Evolutionary dynamics of tumor suppressor gene inactivation

Tumor suppressor genes (TSGs) are important gatekeepers that protect against somatic evolution of cancer. Losing both alleles of a TSG in a single cell represents a step toward cancer. We study how the kinetics of TSG inactivation depends on the population size of cells and the mutation rates for the first and second hit. We calculate the probability as function of time that at least one cell has been generated with two inactivated alleles of a TSG. We find three different kinetic laws: in small, intermediate, and large populations, it takes, respectively, two, one, and zero rate-limiting steps to inactivate a TSG. We also study the effect of chromosomal and other genetic instabilities. Small lesions without genetic instability can take a very long time to inactivate the next TSG, whereas the same lesions with genetic instability pose a much greater risk for cancer progression.