No two without three: Modeling dynamics of the trio RNA virus-defective interfering genomes-satellite RNAs

Abstract

Almost all viruses, regardless of their genomic material, produce defective viral genomes (DVG) as an unavoidable byproduct of their error-prone replication. Defective interfering (DI) elements are a subgroup of DVGs that have been shown to interfere with the replication of the wild-type (WT) virus. Along with DIs, other genetic elements known as satellite RNAs (satRNAs), that show no genetic relatedness with the WT virus, can co-infect cells with WT helper viruses and take advantage of viral proteins for their own benefit. These satRNAs have effects that range from reduced symptom severity to enhanced virulence. The interference dynamics of DIs over WT viruses has been thoroughly modeled at within-cell, within-host, and population levels. However, nothing is known about the dynamics resulting from the nonlinear interactions between WT viruses and DIs in the presence of satellites, a process that is frequently seen in plant RNA viruses and in biomedically relevant pathosystems like hepatitis B virus and its δ satellite. Here, we look into a simple phenomenological mathematical model that describes how a WT virus replicates and produces DIs in presence of a satRNA. The WT virus is subject to mechanisms of complementation, competition, and various levels of interference from DIs and the satRNA. Examining the dynamics analytically and numerically reveals three possible regimes: (i) full extinction, (ii) satellite extinction and virus-DIs coexistence and (iii) full coexistence. Assuming DIs replicate faster than the satRNA owed to their smaller size drives to scenario (ii), which implies that DIs could wipe out the satRNA. In addition, a small region of the parameter space exists wherein the system is bistable (either scenarios (ii) or (iii) are concurrently stable). We have identified transcritical bifurcations in the transitions between scenarios (i) to (iii) and saddle–node bifurcations behind the change from bistability to monostability. Despite the model simplicity, our findings may have applications in biomedicine and agronomy. They will cast light on the dynamics of this three-species system and aid in the identification of scenarios in which the clearance of the satRNAs may be possible thus e.g., allowing for less severe disease symptoms.