Error catastrophe and antiviral strategy.

T term ‘‘error catastrophe,’’ originally introduced in the theory of molecular evolution (1), has become fashionable among virologists. In a recent paper in PNAS (2), it was suggested, on the basis of quantitative sequence studies, that ribavirin, a common antiviral drug, by its mutagenic action drives poliovirus into an error catastrophe of replication, thereby turning a productive infection into an abortive one. Previous studies by Loeb and his group (3, 4) on the AIDS virus (HIV) and by Domingo, Holland, and coworkers (5, 6) on foot-and-mouth disease virus (FMDV) have led to similar conclusions, suggesting a paradigm shift in antiviral strategies (7). A recent issue of PNAS presents a paper by Grande-Pérez et al. (8), which deals with the ‘‘molecular indetermination in the transition to error catastrophe,’’ shedding light on the complexity of the mechanisms involved in virus infection and stressing the need for a careful molecular analysis of the detail, which may differ greatly from one virus to another. Because of its practical relevance for developing potent antiviral drugs and, beyond that, its general importance for an understanding of molecular evolution, this commentary will highlight the theoretical basis and point out the kind of conclusions that can be drawn in discussing experimental results. The term error catastrophe is of a descriptive nature and lacks a clear-cut definition. A catastrophe is usually triggered if certain tolerances are exceeded. For replication, there is indeed such a limiting value of error or mutation rate that must not be surpassed if the wild type is to be kept stable. We call this limit the ‘‘error threshold.’’ Why is it a sharply defined limit? Why does the efficiency of replication not vary monotonically with the error rate? The information stored in the genomic sequence melts like ice at 0°C. This comparison is indeed a very apt one. The information melts away in a process that has all the physical characteristics of a first-order phase transition requiring cooperative behavior with unlimited coherence lengths, as we encounter in the melting of a solid or the evaporation of a liquid at its boiling point. The error threshold is caused by the inherent autocatalytic nature of replication, which represents not only the transfer of information from one generation to the next, as would be the case for a message sent through a transmission channel. Rather, replication provides an exponential proliferation of the information contained in the sequence as a whole. In the population formed, this results in competition among the various slightly differing sequences, which behave as cooperative units. Natural selection is a direct consequence of this competitive replication. It presupposes differences in efficiency of replication without excluding neutral mutants. Neutral copies, all belonging to the group of best-adapted ones, are selected against the rest, but because of their inherently reproductive behavior, they continue to compete with one another in a stochastic manner. Kimura and Ohta (9) called this nondeterministic f luctuating selection ‘‘non-Darwinian,’’ although Darwin himself anticipated it. Kimura and Ohta’s stochastically f luctuating selection reminds us of ‘‘critical phase transitions,’’ as found in ferroor antiferromagnetism or liquid-gas transformation near the critical point where, in analogy to neutrality among replicative units, the densities of the liquid and gaseous phases become equal, with the consequence of density fluctuations on all scales of spatial dimensions manifesting themselves in the phenomenon of ‘‘critical opalescence.’’ However, note that these phase transitions associated with natural selection do not take place in the space–time coordinates of our physical space. They refer rather to an abstract ‘‘information space’’ and are therefore not easy to visualize, because they may appear scattered in physical space and over extended periods of time. Information space is a discrete point space with a metric named after Richard Hamming (10). Each of the possible 4N sequences of length N is assigned to one and only one point, with all neighborhoods among sequences correctly ordered according to their kinship distances. This “spatial” order requires a 22 Ndimensional Hamming space. The dynamical equations of the rise and fall of populations can be written in a fairly general phenomenological form, yielding the quasispecies model (11, 12). A quasispecies is a population structure in information space and is the ‘‘condensed’’ mutant distribution that results from the phase transition representing natural selection. It has been termed ‘‘quasispecies’’ because the whole distribution behaves ‘‘quasi’’ as a single species, because it is determined by one (namely the largest) eigenvalue of its system of dynamical equations. The eigenvalues, being invariants of the equations, are determined as soon as the mutant spectrum is defined, regardless of whether the final stationary population structure is achieved. Rather than elaborating on further details of theory, I shall now discuss the important parameters that determine selection and hence also the behavior of virus populations, as expressed in the work this commentary refers to. Fig. 1 shows a computer simulation of a model case that is representative of the phenomenon of error catastrophe. Such simulations were first performed by Schuster and Swetina (13). The present example was computed by Tarazona (14). It shows the stationary structure of a population consisting of binary sequences of length N 20, in which all sequences have equal values of all their replication rates except for one sequence, which shows a 10-fold higher rate. The error rate (1 q), i.e., the relative number of misincorporations per site, has been assumed to be uniform for all sequences in the distribution. Fig. 1 shows a plot of the relative population number of the steadystate population against the error rate (1 q), the numbers 0, 1, 2, etc., referring to 0 errors ( master sequence) and the sums of all of the 1, 2, 3, error sequences, respectively. The error threshold is seen clearly at 1 q 0.11. Although the individual curves vary quite markedly with the error rate, the order of the quasispecies, represented by the consensus sequence, is clearly conserved up to the ‘‘melting point,’’ i.e., the error threshold. Above the error threshold, each of the 106 (i.e., 2N) possible individual sequences occurs with the same probability of 10 6. Because the distribution was centered around the master sequence (0