High Levels of Extracellular Potassium Can Delay Myxoma Virus Replication by Preventing Release of Virions from the Endosomes.

Potassium (K+) is one of the most abundant cations in the human body. Under normal conditions, the vast majority of K+ is found within cells, and the extracellular [K+] is tightly regulated to within 3.0 to 5.0 mM. However, it has recently been shown that high levels of localized necrosis can increase the extracellular concentration of K+ to above 50 mM. This raises the possibility that elevated extracellular K+ might influence a variety of biological processes that occur within regions of necrotic tissue. For example, K+ has been shown to play a central role in the replication cycles of numerous viral families, and in cases of lytic infection, localized regions containing large numbers of necrotic cells can be formed. Here, we show that the replication of the model poxvirus myxoma virus (MYXV) is delayed by elevated levels of extracellular K+. These increased K+ concentrations alter the cellular endocytic pathway, leading to increased phagocytosis but a loss of endosomal/lysosomal segregation. This slows the release of myxoma virus particles from the endosomes, resulting in delays in genome synthesis and infectious particle formation as well as reduced viral spread. Additionally, mathematical modeling predicts that the extracellular K+ concentrations required to impact myxoma virus replication can be reached in viral lesions under a variety of conditions. Taken together, these data suggest that the extracellular [K+] plays a role in determining the outcomes of myxoma infection and that this effect could be physiologically relevant during pathogenic infection. IMPORTANCE Intracellular K+ homeostasis has been shown to play a major role in the replication of numerous viral families. However, the potential impact of altered extracellular K+ concentrations is less well understood. Our work demonstrates that increased concentrations of extracellular K+ can delay the replication cycle of the model poxvirus MYXV by inhibiting virion release from the endosomes. Additionally, mathematical modeling predicts that the levels of extracellular K+ required to impact MYXV replication can likely be reached during pathogenic infection. These results suggest that localized viral infection can alter K+ homeostasis and that these alterations might directly affect viral pathogenesis.

Classical and resource-based competition: a unifying graphical approach.

A graphical technique is given for determining the outcome of two species competition for two resources. This method is unifying in the sense that the graphical criterion leading to the various outcomes of competition are consistent across most of the spectrum of resource types (from those that fulfill the same growth needs to those that fulfill different needs) regardless of the classification method used, and the resulting graphs bear a striking resemblance to the well-known phase portraits for two species Lotka-Volterra competition. Our graphical method complements that of Tilman. Both include zero net growth isoclines. However, instead of using the consumption vectors at potential coexistence equilibria to determine input resource concentrations leading to specific competitive outcomes, we introduce curves bounding the feasible set (the set where the resource concentrations of any equilibrium solution must be located). The washout equilibrium (corresponding to the supply point) occurs at an intersection of curves defining the feasible set boundary. The resource concentrations of all other equilibria are found where zero net growth isoclines either intersect each other inside the feasible set or they intersect the feasible set boundary. A species has positive biomass at such an equilibrium only if its zero net growth isocline is involved in such an intersection. The competitive outcomes are then determined from the position of the single species equilibria, just as in the phase portrait analysis for classical competition (rather than from information at potential coexistence equilibria as in Tilman's method).

Ecological conditions that favor the evolution of intermediate-virulence in an environmentally transmitted parasite.

In this paper we develop and analyze several population-dynamic models of an environmentally transmitted symbiotic parasite infecting an isolated population of susceptible hosts. In our most basic model infection acts only to decrease the average lifetime of the infected host, parasites are only transmitted to uninfected hosts, there is no recovery from infection, and the rate of parasite transmission is an increasing function of the level of parasite virulence. It is shown that invasion of the parasite-free equilibrium cannot occur for virulence levels that are either too high or too low. We then incorporate a number of modifications to the model, among them the possibility that host fertility is reduced by infection, and that transmission rate depends additionally on susceptible host density. It is shown that the essential nature of the conditions for invasion are preserved. Thus, natural selection for intermediate virulence is a generic property of a broad class of population models.

Global analysis of competition for perfectly substitutable resources with linear response.

We study a model of the chemostat with two species competing for two perfectly substitutable resources in the case of linear functional response. Lyapunov methods are used to provide sufficient conditions for the global asymptotic stability of the coexistence equilibrium. Then, using compound matrix techniques, we provide a global analysis in a subset of parameter space. In particular, we show that each solution converges to an equilibrium, even in the case that the coexistence equilibrium is a saddle. Finally, we provide a bifurcation analysis based on the dilution rate. In this context, we are able to provide a geometric interpretation that gives insight into the role of the other parameters in the bifurcation sequence.