Error threshold in RNA quasispecies models with complementation

A general assumption of quasispecies models of replicons dynamics is that the fitness of a genotype is entirely determined by its sequence. However, a more biologically plausible situation is that fitness depends on the proteins that catalyze metabolic reactions, including replication. In a stirred population of replicons, such as viruses replicating and accumulating within the same cell, the association between a given genome and the proteins it encodes is not tight as it can be replicated by proteins translated from other genomes. We have investigated how this complementation phenomenon affects the error threshold in simple quasispecies mean field models. We first studied a model in which the master and the mutant genomes code for wild-type and mutant replicases, respectively. We assume that the mutant replicase has a reduced activity and that the wild-type replicase does not have increased affinity for the master genome. The whole pool of replicases can bind and replicate both genomes. We then analyze a different model considering a more extreme case of mutant genomes, the defective interfering particles (DIPs) described in many cases of viral infection. DIPs, with a higher replication rate owed to their shorter genomes, do not code for replicase, but they are able of using the replicase translated from the master genome. Our models allow to study how the probability of interaction between the genomes and the whole pool of replicases affects the error threshold. In both systems we characterize the scenario of coexistence between master and mutant genomes, providing the critical values of mutation rate, μc, and the critical interaction rate between master genomes and replicases, γc, at which the quasispecies enters into error catastrophe, a situation in which the mutant genomes dominate the population. In both cases, we showed that the error-threshold transition is given by transcritical-like bifurcations, suggesting a continuous phase transition. We have also found that the region in the parameter space (μ,γ) in which the master sequence survives is reduced when DIPs are introduced into the system.