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.I n 1971, Knudson (1) performed a statistical analysis of the incidence of retinoblastoma in young children. This analysis and subsequent work eventually led to the model invoking two hits of the retinoblastoma gene as rate-limiting steps in tumorigenesis (2-6). In the inherited form, the first mutation is already present in the germ line, whereas the second mutation emerges during somatic cell divisions. These observations led to the concept of a tumor suppressor gene (TSG). In the meantime, a large number of TSGs have been discovered that are involved in various human cancers (7-10). Here, we will calculate the dynamics of inactivating TSGs in populations of dividing cells with or without genetic instability (11-15).A normal cell has two alleles of a TSG. Inactivating the first allele is considered to be a neutral (or almost neutral) mutation. Inactivating the second allele provides the cell with an increased net reproductive rate. Point mutations, small insertions, deletions, structural changes of the chromosome, or chromosomal loss can constitute the first hit, whereas all of these events plus mitotic recombination can occur as the second hit. Usually large deletions or chromosome loss do not account both for the first and second step in one cell, because large homozygous deletions are often lethal for a cell. Denote by u 1 and u 2 the mutation rates for the first and second hit (including all possible mechanisms). It is natural to assume that u 1 is less than u 2 , because there are more possibilities for the second hit.We will now ask the most basic question regarding the somatic evolutionary dynamics of TSGs: how long does it take for a population of N cells to generate a single cell with two inactivated alleles of a TSG?For small populations, N Ͻ 1͞ ͌ u 2 , the first hit takes over the population before the second hit occurs (Fig. 1). There is an intuitive explanation for this threshold: a cell with one hit is a neutral mutant that takes on average N generations to reach fixation, whereas the waiting time for the second hit is 1͞(Nu 2 ). From N Ͻ 1͞(Nu 2 ) we obtain N Ͻ 1͞ ͌ u 2 . In this case, the probability that a single cell wi...