caspase-3 activation......Page 122
8.4 DISC formation and caspase-8 activation......Page 126
8.5 Combined intrinsic and extrinsic apoptosis pathways......Page 131
8.6 Summary and future modelling......Page 133
Exercises......Page 135
9 Cell differentiation......Page 136
9.1 Cell differentiation in the hematopoietic system......Page 137
9.2 Modelling the differentiation of Th lymphocytes......Page 138
9.3 Cytokine memory in single cells......Page 141
9.4.1 Equation for population density Φ......Page 142
9.4.2 Determining the population density Φ......Page 144
9.5 High-dimensional switches in cellular differentiation......Page 145
9.6 Summary......Page 147
Exercises......Page 148
10.1 Cellular senescence and telomeres......Page 150
10.2.1 The probabilistic model of Op den Buijs et al.......Page 151
10.2.2 A continuum model......Page 153
10.3 Asymmetric stem-cell division......Page 156
10.4.1 The Roeder–Loeffler model......Page 159
10.4.2 A deterministic model......Page 162
Exercises......Page 164
11.1 Attributes of cancer......Page 166
11.2 A multiscale model of avascular tumor growth......Page 167
11.2.1 Cellular scale......Page 168
11.2.2 Extracellular scale......Page 169
11.2.3 Subcellular scale......Page 170
11.3 A multiscale model of colorectal cancer......Page 171
11.3.1 Gene level: a Boolean network......Page 172
11.3.2 Cell level: a discrete cell-cycle model......Page 174
11.3.3 Tissue level: colonies of cells and oxygen supply......Page 175
11.4.1 Three types of cells......Page 178
11.4.2 One type of cells......Page 183
Exercises......Page 185
C......Page 187
H......Page 188
M......Page 189
T......Page 190
Z......Page 191
G......Page 192
T......Page 193
Z......Page 194