The age incidence of chronic myeloid leukemia can be explained by a one-mutation model

Abstract

Chronic myeloid leukemia (CML) is associated with the Philadelphia chromosome, which arises by a reciprocal translocation between chromosomes 9 and 22 and harbors the BCR-ABL fusion oncogene. It is unknown whether any other mutations are needed for the chronic phase of the disease. The CML incidence increases as a function of age with an exponent of approximately 3. A slope of 3 could indicate that there are two mutations, in addition to the Philadelphia translocation, that have not yet been discovered. In this work, we explore an alternative hypothesis: We study a model of cancer initiation requiring only a single mutation. A mutated cell has a net reproductive advantage over normal cells and, therefore, might give rise to clonal expansion. The cancer is detected with a probability that is proportional to the size of the mutated cell clone. This model has three waiting times: (i) the time until a mutated cell is produced, (ii) the time of clonal expansion, and (iii) the time until the clone is detected. Surprisingly, this simple process can give rise to cancer incidence curves with exponents up to 3. Therefore, the CML incidence data are consistent with the hypothesis that the Philadelphia translocation alone is sufficient to cause chronic phase CML.

Fig. 1.

The Moran process. Initially, all N cells are wild type and have a relative growth rate of 1. At each time step, a cell is chosen for reproduction proportional to fitness, and its daughter cell replaces another randomly chosen cell. The total number of cells remains strictly constant. Wild-type cells give rise to mutated cells at rate u per cell division. Mutated cells have a relative growth rate r. Cells divide every τ days.

Fig. 2.

Simulation and theory. The figure shows the results of the exact stochastic computer simulation (triangles) and Eq. 1 (lines). Parameter values are mutation rate u = 10⁻⁹, population size N = 1,000, relative fitness of mutated cells r = 1.1, mean cell generation time τ = 1 day, and probability of detection q/N = α = 0.1 for an exponent of 1 (a); u = 10⁻⁵, N = 2,000, r = 1.001, τ = 100, and α = 2 × 10⁻⁵ for an exponent of 2 (b); and u = 10⁻⁶, N = 2,000, r = 1.01, τ = 40, and α = 2 × 10⁻⁵ for an exponent of 3 (c).

Fig. 3.

CML incidence. The figure shows the numerical simulation of Eq. 1 (line) and the adjusted cumulative CML incidence data from Table 1, column 5 (circles). Parameter values are u = 3 × 10⁻⁸, N = 10⁵, r = 1.01, τ = 60, and α = 10⁻³ (a) and 5 × 10⁻¹⁰, N = 10⁶, r = 1.02, τ = 100, and α = 0.1 (b).