Cancer models, genomic instability and somatic cellular Darwinian evolution

Abstract

The biology of cancer is critically reviewed and evidence adduced that its development can be modelled as a somatic cellular Darwinian evolutionary process. The evidence for involvement of genomic instability (GI) is also reviewed. A variety of quasi-mechanistic models of carcinogenesis are reviewed, all based on this somatic Darwinian evolutionary hypothesis; in particular, the multi-stage model of Armitage and Doll (Br. J. Cancer 1954:8;1-12), the two-mutation model of Moolgavkar, Venzon, and Knudson (MVK) (Math. Biosci. 1979:47;55-77), the generalized MVK model of Little (Biometrics 1995:51;1278-1291) and various generalizations of these incorporating effects of GI (Little and Wright Math. Biosci. 2003:183;111-134; Little et al. J. Theoret. Biol. 2008:254;229-238).

Figure 1

Schematic diagram of the Armitage-Doll [1]multi-stage model.

Figure 2

SEER 1973-1999 [164]colon cancer data, and observed data (with 95% confidence intervals (CI), adjusted for overdispersion [165]), taken from Little [99]. The use of double logarithmic (log-log) axes shows that except for the youngest age group (<10 years) the age-incidence relationship is well described by C·[age]^k-1.

Figure 3

Schematic diagram of the two-mutation (MVK) model [2].

Figure 4

Observed absolute risk of lung cancer mortality (+95% CI) and predicted risk associated with the optimal two-mutation and three-mutation models fitted to the Colorado Plateau uranium miner data as a function of cumulative radon-daughter exposure, taken from Little et al. [117]

Figure 5

Schematic diagram of the generalized MVK model [4].

Figure 6

Schematic diagram of generalized cancer model with k cancer-stage mutations and m destabilizing mutations, as in Little et al. [6]. This corresponds to a single type, d, destabilizing mutation (d ∈ [1, r]) with m = m_d destabilizing levels. When there is more than one type of destabilizing mutation, there are multiple copies of this diagram, glued together along the topmost axis (of cells that have not acquired a destabilizing mutation), as in Figure 7.

Figure 7

Schematic diagram of the various destabilizing mutation planes in the model of Little et al. [6], each plane with the structure of Figure 6. Under the assumption of mutually exclusive destabilizing mutations, cells that have committed to one type of GI are not allowed to move between these planes.

Figure 8

Observed colon cancer rate (and 95% CI, adjusted for overdispersion) and model predicted rates for the Caucasian male and female population, taken from Little et al. [6]. Rates are those predicted by the (single multiplicity) models with two cancer-stage mutations and one destabilizing mutation and three cancer-stage mutations and one destabilizing mutation. Also shown are the predicted rates for the models with two cancer-stage mutations with multiplicity two and (1-1) destabilizing mutations (i.e. 2-2-(1-1)), with multiplicity two and (1-2) destabilizing mutations (i.e. 2-2-(1-2)) and with multiplicity three and (1-1-1) destabilizing mutations (i.e. 2-3-(1-1-1)). The stem cell population is fixed at 10⁸ cells [166].