Contents

Preface vii

1. Cancer and somatic evolution 1

1.1 What is cancer? 1

1.2 Basic cancer genetics 2

1.3 Multi-stage carcinogenesis and colon cancer 4

1.4 Genetic instability 6

1.5 Barriers to cancer progression: importance of the microenvironment 8

1.6 Evolutionary theory and Darwinian selection 10

2. Mathematical modeling of tumorigenesis 13

2.1 Ordinary differential equations 14

2.2 Partial differential equations 16

2.3 Discrete, cellular automaton models 20

2.4 Stochastic modeling 22

2.5 Statistics and parameter fitting 25

2.6 Concluding remarks 26

3. Cancer initiation: one-hit and two-hit stochastic models 27

3.1.1 Mutation-selection diagrams and the formulation of a stochastic process 28

3.1.2 Analysis of a one-hit process 30

3.2.1 Process description 35

3.2.2 Two ways to acquire the second hit 36

3.2.3 The regime of tunneling 37

3.2.4 Genuine two-step processes 44

3.2.5 Summary of the two-hit model with a constant population 44

3.3 Modeling non-constant populations 45

3.3.1 Description of the model 45

3.3.2 A one-hit process 47

3.3.3 Three types of dynamics 48

3.3.4 Probability to create a mutant of type "C" 49

3.3.5 A two-hit process 49

3.4 Overview 51

4. Microsatellite and chromosomal instability in sporadic and familial cancers 53

4.1 Some biological facts about genetic instability in colon cancer 55

4.2 A model for the initiation of sporadic colorectal cancers . . 55

4.3 Sporadic colorectal cancers, CIN and MSI 60

4.4 FAP 65

4.5 HNPCC 67

4.6 Insights following from this analysis 68

5. Cellular origins of cancer 71

5.1 Stem cells, tissue renewal and cancer 73

5.2 The basic renewal model 74

5.3 Three scenarios 77

5.4 Mathematical analysis 78

5.5 Implications and data 84

6. Costs and benefits of chromosomal instability 87

6.1 The effect of chromosome loss on the generation of cancer . 88

6.2 Calculating the optimal rate of chromosome loss 90

6.3 Why does CIN emerge? 95

6.4 The bigger picture 98

7. DNA damage and genetic instability 101

7.1 Competition dynamics 102

7.2 Competition dynamics and cancer evolution 107

7.2.1 A quasispecies model 107

7.2.2 Strong apoptosis 115

7.2.3 Weak apoptosis 118

7.3 Summary of mathematical results 119

7.4 Selection for genetic instability 121

7.5 Genetic instability and apoptosis 122

7.6 Can competition be reversed by chemotherapy? 124

8. Tissue aging and the development of cancer 127

8.1 What is aging? 128

8.2 Basic modeling assumptions 129

8.3 Modeling healthy tissue 130

8.4 Modeling tumor cell growth 133

8.5 Checkpoints and basic tumor growth 136

8.6 Tumor growth and the microenvironment 139

8.7 Theory and data 141

9. Basic models of tumor inhibition and promotion 147

9.1 Model 1: Angiogenesis inhibition induces cell death 149

9.2 Model 2: Angiogenesis inhibition prevents tumor cell division 153

9.2.1 Linear stability analysis of the ODEs 155

9.2.2 Conclusions from the linear analysis 156

9.3 Spread of tumors across space 157

9.3.1 Turing stability analysis 158

9.3.2 Stationary periodic solutions 161

9.3.3 Biological implications and numerical simulations . . 161

9.4 Somatic cancer evolution and progression 164

9.5 Clinical implications 168

10. Mechanisms of tumor neovascularization 171

10.1 Emergence of the concept of postnatal vasculogenesis 172

10.2 Relative importance of angiogenesis versus vasculogenesis . 173

10.3 Mathematical models of tumor angiogenesis and vasculogenesis 174

10.4 Mathematical analysis 177

10.5 Applications 180

10.5.1 Dynamics of BM-derived EPCs 180

10.5.2 Re-evaluation of apparently contradictory experimental data 181

10.5.3 Tumor growth kinetics 182

11. Cancer and immune responses 185

11.1 Some facts about immune responses 186

11.2 The model 189

11.3 Method of model analysis 192

11.4 Properties of the model 192

11.5 Immunity versus tolerance 195

11.6 Cancer initiation 196

11.7 Tumor dormancy, evolution, and progression 198

11.8 Immunotherapy against cancers 200

12. Therapeutic approaches: viruses as anti-tumor weapons 205

12.1 Virus-induced killing of tumor cells 207

12.2 Effect of virus-specific CTL 212

12.3 Virus infection and the induction of tumor-specific CTL . . 214

12.4 Interactions between virus-and tumor-specific CTL 218

12.5 Treatment strategies 219

12.6 Evaluating viruses in culture 221

Appendix A Exact formula for total probability of double mutations 223

Bibliography 227

Index

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