Context-dependent selection as the keystone in the somatic evolution of cancer

Abstract

Somatic evolution of cancer involves a series of mutations, and attendant changes, in one or more clones of cells. A "bad luck" type model assumes chance accumulation of mutations. The clonal expansion model assumes, on the other hand, that any mutation leading to partial loss of regulation of cell proliferation will give a selective advantage to the mutant. However, a number of experiments show that an intermediate pre-cancer mutant has only a conditional selective advantage. Given that tissue microenvironmental conditions differ across individuals, this selective advantage to a mutant could be widely distributed over the population. We evaluate three models, namely "bad luck", context-independent, and context-dependent selection, in a comparative framework, on their ability to predict patterns in total incidence, age-specific incidence, stem cell number-incidence relationship and other known phenomena associated with cancers. Results show that among the factors considered in the model, context dependence is necessary and sufficient to explain observed epidemiological patterns, and that cancer evolution is largely selection-limited, rather than mutation-limited. A wide range of physiological, genetic and behavioural factors influence the tissue micro-environment, and could therefore be the source of this context dependence in somatic evolution of cancer. The identification and targeting of these micro-environmental factors that influence the dynamics of selection offer new possibilities for cancer prevention.

Figure 1

The nature of relationships between age, stem cell number, mutation rate and cancer incidence by the bad luck model. The cumulative incidence of cancer increases with age in a threshold relationship. (A) The stem cell number affects the threshold age, but in all cases the trend saturates only at 100% incidence. (B) At any given lifespan, the stem cell number holds a threshold relationship with cancer incidence. For tissues with stem cell numbers below the threshold, the cancer probability is close to zero and above the threshold it rises to almost unity. (C) The mutation rate also influences the threshold age for a given cancer type and given a fixed lifespan, the mutation rates holds a threshold relationship with incidence (D). The age threshold and the sharpness of the threshold measured by the slope at 50% cumulative incidence (I₅₀) have an inverse relationship (E) shown at k = 5 and 8 respectively. If we take only those cancers for which the threshold lies beyond the maximum lifespan, the relationship of stem cell number with lifetime cancer incidence on a log-log plot is linear (F) with the slope = 1. Lifespan and other parameters change the position of the line, but the slope remains unaltered. Shown in the graph are analytical results. Simulations at population size 10,000 and above follow the analytical predictions very closely. Parameters: For A and B, p = 10⁻⁶, n ranges from (curves right to left) 10³ to 10¹⁰. For C and D, n = 10⁹ and p ranges from (curves left to right) 10⁻⁶ to 10⁻⁹. In all results displayed here k = 5 and d = 1000.

Figure 2

The nature of relationships between age, stem cell number, mutation rate and cancer incidence by the CIS model. (A) Similar to the bad luck model, there is a threshold age at which the incidence transits from near zero to near 100%. Saturation of cumulative incidence happens only when the incidence approaches 100%. The threshold age is affected by the stem cell number (A,B) as well as the mutation rate (C,D). The threshold age and the slope at I₅₀ holds an inverse relationship (E) similar to the bad luck model. (F) For the parameter range in which the threshold lies much beyond the lifespan, the log-log relationship between stem cell number and cumulative incidence is linear with a slope > = 1. For A and B, p = 5.603 10⁻⁹, n ranges from (curves right to left respectively) 10⁶ to 10^10.5. For C and D, n = 1.785 10⁸. p ranges from (curves left to right) 10^−6.5 to 10^−10.5. Growth rates progress linearly in the general form, $g_i$ = 0.007 (i + 1), where i = 0 to k and k = 5. Here, Δg = 0.007. k = 5 for all.

Figure 3

Age trend in cumulative incidence with randomized vs fixed p for the population in the CIS case; giving a distribution to p does not reduce the saturation of incidence from 100%, but slows the transition to 100%. In the randomized case, p values were drawn from a uniform distribution with range [3.775 ∗ 10⁻¹¹, 3.06 ∗ 10⁻⁷], while for the fixed case, p = 3.06 * 10⁻⁷; for both, n = 1.785 * 10⁸ and k = 5.

Figure 4

The nature of relationships between age, stem cell number, mutation rate and cancer incidence predicted by the CDS model. In this model the cumulative incidence can saturate much below 100% depending upon the distribution of Δg. The age incidence curve at different n (A,B) and different mutation rates (C,D) show an early saturating trend rather than a threshold phenomenon. The log-log plot between stem cell number and life time incidence may be saturating or linear with a slope < = 1 (E). With a reduction in the mean Δg, the cell number incidence curve saturates early (F). All parameters similar to Fig. 2.