Modelling cholesterol effects on the dynamics of the hypothalamic-pituitary-adrenal (HPA) axis

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

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

Dynamic properties of a nonlinear five-dimensional stoichiometric model of the hypothalamicpituitary-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

Predictive Modeling of the Hypothalamic-Pituitary-Adrenal (HPA) Function. Dynamic Systems Theory Approach by Stoichiometric Network Analysis and Quenching Small Amplitude Oscillations

Two methods for dynamic systems analysis, Stoichiometric Network Analysis (SNA) and Quenching of Small Amplitude Oscillations (QA), are used to study the behaviour of a vital biological system. Both methods use geometric approaches for the study of complex reaction systems. In SNA, methods based on convex polytopes geometry are applied for stability analysis and optimization of reaction networks. QA relies on a geometric representation of the concentration phase space, introduces the concept of manifolds and the singular perturbation theory to study the dynamics of complex processes. The analyzed system, the Hypothalamic-Pituitary-Adrenal (HPA) axis, as a major constituent of the neuroendocrine system has a critical role in integrating biological responses in basal conditions and during stress. Self-regulation in the HPA system was modeled through a positive and negative feedback effect of cortisol. A systematically reduced low-dimensional model of HPA activity in humans was fine-tuned by SNA, until quantitative agreement with experimental findings was achieved. By QA, we revealed an important dynamic regulatory mechanism that is a natural consequence of the intrinsic rhythmicity of the considered system

Predictive modeling of the hypothalamic-pituitary-adrenal (HPA) axis response to acute and chronic stress

Detailed dynamics of the hypothalamic-pituitary-adrenal (I-IPA) 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 four-dimensional 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

Advances in mathematical modelling of the hypothalamic-pituitary-adrenal (HPA) axis dynamics and the neuroendocrine response to stress

Stress is a physiological reaction of an organism to a demand for change that is imposed by external factors or is coming from within by way of physiological strains or self-perceived mental and/or emotional threats (internal factors). It manifests itself through the sudden release of a flood of hormones, including corticosteroids, into the blood, which rouse the body for action. Normally, stress is beneficial, but when lasting or being very strong, it causes major damage to our mind and body. Despite intense research, we still do not understand fully how the stress response axis, whose main function is to respond to challenges while maintaining the normal physiological balance, loses under prolonged exposure to stressors its capacity to maintain homeostasis. Recent applications of mathematical modelling and dynamical systems theory have enabled us to emulate complex neurochemical transformations that underlie the stress response, and help us to acquire deeper understanding of this dynamical regulatory network

Simulation of Complex Oscillations Based on a Model of the Bray-Liebhafsky reaction

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Complex and Chaotic Oscillations in a Model for the Catalytic Hydrogen Peroxide Decomposition under Open Reactor Conditions

Numerous periodic and aperiodic dynamic states obtained in a model for hydrogen peroxide decomposition in the presence of iodate and hydrogen ions (the Bray-Liebhafsky reaction) realized in an open reactor (CSTR) where the flow rate was the control parameter, have been investigated numerically. Between two Hopf bifurcation points, different simple and complex oscillations and different routes to chaos were observed. In the region of the mixed-mode evolution of the system, the transitions between two successive mixed-mode simple states are realized by period doubling of the initial state leading to a chaotic window in which the next dynamic state emerges mixed with the initial one. It appears in increasing proportions in concatenated patterns until total domination. Thus, with increasing the flow rate the period-doubling route to chaos, whereas with decreasing the flow rate, the peak-adding route to chaos was obtained. Moreover, in very narrow regions of flow rates, chaotic mixtures of mixed-mode patterns were observed. This evolution of patterns repeats until the end of the mixed-mode region at high flow rates that corresponds to chaotic mixtures of one large and many small amplitude oscillations. Starting from the reverse Hopf bifurcation point and decreasing the flow rate, simple small amplitude sinusoidal oscillations were encountered and then the period doubling route to chaos. With further decreasing flow rate, the mixed mode oscillations emerge inside the chaotic window.info:eu-repo/semantics/publishe

Determination of quercetin in pharmaceutical formations via its reaction with potassium titanyloxalate. Determination of the stability constants of the quercetin titanyloxalato complex

Asimple, rapid and accurate procedure for the quantitative determination of quercetin in its pure form and in formulations has been developed. The method is based on the spectrophotometric determination of a complex formed between quercetin and potassium titanyloxalate in 50 % ethanolic solutions. To characterize the quercetin titanyloxalato complex, the stability constants of the complex were determinated potentiometrically and spectrophotometrically at different temperatures (T = 26.0 oC, 34 oC and 39.0 oC), as well as at different ionic strengths (I = 5.0Ã10-4 mol dm-3, 3.0Ã10-2 mol dm-3 and 6.0Ã10-2 mol dm-3) and the thermodynamic parameters were calculated. As quercetin is usually conjugated to vitamin C in pharmaceutical formulations, two procedures for the quantitative determination of quercetin by this complexing reaction were tested both in the absence and presence of ascorbic acid. In both procedures, the Beer law was obeyed over the same concentration range of quercetin, i.e., 0.85 mg mL-1Ã16.9 mg mL-1. In the first procedure in the absence of ascobic acid the molar absorptivity coefficient of the quercetin-titanyloxalate complex is a = 2.49Ã104 mol-1 dm3 cm-1, Sandells sensitivity of the method is S = 1.35Ã10-2 mg cm-2 and the detection limit is d = 0.67 mg mL-1. Whereas, in the presence of ascorbic acid (second procedure) a = 3.04Ã104 mol-1 dm3 cm-1, S = 1.11Ã10-2 ug mL-1. The proposed method was verified for the determination of quercetin in pharmaceutical dosage forms