Coupling between phosphate and calcium homeostasis: a mathematical model

Am J Physiol Renal Physiol. 2017 Dec 1;313(6):F1181-F1199. doi: 10.1152/ajprenal.00271.2017. Epub 2017 Jul 26.


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.

MeSH terms

  • Animals
  • Bone and Bones / metabolism*
  • Calcium / blood
  • Calcium / metabolism*
  • Calcium Phosphates / blood
  • Calcium Phosphates / metabolism
  • Cholecalciferol / metabolism
  • Feedback, Physiological
  • Female
  • Fibroblast Growth Factor-23
  • Fibroblast Growth Factors / metabolism
  • Homeostasis
  • Intestinal Mucosa / metabolism*
  • Kidney / metabolism*
  • Male
  • Mice, Inbred C57BL
  • Models, Biological*
  • Parathyroid Hormone / metabolism
  • Phosphates / blood
  • Phosphates / metabolism*
  • Receptors, Calcium-Sensing / metabolism
  • alpha-2-HS-Glycoprotein / metabolism


  • Ahsg protein, rat
  • Calcium Phosphates
  • Fgf23 protein, mouse
  • Fgf23 protein, rat
  • Parathyroid Hormone
  • Phosphates
  • Receptors, Calcium-Sensing
  • alpha-2-HS-Glycoprotein
  • extracellular calcium cation-sensing receptor, rat
  • Cholecalciferol
  • Fibroblast Growth Factors
  • Fibroblast Growth Factor-23
  • calcium phosphate
  • Calcium