Distribution of Spontaneous Mutants and Inferences about the Replication Mode of the RNA Bacteriophage φ6

In recent years, viruses have been increasingly used in the laboratory to study the fitness effects of mutations (1, 4, 8, 10, 14, 15, 16, 25). The increase is likely due to two reasons. First, these fitness effects, which are generally quantified as the distribution of the magnitude, the sign (deleterious versus beneficial), and the interaction (additive versus nonadditive) of the mutations, are key to many evolutionary models, and viruses have become a major focus of evolutionary studies. Much of our predictive theories in evolution have come from population genetic models that make assumptions about the fitness effects of mutations. For example, depending on whether the interaction between deleterious mutations is log-additive, the models predict distinctly different advantages for the evolution of recombination (5, 15). Second, many issues addressed by such models have now also been raised in the context of viruses, especially RNA viruses, which have a much higher mutation rate than DNA viruses (11, 12). Evolutionary topics as wide ranging as the quasi-species concept, game theory, the origin of life, the constancy of the molecular clock, the divergence and convergence of isolated populations, and the evolution of recombination have all been recently considered in relation to viruses (1-3, 5-7, 15, 17, 18, 22, 24, 29, 31, 32). As the more qualitative aspects of the distribution of mutational effects and interactions have become known, it has become desirable to extract more quantitative information. However, more quantitative analyses require also more exact information on another type of distribution, that of mutations and mutants in a population. The distinction between mutations and mutants is important and is made herein. A mutation is the event that changes a nucleotide sequence. The mutated sequence and any copies are mutants. Because mutations are generated randomly, the distribution of mutations across bursts (or across progeny for a virus that does not burst) is expected to be Poisson (27). However, the distribution of mutants across bursts may or may not be Poisson, depending on the mode of viral replication inside the host cell. If the parental virus is the only template used for production of progeny, the distribution remains Poisson because mutants do not replicate. With only one template, the replication model conforms to a “stamping machine” model (28), and the resulting Poisson distribution has the characteristic of having a mean that equals the variance or a variance-to-mean ratio of 1 (27). On the other hand, if the progeny can also serve as templates for additional progeny, the distribution has a variance-to-mean ratio much greater than 1 because mutant progeny produce more mutant viruses. In the worst-case scenario, if a mutant progeny arises as the first progeny virus produced by the parental virus, half of the progeny will be mutant. If all progeny can act immediately as templates, the replication model is effectively exponential or geometric growth, and the resulting distribution conforms to the Luria-Delbruck distribution (20). If only a fraction of the progeny replicate, the replication model is a hybrid between geometric growth and stamping machine and deviates less from a Poisson distribution. Thus, knowing the mean and variance of the distribution of mutants across bursts is not only important for any detailed analysis of the distribution of mutational effects but also useful for inferring the mode of replication of a virus. Luria (19) concluded that the phage T2 replicated by geometric process because the distribution of mutants had a variance that was much greater than the mean. Denhardt and Silver (9) argued for a stamping machine in the phage φX174 because the distribution was Poisson. In this study, we measured the distribution of mutants in the RNA bacteriophage φ6 (26, 30) by assaying the production of wild-type revertants from an amber mutant. φ6 has been used extensively for mutation accumulation experiments (1, 2, 4, 7). It has a double-stranded (ds) genome consisting of 13,383 bp (18). Its replication is known to occur by semiconservative, plus-strand (message-sense) displacement (18). After infecting and entering a host cell, the infecting or parental genome begins replication by synthesizing a new plus strand, which displaces the old plus strand of the parental genome. Although the parental genome is now ready for a second round of replication, the displaced strand is not. It must first be encapsidated and copied to produce the first ds progeny genome. Thus, because the progeny genome may or may not be ready to replicate when the parental genome initiates the second round of replication, the mode of replication may be either by a geometric growth or by a stamping machine model. We find that the distribution of mutants in φ6 deviates only slightly from a Poisson distribution. Thus, replication in φ6 is effectively a stamping machine in which the ds progeny genomes replicate with a very low probability.