Impact of spatial structure on quasi-neutral manifolds in the HV–DIPs–satRNA model

Investigate the impact of spatial structure within host cells on the existence, geometry, and stability of the quasi-neutral curve of coexistence equilibria in the ordinary differential equation model of helper virus (HV), defective interfering genomes (DIPs), and satellite RNA (satRNA) that explicitly includes the RNA-dependent RNA polymerase (RdRp). Determine whether quasi-neutral manifolds persist, are modified, or break down when spatial heterogeneity or spatially distributed replication is incorporated into the within-cell tripartite system characterized by parameters α (HV replication rate), ω (fraction of DIPs produced), β (satRNA replication rate), γ (DIPs replication rate), κ (RdRp production rate), ε (RNA degradation rate), and ε_p (RdRp degradation rate).

Background

The paper introduces and analyzes a four-dimensional ODE model for the early within-cell replication dynamics of a helper virus (HV), its defective interfering genomes (DIPs), and a satellite RNA (satRNA), explicitly modeling the RNA-dependent RNA polymerase (RdRp). A key finding is a global bifurcation—termed quasi-neutral nullcline confluence (QNC)—through which a quasi-neutral curve of coexistence equilibria is created or destroyed depending on the relation α(1−ω)=β and β>γ.

The authors highlight that quasi-neutral manifolds can organize global dynamics and produce long transients with scaling laws near the bifurcation. They note that replication can be spatially structured in cells (e.g., replication factories) and explicitly state that the impact of space on such quasi-neutral manifolds has not yet been addressed, pointing to an unresolved question about how spatial heterogeneity affects the existence and properties of these manifolds in the HV–DIPs–satRNA system.