Examining The Theory of Error Catastrophe

Abstract

This discussion attempts to present a simple explanation of the current theory of error catastrophe and why it does not herald a paradigm shift in antiviral strategy. In the main text of the paper, the workings of a simple model of error catastrophe are examined to demonstrate what actually causes error catastrophe. The Appendix contains a more detailed discussion of the original error threshold model of Eigen and Schuster and how it applies to a viral quasispecies. RNA viruses are said to replicate at the edge of “error catastrophe” (18). Error catastrophe is a term coined to describe the supposed inability of a genetic element to be maintained in a population as the fidelity of its replication machinery decreases beyond a certain threshold value. Error catastrophe has been invoked as a theoretical basis for treatment of viral infection with drugs that would push the error rate for copying of the viral genome beyond this threshold (1, 4, 5, 6, 7, 9, 10, 14, 15, 16, 17, 19, 22, 25, 26, 28, 29, 40). Numerous publications aimed at the detection of virus extinction by error catastrophe induced by viral mutagens have appeared in recent years (8, 11, 12, 13, 24, 27, 33, 34, 35, 36, 38, 39, 46, 47). The catastrophic effect of high error rates was originally predicted in a mathematical model by Eigen and Schuster (20), in which a master genetic sequence replicated in competition with a collection of variants generated by errors in replication of the master sequence. In the simplest versions of the model (41), the variants all typically have a lower replication rate than the master sequence, and the effect of their replication errors is to convert one variant into another. When the distribution of genomes in such a replicating system was calculated to steady state, it was found that beyond a threshold error rate the master sequence effectively disappeared, becoming no more frequent than any single variant sequence. Eigen and Schuster referred to this hypothetical redistribution of the genetic information of the system as an error catastrophe (not to be confused with the theory of ageing that is also called error catastrophe [30, 31, 32]). Various treatments of the basic model have appeared in the literature since publication of Eigen and Schuster's original paper (2, 3, 21, 42, 42, 44, 45). We present here an examination of the theoretical basis for error catastrophe as predicted by the accepted mathematical simulations. For this purpose, we have constructed our own relatively simple model, based on ordinary differential equations, that reproduces error catastrophe. Using this model, we show that an error threshold is predicted to occur solely because of the implausible proposition that all progeny genomes that are not the master sequence continue to replicate at a finite rate no matter how many replication errors they contain, whereas replication of the master sequence is disqualified by a single error in the progeny genome. The disappearance of the master sequence at the error threshold is predicated on competition between the progeny and the master sequence to infinite time. We will show that, without the assumption that all mutants, no matter what their sequences, continue to replicate, mathematical models do not predict error catastrophe.