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

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 μ_c=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.

[Mobbing. Psychologic abuse in the work setting]

Mobbing is a relatively recent study phenomenon, lying in the realm of abuses. It is especially well-known as a form of psychological mistreatment at the work place. It develops due to an asymmetric power relationship among 2 or more people and its fundamental essence is jealousy and the ambition to hold power by at least one of these people.

Properties of Asp212----Asn bacteriorhodopsin suggest that Asp212 and Asp85 both participate in a counterion and proton acceptor complex near the Schiff base

The gene coding for bacteriorhodopsin was modified in vitro to replace Asp212 with asparagine and expressed in Halobacterium halobium. X-ray diffraction measurements showed that the major lattice dimension of purple membrane containing the mutated bacteriorhodopsin was the same as wild type. At pH greater than 7, the Asp212----Asn chromophore was blue (absorption maximum at 585 nm) and exhibited a photocycle containing only the intermediates K and L, i.e. a reaction sequence very similar to that of wild-type bacteriorhodopsin at pH less than 3 and the blue form of the Asp85----Glu protein at pH less than 9. Since in the latter cases these effects are attributed to protonation of residue 85, it now appears that removal of the carboxylate of Asp212 has similar consequences as removing the carboxylate of Asp85. However, an important difference is that only Asp85 affects the pKa of the Schiff base. At pH less than 7, the Asp212----Asn protein was purple (absorption maximum at 569 nm) but photoexcitation produced only 15% of the normal amount of M and the transport activity was partial. The reactions of the blue and purple forms after photoexcitation are both quantitatively accounted for by a proposed scheme, K in equilibrium with L1 in equilibrium with L2----BR, but with the addition of an L1 in equilibrium with M reaction with unfavorable pKa for Schiff base deprotonation in the purple form. The latter hinders the transient accumulation of M, and the consequent branching at L1 allows only partial proton transport activity. The results are consistent with the existence of a complex counterion for the Schiff base proposed earlier (De Groot, H. J. M., Harbison, G. S., Herzfeld, J., and Griffin, R. G. (1989) Biochemistry 28, 3346-3353) and suggest that Asp85, Asp212, and at least one other protonable residue participate in it.