Figure 1.
Schematic of the HPA axis. A) Stress is processed in the central nervous system and a signal is relayed to the PVN in the hypothalamus to activate CRH secretion into the hypophyseal portal system. B) CRH diffuses to the pituitary gland and activates ACTH secretion. ACTH travels down to the adrenal cortex to activate cortisol (CORT) release. Cortisol inhibits both CRH and ACTH secretion to downregulate its own production, forming a closed loop. C) Negative feedback of cortisol suppresses CRH synthesis in the PVN, ultimately reducing the amount of stored CRH and its subsequent release. External inputs, such as stressors and circadian inputs, directly affect the release rate of CRH at the axonal terminal. D) CRH released by the PVN stimulates the protein kinase A (PKA) pathway to activate release of CRH by the anterior pituitary, contributing to ACTH secretion in an auto/paracrine fashion.
Table 1.
Parameters and their effects on nullcline structure
| Parameter | Description | Effects on nullclines (when increased) |
|---|---|---|
| q0 | maximum release rate of CRH in basal state | an upward shift of the upper branch and a leftward shift of both knees of the c-nullcline |
| q1 | circulating CRH for half-maximum self-upregulation | an upward shift of the upper branch and a leftward shift of both knees of the c-nullcline |
| q2 | ratio of CRH and cortisol decay rates | a downward shift of the upper branch and a rightward shift of both knees of the c-nullcline |
| gc,max | maximum auto/paracrine effect of CRH in the pituitary | a rightward shift of the lower and upper knees of the c-nullcline and an upward shift of the upper branch |
| n | Hill coefficient of gc(c) describing the self-upregulation of CRH | a leftward shift of the left knee and a rightward shift of the right knee of the c-nullcline |
| k | relates stored CRH to CRH release rate | a leftward shift of the middle branch of the c-nullcline and an upward shift of the lower branch of the c-nullcline |
| b | relates cortisol to stored CRH level | a leftward shift of the middle branch of the cs-nullcline |
| p2 | (or)-complex level for half-maximum negative feedback | a rightward shift and elongation of the oscillatory regime of the cs-nullcline |
| p3 | ratio of ACTH and cortisol decay rates | a rightward shift and elongation of the oscillatory regime of the cs-nullcline |
| p4 | (or)-complex level for half-maximum positive feedback on r production | elongation of the oscillatory branch of the cs-nullcline |
| p5 | basal GR production rate by pituitary | shortening of the oscillatory branch of the cs-nullcline |
| p6 | ratio of GR and cortisol decay rates | a rightward shift and shortening of the oscillatory branch of the cs-nullcline |
| td | delay in the adrenal cortex in response to ACTH | elongation of the oscillatory branch of the cs-nullcline (Walker, Terry, & Lightman, 2010). |
Figure 2.
Effects of changing parameters on the c-nullcline. One of the nondimensionalized six parameters that affect the c-nullcline is varied over a range of values (from 80% to 120% of the reference values), and the corresponding c-nullclines are plotted. The dashed segment of the nullcline indicates the unstable steady states. Darker curves (in the direction of the arrows) are associated with greater values of the corresponding parameter. When not varied, parameters are set to the reference values q0 = 28.0(I = 1),q1 = 0.04,q2 = 1.8,gc, max = 42,n = 6, and k = 2.83. A) The value of q0 is varied from 22.4 to 33.6. B) The value of q1 is varied from 0.032 to 0.48. C) The value of q2 is varied from 1.44 to 2.16. D) The value of gc,max is varied from 33.6 to 50.4. E) The value of n is varied from 1 to 8. A saddle-node bifurcation occurs between n = 4 and n = 5. F) The value of k is varied from 2.26 to 3.40.
Figure 3.
Effect of changing parameters on cs-nullcline. One of the six parameters that affect the cs-nullcline is varied over a range of values (from 80% to 120% of the reference values), and corresponding cs-nullclines are plotted. The dashed segment of the nullcline indicates the time-averaged value of cs over the limit cycle corresponding to the value of c (Equations 9 and 10). Darker colored curves (in the direction of the arrows) are associated with greater values of the corresponding parameter. When not varied, these parameters are set at the reference values: td = 1.44,b = 0.6,p2 = 15,p3 = 7.2,p4 = 0.05,p5 = 0.11, and p6 = 2.9. A) The value of b is varied from 0.48 to 0.71. B) The value of p2 is varied from 1.5 to 27. C) The value of p3 is varied from 3.6 to 7.92. D) The value of p4 is varied from 0.04 to 0.06. E) The value of p5 is varied from 0.09 to 0.14. F) The value of p6 is varied from 2.3 to 3.8.
Figure 4.
Numerical simulation of DEX challenge test on normal and PTSD subjects. A) Numer ical simulation of cortisol response in a “normal” subject during DEX suppression test. The aver age percentage suppression of cortisol in this scenario is 〈sN〉 = 63%. B) Numerical simulation of cortisol response in a PTSD subject during DEX suppression test. Here the average percentage suppression of cortisol is 〈sD〉 = 73%, significantly greater than that of a normal subject. C) Inter sections of the c-nullcline with pre-DEX (light blue) and post-DEX (blue) cs-nullclines. Normal and PTSD subjects are represented as black circles and red triangles, respectively. D) The values of fa(or) pre- and post-DEX treatment are plotted for normal (black circles) and PTSD states (red triangles).
Figure 5.
Numerical solutions of ACTH stimulation test. A) The oscillating stable state of the system with normal (solid) and hyporeactive (dashed) adrenal gland sensitivity is plotted. The non dimensionalized o is scaled by the same factor (the normal adrenal sensitivity) in both cases for direct comparison. Details of the scaling of the state variables are provided in Kim et al. (2017, Appendix A). The hyporeactive subject with p2 and p4 adjusted to represent lower adrenal sensitivity exhibited slightly higher basal cortisol levels. B) Cortisol response to exogenous ACTH administration is plotted for normal (solid) and for hyporeactive (dashed) adrenal sensitivity. The phase of the oscillation at the time of administration was different in each simulation. C) The peak cortisol levels reached during exogenous ACTH administration are plotted as a function of the phase of the intrinsic oscillations at the time of ACTH administration for normal (solid red) and hyporeactive (dashed red) subjects. The phase and the peaks shown in B are marked in the plot as an example. The maximum peak cortisol level of the hyposensitive subject and the minimum peak cortisol level of the hyporeactive subject are both approximately o = 8.
