Storyboard

The hormonal system uses chemical messengers (hormones) secreted in endocrine glands that travel through the blood to target organs. The kinetics are first order: the steady-state concentration C_ss = S/k_elim depends on the secretion rate and the plasma half-life. The half-life varies greatly between hormones (insulin: 5 min; cortisol: 6090 min; T4: 7 days), which determines how quickly the system responds.

The HPA (hypothalamus-pituitary-adrenal) axis is the canonical example of hormonal negative feedback: stress activates the hypothalamus (CRH) pituitary (ACTH) adrenal (cortisol) negative feedback on hypothalamus and pituitary (cortisol inhibits CRH and ACTH). The three-compartment dynamic system produces ultradian oscillations (~2 h) and the circadian rhythm (peak 8 AM, nadir 2 AM) of cortisol.

The Goodwin model (three-step delay repressor) explains the generation of circadian oscillations (~24 h): the mRNA (X) produces protein (Y) that forms a repressor (Z) that inhibits the transcription of X. With sufficient delay and non-linearity (n 3 in the inhibition function), the system oscillates spontaneously. This model describes the circadian molecular clock (CLOCK/BMAL1/PER/CRY genes in mammals).

The fraction of occupied receptors (Hill isotherm) determines the biological response: E = E_max × [H]^n/([H]^n + K_D^n). In hormonal resistance (hypothyroidism with elevated TSH but normal T4, insulin resistance), the effective K_D is increased (or n reduced): more hormone is needed for the same effect. Diagnosis is made with stimulation or suppression tests that evaluate the responsiveness of the target tissue.

The thyroid axis (TSH T4 T3 feedback on TSH) has the most sensitive and precise feedback from the endocrine system: the TSH-free T4 relationship is log-linear with n_T 23 (Hill), implying that small changes in free T4 produce large changes in TSH. That is why TSH is the best functional marker of the thyroid: a normal TSH (0.44 U/mL) practically rules out clinically significant thyroid dysfunction.

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