The apparent hysteresis in hormone-agonist relationships.

It has been noted in multiple studies that the calcium-PTH axis, among others, is subject to an apparent hysteresis. We sought to explain a major component of the observed phenomenon by constructing a simple mathematical model of a hormone and secretagogue system with concentration dependent secretion and containing two delays. We constructed profiles of the hormone-agonist axis in this model via four types of protocols, three of which emulating experiments from the literature, and observed a delay- and load-dependent hysteresis that is an expected mathematical artifact of the system described. In particular, the delay associated with correction allows for over-secretion of the hormone influencing the corrective mechanism; thus rate dependence is an artifact of the corrective mechanism, not a sensitivity of the gland to the magnitude of change. From these observations, the detected hysteresis is due to delays inherent in the systems being studied, not in the secretory mechanism.