Modeling Dynamics of the Hypothalamic-Pituitary-Adrenal Axis

The hypothalamic–pituitary–adrenal (HPA) axis forms a tightly regulated neuroendocrine network linking the hypothalamus, pituitary and adrenal glands to coordinate stress responses and maintain homeostasis. External or internal stressors trigger the release of corticotrophin-releasing hormone (CRH) from the hypothalamus and adrenocorticotropic hormone (ACTH) from the pituitary, leading to glucocorticoid secretion by the adrenal cortex. Circulating glucocorticoids then exert negative feedback at both central and peripheral sites. Mathematical frameworks—ranging from ordinary differential equations to impulsive time-delay models—have captured its characteristic ultradian and circadian oscillations, pulsatility and nonlinear feedback loops. More recent approaches integrate gland-mass dynamics and phase-dependent interactions to explain hormone rhythms over timescales of hours to weeks. These models shed light on mechanisms of resilience and dysregulation in stress-related and mood disorders, offering predictive tools for experimental design and therapeutic optimisation.

Research from Nature Portfolio

An impulsive time-delay differential equation model has clarified the origin of hormonal pulsatility by treating ACTH secretion as discrete impulses and glucocorticoid release with downstream delays. Numerical simulations reveal that intrinsic pituitary pulses can drive ultradian oscillations independently of adrenal time delays, with external circadian or stress-related inputs causing predictable phase shifts. This work highlights pulse-modulated control as a robust regulatory strategy of the HPA axis and identifies the isolated pituitary as a source of intrinsic rhythmicity, providing a unifying framework to interpret physiological and pathological hormone profiles.

Modeling Dynamics of the Hypothalamic-Pituitary-Adrenal Axis publication trend

The graph below shows the total number of articles in modeling dynamics of the hypothalamic-pituitary-adrenal axis across all publications each year (not limited to Nature Index journals).

Technical terms

HPA axis: The neuroendocrine system linking hypothalamus, pituitary and adrenal glands that regulates stress responses and homeostasis.

Ultradian rhythm: Repeated cycles of hormone secretion with a period shorter than 24 hours.

Bistability: The property of a dynamical system to exhibit two distinct stable steady states under the same set of parameters.

Dynamical compensation: A mechanism in which slow adaptive processes adjust internal variables to maintain stable system output despite changes in parameters.

Time-delay differential equation: A mathematical formulation in which the rate of change of a variable depends on its past values at specified delays.

References

1. Major depressive disorder and bistability in an HPA-CNS toggle switch. PLOS Computational Biology (2023).
2. A new model for the HPA axis explains dysregulation of stress hormones on the timescale of weeks. Molecular Systems Biology (2020).
3. Characterizing Dynamic Interactions between Ultradian Glucocorticoid Rhythmicity and Acute Stress Using the Phase Response Curve. PLOS ONE (2012).
4. Onset, timing, and exposure therapy of stress disorders: mechanistic insight from a mathematical model of oscillating neuroendocrine dynamics. Biology Direct (2016).
5. Modeling pulsativity in the hypothalamic–pituitary–adrenal hormonal axis. Scientific Reports (2022).