Cancer initiation with epistatic interactions between driver and passenger mutations.

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 the 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.