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OSCILLATORY dynamics appears to be essential for self-organization and self-regulation in living systems. Oscillations with different periodicity, from millisecond to annual range, are implemented at all levels of organization of living organisms, from the molecular to the biosphere level, occurring in processes as diverse as gene transcription in the cell nuclei to seasonal migrations of species between ecosystems [1, 2]. The hypothalamic-pituitary-adrenal (HPA) axis, a neuroendocrine system involved in maintaining homeostasis in mammalian organisms under physiological conditions and stress [3][4][5], is no exception to that rule. Cortisol, the HPA axis principal hormone in humans, exhibits complex dynamic behavior with two char- Abstract. Detailed dynamics of the hypothalamic-pituitary-adrenal (HPA) axis is complex, depending on the individual metabolic load of an organism, its current status (healthy/ill, circadian phase (day/night), ultradian phase) and environmental impact. Therefore, it is difficult to compare the HPA axis activity between different individuals or draw unequivocal conclusions about the overall status of the HPA axis in an individual using single time-point measurements of cortisol levels. The aim of this study is to identify parameters that enable us to compare different dynamic states of the HPA axis and use them to investigate self-regulation mechanisms in the HPA axis under acute and chronic stress. In this regard, a fourdimensional stoichiometric model of the HPA axis was used. Acute stress was modeled by inducing an abrupt change in cortisol level during the course of numerical integration, whereas chronic stress was modeled by changing the mean stationary state concentrations of CRH. Effects of acute stress intensity, duration and time of onset with respect to the ultradian amplitude, ultradian phase and the circadian phase of the perturbed oscillation were studied in detail. Bifurcation analysis was used to predict the response of the HPA axis to chronic stress. Model predictions were compared with experimental findings reported in the literature and relevance for pharmacotherapy with glucocorticoids was discussed.Key words: HPA axis, Stress, Cortisol, Predictive modeling, Circadian and ultradian rhythmicity acteristic frequencies: ultradian oscillations, with a period of 20-120 min [4-6] superimposed on circadian oscillations, with a period of about 24 h. The importance of circadian rhythms for adequate functioning of the HPA axis has been recognized for years [7, 8]; in addition, new experimental [9-15] and theoretical [16][17][18][19][20][21][22][23][24][25][26][27] results offer enough evidence to support the indispensable roles of ultradian oscillatory dynamics of HPA hormones levels for normal physiology. Since ultradian and circadian oscillations operate on different time scales, their effects are manifested in different biological realms. However, being coupled they seem to contribute synergistically to better integration and adaptation of an organism to the unpredictable ...

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A mathematical model of the hypothalamic-pituitary-adrenal (HPA) axis with cholesterol as a dynamical variable was derived to investigate the effects of cholesterol, the primary precursor of all steroid hormones, on the ultradian and circadian HPA axis activity. To develop the model, the parameter space was systematically examined by stoichiometric network analysis to identify conditions for ultradian oscillations, determine conditions under which dynamic transitions, i.e. bifurcations occur and identify bifurcation types. The bifurcations were further characterized using numerical simulations. Model predictions agree well with empirical findings reported in the literature, indicating that cholesterol levels may critically affect the global dynamics of the HPA axis. The proposed model provides a base for better understanding of experimental observations, it may be used as a tool for designing experiments and offers useful insights into the characteristics of basic dynamic regulatory mechanisms that, when impaired, may lead to the development of some modern-lifestyle-associated diseases.