Zusammenfassung
Cells of every organism undergo somatic mutations. Many mutations
do not significantly affect the gene’s function, while other mutations impair
the gene’s function. Often, this impairment leads to decreased survival
chance of the cell, such that the cell dies. If necessary, this cell can be
unproblematically be replaced. Sometimes, however, that impairment
disturbs the cell’s life cycle in a way that decreases its chance of cell death, or
apoptosis, or increases its rate of cell division. Uncontrolled cell proliferation
can then lead to the formation of cancer, and ultimately to a tumor. Usually
not only one, but a handful of mutations are necessary to affect different
safety mechanisms of the cell.
Often, genes influence each other, which is called epistasis. Also some
oncogenes underlie epistatic interactions. In the Burkitt Lymphoma the hallmark
mutation – an IG/MYC translocation – is believed to actually lower the
cell’s chance of survival. In concert with other mutations, however, it forms a
lymphoma. Basic knowledge about the initiation of cancers where the genes
of the cancerous mutations underlie epistatic interactions is rare and difficult
to acquire in experimental system.
The work described in this thesis is a theoretical analysis of systems with
epistatic interactions in cancer initiation. The population dynamics of an abstract
system with two different types of mutations between which epistatic
interactions exist is analyzed. One type is deleterious by itself, the other one
is (nearly) neutral. If the deleterious mutation is accompanied by enough mutations
of the other types, the cell has a fitness advantage. We find, amongst
others, that the cancer deploying cell lineage has most likely acquired that
specific mutation only subsequently to the other, non-deleterious mutations,
which inhibit the negative effect of that particular mutation. It is conceivable
that epistatic effects could change the order of mutations not only in
the survival and proliferation rates of the cell, but also in the mutation rates.
Hence, we further pursue the question: “If the deleterious mutation increases
the mutation rate for acquiring the necessary, additional mutations, how does
this change the probability for the order of mutations?”. We develop a recursive
algorithm for the computation of the probability density functions of the
different mutational pathways over time. Finally, we develop a model aiming
at describing the initiation of Burkitt Lymphoma. Lastly, an outlook is given
explaining future research directions based on epistasis in cancer initiation.
