Compound 3 kinetics and chemiluminescence in oscillatory oxidation reactions catalyzed by horseradish peroxidase

Complex dynamics in an unexplored simple model of the peroxidase-oxidase reaction

A previously overlooked version of the so-called Olsen model of the peroxidase-oxidase reaction has been studied numerically using 2D isospike stability and maximum Lyapunov exponent diagrams and reveals a rich variety of dynamic behaviors not observed before. The model has a complex bifurcation structure involving mixed-mode and bursting oscillations as well as quasiperiodic and chaotic dynamics. In addition, multiple periodic and non-periodic attractors coexist for the same parameters. For some parameter values, the model also reveals formation of mosaic patterns of complex dynamic states. The complex dynamic behaviors exhibited by this model are compared to those of another version of the same model, which has been studied in more detail. The two models show similarities, but also notable differences between them, e.g., the organization of mixed-mode oscillations in parameter space and the relative abundance of quasiperiodic and chaotic oscillations. In both models, domains with chaotic dynamics contain apparently disorganized subdomains of periodic attractors with dinoflagellate-like structures, while the domains with mainly quasiperiodic behavior contain subdomains with periodic attractors organized as regular filamentous structures. These periodic attractors seem to be organized according to Stern-Brocot arithmetics. Finally, it appears that toroidal (quasiperiodic) attractors develop into first wrinkled and then fractal tori before they break down to chaotic attractors.

Nucleation of stem cell domains in a bistable activator-inhibitor model of the shoot apical meristem

Shoot apical meristems (SAMs) give rise to all above-ground tissues of a plant. Expansion of meristematic tissue is derived from the growth and division of stem cells that reside in a central zone of the SAM. This reservoir of stem cells is maintained by expression of a transcription factor WUSCHEL that is responsible for the development of stem cells in the central zone. WUSCHEL expression is self-activating and downregulated by a signaling pathway initiated by CLAVATA proteins, which are upregulated by WUSCHEL. This classic activator-inhibitor network can generate localized patterns of WUSCHEL activity by a Turing instability provided certain constraints on reaction rates and diffusion constants of WUSCHEL and CLAVATA are satisfied, and most existing mathematical models of nucleation and confinement of stem cells in the SAM rely on Turing's mechanism. However, Turing patterns have certain properties that are inconsistent with observed patterns of stem cell differentiation in the SAM. As an alternative mechanism, we propose a model for stem cell confinement based on a bistable-switch in WUSCHEL-CLAVATA interactions. We study the bistable-switch mechanism for pattern formation in a spatially continuous domain and in a discrete cellularized tissue in the presence of a non-uniform field of a rapidly diffusing hormone. By comparing domain formation by Turing and bistable-switch mechanisms in these contexts, we show that bistable switching provides a superior account of nucleation and confinement of the stem cell domain under reasonable assumptions on reaction rates and diffusion constants.

Complexity in subnetworks of a peroxidase-oxidase reaction model

The peroxidase-oxidase (PO) reaction is a paradigmatic (bio)chemical system well suited to study the organization and stability of self-sustained oscillatory phases typically present in nonlinear systems. The PO reaction can be simulated by the state-of-the-art Bronnikova-Fedkina-Schaffer-Olsen model involving ten coupled ordinary differential equations. The complex and dynamically rich distribution of self-sustained oscillatory stability phases of this model was recently investigated in detail. However, would it be possible to understand aspects of such a complex model using much simpler models? Here, we investigate stability phases predicted by three simple four-variable subnetworks derived from the complete model. While stability diagrams for such subnetworks are found to be distorted compared to those of the complete model, we find them to surprisingly preserve significant features of the original model as well as from the experimental system, e.g., period-doubling and period-adding scenarios. In addition, return maps obtained from the subnetworks look very similar to maps obtained in the experimental system under different conditions. Finally, two of the three subnetwork models are found to exhibit quint points, i.e., recently reported singular points where five distinct stability phases coalesce. We also provide experimental evidence that such quint points are present in the PO reaction.

Complexity of a peroxidase-oxidase reaction model

The peroxidase-oxidase oscillating reaction was the first (bio)chemical reaction to show chaotic behaviour. The reaction is rich in bifurcation scenarios, from period-doubling to peak-adding mixed mode oscillations. Here, we study a state-of-the-art model of the peroxidase-oxidase reaction. Using the model, we report systematic numerical experiments exploring the impact of changing the enzyme concentration on the dynamics of the reaction. Specifically, we report high-resolution phase diagrams predicting and describing how the reaction unfolds over a quite extended range of enzyme concentrations. Surprisingly, such diagrams reveal that the enzyme concentration has a huge impact on the reaction evolution. The highly intricate dynamical behaviours predicted here are difficult to establish theoretically due to the total absence of an adequate framework to solve nonlinearly coupled differential equations. But such behaviours may be validated experimentally.

