Coupling between phosphate and calcium homeostasis: a mathematical model

We developed a mathematical model of calcium (Ca) and phosphate (PO ) homeostasis in the rat to elucidate the hormonal mechanisms that underlie the regulation of Ca and PO balance. The model represents the exchanges of Ca and PO between the intestine, plasma, kidneys, bone, and the intracellular compartment, and the formation of Ca-PO -fetuin-A complexes. It accounts for the regulation of these fluxes by parathyroid hormone (PTH), vitamin D , fibroblast growth factor 23, and Ca -sensing receptors. Our results suggest that the Ca and PO homeostatic systems are robust enough to handle small perturbations in the production rate of either PTH or vitamin D The model predicts that large perturbations in PTH or vitamin D synthesis have a greater impact on the plasma concentration of Ca ([Ca ] ) than on that of PO ([PO ] ); due to negative feedback loops, [PO ] does not consistently increase when the production rate of PTH or vitamin D is decreased. Our results also suggest that, following a large PO infusion, the rapidly exchangeable pool in bone acts as a fast, transient storage PO compartment (on the order of minutes), whereas the intracellular pool is able to store greater amounts of PO over several hours. Moreover, a large PO infusion rapidly lowers [Ca ] owing to the formation of CaPO complexes. A large Ca infusion, however, has a small impact on [PO ] , since a significant fraction of Ca binds to albumin. This mathematical model is the first to include all major regulatory factors of Ca and PO homeostasis.