  We investigate the dynamics of cancer initiation in a mathematical model with
one driver mutation and several passenger mutations. Our analysis is based on a
multi type branching process: We model individual cells which can either divide
or undergo apoptosis. In case of a cell division, the two daughter cells can
mutate, which potentially confers a change in fitness to the cell. In contrast
to previous models, the change in fitness induced by the driver mutation
depends on the genetic context of the cell, in our case on the number of
passenger mutations. The passenger mutations themselves have no or only a very
small impact on the cell's fitness. While our model is not designed as a
specific model for a particular cancer, the underlying idea is motivated by
clinical and experimental observations in Burkitt Lymphoma. In this tumor, the
hallmark mutation leads to deregulation of the MYC oncogene which increases the
rate of apoptosis, but also the proliferation rate of cells. This increase in
the rate of apoptosis hence needs to be overcome by mutations affecting
apoptotic pathways, naturally leading to an epistatic fitness landscape. This
model shows a very interesting dynamical behavior which is distinct from the
dynamics of cancer initiation in the absence of epistasis. Since the driver
mutation is deleterious to a cell with only a few passenger mutations, there is
a period of stasis in the number of cells until a clone of cells with enough
passenger mutations emerges. Only when the driver mutation occurs in one of
those cells, the cell population starts to grow rapidly.
