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.

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The possibility to target noncanonical guanine structures with specific ligands for therapeutic purposes inspired numerous theoretical and experimental investigations of a guanine quartet and its stacked composites. In this work, we employed the interacting quantum atoms methodology to study interactions among different fragments in complexes composed of a guanine quartet and alkali (Li+, Na+, K+) or alkaline earth (Be2+, Mg2+, Ca2+) cations in vacuo: metal–quartet interaction, influence of the cation on guanine–guanine interaction, as well as hydrogen bond cooperativity in the guanine quartet and its complexes with metal ions. Interestingly, although the presence of a cation intensifies interaction among guanine molecules, it lowers their binding energy because of notable quartet’s distortion which is responsible for guanines’ substantial deformation energy. This phenomenon is particularly pronounced with Be2+ which, out of the six analyzed cations, enhances hydrogen bond cooperativity to the greatest extent.

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 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.