Ljiljana Kolar-Anić

Mechanism of the Bray–Liebhafsky reaction: effect of the oxidation of iodous acid by hydrogen peroxide

The mechanism of the Bray–Liebhafsky oscillatory reaction is considered. The additional reaction of oxidation of the iodine in HIO2 by hydrogen peroxide is added to the main subset common to all the variants of the previously postulated model for the overall process. A stability analysis of the proposed mechanism has been carried out. A better accordance between the theoretical model and experimental observations is obtained. In particular, the clear iodide maximum at the beginning of reaction followed by the period of smooth catalysis of hydrogen peroxide decomposition prior to the commencement of oscillations, which are the well-known experimental features taking place at sufficiently large acidities and hydrogen peroxide concentrations, are simulated numerically.

PSEUDO-STEADY STATES IN THE MODEL OF THE BRAY-LIEBHAFSKY OSCILLATORY REACTION

The main pseudo-steady states in the process of catalytic hydrogen peroxide decomposition are analysed. The dominant steady states during the monotonic and oscillatory evolution, well known experimentally, are defined by stoichiometric network analysis of the model for this process. The trajectories for the evolution of the system in the phase space in the vicinity of the unstable pseudo-steady state where oscillatory behaviour is obtained, are also calculated. The adjustment of the phase trajectory to the corresponding oscillation is proposed as an additional criterion for the selection of the kinetic parameters necessary for numerical simulation. The calculation procedure is general, independent of the model under consideration.

Kinetic aspects of the Bray–Liebhafsky oscillatory reaction

The decomposition of hydrogen peroxide in the presence of potassium iodate and sulphuric acid (the Bray–Liebhafsky oscillatory reaction) at constant temperature is elucidated. The forms of the time evolution of this process and some kinetic parameters are presented as a function of the concentrations of the reactants.

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. This powerful method for the analysis of steady-states stability is also used to transform the classical differential equations into dimensionless equations. This transformation is easy and leads to a form of the equations combining the advantages of classical dimensionless equations with the advantages of the SNA. The used dimensionless parameters have orders of magnitude given by the experimental information about concentrations and currents. This simplifies greatly the study of the slow manifold and shows which parameters are essential for controlling its shape and consequently have an important influence on the trajectories. The effectiveness of these equations is illustrated on two examples: the study of the bifurcations points and a simple sensitivity analysis, different from the classical one, more based on the chemistry of the studied system.

Determination of Cl–, Br–, I–, Mn2+, malonic acid and quercetin by perturbation of a non-equilibrium stationary state in the Bray–Liebhafsky reaction

A new method applying a non-linear chemical system under conditions far from thermodynamic equilibrium in microvolume/microconcentration quantitative analysis is described. The chemical system used as a matrix is the Bray–Liebhafsky reaction in a non-equilibrium stationary state close to a bifurcation point. The method is based on monitoring the response of this system to perturbations by Cl–, Br–, I–, Mn2+, malonic acid and quercetin analyte solutions, which are followed potentiometrically either by an Ag+/S2– ion-sensitive or by a Pt electrode. A linear response of the potential shift versus the logarithm of the analyte concentrations is found in the following ranges: 1.3 × 10–6 mol dm–3 ≤ [Cl–] ≤ 1.6 × 10–4 mol dm–3, 1.0 × 10–6 mol dm–3 ≤ [Br–] ≤ 8.3 × 10–5 mol dm–3, 2.0 × 10–6 mol dm–3 ≤ [I–] ≤ 1.0 × 10–4 mol dm–3, 8.4 × 10–7 mol dm–3 ≤ [Mn2+] ≤ 8.3 × 10–5 mol dm–3, 3.8 × 10–7 mol dm–3 ≤ [malonic acid] ≤ 2.1 × 10–5 mol dm–3 and 1.5 × 10–8 mol dm–3 ≤ [quercetin] ≤ 3.7 × 10–5 mol dm–3. Under the investigated conditions an improved detection limit for all halides tested is obtained. Unknown concentrations of the analytes can be determined from a standard series of calibration curves to an accuracy within ±5%. In addition, the application of potentiometric measurements in microvolume/microconcentration quantitative analysis is diversified.

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.

Investigation of dynamic behavior of the Bray–Liebhafsky reaction in the CSTR. Properties of the system examined by pulsed perturbations with I−

In order to investigate the properties of the dynamic states in the Bray–Liebhafsky (BL) reaction, pulsed perturbations with iodide are applied. In particular, the excitability thresholds of several stable stationary states corresponding to the same non-equilibrium stationary state branch, as well as the excitability thresholds and phase response behavior of one oscillatory state, are investigated and characterized quantitatively. In the oscillatory state, the phase response behavior corresponding to perturbations of different strengths is determined, and characterized by phase response curves (PRC and PTC). Finally, all values obtained experimentally are also calculated, using one variant of a model of the Bray–Liebhafsky reaction.

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.

Contraction of the model for the Bray–Liebhafsky oscillatory reaction by eliminating intermediate I2O

The existing model for the Bray–Liebhafsky reaction aimed at simulating the largest possible number of various self-organization phenomena observed experimentally, is reduced herewith with the purpose of removing the intermediate I2O preserving the main characteristics of the parent model. The stoichiometric network analysis is applied.

The state space of a model for the Bray-Liebhafsky oscillating reaction

It has been known for a long time that the decomposition of hydrogen peroxide catalyzed by hydrogen and iodate ions, the Bray-Liebhafsky reaction, can generate oscillations in a batch reactor. Recently, mixed-mode oscillations and chaos have also been observed in a CSTR. The model we had previously proposed to explain the kinetics in a batch reactor can also simulate these new complex behaviors. Time series give only a limited view of the features of the calculated behaviors and more information is obtained studying the properties of the state space. We use projections of the trajectories, calculation of the correlation dimension of the attractor, Poincaré sections, and return maps. As the state space of the model is six-dimensional, we try to answer the questions of whether the projections into a 3D subspace give correct pictures of the real trajectories and whether we have reasons to prefer a special subspace.