Narrow Results

A mathematical model of competition between plasmid-bearing and plasmid-free organisms for a single limiting resource in a chemostat with distinct removal rates and in the presence of an external inhibitor is analyzed. This model was previously introduced in the special case where the growth rate functions and the absorption rate of the inhibitor follow the Monod kinetics and the removal rates are the same as the dilution rate. Here, we consider the general case of monotonic growth and absorption functions, and distinct removal rates. Through the three operating parameters of the model, represented by the dilution rate, the input concentrations of the substrate and the inhibitor, we give necessary and sufficient conditions for existence and stability of all equilibria. To better understand the richness of the model’s behavior with respect to those operating parameters, we determine the operating diagram theoretically and numerically. This diagram is very useful to understand the model from both the mathematical and biological points of view.

Metal ions have a major effect on the metabolic processes in cells either as inhibitors or as integral components of enzymes. The inhibition of enzymes can take place either through the inhibition of gene expression or through inhibition of protein function. A particularly interesting example of the effect of a metal ion on metabolism is the observed inhibition of Krebs cycle and alteration of energy metabolism by zinc (II) cations. In this particular case metal ion inhibition of enzyme is linked to one of the major functions of prostate cells of accumulation and excretion of citrate. Experimental results have shown that increase in concentration of zinc (II) in prostate cells effectively blocks progression of a part of the Krebs cycle leading to change in the concentration of several metabolites with largest effect in the accumulation of citrate. Based on previously reported experimental results, several distinct mechanisms for zinc (II) inhibition of Krebs cycle were proposed. In order to determine the precise mechanism of inhibition in this system, a mathematical model of glycolysis and Krebs cycle was constructed. Three different types of inhibition were analyzed, including competitive and uncompetitive inhibition as well as inhibition through the alteration of the expression level of m-aconitase. The effects of different inhibition models on metabolite concentrations were investigated as a time course simulation of the system of reactions. Several kinetic parameters in the model were optimized in order to best resemble experimental measurements. The simulation shows that only competitive inhibition leads to an agreement with experimental data.