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

Modelling of the thyroid hormone synthesis as a part of nonlinear reaction mechanism with feedback

The synthesis of thyroid hormones in the hypothalamic-pituitary-thyroid (HPT) axis was studied. For this purpose, a reaction model for HPT axis with stoichiometric relations between the main reaction species was postulated. Using the law of mass action, this model has been transformed into a set of nonlinear ordinary differential equations. This new model has been examined by stoichiometric network analysis (SNA) with the aim to see if it possesses the ability to reproduce oscillatory ultradian dynamics founded on the internal feedback mechanism. In particular, a feedback regulation of TSH production based on the interplay between TRH, TSH, somatostatin and thyroid hormones was proposed. Besides, the ten times larger amount of produced T₄ with respect to T₃ in the thyroid gland was successfully simulated. The properties of SNA in combination with experimental results, were used to determine the unknown parameters (19 rate constants of particular reaction steps) necessary for numerical investigations. The steady-state concentrations of 15 reactive species were tuned to be consistent with the experimental data. The predictive potential of the proposed model was illustrated on numerical simulations of somatostatin influence on TSH dynamics investigated experimentally by Weeke et al. in 1975. In addition, all programs for SNA analysis were adapted for this kind of a large model. The procedure of calculating rate constants from steady-state reaction rates and very limited available experimental data was developed. For this purpose, a unique numerical method was developed to fine-tune model parameters while preserving the fixed rate ratios and using the magnitude of the experimentally known oscillation period as the only target value. The postulated model was numerically validated by perturbation simulations with somatostatin infusion and the results were compared with experiments available in literature. Finally, as far as we know, this reaction model with 15 variables is the most dimensional one that have been analysed mathematically to obtain instability region and oscillatory dynamic states. Among the existing models of thyroid homeostasis this theory represents a new class that may improve our understanding of basic physiological processes and helps to develop new therapeutic approaches. Additionally, it may pave the way to improved diagnostic methods for pituitary and thyroid disorders.

Influence of arginine vasopressin on the ultradian dynamics of Hypothalamic-Pituitary-Adrenal axis

Numerous studies on humans and animals have indicated that the corticotrophin-releasing hormone (CRH) and arginine vasopressin (AVP) stimulate both individually and synergistically secretion of adrenocorticotropic hormone (ACTH) by corticotropic cells in anterior pituitary. With aim to characterize and better comprehend the mechanisms underlying the effects of AVP on Hypothalamic-Pituitary-Adrenal (HPA) axis ultradian dynamics, AVP is here incorporated into our previously proposed stoichiometric model of HPA axis in humans. This extended nonlinear network reaction model took into account AVP by: reaction steps associated with two separate inflows of AVP into pituitary portal system, that is synthesized and released from hypothalamic parvocellular and magnocellular neuronal populations, as well as summarized reaction steps related to its individual and synergistic action with CRH on corticotropic cells. To explore the properties of extended model and its capacity to emulate the effects of AVP, nonlinear dynamical systems theory and bifurcation analyses based on numerical simulations were utilized to determine the dependence of ultradian oscillations on rate constants of the inflows of CRH and AVP from parvocellular neuronal populations, the conditions under which dynamical transitions occur due to their synergistic action and, moreover, the types of these transitions. The results show that under certain conditions, HPA system could enter into oscillatory dynamic states from stable steady state and vice versa under the influence of synergy reaction rate constant. Transitions between these dynamical states were always through supercritical Andronov-Hopf bifurcation point. Also, results revealed the conditions under which amplitudes of ultradian oscillations could increase several-fold due to CRH and AVP synergistic stimulation of ACTH secretion in accordance with results reported in the literature. Moreover, results showed experimentally observed superiority of CRH as a stimulator of ACTH secretion compared to AVP in humans. The proposed model can be very useful in studies related to the role of AVP and its synergistic action with CRH in life-threatening circumstances such as acute homeostasis dynamic crisis, autoimmune inflammations or severe hypovolemia requiring instant or several-days sustained corticosteroid excess levels. Moreover, the model can be helpful for investigations of indirect AVP-induced HPA activity by exogenously administered AVP used in therapeutic treatment.

