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Mathematical models of cell population dynamics


Werner,  Benjamin
Research Group Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society;


Traulsen,  Arne
Research Group Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society;

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Werner, B. (2013). Mathematical models of cell population dynamics. PhD Thesis, University, Lübeck.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0026-A6E4-B
Cancers result from altered cell proliferation properties, caused by mutations in specific genes. An accumulation of multiple mutations within a cell increases the risk to develop cancer. However, mechanisms evolved to prevent such multiple mutations. One such mechanism is a hierarchically organized tissue structure. At the root of the hierarchy are a few, slow proliferating stem cells. After some cell differentiations all functional cells of a tissue are obtained. In the first two chapters of this thesis, we mathematically and computationally evaluate a multi compartment model that is an abstract representation of such hierarchical tissues. We find analytical expressions for stem cell and non stem cell driven cell populations without further mutations. We show that non stem cell mutations give raise to clonal waves, that travel trough the hierarchy and are lost in the long run. We calculate the average extinction times of such clonal waves. In the third chapter we allow for arbitrary many mutations in hierarchically organized tissues and find exact expressions for the reproductive capacity of cells, highlighting that multiple mutations are strongly suppressed by the hierarchy. In the fourth chapter we turn to a related problem, the evolution of resistance against molecular targeted cancer drugs. We develop a minimalistic mathematical model and compare the predicted dynamics to experimental derived observations. Interestingly we find that resistance can be induced either by mutation or intercellular processes such as phenotypic switching. In the fifth chapter of this thesis, we investigate the shortening of telomeres in detail. The comparison of mathematical results to experimental data reveals interesting properties of stem cell dynamics. We find hints for an increasing stem cell pool size with age, caused by a small number of symmetric stem cell divisions. We also implement disease scenarios and find exact expressions how the patterns of telomere shortening differ for healthy and sick persons. Our model provides a simple explanation for the pronounced increase of telomere shortening in the first years of live, followed by an almost linear decrease for healthy adults. In the final chapter, we implement a method to introduce arbitrary many random mutations into the framework of frequency dependent selection. We show how disadvantageous mutations can reach fixation under a deterministic scenario and discuss possible applications to cancer modeling.