Robustness to Mutations Depends on whether RNA Virus Replication Occurs Geometrically or Via a Stamping Machine

Regardless genome polarity, during viral replication intermediaries of complementary sense must be synthesized and used as templates for the synthesis of new genomic strands. Depending on whether the newly synthesized genomic molecules become themselves templates for producing extra antigenomic strands, thus giving rise to a geometric growth, or only the firstly synthetized antigenomic strands can be used to this end, thus following Luria's stamping machine model, the abundance and distribution of mutant genomes will be different. Mathematical models of virus replication have largely ignored this fact and generally assumed a pure geometric growth. Here we propose mathematical and bit string quasispecies models that allow to distinguish between linear and geometric replication and also incorporating the existence of antigenomic intermediates of replication. We have observed that the error threshold increases as the mechanism of replication switches from purely geometric to stamping machine. We also found that for a wide range of mutation rates, large effect mutations do not accumulate regardless the scheme of replication. However, mild mutational effects accumulate more in the geometrical mode. Furthermore, at high mutation rates, geometric growth leads to a sooner population collapse for intermediate values of mutational effects at which the stamping machine still produces non mutated genomes. Finally, at increasing mutation rates, the highest production of virions is found for close-to-linear replication and high replicase production. In conclusion, we have shown that by selecting a stamping machine replication strategy, RNA viruses may increase their robustness against the accumulation of deleterious mutations.