Viral replication modes in single-peak fitness landscapes: a dynamical systems analysis

Positive-sense, single-stranded RNA viruses are important pathogens infecting almost all types of organisms. Experimental evidences from mutant distributions and amplification kinetics of viral RNA suggest that these pathogens may follow different RNA replication modes, ranging from the stamping machine replication (SMR) to the geometric replication (GR) modes. Despite previous theoretical works have focused on the evolutionary dynamics of RNA viruses amplifying their genomes with different strategies, few is known in terms of the bifurcations and transitions involving error thresholds (mutation-induced dominance of mutants) and lethal mutagenesis (mutation-induced extinction of all sequences). Here we analyze a dynamical system describing the intracellular amplification of viral RNA genomes evolving on a single-peak fitness landscape focusing on three cases considering neutral, deleterious, and lethal mutants spectra. In our model, the different replication modes are introduced with parameter α: with α ≳ 0 for the SMR and α = 1 for the GR. We analytically derive the critical mutation rates causing lethal mutagenesis and error catastrophe, governed by transcritical bifurcations that depend on parameters α, k1 (replicative fitness of mutants), and on the spontaneous degradation rates of the sequences, e. For the lethal case the critical mutation rate involving lethal mutagenesis is μc = 1−e√α−1. Here, the SMR involves lower critical mutation rates, being the system more robust to lethal mutagenesis replicating closer to the GR mode. This result is also found for the neutral and deleterious cases, but for these later cases lethal mutagenesis can shift to the error catastrophe once the replication mode surpasses a threshold given by √α = e/k1.