Cell selection as driving force in lung and colon carcinogenesis

Abstract

Carcinogenesis is the result of mutations and subsequent clonal expansions of mutated, selectively advantageous cells. To investigate the relative contributions of mutation versus cell selection in tumorigenesis, we compared two mathematical models of carcinogenesis in two different cancer types: lung and colon. One approach is based on a population genetics model, the Wright-Fisher process, whereas the other approach is the two-stage clonal expansion model. We compared the dynamics of tumorigenesis predicted by the two models in terms of the time period until the first malignant cell appears, which will subsequently form a tumor. The mean waiting time to cancer has been calculated approximately for the evolutionary colon cancer model. Here, we derive new analytic approximations to the median waiting time for the two-stage lung cancer model and for a multistage approximation to the Wright-Fisher process. Both equations show that the waiting time to cancer is dominated by the selective advantage per mutation and the net clonal expansion rate, respectively, whereas the mutation rate has less effect. Our comparisons support the idea that the main driving force in lung and colon carcinogenesis is Darwinian cell selection.

Figure 1

Schematic representation of the WF process. Illustrated are five generations of a single realization of the WF process with a constant population size of N = 6 cells. In each generation, cells are drawn randomly from the previous generation. Initially, in generation 1, all cells are wild-type (white). In generation 2, the first cell with one mutation appears (gray). Cells with additional mutations have a selective advantage: they are more likely to generate offspring and will, on average, outcompete cells with fewer mutations. In this realization, the first cell with two mutations occurs in generation 5 (black), and the waiting time for k = 2 mutations is T_WF = 4 generations; see Eq. 1.

Figure 2

Conceptual view of the two-stage model with clonal expansion. Normal cells (N) can develop into initiated (or intermediate) cells (I). I-cells have sustained the first rate-limiting event in the pathway to malignancy at rate μ₁, the parameter defining the rate of critical genomic events involved in initiation. An I-cell can divide into two I-cells with rate α; it dies or differentiates with rate β; it divides asymmetrically into one I-cell and one cell that has sustained the second event [malignant cells (M)] with rate μ₂. The M-cells are assumed to develop into a tumor (T) after a deterministic lag time, t_lag.