Evolutionary dynamics of tumor suppressor gene inactivation - PubMed (original) (raw)

Evolutionary dynamics of tumor suppressor gene inactivation

Martin A Nowak et al. Proc Natl Acad Sci U S A. 2004.

Abstract

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.

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Figures

Fig. 1.

Fig. 1.

Inactivating a TSG requires two, one, or zero rate-limiting steps depending on the population size. (a) Cells of type 0, 1, and 2 have, respectively, 0, 1, and 2 inactivated alleles of the TSG. The mutation rate for inactivating the first and second allele are given by _u_1 and _u_2. Initially all cells are of type 0. (b) In small populations, formula image, type 1 cells will reach fixation before a cell of type 2 has been generated. The resulting kinetics have two rate-limiting steps (Eq. 1). (c) In intermediate populations, 1/_u_1 < formula image, a lineage of type 1 cells generates a type 2 cell before reaching fixation. The resulting kinetics have one rate-limiting step (Eq. 2). (d) In large populations, 1/_u_1 < N, type 1 cells are generated immediately and accumulate as a linear function of time. After some (short) time a type 2 cell will be generated. The kinetics involve two steps, none of which is rate-limiting for overall cancer progression (Eq. 3). This classification allows us to analyze the effect of cell number and mutation rate on the kinetics of TSG inactivation.

Fig. 2.

Fig. 2.

Perfect agreement between exact numerical simulations and the analytic approximations given by Eqs. 1–3. Population sizes are (a) N = 2, (b) N = 100, and (c) N = 107. (d) T_1/2 denotes the half-time of TSG inactivation, defined as the time until the probability of generating at least one cell of type 2 has become 1/2. Shown is log_T_1/2 vs. log_N. The numerical data (dots) can be approximated by three straight lines derived from Eqs. 1–3. For small N, we have _T_1/2 = log2/_u_1. For intermediate N, we have formula image). For large N, we have formula image. For reasonably fast computing time, we used the mutation rates _u_1 = 10–5 and _u_2 = 0.002 and performed 104 independent runs for every N.

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