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要旨:
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.
