STOCHASTIC MODELING OF LOSS- AND GAIN-OF-FUNCTION MUTATIONS IN CANCER

Abstract

Here we review some spatial and non-spatial stochastic methods developed to study the dynamics of cancer progression. We illustrate the methodology with applications to the two most common patterns in cancer initiation and progression: loss-of-function and gain-of-function mutations. An example of a gain-of-function mutation is an activation of an oncogene; for such mutations we are interested in the process of mutant take-over. An example of a loss-of-function mutation is an inactivation of a tumor suppressor gene; for such processes we calculate the rate of production of double-hit mutants. We consider three stochastic models of cell populations with a constant size: a simple mass-action model, a spatial model and a hierarchical model which contains stem cells and daughter cells. Interestingly, the process of mutation accumulation and spread develops differently in different models. This suggests that simple mass-action models can be misleading when studying cancer dynamics. Moreover, our results also allow us to think about various types of tissue architecture and its protective role against cancer. In particular, we show that hierarchical tissue organization lowers the risk of cancerous transformations. Also, cellular motility and long-range signaling can decrease the risk of cancer in solid tissues.