A mathematical model for copper homeostasis in Enterococcus hirae

Copper is an essential micronutrient for life. It is required by a wide range of species, from bacteria to yeast, plants and mammals including humans. To prevent the consequences of the excess or deficit of copper, living organisms have developed molecular mechanisms that regulate the uptake, efflux, storage and use of the metal. However, the limits of homeostatic regulation are not known. Here, we take advantage of a simple biological mechanism involved in copper metabolism of Enterococcus hirae, to explore how the regulation is achieved by using a set of four proteins codified in the cop operon: two P-type ATP-ases copper transporters, one copper chaper-one and one Cu-response transcription factor. We propose a mathematical model, based on differential equations and the power-law formalism (see M.A. Savageau, Chaos 11(1) (2001) 142–159), for the behavior of the cop operon and we show that homeostasis is a result of transient dynamics. The results derived from the mathematical model allow to measure qualitatively the adaptability of the system to its environment. This detailed model has been possible thanks to the available experimental biological information provided in a sequence of recent works by Solioz and co-workers.