Noise-induced bistability in the quasi-neutral coexistence of viral RNAs under different replication modes

Abstract

Evolutionary and dynamical investigations into real viral populations indicate that RNA replication can range between the two extremes represented by so-called 'stamping machine replication' (SMR) and 'geometric replication' (GR). The impact of asymmetries in replication for single-stranded (+) sense RNA viruses has been mainly studied with deterministic models. However, viral replication should be better described by including stochasticity, as the cell infection process is typically initiated with a very small number of RNA macromolecules, and thus largely influenced by intrinsic noise. Under appropriate conditions, deterministic theoretical descriptions of viral RNA replication predict a quasi-neutral coexistence scenario, with a line of fixed points involving different strands' equilibrium ratios depending on the initial conditions. Recent research into the quasi-neutral coexistence in two competing populations reveals that stochastic fluctuations fundamentally alter the mean-field scenario, and one of the two species outcompetes the other. In this article, we study this phenomenon for viral RNA replication modes by means of stochastic simulations and a diffusion approximation. Our results reveal that noise has a strong impact on the amplification of viral RNAs, also causing the emergence of noise-induced bistability. We provide analytical criteria for the dominance of (+) sense strands depending on the initial populations on the line of equilibria, which are in agreement with direct stochastic simulation results. The biological implications of this noise-driven mechanism are discussed within the framework of the evolutionary dynamics of RNA viruses with different modes of replication.

Stationary distributions of systems with discreteness-induced transitions

“…The paper raised much interest and similar effects have been observed in more complicated and realistic models, e.g., large scale networks [2], particle systems with finite interaction radius [3], reaction-diffusion systems [4], models of ant foraging [5], chiral autocatalysis [6], tumor growth [7], spatial models [8], and viral replication [9].…”

“…The paper raised much interest and resulted in similar effects being observed in more complicated and realistic models in physics, biology and elsewhere, e.g. in large-scale networks [2], particle systems with finite interaction radius [3], reaction-diffusion systems [4], models of receptor oligomerization by bivalent ligand [5], models of ant foraging [6], chiral autocatalysis [7], tumour growth [8], spatial models [9], viral replication [10] and noise control in synthetic biology [11]. Thus, the phenomomen of DITs is widespread in nature.…”

“…The conditional stationary distribution π(a1|n), cf (7). from simulation (grey histograms) and from(9) in Theorem 1 (red lines). Parameters are chosen according to(11) withκ i = 1, δ i = λ i = D = 0.01 for i = 1, 2.The volume parameter V differs in the three panels to illustrate the effect of scaling, and n is chosen as the mean of ν(n), which is 4000, 400, and 40, respectively; implying that the mean of the scaled process X/V is (1, 1) in all three cases.…”

Critical slowing down close to a global bifurcation of a curve of quasi-neutral equilibria

“…Quasi-neutral manifolds have been investigated in the dynamics of allele fixation [45,46], in two-species Lotka-Volterra models [47] and in models of sexual in diploid populations [48,49]. These manifolds have been also studied analytically and computationally in epidemiology [50] and in RNA viruses with different replication modes ranging between geometric and stamping machine modes [51]. Quasi-neutral curves imply coexistence within the phase space with different equilibrium states for different initial conditions.…”

“…CQNE are formed by a continuum of equilibrium values: once an orbit reaches the CQNE, the dynamics stops. This dynamics is fundamentally altered in the presence of noise, which have been also been an important subject of recent research in the context of noise-induced bistability [47,50,51].…”