Chaos in the peroxidase-oxidase oscillator

The peroxidase-oxidase (PO) reaction involves the oxidation of reduced nicotinamide adenine dinucleotide by molecular oxygen. When both reactants are supplied continuously to a reaction mixture containing the enzyme and a phenolic compound, the reaction will exhibit oscillatory behavior. In fact, the reaction exhibits a zoo of dynamical behaviors ranging from simple periodic oscillations to period-doubled and mixed mode oscillations to quasiperiodicity and chaos. The routes to chaos involve period-doubling, period-adding, and torus bifurcations. The dynamic behaviors in the experimental system can be simulated by detailed semiquantitative models. Previous models of the reaction have omitted the phenolic compound from the reaction scheme. In the current paper, we present new experimental results with the oscillating PO reaction that add to our understanding of its rich dynamics, and we describe a new variant of a previous model, which includes the chemistry of the phenol in the reaction mechanism. This new model can simulate most of the experimental behaviors of the experimental system including the new observations presented here. For example, the model reproduces the two main routes to chaos observed in experiments: (i) a period-doubling scenario, which takes place at low pH, and a period-adding scenario involving mixed mode oscillations (MMOs), which occurs at high pH. Our simulations suggest alternative explanations for the pH-sensitivity of the dynamics. We show that the MMO domains are separated by narrow parameter regions of chaotic behavior or quasiperiodicity. These regions start as tongues of secondary quasiperiodicity and develop into strange attractors through torus breakdown.

On the mechanism of oscillations in neutrophils

We have investigated the regulation of the oscillatory generation of H(2)O(2) and oscillations in shape and size in neutrophils in suspension. The oscillations are independent of cell density and hence do not represent a collective phenomena. Furthermore, the oscillations are independent of the external glucose concentration and the oscillations in H(2)O(2) production are 180 degrees out of phase with the oscillations in NAD(P)H. Cytochalasin B blocked the oscillations in shape and size whereas it increased the period of the oscillations in H(2)O(2) production. 1- and 2-butanol also blocked the oscillations in shape and size, but only 1-butanol inhibited the oscillations in H(2)O(2) production. We conjecture that the oscillations are likely to be due to feedback regulations in the signal transduction cascade involving phosphoinositide 3-kinases (PI3K). We have tested this using a simple mathematical model, which explains most of our experimental observations.

Oscillations in peroxidase-catalyzed reactions and their potential function in vivo

The peroxidase-oxidase reaction has become a model system for the study of oscillations and complex dynamics in biochemical systems. In the present paper we give an overview of previous experimental and theoretical studies of the peroxidase-oxidase reaction. Recent in vitro experiments have raised the question whether the reaction also exhibits oscillations and complex dynamics in vivo. To investigate this possibility further we have undertaken new experimental studies of the reaction, using horseradish extracts and phenols which are widely distributed in plants. The results are discussed in light of the occurrence and a possible functional role of oscillations and complex dynamics of the peroxidase-oxidase reaction in vivo.

Human myeloperoxidase catalyzes an oscillating peroxidase-oxidase reaction

We have studied the peroxidase-oxidase reaction catalyzed by human myeloperoxidase in an open system where both substrates-molecular oxygen and NADH-are supplied continuously to the reaction mixture. The reaction shows oscillatory kinetics at pH values around 5, provided that the reaction medium in addition to the enzyme and the substrates also contains an aromatic electron mediator such as melatonin or 4-hydroxybenzoic acid and chloride ions at concentrations >1mM. The experimental findings can be simulated by a detailed model of the reaction. The results are important for our understanding of oxidant production in neutrophils.

Computer simulation of damped oscillations during peroxidase-catalyzed oxidation of indole-3-acetic acid

Oscillation patterns in horseradish peroxidase (HRP)-catalyzed oxidation of indole-3-acetic acid (IAA) at neutral pH were studied using computer simulation. Under certain conditions, such as the presence of a reaction promoter and continuous intake of oxygen from the gaseous phase, the simulated system exhibits damped oscillations of the concentrations of oxygen in the aqueous phase, [O(2)](aq), and of all the reaction intermediates. The critical concentration of oxygen in aqueous phase, [O(2)](cr)(aq), was used to describe the nature of the oscillations. The critical concentration is the concentration at which the system abruptly changes its properties. If [O(2)](aq) is higher than [O(2)](cr)(aq) then the reaction develops as an avalanche, otherwise, the reaction stops. The nature of oscillations is accounted for by the interaction of two processes: the consumption/accumulation of oxygen and the accumulation/consumption of reaction intermediates. Oscillations are always damped. Neither HRP or umbelliferone (Umb) deactivation nor IAA consumption can account for the damping. The nature of the damping is determined by the termination reactions of free radical intermediates and ROOH. The three major parameters of oscillations: period of oscillations, initial amplitude of oscillations and the rate of damping were studied as functions of: (i) oxygen concentration in the gaseous phase, (ii) initial oxygen concentration in aqueous phase, (iii) the concentration of IAA and (iv) the initial concentration of HRP.

