Theory

The replication of riboviruses whose chromosomes are composed of single-stranded RNA follows a simple scheme (Fig. 1). A cell is infected with one (or more) virus particles. Each infecting genome is copied iteratively such that complementary strands accumulate. Subsequently, the complementary strands are themselves copied iteratively, producing final strands of the same polarity as the infecting strand, and these final strands are packaged and released. We make the reasonable assumption that “final” strands rarely or never reenter the beginning of the cycle within a single infection. The key attribute of iterative replication is that the mutation frequency f equals the mutation rate μ per copying event: if n complementary strands are copied from a template and if μ is the mutation rate per copying event, then the number of mutations will be nμ, and f = nμ/n = μ.

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Figure 1

The accumulation of mutations during a single round of infection. The diagram shows the consequences of an arbitrary μ_g = 0.2 at both the first and second rounds, and the scheme is simplified by setting n₂ = 20 for all second rounds of copying. The burst size is n₁n₂ = 100. ○, unmutated genomes; ➊, genomes with a single mutation; ➋, genomes with two mutations, which may arise in sequential replications (as in the fourth line) or during a single replication (as in the bottom line).

When a ribovirus infects a cell, the population of complementary strands accumulating from the first round of repeated copying has f₁ = μ₁. Ignoring rare precise back mutations and in the absence of selection, this mutant subpopulation will persist at the frequency f₁. In the second round of repeated copying, a new fraction of mutations will be contributed, amounting to f₂ = μ₂. Thus, in one cycle of cell infection, f = f₁ + f₂ = μ₁ + μ₂. It is presently unknown whether μ₁ and μ₂ differ, and we must combine them into f = 2μ. This process of linear accumulation will continue as a virus stock grows through c cycles of cell infection; c will generally be a small (but not necessarily an integer) number, from one for a single round of infection (high multiplicity of infection), to perhaps four or five for a large population of host cells and a small inoculum. For stocks grown to a size sufficient to accumulate numerous mutations, the general formulation is f = 2cμ. Note that this expression holds only in the absence of selection, which is likely to be weak or absent during the first cycle of infection but may become strong in subsequent cycles. The mutational targets used in the studies we cite are believed to be largely free of selection. Given specific information about selection coefficients, it is possible to describe their effects on mutation accumulation over multiple cycles.

An alternative approach, used frequently with DNA-based microbes and occasionally with riboviruses, is the null-class method (6). In this method, numerous parallel cultures are each seeded with a small amount of virus and grown to a population size such that only roughly half of the cultures have accumulated any mutants. Each culture is then screened simply for the presence or absence of mutants, and the average number N of virus particles per culture is also determined. On the assumption that mutational events are randomly distributed among replication events and because the number of replication events per culture is close to N, the proportion of cultures with no mutants P(0) = e^−Nμ.

Calculations

Discussion

The mutation process in riboviruses can be described by a simple linear equation that reflects the repeated copying of templates that is characteristic of these organisms. The mutational consequences of iterative replication have not been explored much in the several decades since the primordial analysis of a “stamping machine” model (22). An exception is the single-stranded DNA bacteriophage φX174. This phage replicates in a complicated but fundamentally linear manner (23, 24), such that the mutation equations (25, 26) are similar to the equation used here for riboviruses, although the observed rates are far lower than those of riboviruses and are instead characteristic of DNA-based microbes (3). However, uncertainty persists concerning the extent to which second-generation strands reenter the beginning of the cycle within a single φX174 infection (24).

Applying mainly mutation-accumulation or null-class analyses to published data yields a set of nine rates of mutation per genome per replication that vary fairly smoothly over about an order of magnitude (Table 1). Just such variation is expected from the tiny mutational target sizes characteristic of the cited measurements: 1/3 base for seven entries, 2/3 base for two entries, and roughly 7.5 bases for the measles-virus entry. Most mutational spectra display a wide range of site-specific mutabilities, and even a specific substitution such as G:C → A:T in DNA can vary by over 2,000-fold depending on the neighboring sequences (27). The smooth spread of values in Table 1 and the similarity of mean and median lead us to propose the median (0.76) as the best current value for the rate of spontaneous mutation in riboviruses generally. A similar value, 1.2, was recently obtained by applying the fundamentally different Bateman–Mukai analysis to data obtained with VSV (28). These values are very high in comparison to values in other organisms but were anticipated in classical studies of mutation in an RNA phage (15, 16) and have long been known to be generally high (29).

