Mathematical models for siderophore production and siderophore mediated antagonism in bacterial populations under iron limitation
Although iron is the most abundant transition metal on earth, its solubility is very low and therefore its bioavailability is poor. Many microorganisms have developed iron chelating systems and often produce siderophores which are iron chelators secreted by the cell. In particular, Pseudomonads are prominent producers of a siderophore called pyoverdine that has a high iron binding capability. The pseudomonas-pyoverdine system is modeled through a system of nonlinear differential equations that explicitly takes into account the transient adaptation (lag phase) of the average physiological state of the population to the environmental conditions. Various lag phase models are considered and a parameter identification study is conducted. The theoretical properties of the model, the model behavior at small and large times, and local stability are analyzed. A new competition model based on iron chelation is also developed. A population of a chelator microorganism (e.g., Pseudomonas) and a non-chelator (e.g., a pathogen) is considered. The chelator is assumed to produce an iron-chelating siderophore which binds ferric ions and makes them available only to the chelator and not to the competing microorganism. A qualitative analysis of the model for the batch case (no inflow or outflow) is carried out and the global behavior of the model variables is studied. For the chemostat case, the equilibrium points are derived and their local stability is studied. The principle of competitive exclusion that bases survivability of the competing species on their break even points is found not to apply. An optimal finite-time control strategy is proposed that aims at manipulating the microbial community by preemptive colonization to displace the pathogenic bacteria through competition for iron. Pontryagin's Minimum Principle is used to characterize the optimal control and the optimality system composed of state and adjoint differential equations is numerically solved. Existence results are established and various simulations are carried out to illustrate the technique. It is found that through the optimal feeding strategy, it is possible to move from an existing non-desired equilibrium whereby the pathogen outcompetes Pseudomonas to a more desirable equilibrium where the pathogen gets extinct.