Speaker: Deena Schmidt (IMA)
Title: Waiting for k mutations: with applications to DNA regulatory sequence evolution and cancer
Abstract: We consider the population genetics problem: How long does it take before some member of the population has k specified mutations? The case k=2 is relevant to the onset of cancer due to the inactivation of both copies of a tumor suppresor gene. Results of Nowak and collaborators give the waiting time distribution in this case and the time until the mutant phenotype becomes fixed in the population. Here we apply these results to obtain insights into regulatory sequence evolution in Drosophila and humans. In particular, we examine the waiting time for a pair of mutations, the first of which inactivates an existing transcription factor binding site and the second which creates a new one. Consistent with recent experimental observations for Drosophila, we find that a few million years is sufficient, but for humans with a much smaller effective population size, this type of change would take more than 100 million years. In addition, we'll discuss models for larger k, which are needed for colon cancer and other diseases where a sequence of mutations leads to cells with uncontrolled growth.