Source: Theoretical Biology and Medical Modelling
        Vol 4, #1, p 8
Date:   February 14, 2007
URL:    http://www.tbiomed.com/content/pdf/1742-4682-4-8.pdf
        http://www.tbiomed.com/content/4/1/8


Inclusion of the glucocorticoid receptor in a hypothalamic pituitary adrenal
axis model reveals bistability
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Shakti Gupta, Eric Aslakson*, Brian M. Gurbaxani, Suzanne D. Vernon 
Division of Viral and Rickettsial Diseases, National Center for Zoonotic,
Vector- Borne, and Enteric Diseases, Centers for Disease Control and
Prevention, 600 Clifton Rd, MS-A15, Atlanta, Georgia USA 30333
* Corresponding author 
Email addresses: Shakti Gupta: shaktig@gmail.com, Eric Aslakson: btl0@cdc.gov,
Brian M. Gurbaxani: buw8@cdc.gov, Suzanne D. Vernon: svernon@cdc.gov 


Abstract 

Background 
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.

Results 
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).

Conclusions 
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.


Background 

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

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 [1,2]. These widespread and
potent effects of cortisol demand that the feed forward and feedback loops
of the HPA axis are tightly regulated. Disruption of HPA axis regulation is
known to contribute to a number of stress-related disorders. For example,
increased cortisol (hypercortisolism) has been shown in patients with major
depressive disorder (MDD) [3, 4], and decreased cortisol (hypocortisolism)
has been observed in people with post-traumatic stress disorder (PTSD), Gulf
War illness, post infection fatigue and chronic fatigue syndrome (CFS)[5-9]. 
While it is not clear if dysregulation of the HPA axis is a primary or
secondary effect of these disorders, there is evidence that stress-related
disorders are influenced by early life adverse experiences that affect the
neural architecture and gene expression in the brain [10]. Childhood events
such as severe infection, malnutrition, physical, sexual and emotional abuse
are associated with many chronic illnesses later in life [11].

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 [12], it is a system that is amenable to modelling. Models of the
HPA axis have been constructed using deterministic coupled ordinary
differential equations [13-17]. These models were successful in capturing
features such as negative feedback control and diurnal cycling of the HPA
axis. Our goal was to understand the dynamic effects of CRH, ACTH and
cortisol with a mathematically parsimonious model to gain insight into HPA
axis regulation. This model is novel in that it incorporates expression of
the glucocorticoid receptor (GR) in the pituitary and demonstrates that
repeated stress and GR expression reveals the bistability inherent in the
HPA axis given the enhanced model.


Model 

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:

dC                      O
--  = (K_c + F ) * (1 - -- ) - K_cd C                    (1)
dT                      K_i1

In this equation, - K_cd C models a constant degradation rate of CRH in the 
blood of the portal vein.  O
The term  (K_c + F) * (1 - -- ) models a circadian production term K_c and a
                           K_i1
stress term  F , both reduced by a linear inhibition term represented by 
     O               O                                   O       K_c + F
(1 - -- ). For small --  , we may write (K_c + F) * (1 - -- ) ~~ -------  .
     K_i1            K_i1                                K_i1    1 + O/K_i1
                 K_c + F
The latter form, -------    corresponds to standard linear inhibition of
                 1 + O/K_i1
(K_+F) with inhibition constant K_i1. This form also guarantees positive 
ACTH concentrations. We write for the hypothalamus: 

dC   K_c + F
-- = ------- - K_cd C                                    (2)
dT   1 + O/K_i1

For the pituitary:

dA   K_a C
-- = -------------- - K_ad A                             (3)
dT   1 + O/K_i2

Equation 3 models a constant degradation rate of ACTH by the term - K_ad A 
and an ACTH production term,  K_a C  , with a cortisol inhibition factor 
similar to (2).               -----
                              1 + O/K_i2
For the adrenal: 

dO
-- = K_o A - K_od O                                      (4)
dT

Equation 4 models a constant degradation rate of cortisol - K_ad O and a 
cortisol production rate K_o A linearly dependent on ACTH. 

