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

Joan Fornés, J. Tomás Lázaro, Tomás Alarcón, Santiago F. Elena, Josep Sardanyés

    Research output: Contribution to journalArticleResearch

    3 Citations (Scopus)

    Abstract

    © 2018 Elsevier Ltd Positive-sense, single-stranded RNA viruses are important pathogens infecting almost all types of organisms. Experimental evidence from distributions of mutations and from viral RNA amplification suggest that these pathogens may follow different RNA replication modes, ranging from the stamping machine replication (SMR) to the geometric replication (GR) mode. Although previous theoretical work has focused on the evolutionary dynamics of RNA viruses amplifying their genomes with different strategies, little is known in terms of the bifurcations and transitions involving the so-called error threshold (mutation-induced dominance of mutants) and lethal mutagenesis (extinction of all sequences due to mutation accumulation and demographic stochasticity). 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. We analytically derive the critical mutation rates causing lethal mutagenesis and error threshold, governed by transcritical bifurcations that depend on parameters α (parameter introducing the mode of replication), replicative fitness of mutants (k1), and on the spontaneous degradation rates of the sequences (ϵ). Our results relate the error catastrophe with lethal mutagenesis in a model with continuous populations of viral genomes. The former case involves dominance of the mutant sequences, while the latter, a deterministic extinction of the viral RNAs during replication due to increased mutation. For the lethal case the critical mutation rate involving lethal mutagenesis is μc=1−ɛ/α. 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 threshold once the replication mode surpasses a threshold given by α=ϵ/k1.
    Original languageEnglish
    Pages (from-to)170-183
    JournalJournal of Theoretical Biology
    Volume460
    DOIs
    Publication statusPublished - 7 Jan 2019

    Keywords

    • Bifurcations
    • Dynamical systems
    • Error threshold
    • Replication modes
    • RNA viruses
    • Single-peak fitness landscape

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