As cancer tumours develop, competition between cells will favour those with some mutations over others, creating a dynamic heterogeneous system made up of different cell populations, called sub-clones. This heterogeneity poses a challenge for treatment, as this variety serves to ensure there is almost always a portion of the cells which are resistant to any one targeted therapy. This can be avoided by combining therapies, but finding viable combinations experimentally is expensive and time-consuming. However, there is also cooperation between sub-clones, and being able to better model and predict these dynamics could allow this interdependence to be exploited.

In order to investigate how best to tackle tumour heterogeneity, while avoiding acquired resistance, I have developed the first comprehensive computational model of the gene regulatory network in breast cancer focused on the c-myc oncogene and the differences between sub-clones. I model the system as a discrete, qualitative network, which can reproduce the conditions in heterogeneous tumours, as well as predict the effect of perturbations mimicking mutations or application of therapy.

Together with experimental collaborators, I apply my computational model to an \textit{in vivo} mouse model of MMTV-Wnt1 driven breast cancer, which has high and low c-myc expressing sub-clones. I show that the computational model is able to reproduce the behaviour of this system, and predict how best to target either one sub-clone individually or the tumour as a whole. I show how combination therapies offer more paths to attack the tumour, and how two drugs can work synergistically. For example, I predict how Mek inhibition will preferentially affect one sub-clone, but the addition of COX2 inhibition improves effectiveness across the tumour as a whole.

In this thesis, I show how a computational network model can predict treatments in breast cancer, and assess the effects on different clones of different treatment combinations. This model can be easily extended with new data, as well as adapted to different types of cancer. This therefore represents a novel method to find viable combination therapies computationally and speed up the development of new cancer treatments.