We have augmented this model by including synthesis and regulation of the
glucocorticoid receptor (R) in the pituitary [18, 19]. In the pituitary,
cortisol enters the cell and binds the glucocorticoid receptor in the
cytoplasm, causing the receptor to dimerize. This dimerization causes the
complex to translocate to the nucleus (dimerization, translocation, and
transcription factor binding are not modelled, but assumed to be fast),
where it up regulates glucocorticoid receptor (R) synthesis and down
regulates production of ACTH (A).

The following are the differential equations written for the HPA axis model
that includes glucocorticoid receptor synthesis and regulation in the
pituitary (Figure 1).

For the hypothalamus: 

dC   K_c + F
-- = -------   - K_cd C                                  (5)
dT   1 + O/K_i1

For the pituitary: 

dA   K_a C
-- = ------- - K_ad A                                    (6)
dT   1 + OR/K_i2

dR   K_r (OR)^2
-- = ----------- + K_cr - K_rd R                         (7)
dT   K + (OR)^2

For the adrenal:

dO 
-- = K_o A - K_od O                                      (8)
dT

Equation (7) describes the production of GR in the pituitary. The term 
K_r (OR)^2
---------- in equation 7 is in Michaelis-Menten form since we assume the
K + (OR)^2

bound glucocorticoid receptor (OR) dimerizes with fast kinetics, so that the
amount of dimer is in constant quasi-equilibrium, depending on the abundance
of OR and the equilibrium binding affinity (K). The model further assumes
that cortisol (O) and the glucocorticoid receptor (R) bind to each other
with very fast kinetics compared to the rate of change of the 4 state
variables (A, C, O, and R), so that OR stays in quasi- equilibrium as well. 
These are reasonable assumptions, given that high affinity receptor-ligand
kinetics are often much faster than enzyme kinetics (as is assumed in the
standard Michaelis-Menten equation) or than steps requiring transcription
and/or translation for protein synthesis. Equation (7) also models a linear
production term K_cr and a degradation term - K_rd R for pituitary GR
production. Equation (6) reflects the inhibition dependence of
glucocorticoid receptor (R) and cortisol (O) with an inhibition constant
K_i2.

Scaling of the equations (5)-(8) has been done to reduce the parameters used 
in simulations. The scaled variables are defined as; 
                 K_od C        K^2_od A       K^3_od O
t = K_od T , c = ------- , a = -------- , o = -----------
                 K_c           K_c K_a        K_c K_a K_o

    K_od R          K_cd          K_ad           K_rd
r = ------ , k_cd = ---- , k_ad = ----  , k_rd = ----
    K_r             K_c           K_od           K_ad

The scaled equations thereby obtained are; 

dc    1 + f
-- = -----   - k_cd c                                    (9)
dt   1 + o/ki1

da      c
-- = ------- - k_ad a                                    (10)
dt   1 + or/ki2

dr    (or)^2
-- = ---------- + k_cr - k_rd r                          (11)
dt   k + (or)^2

do
-- = a - o                                               (12)
dt

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, k_cd=1, k_ad=10, k_rd=0.9, k_cr=0.05, k=0.001,
k_i1=0.1 and k_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
serum cortisol data [9].


Results 

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 2, equation 4 predicts a fit
that is very similar to the actual cortisol production in this healthy human
subject. Experimental fitting of ACTH is not possible since hypothalamic
derived CRH cannot be measured.


Steady States 

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 3 shows the variation of
GR and cortisol steady state with respect to parameter k_rd. Variations in
k_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 k_rd, there
exists only a low GR concentration steady state. As the value of k_rd
decreases, these equations produce two more steady states, one stable and
another unstable in GR concentration. As k_rd decreases further, a low GR
concentration state disappears and only a high GR concentration state exists
(Figure 3a). In this model, we postulate that the low GR concentration
represents the normal steady state, and high GR concentration denotes a
dysregulated HPA axis steady state as it results in persistent low cortisol
levels (hypocortisolism) (Figure 3b). Hypocortisolism results from the
negative feedback between GR (i.e. the symbol "R" in Figure 1) and ACTH
(A), and hence cortisol (O) produced downstream of it, as shown in Figure 1
and reflected by the inverse relationship between cortisol and GR in Figure
3. Thus individuals with very large values of k_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 k_rd would be
constitutively unhealthy.


