Parathyroid hormone secretion by multiple distinct cell populations, a time dynamic mathematical model

Abstract

The acute response of parathyroid hormone to perturbations in serum ionized calcium ([Ca2+]) is physiologically complex, and poorly understood. The literature provides numerous observations of quantitative and qualitative descriptions of parathyroid hormone (PTH) dynamics. We present a physiologically based mathematical model of PTH secretion constructed from mechanisms suggested in the literature, and validated against complex [Ca2+] clamping protocols from human data. The model is based on two assumptions. The first is that secretion is a fraction of cellular reserves, with the fraction being determined by the kinetics of [Ca2+] with its receptor. The second is that there are multiple distinct populations of parathyroid cells, with different secretory parameters. The steady state and transient PTH secretion responses of the model are in agreement with human experimental PTH responses to different hypocalcemia and hypercalcemia stimuli. This mathematical model suggests that a population of secreting cells is responsible for the PTH secretory dynamics observed experimentally.

A model of calcium homeostasis in the rat

“…When [Ca 2ϩ ]p is well below R, n(Ca) tends towards high values (Ͼ100), as commonly used to fit hypocalcemia profiles (1,73,80). Conversely, when [Ca 2ϩ ]p rises above R, n(Ca) takes on a lower value.…”

“…This function accounts for the inhibition of PTH secretion by CaSR (73): ␤ exo PTH g is the maximal rate of PTH secretion from the gland, ␥ exo PTH g characterizes the degree to which CaSR can maximally inhibit secretion, KCa is the binding affinity of Ca 2ϩ to CaSR, and n(Ca) is a steepness factor. As discussed by Shresta et al (80), to properly account for the effects of both hypercalcemia and hypocalcemia on PTH secretion, it is necessary to use an adaptive n, which can be calculated as:…”