(Submitted on 4 Oct 2013)
We investigate the dynamics of cancer initiation in a model with one driver mutation and several passenger mutations. In contrast to previous models, the change in fitness induced by the driver mutation depends on the genetic background 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. This approach is motivated by the Burkitt Lymphoma, where the hallmark mutation, a translocation between the MYC gene and an immunoglobulin gene, alters the rate of apoptosis, but also the proliferation rate of cells. This way we obtain an epistatic fitness landscape, where the fitness of cells with the driver mutation is advantageous only if enough passenger genes have mutated. Otherwise the fitness might even be deleterious. Our analysis is based on an individual cell model in which the cells can divide or undergo apoptosis. In case of division the two daughter cells can mutate. This model shows a very interesting dynamical behavior. Since the driver mutation is deleterious on a background with only a few passenger mutations, there is a long period of stasis in the number of cells until a clone of cells has evolved with enough passenger mutations. Only when the driver mutation occurs in one of those cells, the cell population starts to grow exponentially.