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The body's primary stress management system is the hypothalamic pituitary adrenal (HPA) axis. The HPA axis responds to physical and mental challenge to maintain homeostasis in part by controlling the body's cortisol level. Dysregulation of the HPA axis is implicated in numerous stress-related diseases.

We developed a structured model of the HPA axis that includes the glucocorticoid receptor (GR). This model incorporates nonlinear kinetics of pituitary GR synthesis. The nonlinear effect arises from the fact that GR homodimerizes after cortisol activation and induces its own synthesis in the pituitary. This homodimerization makes possible two stable steady states (low and high) and one unstable state of cortisol production resulting in bistability of the HPA axis. In this model, low GR concentration represents the normal steady state, and high GR concentration represents a dysregulated steady state. A short stress in the normal steady state produces a small perturbation in the GR concentration that quickly returns to normal levels. Long, repeated stress produces persistent and high GR concentration that does not return to baseline forcing the HPA axis to an alternate steady state. One consequence of increased steady state GR is reduced steady state cortisol, which has been observed in some stress related disorders such as Chronic Fatigue Syndrome (CFS).

Inclusion of pituitary GR expression resulted in a biologically plausible model of HPA axis bistability and hypocortisolism. High GR concentration enhanced cortisol negative feedback on the hypothalamus and forced the HPA axis into an alternative, low cortisol state. This model can be used to explore mechanisms underlying disorders of the HPA axis.

The hypothalamic pituitary adrenal (HPA) axis represents a self-regulated dynamic feedback neuroendocrine system that is essential for maintaining body homeostasis in response to various stresses. Stress can be physical (e.g. infection, thermal exposure, dehydration) and psychological (e.g. fear, anticipation). Both physical and psychological stressors activate the hypothalamus to release corticotropin releasing hormone (CRH). The CRH is released into the closed hypophyseal portal circulation, stimulating the pituitary to secrete adrenocorticotropic hormone (ACTH). ACTH is released into the blood where it travels to the adrenals, inducing the synthesis and secretion of cortisol from the adrenal cortex. Cortisol has a negative feedback effect on the hypothalamus and pituitary that further dampens CRH and ACTH secretion [

Cortisol affects a number of cellular and physiological functions to maintain body homeostasis and health. Cortisol suppresses inflammation and certain immune reactions, inhibits the secretion of several hormones and neuropeptides and induces lymphocyte apoptosis [

Definitive research on HPA axis function in chronic diseases has been hampered by the complexity of the numerous systems affected by the HPA axis, such as the immune and neuroendocrine systems, the lack of known or accessible brain lesions and the correlative nature of much of the existing data. Since the organization of the HPA axis has been characterized to detail the feedback and feed forward signalling that regulates HPA axis function [

The HPA axis has three compartments representing the hypothalamus, pituitary and adrenals regulated by simple, linear mass action kinetics for the production and degradation of the primary chemical product of each compartment. In this model, stress to the HPA axis (F) stimulates the hypothalamus to secrete CRH (C). CRH (C) signals the induction of ACTH synthesis (A) in the pituitary. ACTH (A) signals to the adrenal gland and activates the synthesis and release of cortisol (O). Cortisol (O) regulates its own synthesis via inhibiting the synthesis of CRH (C) in the hypothalamus, and ACTH (A) in the pituitary. The equation for the hypothalamus can be written as:

In this equation, -_{cd}_{c }+ _{c }and a stress term _{c }+ _{c }+ _{i1}. This form also guarantees positive ACTH concentrations. We write for the hypothalamus:

For the pituitary:

Equation 3 models a constant degradation rate of ACTH by the term -_{ad}

For the adrenal:

Equation 4 models a constant degradation rate of cortisol -_{od}_{o}

We have augmented this model by including synthesis and regulation of the glucocorticoid receptor (R) in the pituitary [

The following are the differential equations written for the HPA axis model that includes glucocorticoid receptor synthesis and regulation in the pituitary (Figure

F is an external stress that triggers the hypothalamus to release CRH (C) that signals to the pituitary to release ACTH (A) stimulating the synthesis and release of cortisol (O) from the adrenals. Release of cortisol negatively regulates CRH and ACTH after binding to the glucocorticoid receptor (R) in the pituitary. Here, GR and cortisol regulate further GR synthesis.

For the hypothalamus:

For the pituitary:

For the adrenal:

Equation (7) describes the production of GR in the pituitary. The term _{cr }and a degradation term -_{rd}_{i2}.

Scaling of the equations (5) – (8) has been done to reduce the parameters used in simulations. The scaled variables are defined as;

The scaled equations thereby obtained are;

These scaled equations were used in the simulations. The advantage of scaling is that it obviates the need for knowledge of unknown parameter values such as the synthesis rate of CRH in the hypothalamus and ACTH and GR in the pituitary. The parameter values that can be measured are the degradation rates of CRH, ACTH, and cortisol. The scaled parameter values used in simulation were, _{cd }= 1, _{ad }= 10, _{rd }= 0.9, _{cr }= 0.05, _{i1 }= 0.1, and _{i2 }= 0.1. Further, these simulated results for CRH, ACTH and cortisol are converted back to their commonly used dimensions and values obtained in experiments. The simulated time course plots ignore the circadian input to the hypothalamus.

Models were programmed in Matlab (The Mathworks, Natick, MA). The meta-modeling of bi-stability used the CONTENT freeware package. All Matlab code will be provided upon request. Dr. Leslie Crofford provided the human subject serum cortisol data [

To determine if these equations could predict the general features of cortisol production, the experimental data was compared to a cortisol curve generated using equation 4. As shown in Figure

Experimental ACTH and cortisol from a human subject shown in blue and red in top and bottom panels respectively. Modelled cortisol using equation 4 displayed with solid black line in lower panel.

