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Mathematical Classification of the Modes of Tumour Evolution

Manojlovic, V. (2023). Mathematical Classification of the Modes of Tumour Evolution. (Unpublished Doctoral thesis, City, University of London)


Determining the mode of tumour evolution is a fundamental question in cancer biology. Knowledge of the evolutionary dynamics of tumours could lead to improved diagnosis and treatment through the identification of key patterns in the data. In this thesis, I present a multi-pronged approach to the study of tumour evolution by further developing methods for the analysis of phylogenetic trees, investigating how different measures of tree properties evolve with time, and narrowing down the consideration of evolutionary models to those that are most relevant in colorectal cancer.

A recently introduced tree balance index, J1, unlike prior definitions, permits meaningful comparison of trees with arbitrary outdegree distributions and node sizes, thus overcoming the shortcomings of conventional methods. I quantify the accuracy of approximations to the expected values of J1 for two important null models: the Yule process and the uniform model, and prove that, for the Yule process, the approximation converges to the true expectation in the limit of large trees. I further investigate the minima of J1 for certain important tree families. These results help establish J1 as a universal, cross-disciplinary index of tree balance that generalizes and supersedes prior approaches.

As balance is only one of several properties that can be used to characterise phylogenetic trees, I also investigate the evolution of other metrics used in the study of phylogenies. By recapitulating the results of a previous study with a slightly altered methodology, and by expanding the analysis to include a new, more comprehensive set of tree indices, I discuss how these methods could be used to examine the evolutionary dynamics of tumours.

Finally, I develop an agent-based model of colorectal cancer evolution which is informed by multi-site DNA methylation data. I use this model to infer properties of multiple tumours and draw conclusions about the rate of tumour growth and strength of selection acting on the tumour. I find that the model is able to reproduce the observed data but not detailed enough to infer the strength of selection within tumour glands.

Publication Type: Thesis (Doctoral)
Subjects: Q Science > Q Science (General)
Q Science > QA Mathematics
R Medicine > RZ Other systems of medicine
T Technology > T Technology (General)
Departments: School of Science & Technology > Mathematics
School of Science & Technology > School of Science & Technology Doctoral Theses
Doctoral Theses
[thumbnail of Manojlovic thesis 2023 PDF-A.pdf]
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