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1 | (5) |
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1 | (1) |
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1.2 Intracellular processes, cell states and cell fate: overview of the chapters |
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2 | (1) |
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1.3 On mathematical modelling of biological phenomena |
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3 | (2) |
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1.4 A brief note on the organization and use of the book |
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5 | (1) |
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5 | (1) |
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2 From molecules to a living cell |
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6 | (12) |
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2.1 Cell compartments and organelles |
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6 | (3) |
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2.2 The molecular machinery of gene expression |
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9 | (3) |
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2.3 Molecular pathways and networks |
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12 | (3) |
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15 | (1) |
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References & further readings |
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16 | (2) |
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3 Mathematical and computational modelling tools |
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18 | (26) |
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18 | (4) |
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3.2 Ordinary differential equations (ODEs) |
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22 | (3) |
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3.2.1 Theorems on uniqueness of solutions |
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22 | (1) |
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3.2.2 Vector fields, phase space, and trajectories |
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23 | (1) |
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3.2.3 Stability of steady states |
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24 | (1) |
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3.3 Phase portraits on the plane |
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25 | (2) |
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27 | (2) |
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3.5 Bistability and hysteresis |
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29 | (1) |
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30 | (2) |
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3.7 Singular perturbations |
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32 | (1) |
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3.8 Partial differential equations (PDEs) |
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33 | (3) |
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3.8.1 Reaction-diffusion equations |
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33 | (1) |
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34 | (1) |
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3.8.3 Dirichlet, Neumann and third-boundary-value problems |
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35 | (1) |
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3.9 Well posed and ill posed problems |
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36 | (1) |
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37 | (3) |
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3.10.1 Conservation of mass equation |
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37 | (1) |
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3.10.2 Method of characteristics |
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38 | (2) |
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3.11 Stochastic simulations |
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40 | (1) |
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3.12 Computer software platforms for cell modelling |
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41 | (1) |
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42 | (1) |
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42 | (2) |
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4 Gene-regulatory networks: from DNA to metabolites and back |
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44 | (21) |
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4.1 Genome structure of Escherichia coli |
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44 | (1) |
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45 | (2) |
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4.3 A model of the Trp operon |
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47 | (3) |
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4.4 Roles of the negative feedbacks in the Trp operon |
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50 | (2) |
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52 | (2) |
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4.6 Experimental evidence and modelling of bistable behavior of the lac operon |
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54 | (1) |
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4.7 A reduced model derived from the detailed lac operon network |
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55 | (6) |
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4.8 The challenge ahead: complexity of the global transcriptional network |
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61 | (1) |
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62 | (1) |
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63 | (2) |
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5 Control of DNA replication in a prokaryote |
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65 | (14) |
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5.1 The cell cycle of E. coli |
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65 | (2) |
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5.2 Overlapping cell cycles: coordinating growth and DNA replication |
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67 | (1) |
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5.3 The oriC and the initiation of DNA replication |
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67 | (2) |
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5.4 The initiation-titration-activation model of replication initiation |
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69 | (5) |
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5.4.1 DnaA protein synthesis |
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70 | (1) |
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5.4.2 DnaA binding to boxes arid initiation of replication |
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71 | (2) |
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5.4.3 Changing numbers of oriCs and dnaA boxes during chromosome replication |
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73 | (1) |
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5.4.4 Death and birth of oriCs |
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74 | (1) |
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5.4.5 Inactivation of dnaA-ATP |
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74 | (1) |
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74 | (1) |
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5.6 Robustness of initiation control |
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75 | (2) |
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77 | (1) |
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78 | (1) |
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6 The eukaryotic cell-cycle engine |
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79 | (17) |
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6.1 Physiology of the eukaryotic cell cycle |
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79 | (1) |
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6.2 The biochemistry of the cell-cycle engine |
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80 | (2) |
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6.3 Embryonic cell cycles |
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82 | (3) |
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6.4 Control of MPF activity in embryonic cell cycles |
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85 | (2) |
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6.5 Essential elements of the basic eukaryotic cell-cycle engine |
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87 | (6) |
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93 | (2) |
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95 | (1) |
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95 | (1) |
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96 | (12) |
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7.1 Cell-cycle checkpoints |
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96 | (1) |
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7.2 The restriction point |
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97 | (1) |
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7.3 Modelling the restriction point |
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98 | (3) |
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7.3.1 The G1-S regulatory network |
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98 | (2) |
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100 | (1) |
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7.4 The G2 DNA damage checkpoint |
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101 | (3) |
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7.5 The mitotic spindle checkpoint |
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104 | (2) |
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106 | (1) |
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107 | (1) |
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108 | (17) |
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8.1 Background on the biology of apoptosis |
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108 | (1) |
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8.2 Intrinsic and extrinsic caspase pathways |
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109 | (2) |
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8.3 A bistable model for caspase-3 activation |
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111 | (4) |
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8.4 DISC formation and caspase-8 activation |
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115 | (5) |
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8.5 Combined intrinsic and extrinsic apoptosis pathways |
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120 | (2) |
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8.6 Summary and future modelling |
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122 | (2) |
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124 | (1) |
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124 | (1) |
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125 | (14) |
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9.1 Cell differentiation in the hematopoietic system |
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126 | (1) |
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9.2 Modelling the differentiation of Th lymphocytes |
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127 | (3) |
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9.3 Cytokine memory in single cells |
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130 | (1) |
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9.4 Population of differentiating Th lymphocytes |
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131 | (3) |
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9.4.1 Equation for population density φ |
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131 | (2) |
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9.4.2 Determining the population density φ |
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133 | (1) |
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9.5 High-dimensional switches in cellular differentiation |
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134 | (2) |
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136 | (1) |
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137 | (1) |
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137 | (2) |
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10 Cell aging and renewal |
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139 | (16) |
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10.1 Cellular senescence and telomeres |
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139 | (1) |
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10.2 Models of tissue aging and maintenance |
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140 | (5) |
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10.2.1 The probabilistic model of Op den Buijs et al. |
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140 | (2) |
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142 | (3) |
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10.3 Asymmetric stem-cell division |
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145 | (3) |
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10.4 Maintaining the stem-cell reservoir |
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148 | (5) |
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10.4.1 The Roeder-Loeffler model |
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148 | (3) |
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10.4.2 A deterministic model |
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151 | (2) |
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153 | (1) |
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153 | (2) |
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11 Multiscale modelling of cancer |
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155 | (21) |
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11.1 Attributes of cancer |
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155 | (1) |
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11.2 A multiscale model of avaseular tumor growth |
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156 | (4) |
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157 | (1) |
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11.2.2 Extracellular scale |
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158 | (1) |
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159 | (1) |
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11.3 A multiscale model of colorectal cancer |
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160 | (7) |
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11.3.1 Gene level: a Boolean network |
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161 | (2) |
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11.3.2 Cell level: a discrete cell-cycle model |
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163 | (1) |
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11.3.3 Tissue level: colonies of cells and oxygen supply |
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164 | (3) |
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11.4 Continuum models of solid tumor growth |
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167 | (7) |
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11.4.1 Three types of cells |
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167 | (5) |
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172 | (2) |
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174 | (1) |
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174 | (2) |
Glossary |
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176 | (5) |
Index |
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181 | |