Curated HPA-Axis Models
A mechanistic model of ACTH-stimulated cortisol secretion
Although this model  is bit old, it can capture mechanistic behavior of the ACTH stimulated cortisol secretion. GPCR signaling part is very much outdated and model does not consider the cholesterol uptake through LDL receptors pathway which is crucial for maximal steroid production. In fact "neither endogenous cellular cholesterol synthesis nor mobilization of stored cholesteryl esters is sufficient to support maximal steroid production, since hormone-stimulated steroid production is markedly augmented in the presence of lipoproteins" . Apart from this authors themselves suggest - "The model does fail to explain some known characteristics of cortisol secretion. Because the model is driven by the concentration of ACTH, there is no explanation for dependence on the rate of presentation of ACTH. Since a measurable decrease in ACTH concentration from arterial to venous blood has been shown (II), this effect may be a property of the intact gland rather than the cell. Indeed, without hormone consumption, sensitivity to presentation rate appears physically unrealizable. The model also cannot account for an absolute delay between increased concentration of ACTH and increased secretion of cortisol. An absolute delay of 1-2 min was described by Miller and associates (27) and Urquhart and Li (42), though Lake and Gann (25) found elevated secretion rates of cortisol 1 min after ACTH was given. In the gland, an absolute delay may be incurred in the activation of one or more of the rate constants. This, of course, cannot be duplicated with the first-order equations we have employed".
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