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.

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.

Intermittent Chaos in the CSTR Bray-Liebhafsky Oscillator-Specific Flow Rate Dependence.

Dynamic states with intermittent oscillations consist of a chaotic mixture of large amplitude relaxation oscillations grouped in bursts, and between them, small-amplitude sinusoidal oscillations, or even the quiescent parts, known as gaps. In this study, intermittent dynamic states were generated in Bray-Liebhafsky (BL) oscillatory reaction in an isothermal continuously-fed, well-stirred tank reactor (CSTR) controled by changes of specific flow rate. The intermittent states were found between two regular periodic states and obtained for specific flow rate values from 0.

Stoichiometric network analysis of a reaction system with conservation constraints.

Stoichiometric Network Analysis (SNA) is a powerful method that can be used to examine instabilities in modelling a broad range of reaction systems without knowing the explicit values of reaction rate constants. Due to a lack of understanding, SNA is rarely used and its full potential is not yet fulfilled. Using the oscillatory carbonylation of a polymeric substrate [poly(ethylene glycol)methyl ether acetylene] as a case study, in this work, we consider two mathematical methods for the application of SNA to the reaction models when conservation constraints between species have an important role.

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.

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.

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

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.

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.

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

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.

Stoichiometric network analysis and associated dimensionless kinetic equations. Application to a model of the Bray-Liebhafsky reaction.

The stoichiometric network analysis (SNA) introduced by B. L. Clarke is applied to a simplified model of the complex oscillating Bray-Liebhafsky reaction under batch conditions, which was not examined by this method earlier.

Malonic acid concentration as a control parameter in the kinetic analysis of the Belousov-Zhabotinsky reaction under batch conditions.

The influence of the initial malonic acid concentration [MA]0 (8.00 x 10(-3) < or = [MA]0 < or = 4.30 x 10(-2) mol dm(-3)) in the presence of bromate (6.

Determination of ascorbic acid in pharmaceutical dosage forms and urine by means of an oscillatory reaction system using the pulse perturbation technique.

A simple and reliable method for the determination of ascorbic acid (AA) is proposed and validated. It is based on potentiometric monitoring of the concentration perturbations of an oscillatory reaction system in a stable nonequilibrium stationary state close to the bifurcation point. The response of the Bray-Liebhafsky (BL) oscillatory reaction as a matrix, to the perturbation by different concentrations of AA, is followed by a Pt electrode.

Kinetic determination of morphine by means of Bray-Liebhafsky oscillatory reaction system using analyte pulse perturbation technique.

A novel kinetic method for micro-quantitative determinations of morphine (MH) is proposed and validated. The method is based on the potentiometric monitoring of the concentration perturbations of the oscillatory reaction system being in a stable non-equilibrium stationary state close to the bifurcation point between stable and oscillatory state. The response of the Bray-Liebhafsky (BL) oscillatory reaction as a matrix system, to the perturbations by different concentrations of morphine, is followed by a Pt-electrode.

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.

Determination of paracetamol in pure and pharmaceutical dosage forms by pulse perturbation technique.

A new procedure for kinetic determination of paracetamol in pharmaceuticals is proposed. The method is based on potentiometric monitoring of the concentration perturbations of the matrix reaction system being in a stable non-equilibrium stationary state close to the bifurcation point. In the case considered as the matrix system, the Bray-Liebhafsky oscillatory reaction is used.

Numerically simulated pH-induced reactivation of catalytic activity of horseradish peroxidase.

A model mechanism that accounts for the experimentally observed pH-dependent enhancement of enzymatic activity of horseradish peroxidase through the catalase-like pathway is proposed. Predictions of the model are tested against a number of experimental results to confirm that kinetic constants used in the numerical simulation are correctly chosen and that the model can be used to emulate the reaction between horseradish peroxidase and hydrogen peroxide in a wide range of conditions.

Mathematical modeling of the hypothalamic-pituitary-adrenal system activity.

Mathematical modeling has proven to be valuable in understanding of the complex biological systems dynamics. In the present report we have developed an initial model of the hypothalamic-pituitary-adrenal system self-regulatory activity. A four-dimensional non-linear differential equation model of the hormone secretion was formulated and used to analyze plasma cortisol levels in humans.

Microquantitative determination of hesperidin by pulse perturbation of the oscillatory reaction system.

A simple and reliable kinetic method for the determination of hesperidin (Hesp) is developed. It is based on potentiometric monitoring of the concentration perturbations of the matrix reaction system which is in a stable non-equilibrium stationary state close to the bifurcation point. The Bray-Liebhafsky oscillatory reaction is used as the matrix system.