Equations (9)–(12) permit one or three positive steady states depending upon the parameter values. The three positive steady states exist because of homodimerization of the GR with cortisol. Figure _{rd}. Variations in _{rd }from person to person may be expected due to genetic differences in the details of GR production and degradation. For a high value of _{rd}, there exists only a low GR concentration steady state. As the value of _{rd }decreases, these equations produce two more steady states, one stable and another unstable in GR concentration. As _{rd }decreases further, a low GR concentration state disappears and only a high GR concentration state exists (Figure _{rd }would be constitutively healthy in this model, i.e. impervious to a dysregulated HPA-axis no matter how much they are stressed, and those with very low values of _{rd }would be constitutively unhealthy.

Variations of steady state (a) GR and (b) cortisol with _{rd}. Solid and dashed lines denote the stable and unstable steady states, respectively. If _{rd }for a given patient is in the region where GR and cortisol are multivalued, then the given patient can be pushed from one value of steady state GR or cortisol to equally valid altered steady state levels by the application of an extreme stress.

The response of the normal HPA axis to small perturbations is essential to the survival of an organism. Stress activates the HPA axis to regulate various body functions; first by increasing ACTH synthesis followed by increased cortisol production and then returning to the original state. Figure

The response of the HPA axis following a short stress. Short time stress as indicated by the shaded larea was given for 0<T<1 hr.

The robustness of the system was illustrated by the fact that short stress produced small transients that returned to the original, normal steady state. To simulate adaptation of the HPA axis to repeated stress, recursive stress was applied at T = 0, 8 and 16 hours for 2 hour periods. The simulation results showed the continuous decrease in maximum ACTH and cortisol concentration after every stress (Figure

Transient responses of HPA axis to recursive stresses. Initially HPA axis was at a lower GR steady state and stress was given at T = 0, 8 and 16 for 2 hours. Repeated stresses are shown by shaded areas.

To simulate the response to chronic stress, a long stress was given for 0<T<10 hours to perturb the normal steady state of the HPA axis. Simulation results show the bistability in the HPA axis; a long stress forces the HPA axis to an alternate steady state (Figure

Transient responses of HPA axis to chronic stress. Extended length stress was given for 0<T<10. Stress is indicated with shading.

Psychologic stress, CRH and dexamethasone (DEX) tests are used to assess HPA axis function. The model was used to simulate these various HPA axis function tests. To simulate a psychologic stress experiment, the same stress was given with two different initial conditions: normal steady state (low GR concentration) that would occur in a control group, and low cortisol state (high GR concentration) that would occur in a hypocortisolemic patient group. Because the high concentration GR inhibited ACTH synthesis, the patient group exhibited continued low cortisol and ACTH responses compared to the control (Figures

Transient responses of HPA axis a simulated stress experiment. The same stress was given with two different initial conditions; normal steady state (low GR concentration) that would occur in a control group, and low cortisol state (high GR concentration) that would occur in a patient group. Stress was given for 0<Time<1 hr. Dash and solid lines indicate the normal and dysregulated HPA axis responses respectively and stress is indicated with shading.

Transient responses of HPA axis to CRH test. The exogenous CRH was injected at T = 0. Dashed and solid lines indicate the normal and dysregulated HPA axis responses respectively.

Previous models of the HPA axis have not demonstrated bistability in steady state cortisol or ACTH. We believe this is because none of the previous models have explicitly accounted for nonlinear kinetics, such as the homodimerization of GR after cortisol activation [

GR is found in cells throughout the human brain and body. However, GR synthesis and regulation is tissue and organ specific. For example, while corticosterone injection in rats inhibits the synthesis of GR-mRNA in lymphocyte, hypothalamic and hippocampal cells [

We were also able to demonstrate that these simulation results are qualitatively similar to cortisol levels measured in a human subject (Figure

There may be other physiologically plausible mechanisms that produce bi-stability other than the anterior pituitary GR homodimerization mechanism investigated here. The point of this investigation is not to conclusively prove that pituitary GR dimerization is the cause of hypocortisolism, but rather to demonstrate that there are physiologically plausible mechanisms for producing bistability in the HPA-axis that are stress modulated. Further mining of the experimental literature together with mathematical modelling will reveal additional plausible mechanisms.

Moderate, short-lived stress responses that result in transient increases in cortisol are important and necessary for maintaining body homeostasis and health. Strong and prolonged stress can force the HPA axis into an altered steady state. We demonstrate bistability in the HPA axis due to pituitary GR synthesis. This altered steady state, characterized by hypocortisolism, is observed in a number of stress-related illnesses. The elucidation of bistability in this model of the HPA axis through the action of pituitary GR effects may lead to targeted treatments of stress-related illness where hypocortisolism is the primary clinical manifestation.

SG was responsible for programming the differential equation models, producing the mathematics for the meta-analysis on stress response and bistability, and writing of the manuscript. EA and SDV were responsible for the concept, the design of this study and preparation, validation, writing, and critical review of the manuscript. BMG provided assistance on the mathematical analysis and was responsible for critical review and editing of the manuscript.

The findings and conclusions in this report are those of the author(s) and do not necessarily represent the views of the funding agency.

The author(s) declare that they have no competing interests.

The funding for this project was made possible by funding from DARPA MIPR number 05-U357. We would also like to acknowledge the Dr. Leslie Crofford and the University of Michigan (GCRC M01-RR00042 and R01-AR43148) for providing experimental data.