Bacteriophage φ6 has a segmented, double-stranded RNA genome and thus differs profoundly from the viruses in Table 1. Nevertheless, the φ6 mutation rate must be much higher than that of DNA-based microbes, because stocks accumulate about 0.5% temperature-sensitive mutations (30). Nonsense mutations in φ6 display revertant frequencies ≥10⁻⁴ in stocks where c ≈ 5 (L. Chao, personal communication). For φ6, G = 13,379 (31). Assuming negligible selection and T = 1.5, μ_g ≥ 0.13, a value compatible with the values shown in Table 1. Thus, the high ribovirus mutation rate seems to encompass both animal viruses and phages.

The viral particles emerging from individual infected cells contain occasional mutant clones descended from new mutations. Mutation in riboviruses should produce mutant clone size distributions very different from those characteristic of exponentially replicating chromosomes. In riboviruses, fewer mutations will occur in the first round of genome copying than in the second round, because fewer copying events occur in the first round. Therefore, a few clones will contain several mutants, whereas most clones will contain only one mutant. This prediction has already been verified for the single-stranded DNA phage φX174, where roughly 5 large clones and about 309 single mutants (clones of size 1) were observed; the uncertainties reflect probable coincidences of clones of size 1 and a few preexisting mutations producing large clones (23). In riboviruses, the mutant clone size distribution can be described in terms of the mutation rates characteristic of the first and second rounds of copying (μ₁ and μ₂, respectively) and the mean numbers of genomes produced per template in the first and second rounds (n₁ and n₂, respectively). Specifically, the first round contributes μ₁n₁ mutant clones of mean size n₂; the second round contributes μn₁n₂ mutant clones of size 1; and the total virus progeny per cell is n₁n₂. These are experimentally resolvable parameters.

Because a single cycle of infection produces a mutant frequency twice that of the rate per genome replication, few progeny viruses escape mutation. In general, for 1.5c mutations distributed randomly among genomes, the mutation-free fraction of a population would be e^−1.5c (0.22 for c = 1; 0.05 for c = 2; etc.). However, many or most mutations in riboviruses are deleterious, and selection against deleterious mutations will reduce both mutant frequency and virus yield even within a single cycle of infection. Their high mutation rate renders the riboviruses particularly vulnerable to the consequences of rate increases, and both poliovirus and VSV populations are extinguished by chemical mutagenesis sufficient to increase the rate by a mere 2.5-fold (32). Merely tripling the viral mutation rate, if this increase could be achieved without harming the host, could cure ribovirus infections. Conversely, the normal mutation rate does not seem to be limiting for adaptation (29, 33).

Another consequence of this high rate of mutation is that all but the most mild mutator mutations will be lethal. Mutation pressure alone is likely to generate many mutator mutations, and an analysis of the VSV polymerase gene, encompassing almost 0.6 of the genome, suggested considerable polymerase compositional variation within a population (34). Influenza virus populations seem to accumulate a high frequency (≈12%) of mutators, but these increase mutation rates only by 2- to 4-fold (35); stronger mutators probably die out rapidly. The strength of a VSV mutator (36) cannot be quantitated.

Because recombination can regenerate unmutated genomes, it can reduce the danger of a very high mutation rate. Crossing over is frequent among many riboviruses, and independent assortment of segmented genomes also occurs (30). Perhaps most importantly, however, riboviruses have high fecundity, with yields of 100–10,000 per infected cell, such that the product of yield times the proportion of mutation-free progeny tends to exceed unity.