Modelling chromosome missegregation in tumour evolution

................................................................................................................................... 7 Contents .................................................................................................................................. 9 List of Figures ......................................................................................................................... 14 List of Tables .......................................................................................................................... 29 1. Introduction .................................................................................................................... 31 1.1. Research Problem: Aneuploidy in Cancer ........................................................................... 33 1.2. Hypothesis ............................................................................................................................ 34 1.3. Scope of the Project ............................................................................................................. 36 1.4. Objectives ............................................................................................................................. 36 1.5. Thesis Contributions ............................................................................................................ 37 1.6. Publications .......................................................................................................................... 38 1.7. Thesis Overview ................................................................................................................... 39 2. Background ..................................................................................................................... 41 2.1. The Biology of Cancer ......................................................................................................... 41 2.1.1. Introduction to Cancer Biology .................................................................................... 42 2.1.2. On the Origins of a Tumour .......................................................................................... 44 2.1.3. Oncogenes and Tumour Suppressors ........................................................................... 48 2.1.4. Aneuploidy in Cancer ................................................................................................... 50 2.1.5. Summary of Biological Background ............................................................................. 52 2.2. The Modelling of Cancer ..................................................................................................... 53 2.2.1. Introduction to Cancer Modelling ................................................................................ 53 10 2.2.2. Spectrum of Cancer Models .......................................................................................... 54 2.2.3. Differential Equations Models ...................................................................................... 56 2.2.4. Stochastic Models ......................................................................................................... 58 2.2.5. Markov Chain Models .................................................................................................. 60 2.2.6. Boolean Network Models .............................................................................................. 62 2.2.7. Bayesian Network Models ............................................................................................ 64 2.2.8. Cellular Automata Models ............................................................................................ 66 2.2.9. Agent-Based Models ..................................................................................................... 70 2.2.10. Modelling Chromosome Instability ............................................................................ 73 2.2.11. Summary on Cancer Modelling .................................................................................. 76 2.3. Conclusions .......................................................................................................................... 77 3. Research Methodology ................................................................................................... 78 3.1. Introduction .......................................................................................................................... 78 3.2. Computational Modelling Methodology .............................................................................. 79 3.3. Model Assessment Methodology ......................................................................................... 82 3.4. Biological Modelling Methodology ..................................................................................... 86 3.5. Selecting the Modelling Paradigm ....................................................................................... 90 3.6. Summary .............................................................................................................................. 94 4. The Model ...................................................................................................................... 96 4.1. Introduction .......................................................................................................................... 96 4.2. Abstracting biological concepts ........................................................................................... 97 4.2.1. Concepts Modelled ....................................................................................................... 97 4.2.2. Concepts not Modelled ............................................................................................... 100 4.3. Model Version 1: Homeostasis and Aneuploidy ............................................................... 101