Rebuttal: Adaptive Point Mutation (Rosenberg and Hastings)

Rosenberg and Hastings (4) commit the same logical fallacy as do Roth and Andersson (5). They first state that there are three models to explain adaptive mutation: directed mutation, hypermutation, and cryptic growth. Then they argue against directed mutation and cryptic growth, leaving hypermutation as the only alternative. But, they ignore the alternative model that I presented in my review (2), which involves neither directed mutation nor cryptic growth. My model postulates one underlying mutational mechanism in which all cells can engage; but, in a few cells (the hypermutators) the process is more mutagenic than in the majority because Pol IV is highly expressed and mismatch repair is deficient. The majority produces 90% and the hypermutators produce 10% of the Lac⁺ mutations, but hypermutators produce all of the multiple mutations.

The conclusion that only a few Lac⁺ mutations arise in hypermutators is based, in part, on the higher than expected frequency of Lac⁺ cells with two other mutations. Rosenberg and Hastings argue that this is because some cells spend more time in the hypermutable state and thus have more mutations. It is true that the proportion of cells with multiple mutations increases with time during lactose selection (3). But this effect is not large enough to account for the frequency of triple mutants. The argument is as follows (J. Cairns, personal communication).

Consider a homogeneous population of cells accumulating three mutations, Lac⁺, A, and B, each at a constant rate. The frequency of cells with any one mutation will increase linearly with time, with any two as the square of time and with all three as the cube of time. Simple calculus shows that at time T, the proportion of mutation A that occurs in cells that already have another mutation is equal to (k_A)(T/2), where k_A is the mutation rate constant for A; the proportion of mutation A that occurs in cells that already have two other mutations is equal to (k_A)(2T/3). Thus, by time T, mutation A will be more common in the accumulated Lac⁺ B cells than in the accumulated Lac⁺ cells by the factor (2T/3)/(T/2) = 4/3. Thus, A mutations should be a mere 33% more common in Lac⁺ B cells than in Lac⁺ cells, not the 10- to 35- fold that has been observed (3, 6). This must mean that only a minority of the Lac⁺ mutants arise in hypermutators (1).

Finally, Rosenberg and Hastings argue (see Fig. 2 in reference 4) that their model is simpler because it has only one mutating population, whereas our model has two. But the Rosenberg-Hastings model also evokes two populations; a minority that are mutating and a majority that are not. So, Occam's razor does not apply here.