Subcellular phenomena in colorectal cancer

The Wnt signalling pathway is involved in stem cell maintenance, differentiation and tissue development, and in so doing plays a key role in controlling the homeostasis of colorectal crypts. In response to an external Wnt stimulus, the intracellular levels of the protein beta-catenin are regulated by the proteins which make up the Wnt signalling pathway. Abnormalities in the Wnt signalling pathway have been implicated in the initiation of colorectal and other cancers. In this thesis we analyse and simplify existing models of the Wnt signalling pathway, formulate models for Wnt's control of the cell cycle in a single cell, and incorporate these into a multiscale model to describe how Wnt may control the patterns of proliferation in a colorectal crypt. A systematic asymptotic analysis of an existing ODE-based model of the Wnt signalling pathway is undertaken, highlighting the operation of different pathway components over three different timescales. Guided by this analysis we derive a simplified model which is shown to retain the essential behaviour of the Wnt pathway, recreating the accumulation and degradation of beta-catenin. We utilise our simple model by coupling it to a model of the cell cycle. Our findings agree well with the observed patterns of proliferation in healthy colon crypts. Furthermore, the model clarifies a mechanism by which common colorectal cancer mutations may cause elevated beta-catenin and Cyclin~D levels, leading to uncontrolled cell proliferation and thereby initiating colorectal cancer. A second model for the influence of the Wnt pathway on the cell cycle is constructed to incorporate the results of a recent set of knockout experiments. This model reproduces the healthy proliferation observed in crypts and additionally recreates the results of knockout experiments by additionally including the influence of Myc and CDK4 on the cell cycle. Analysis of this model leads us to suggest novel drug targets that may reverse the effects of an early mutation in the Wnt pathway. We have helped to build a flexible software environment for cell-based simulations of healthy and cancerous tissues. We discuss the software engineering approach that we have used to develop this environment, and its suitability for scientific computing. We then use this software to perform multiscale simulations with subcellular Wnt signalling models inside individual cells, the cells forming an epithelial crypt tissue. We have used the multiscale model to compare the effect of different subcellular models on crypt dynamics and predicting the distribution of beta-catenin throughout the crypt. We assess the extent to which a common experiment reveals the actual dynamics of a crypt and finally explain some recent mitochondrial-DNA experiments in terms of cell dynamics