Cancer is a disease driven by somatic mutations that accumulate in the genome during an individual`s lifetime. Recent advances in DNA sequencing technologies are enabling the measurement of these mutations in many cancer samples. However, distinguishing
functional driver mutations responsible for cancer from random passenger mutations remains a challenge. We develop two mathematical models to address this challenge. These models rely on the observation that driver mutations target a relatively small number of signaling and regulatory networks in the cell. In the first model, we use a diffusion process on graphs and a novel statistical test to identify groups of interacting genes, or pathways, that are mutated in a significant number of cancer samples. In the second model, we use a Markov Chain Monte Carlo approach to identify groups of genes
whose mutations are mutually exclusive (or nearly so) in a large number of samples. I will focus on the mathematics and algorithmic aspects of the work and illustrate applications of our approaches to real mutation data from The Cancer Genome Atlas.
This is joint work with Ben Raphael and Fabio Vandin from Brown University.