Title: Is stochastic modeling useful in cancer research?
Abstract: The mathematical sciences have contributed substantially to our understanding of many aspects of biology and medicine. For example, stochastic process and statistical methods have been important in population and evolutionary genetics, and computer science and machine learning play a key role in applications of genomics to human health. Conversely, questions in biology and medicine have led to novel mathematics. In this talk I will discuss a relative newcomer to the world of “mathematical biology”, namely cancer evolution.
Cancer is a disease of the genome, so my focus will be on mutations in DNA and what they tell us about tumor evolution. After a brief introduction to cancer evolution, I will focus on aspects of tumor heterogeneity, the DNA sequence variation observed between tumors and within them. I will illustrate the theme with two examples: the evolution of colon crypts, and stem cells in colorectal cancer. In both examples, approximate Bayesian computation is used for inference in these mechanistic stochastic models. I hope to make the case that mathematical modeling is essential to understanding how tumors evolve, and is likely to become an important aspect of the personalized treatment of patients.