Abstract
Genome instability is a characteristic of most cancers, contributing to the acquisition of genetic alterations that drive tumor progression. One important source of genome instability is linked to telomere dysfunction in cells with critically short telomeres that lack p53-mediated surveillance of genomic integrity. Here we research the probability that cancer emerges through an evolutionary pathway that includes a telomere-induced phase of genome instability. To implement our models we use a hybrid stochastic-deterministic approach, which allows us to perform large numbers of simulations using biologically realistic population sizes and mutation rates, circumventing the traditional limitations of fully stochastic algorithms. The hybrid methodology should be easily adaptable to a wide range of evolutionary problems. In particular, we model telomere shortening and the acquisition of two mutations: Telomerase activation and p53 inactivation. We find that the death rate of unstable cells, and the number of cell divisions that p53 mutants can sustain beyond the normal senescence setpoint determine the likelihood that the first double mutant originates in a cell with telomere-induced instability. The model has applications to an influential telomerase-null mouse model and p16 silenced human cells. We end by discussing algorithmic performance and a measure for the accuracy of the hybrid approximation.