Coupling between phosphate and calcium homeostasis: a mathematical model

Abstract

We developed a mathematical model of calcium (Ca) and phosphate (PO₄) homeostasis in the rat to elucidate the hormonal mechanisms that underlie the regulation of Ca and PO₄ balance. The model represents the exchanges of Ca and PO₄ between the intestine, plasma, kidneys, bone, and the intracellular compartment, and the formation of Ca-PO₄-fetuin-A complexes. It accounts for the regulation of these fluxes by parathyroid hormone (PTH), vitamin D₃, fibroblast growth factor 23, and Ca²⁺-sensing receptors. Our results suggest that the Ca and PO₄ homeostatic systems are robust enough to handle small perturbations in the production rate of either PTH or vitamin D₃ The model predicts that large perturbations in PTH or vitamin D₃ synthesis have a greater impact on the plasma concentration of Ca²⁺ ([Ca²⁺]_p) than on that of PO₄ ([PO₄]_p); due to negative feedback loops, [PO₄]_p does not consistently increase when the production rate of PTH or vitamin D₃ is decreased. Our results also suggest that, following a large PO₄ infusion, the rapidly exchangeable pool in bone acts as a fast, transient storage PO₄ compartment (on the order of minutes), whereas the intracellular pool is able to store greater amounts of PO₄ over several hours. Moreover, a large PO₄ infusion rapidly lowers [Ca²⁺]_p owing to the formation of CaPO₄ complexes. A large Ca infusion, however, has a small impact on [PO₄]_p, since a significant fraction of Ca binds to albumin. This mathematical model is the first to include all major regulatory factors of Ca and PO₄ homeostasis.

Keywords: FGF23; PTH; calcium; homeostasis; mathematical model; phosphate; vitamin D3.