The HPA axis and ethanol: a synthesis of mathematical modelling and experimental observations

Stress and alcohol use are interrelated-stress contributes to the initiation and upholding of alcohol use and alcohol use alters the way we perceive and respond to stress. Intricate mechanisms through which ethanol alters the organism's response to stress remain elusive. We have developed a stoichiometric network model to succinctly describe neurochemical transformations underlying the stress response axis and use numerical simulations to model ethanol effects on complex daily changes of blood levels of cholesterol, 6 peptide and 8 steroid hormones. Modelling suggests that ethanol alters the dynamical regulation of hypothalamic-pituitary-adrenal (HPA) axis activity by affecting the amplitude of ultradian oscillations of HPA axis hormones, which defines the threshold with respect to which the response to stress is being set. These effects are complex-low/moderate acute ethanol challenge (<8 mM) may reduce, leave unaltered or increase the amplitude of ultradian cortisol (CORT) oscillations, giving rise to an intricate response at the organism level, offering also a potential explanation as to why apparently discordant results were observed in experimental studies. In contrast, high-dose acute ethanol challenge (>8 mM) increases instantaneous CORT levels and the amplitude of ultradian CORT oscillations in a dose-dependent manner, affecting the HPA axis activity also during the following day(s). Chronic exposure to ethanol qualitatively changes the HPA axis dynamics, whereas ethanol at intoxicating levels shuts down this dynamic regulation mechanism. Mathematical modelling gives a quantitative biology-based framework that can be used for predicting how the integral HPA axis response is perturbed by alcohol.

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

Changes in the hypothalamic-pituitary-adrenal (HPA) axis activity constitute a key component of bipolar mania, but the extent and nature of these alterations are not fully understood. We use here the lateral hypothalamic-kindled (LHK) rat model to deliberately induce an acute manic-like episode and measure serum corticosterone concentrations to assess changes in HPA axis activity. A mathematical model is developed to succinctly describe the entwined biochemical transformations that underlay the HPA axis and emulate by numerical simulations the considerable increase in serum corticosterone concentration induced by LHK. Synergistic combination of the LHK rat model and dynamical systems theory allows us to quantitatively characterize changes in HPA axis activity under controlled induction of acute manic-like states and provides a framework to study in silico how the dynamic integration of neurochemical transformations underlying the HPA axis is disrupted in these states.

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

Living organisms are highly complex systems that must maintain a dynamic equilibrium or homeostasis that requires energy to be sustained. Stress is a state in which several extrinsic or intrinsic disturbing stimuli, the stressors, threaten, or are perceived as threatening, homeostasis. To achieve homeostasis against the stressors, organisms have developed a highly sophisticated system, the stress system, which provides neuroendocrine adaptive responses, to restore homeostasis. These responses must be appropriate in terms of size and/or duration; otherwise, they may sustain life but be associated with detrimental effects on numerous physiologic functions of the organism, leading to a state of disease-causing disturbed homeostasis or cacostasis. In addition to facing a broad spectrum of external and/or internal stressors, organisms are subject to recurring environmental changes associated with the rotation of the planet around itself and its revolution around the sun. To adjust their homeostasis and to synchronize their activities to day/night cycles, organisms have developed an evolutionarily conserved biologic system, the "clock" system, which influences several physiologic functions in a circadian fashion. Accumulating evidence suggests that the stress system is intimately related to the circadian clock system, with dysfunction of the former resulting in dysregulation of the latter and vice versa. In this review, we describe the functional components of the two systems, we discuss their multilevel interactions, and we present how excessive or prolonged activity of the stress system affects the circadian rhythm of glucocorticoid secretion and target tissue effects.