Coupling between phosphate and calcium homeostasis: a mathematical model.

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.

A model of calcium homeostasis in the rat.

We developed a model of calcium homeostasis in the rat to better understand the impact of dysfunctions such as primary hyperparathyroidism and vitamin D deficiency on calcium balance. The model accounts for the regulation of calcium intestinal uptake, bone resorption, and renal reabsorption by parathyroid hormone (PTH), vitamin D3, and Ca2+ itself. It is the first such model to incorporate recent findings regarding the role of the calcium-sensing receptor (CaSR) in the kidney, the presence of a rapidly exchangeable pool in bone, and the delayed response of vitamin D3 synthesis. Accounting for two (fast and slow) calcium storage compartments in bone allows the model to properly predict the effects of bisphophonates on the plasma levels of Ca2+ ([Ca2+]p), PTH, and vitamin D3 Our model also suggests that Ca2+ exchange rates between plasma and the fast pool vary with both sex and age, allowing [Ca2+]p to remain constant in spite of sex- and age-based hormonal and other differences. Our results suggest that the inconstant hypercalciuria that is observed in primary hyperparathyroidism can be attributed in part to counterbalancing effects of PTH and CaSR in the kidney. Our model also correctly predicts that calcimimetic agents such as cinacalcet bring down [Ca2+]p to within its normal range in primary hyperparathyroidism. In addition, the model provides a simulation of CYP24A1 inactivation that leads to a situation reminiscent of infantile hypercalcemia. In summary, our model of calcium handling can be used to decipher the complex regulation of calcium homeostasis.