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.

► We model a simplified agonist–hormone relationship.
► The model shows hysteresis is an artifact of the lag between hormonal secretion and hormonal action.
► The hysteresis shape is dependent on the delay, not the magnitude of the stimulus.
► The magnitude of the stimulus determines the degree of hysteresis.