Normal stress response 

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 4 shows a simulation of the response of the HPA axis to a short
stress. The initial condition of the HPA axis was set to a normal steady
state and at T=0, a stress was given for 0<T<1. The HPA axis responded to
this disturbance by secreting CRH. The synthesis of CRH induced the
synthesis of ACTH and cortisol (Figures 4a and 4b). The synthesis of CRH
stopped once the stress ended, and the concentration of CRH quickly
decreased due to CRH degradation (Figure 4c). CRH returned to steady state
meanwhile stimulating the release of ACTH that also peaked shortly after the
short stress ended (Figure 4b). Synthesis of cortisol followed the peak
ACTH secretion (Figure 4a). The concentration of GR was only slightly
elevated following the short stress and then returned to baseline (Figure
4d).


Adaptation of HPA axis 

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 5a and b) while CRH is
relatively unaffected (Figure 5c). The decrease in secretion of ACTH and
cortisol occurred because of an increase in pituitary GR concentration and
the fact that the system was pulsed with the stresses before it had time to
fully recover (Figure 5d).


Chronic stress response 

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 6). The HPA axis
secreted cortisol in response to stress. The increased concentration of
cortisol induced the synthesis of GR and the inhibition of pituitary ACTH. 
When stress was applied for long periods, GR synthesis continued and crossed
the threshold middle unstable steady state of GR (Figure 3a). At this
point, the HPA axis reached the basin of attraction of the second stable
steady state and remained there even after the removal of stress. The higher
concentration of GR triggered further pituitary ACTH inhibition, resulting
in a lower basal level ACTH and cortisol production (Figures 6a and b).


HPA axis challenge 

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 7a and b). To simulate the CRH test, e.g., one that
requires exogenous CRH administration, CRH concentration was increased by a
constant amount. This resulted in increased pituitary and adrenal gland
synthesis of ACTH and cortisol respectively. The high concentration of
pituitary GR in the patient group blunted both responses compared to the
control (Figures 8a and b). Both Figures 7 and 8 demonstrate that the
model behaves in a qualitatively similar fashion to observed experimental
results.


Discussion 

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 [18, 19]. This is
essential for the negative feedback control of the HPA axis. This
homodimerization engenders the existence of two stable steady states and one
unstable steady state in GR expression in the pituitary. While increased
cortisol following a short period of stress produces a small perturbation in
GR concentration, long and repeated periods of stress resulting in elevated
cortisol levels produce a large perturbation in GR concentration that force
the HPA axis into an alternate steady state. Because of the existence of
two stable steady states in this model, a small increase GR concentration
can be regulated, but a large perturbation in GR concentration is sustained
even after the removal of the long duration stress. A higher concentration
of GR increases the concentration of cortisol-GR complexes that in turn
enhance the inhibition of ACTH synthesis in the pituitary. Since ACTH
stimulates the production of cortisol, less ACTH results in lower cortisol
secretion and a decrease HPA axis activity.

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 [20, 21], it induces the
synthesis of GR-mRNA and increases the sensitivity in the anterior pituitary
[22, 23]. Our model incorporates the increased synthesis of GR in the
anterior pituitary. Increased GR makes anterior pituitary cells more
sensitive to cortisol and enhances the negative feedback effect of cortisol
on ACTH production. Enhanced negative feedback control of ACTH production
in the anterior pituitary may produce a hypocortisol state.

We were also able to demonstrate that these simulation results are
qualitatively similar to cortisol levels measured in a human subject (Figure
2). A large number of studies have investigated alterations of the HPA axis
in CFS, including both studies of basal HPA axis activity as well as studies
of HPA axis responsiveness to challenge (for review see [24]). A
hypocortisol steady state, such as was demonstrated in this modelling and
simulation study, is in keeping with many of these studies

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.


Conclusions 

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.


Authors' contributions 

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.


Acknowledgements 

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.


Disclaimer 

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

Declaration of competing interests 

The authors declare that they have no competing interests. 


Figure captions

Figure 1 
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. The left panel shows the existing model, the right panel shows
the additional added pituitary sub compartment in the new model.

Figure 2
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.

Figure 3
Variations of steady state (a) GR and (b) cortisol with k_rd. Solid and
dashed lines denote the stable and unstable steady states, respectively. 
If k_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.

Figure 4 
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.

Figure 5
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.

Figure 6
Transient responses of HPA axis to chronic stress. Extended length stress
was given for 0<T<10. Stress is indicated with shading.

Figure 7
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.

Figure 8
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.


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