Pharmacodynamic Model of Parathyroid Hormone Modulation by a Negative Allosteric Modulator of the Calcium-Sensing Receptor

In this study, a pharmacodynamic model is developed, based on calcium–parathyroid hormone (PTH) homeostasis, which describes the concentration–effect relationship of a negative allosteric modulator of the calcium-sensing receptor (CaR) in rats. Plasma concentrations of drug and PTH were determined from plasma samples obtained via serial jugular vein sampling following single subcutaneous doses of 1, 5, 45, and 150 mg/kg to male Sprague–Dawley rats (n = 5/dose). Drug pharmacokinetics was described by a one-compartment model with first-order absorption and linear elimination. Concentration-time profiles of PTH were characterized using a model in which the compound allosterically modulates Ca+2 binding to the CaR that, in turn, modulates PTH through a precursor-pool indirect response model. Additionally, negative feedback was incorporated to account for tolerance observed at higher dose levels. Model fitting and parameter estimation were conducted using the maximum likelihood algorithm. The proposed model well characterized the data and provided compound specific estimates of the Ki and cooperativity constant (α) of 1.47 ng/mL and 0.406, respectively. In addition, the estimated model parameters for PTH turnover were comparable to that previously reported. The final generalized model is capable of characterizing both PTH–Ca+2 homeostasis and the pharmacokinetics and pharmacodynamics associated with the negative allosteric CaR modulator. As such, the model provides a simple platform for analysis of drugs targeting the PTH–Ca+2 system.