Estimation of parameters for a mathematical model of growth hormone secretion

Here, we describe partial calibration of a parsimonious mathematical model of growth hormone (GH) secretion. From first principles, we derived a model of the effects on GH secretion from pituitary somatotrophs of stimulation by GH-releasing factor (GRF) or GH secretagogue, and of inhibition by somatostatin. We obtained a concise model by collapsing the many processes of the signal transduction cascade into a single step broadly reflecting the initial binding of GRF to its receptors. In the model, GH secretion is proportional to the rate of binding of GRF to activatable receptors. Desensitization occurs because of reduction of free receptors/available effector units, and resensitization occurs as those lost are replaced. This replacement is speeded up in the presence of somatostatin, which also inhibits GH secretion by reducing the constant of proportionality between the rate of GH secretion and the rate of GRF binding. We derived simple mathematical equations for the rate of GH secretion and cumulative secretion. Using these, we tested the model against data obtained from experiments performed in vitro, and made it quantitative using rigorous statistical approaches to optimize parameter estimates. The behaviour of the calibrated model matches experimental observations closely.