Four-parameter model of the sigmoidal relationship between parathyroid hormone release and extracellular calcium concentration in normal and abnormal parathyroid tissue.

We employed a computer program to curve-fit data relating PTH release in vitro to the extracellular calcium concentration in parathyroid cells prepared from normal bovine and human as well as pathological human parathyroid tissue. In bovine cells and 82% of human cell preparations in which PTH release was more than 50% suppressible by high calcium concentrations, the data were successfully fitted to symmetrical sigmoidal curves. Such curves were defined by four parameters [A = maximum PTH release, B = slope of the curve at the setpoint, C = set-point (calcium concentration causing half-maximal inhibition of secretion), and D = minimum PTH release]. There was excellent agreement between the predicted values for these parameters and those we have obtained previously using visual fits. We also generated theoretical curves with the program to assess the possible contribution of changes in parameters A through D to hypersecretion of PTH in hyperparathyroidism. These analyses suggested that changes in maximal PTH secretion, slope of the curve, set-point, and maximal suppressibility of PTH release all might contribute to hormonal hypersecretion. On a quantitative basis, however, changes in the set-point produced the largest alteration in secretory rate for a given change in the value of a parameter. These results provide a mathematical model for the relationship between PTH release and the extracellular calcium concentration. Moreover, they provide a means of analyzing theoretically the contribution of various qualitative changes in this relationship to states of hypo- and hypersecretion of PTH.