Modeling cortisol dynamics in the neuro-endocrine axis distinguishes normal, depression, and post-traumatic stress disorder (PTSD) in humans
Open accessAbstract
Cortisol, secreted in the adrenal cortex in response to stress, is an informative biomarker that distinguishes anxiety disorders such as major depression and post-traumatic stress disorder (PTSD) from normal subjects. Yehuda et al. proposed a hypothesis that, in humans, the hypersensitive hypothalamus-pituitary-adrenal (HPA) axis is responsible for the occurrence of differing levels of cortisol in anxiety disorders. Specifically, PTSD subjects have lower cortisol levels during the late subjective night in comparison to normal subjects, and this was assumed to occur due to strong negative feedback loops in the HPA axis. In the present work, to address this hypothesis, we modeled the cortisol dynamics using nonlinear ordinary differential equations and estimated the kinetic parameters of the model to fit the experimental data of three categories, namely, normal, depressed, and PTSD human subjects. We concatenated the subjects (n = 3) in each category and created a model subject (n = 1) without considering the patient-to-patient variability in each case. The parameters of the model for the three categories were simultaneously obtained through global optimization. Bifurcation analysis carried out with the optimized parameters exhibited two supercritical Hopf points and, for the choice of parameters, the oscillations were found to be circadian in nature. The fitted kinetic parameters indicate that PTSD subjects have a strong negative feedback loop and, as a result, the predicted oscillating cortisol levels are extremely low at the nadir in contrast to normal subjects, albeit within the endocrinologic range. We also simulated the phenotypes for each of the categories and, as observed in the clinical data of PTSD patients, the simulated cortisol levels are consistently low at the nadir, and correspondingly the negative feedback was found to be extremely strong. These results from the model support the hypothesis that high stress intensity and strong negative feedback loop may cause hypersensitive neuro-endocrine axis that results in hypocortisolemia in PTSD.
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The models by (24), (27), and (25) had MAPE results close to 90% for cortisol.
“In this case, the models by (24), (27), and (25) underestimated cortisol significantly, thus leading to MAPE results close to 90% which represent an order of magnitude difference between simulations and data.”
From Modeling the hypothalamus-pituitary-adrenal axis: A review and extension (2015) · cites this paper as [25]
In Results > Parameter estimation (page unavailable), the paper reports good agreement between its predicted and experimental cortisol time series for all three groups, rather than substantial underestimation. It does not report MAPE near 90% or an order-of-magnitude difference between simulations and data. (LLM, conf=0.84)
Checked by a reasoning model — may be wrong.
Experimental — accuracy not yet measuredPrevious HPA axis models offer conflicting results on the possibility of getting ultradian and/or circadian oscillations from the structure of the HPA axis itself.
“Previous models have included different structures, rest on a variety of assumptions, and offer conflicting results on the possibility of getting ultradian and/or circadian oscillations from the structure of the HPA axis itself (24–27).”
From Modeling the hypothalamus-pituitary-adrenal axis: A review and extension (2015) · cites this paper as [25]
Five models from the literature met the criteria for replication.
“Five models from the literature fit these criteria (24–27, 30).”
From Modeling the hypothalamus-pituitary-adrenal axis: A review and extension (2015) · cites this paper as [25]
The five replicated models were all deterministic ordinary differential equation models that captured the interactions in the HPA axis and their evolution through time.
“They were all deterministic ordinary differential equation models that captured the interactions in the HPA axis and their evolution through time.”
From Modeling the hypothalamus-pituitary-adrenal axis: A review and extension (2015) · cites this paper as [25]
The models by (24), (27), and (25) underestimated cortisol significantly.
“In this case, the models by (24), (27), and (25) underestimated cortisol significantly, thus leading to MAPE results close to 90% which represent an order of magnitude difference between simulations and data.”
From Modeling the hypothalamus-pituitary-adrenal axis: A review and extension (2015) · cites this paper as [25]
In model (25), dropping the nonlinear elimination terms did not eliminate the circadian oscillation.
“However, dropping those terms in the model did not eliminate the oscillation.”
From Modeling the hypothalamus-pituitary-adrenal axis: A review and extension (2015) · cites this paper as [25]
The Materials and Methods section describes nonlinear Michaelis–Menten elimination in the model, and the Discussion links that kinetics to intrinsic oscillations. Neither section reports what happens when the elimination terms are dropped; searches for their removal and for oscillations without enzymatic degradation found no such test in our copy. Page numbers were not available. (LLM, conf=0.72)
Experimental — accuracy not yet measuredThe high Um values in the models of (25) and (26) indicate that the error is mostly due to bias.
“The high Um values in the models of (25) and (26) indicate that the error is mostly due to bias.”
From Modeling the hypothalamus-pituitary-adrenal axis: A review and extension (2015) · cites this paper as [25]
The Results > Parameter estimation passage describes a weighted least-squares measure of differences between observed and predicted cortisol, but does not discuss Um or attribute model error to bias. Searches for “high Um values,” “bias proportion,” and models (25) and (26) found no passage addressing the claim; page numbers were not available in our copy. (LLM, conf=0.74)
Experimental — accuracy not yet measured
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- Authors
- Sriram, K., Rodriguez-Fernandez, M., & Doyle, F. J.
- Affiliations
- University of California, Santa Barbara (US)
- Corresponding author
- Doyle, Francis J.
- Venue
- PLoS Computational Biology
- Publisher
- Public Library of Science (PLoS)
- Published
- 2012-02-16
- Volume
- 8
- Issue
- 2
- Pages
- e1002379
- ISSN
- 1553-734X (ISSN-L)
- 1553-7358
- PMC
- PMC3280965
- OpenAlex
- W2068945449
- Cited by
- 134
- References
- 62
- Citations by year
- 2026: 6 · 2025: 4 · 2024: 7 · 2023: 6 · 2022: 7 · 2021: 12 · 2020: 10 · 2019: 8 · 2018: 11 · 2017: 13 · 2016: 10 · 2015: 13 · 2014: 15 · 2013: 6 · 2012: 6
- FWCI
- 5.31
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- PLoS Computational Biology (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Figshare (submittedVersion, cc-by)
- Funders
- Army Research Office (#W911NF-09-D-0001, W911NF-10-2- 0111, W911NF)
- Institute for Collaborative Biotechnologies (W911NF‐09‐D‐0001)
- Topics
- Life Sciences › Neuroscience › Behavioral Neuroscience › Stress Responses and Cortisol
- Health Sciences › Medicine › Endocrinology, Diabetes and Metabolism › Adrenal Hormones and Disorders
- Social Sciences › Psychology › Clinical Psychology › Posttraumatic Stress Disorder Research
- Keywords
- hypothalamic-pituitary-adrenal axis, post-traumatic stress disorder, major depressive disorder, adrenal insufficiency, negative feedback loop, nonlinear ordinary differential equations, kinetic parameter estimation, bifurcation analysis, Hopf bifurcation, stress response
- MeSH terms
- Depression, Endocrine System, Humans, Hydrocortisone, Kinetics, Models, Biological, Neurosecretory Systems, Phenotype, Stress Disorders, Post-Traumatic, Stress, Psychological, Models, Statistical, Biomarkers, Comorbidity, Computational Biology
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