Dynamic transitions in a model of the hypothalamic-pituitary-adrenal axis

Abstract

Dynamic properties of a nonlinear five-dimensional stoichiometric model of the hypothalamic-pituitary-adrenal (HPA) axis were systematically investigated. Conditions under which qualitative transitions between dynamic states occur are determined by independently varying the rate constants of all reactions that constitute the model. Bifurcation types were further characterized using continuation algorithms and scale factor methods. Regions of bistability and transitions through supercritical Andronov-Hopf and saddle loop bifurcations were identified. Dynamic state analysis predicts that the HPA axis operates under basal (healthy) physiological conditions close to an Andronov-Hopf bifurcation. Dynamic properties of the stress-control axis have not been characterized experimentally, but modelling suggests that the proximity to a supercritical Andronov-Hopf bifurcation can give the HPA axis both, flexibility to respond to external stimuli and adjust to new conditions and stability, i.e., the capacity to return to the original dynamic state afterwards, which is essential for maintaining homeostasis. The analysis presented here reflects the properties of a low-dimensional model that succinctly describes neurochemical transformations underlying the HPA axis. However, the model accounts correctly for a number of experimentally observed properties of the stress-response axis. We therefore regard that the presented analysis is meaningful, showing how in silico investigations can be used to guide the experimentalists in understanding how the HPA axis activity changes under chronic disease and/or specific pharmacological manipulations.

Stress-Related and Circadian Secretion and Target Tissue Actions of Glucocorticoids: Impact on Health

“…Importantly, in parallel with the tremendous progress of molecular, cellular, and structural biology, significant advances in the field of mathematical and computer biosciences will undoubtedly help us have a deeper understanding of system interrelations. Interestingly, accumulating evidence suggests that stress-related “static” signaling pathways can be effectively transformed into functionally predictive computerized kinetic models (126–129). Such efforts will be useful for accurate predictions of a system response to acute or chronic stress, as well as to pharmacotherapy with novel medications.…”

Corticosterone oscillations during mania induction in the lateral hypothalamic kindled rat—Experimental observations and mathematical modeling

“…We have recently developed a five-dimensional reaction model of human HPA axis, with concentrations of corticotrophin releasing hormone ([CRH]), adrenocorticotrophic hormone ([ACTH]), cortisol ([CORT]), aldosterone ([ALDO]) and cholesterol ([CHOL]) as dynamic variables [69,70]. This core model was systematically fine-tuned by Stoichiometric Network Analysis (SNA), a general flux balance analysis method for optimization of reaction networks and determination of instability regions [72–75].…”

Advances made by Belgrade's group in research of oscillatory reactions

“…Details of the reaction mechanism were studied in the model of the BZ reaction (Fig. 1B) and complex oscillations were also discovered there (Blagojević et al 2011;Blagojević et al 2013 and Much of our work in the last decade was dedicated to the investigation of the HPA axis, and influences of several perturbing substances on its dynamics (Marković et al 2011b;Marković et al 2016;Čupić et al 2016b;Čupić et al in press). Due to inherent ultradian oscillations, our model of the HPA axis has a phase sensitive response on perturbations.…”

“…Furthermore, various methods were developed for formal kinetics of homogenous oscillatory process (Anić et al 1986a;Anić et al 1987;Anić et al 1988;Anić et al 1996;Anić et al 2007), as well as for the stability analysis of the postulated models (Kolar- Anić et al 1995b;Schmitz et al 2000). All investigations were used for different purposes, starting with the development of new analytical methods Pejić et al 2003;Pejić et al 2005;Pejić et al 2006;Pejić et al 2007a;Pejić et al 2007b;Pejić et al 2007c;Pejić et al 2009;Pejić et al 2011;Pejić et al 2012;Pejić et al 2013;Pejić et al 2014a;Pejić et al 2014b;Pejić et al 2016;Vukojević et al 1999;Vukojević et al 2001) and the methods for determining the catalyst's activity Terlecki-Baričević et al 1995;Pejić et al 2001;Anić et al 2009;Maksimović et al 2011), as well as the influence of external fields on the evolution of the chemical oscillator (Stanisavljev et al 2004;Stanisavljev et al 2005;Stanisavljev et al 2006;Stanisavljev et al 2014) to modelling of biochemical processes (Jelić et al 2008;Jelić et al 2009;Čupić et al 2016b;Čupić et al in press;Kolar-Anić 2017d;Marković at. al 2011a;Čupić et al in press;Marković et al 2011b;…”

“…It depends very much on the system under consideration. For this purpose, theory of the Stoichiometric Network Analysis was improved and used for identification of the instability regions in several models of the oscillatory reactions (Jelić et al 2008;Schmitz et al 2008;Jelić et al 2009;Kolar-Anić et al 2010;Čupić et al 2011;Marković et al 2011a;Maćešić et al 2012;Maćešić et al 2015a;Maćešić et al 2015b;Maćešić et al 2016;Čupić et al 2016b;Čupić et al 2016c). Here, as in the case of formal kinetics, the main steps in modelling procedure were developed on the BL reaction and then applied to the other systems.…”