Kinetic studies of the oscillatory dynamics in the peroxidase-oxidase reaction catalyzed by four different peroxidases

Oscillatory kinetics in the peroxidase-oxidase reaction catalyzed by structurally different peroxidases were investigated using NADH as a substrate. For horseradish peroxidase, lactoperoxidase, and soybean peroxidase the oscillatory waveforms of their dominating enzyme intermediates, ferric peroxidase and compound III, are similar. Coprinus peroxidase, on the other hand, has ferrous peroxidase and compound III as the dominating intermediates. The oscillatory waveform of its compound III differs from the waveforms of compound III of the three other peroxidases. Also, the phase plot of the signal for compound III versus the oxygen concentration for Coprinus peroxidase differs from the corresponding phase plots obtained using other peroxidases. A detailed model of the reaction mechanism is proposed, which is able to simulate these different kinds of behaviour. Substituting NADH with dihydroxyfumaric acid as a substrate, oscillations in the oxygen concentration were observed for about 1.5 h when a concentrated solution of this substrate was continuously fed to a solution containing horseradish peroxidase. This is the first demonstration of sustained oscillations with this substrate.

Free radicals and excited species in the metabolism of indole-3-acetic acid and its ethyl ester by horseradish peroxidase and by neutrophils

The peroxidative metabolization of indole-3-acetic acid, a biologically important process, has been followed by EPR spectroscopy with the aim of obtaining information on the mechanism of generation of electronically excited species. The skatole-3-methylene radical detected during oxidation by horseradish peroxidase, does not appear to be involved in a major oxygen consuming process or in the generation of singlet oxygen. The chemiluminescence spectrum exhibits several maxima, which are also observed when the ethyl ester of indole-3-acetic acid is metabolized by horseradish peroxidase or by myeloperoxidase in neutrophils. When the ester is metabolically activated in either of these systems, the EPR spectrum indicates a tertiary carbon-centered radical. This radical centered on the carbon in the 3-position participates in a chemiexcitation/emissive route. Within the cell, this emissive process is responsible for a large part of the oxygen consumed. Some of the emitters originate in the cleavage of the 2,3 double bond. The ester, which is capable of penetrating into the cells, also emits with other myeloperoxidase-containing cells. This compound may have useful applications as an intracellular chemiluminescent probe for the presence of myeloperoxidase.

Computer simulation of sustained oscillations in peroxidase-oxidase reaction

A system of differential equations of second order exhibiting transitional behaviour and sustained oscillations has been obtained for a complete scheme of the peroxidase-oxidase reaction. The concentrations of hydrogen peroxide and of hydrogen donor radicals are slow variables of the system. The most essential reactions responsible for oscillations have been selected. Analysis of the system in phase plane and in parameter space has been carried out. The dependence of oscillation period and amplitude on the parameter values has been investigated.

The oscillating peroxidase-oxidase reaction in an open system. Analysis of the reaction mechanism

1. The oscillations in the peroxidase-oxidase reaction in an open system with NADH as the hydrogen donor are caused by the reaction starting and stopping at critical concentrations of the substrates O2 and NADH. The existence of such critical concentrations is typical of branched chain reactions. 2. The critical concentrations of O2 and NADH that determine the initiation of the reaction are mutually dependent. 3. The branching reactions that determine these critical concentrations involve compounds I and II. 4. Superoxide may be involved in the branching reactions by reacting with NADH and ferriperoxidase. At pH 5.1 the rate constant for the latter reaction is determined as 1.5 . 10(5) M-1 . s-1, whereas for the former reaction only an upper limit for the rate constant of 3.5 . 10(4) M-1 . s-1 could be estimated. These relatively low rate constants suggest that alternative branching reactions may also be involved.

Oscillatory kinetics of the peroxidase-oxidase reaction in an open system. Experimental and theoretical studies

1. The oscillations in the peroxidase (donor: hydrogen-peroxide oxidoreductase, EC 1.11.1.7)-catalyzed reaction between NADH and O2 are undamped when the reaction is carried out in a system open to both substrates and when 2,4-dichlorophenol and methylene blue are present in the solution. 2. The waveform of the oscillations changes when the concentration of peroxidase is varied. 3. The waveforms obtained experimentally can be simulated by a branched chain reaction model in which the branching is quadratic. 4. A correlation between the present knowledge of the reaction and the model can be made by combining well established and hypothetical reaction steps into a few reaction schemes. A selection among schemes however, is not possible at the present time. 5. Compound III participates in the reaction as an active intermediate. This is possible because dichlorophenol stimulates the break down of compound III.

Chaos in an enzyme reaction

Dynamic systems are usually thought to have either monotonic or periodic behaviour. Although the possibility of other types of behaviour has been recognised for many years, the existence of non-monotonic, non-periodic behaviour in dynamic systems has been firmly established only recently. It is termed chaotic behaviour. A review on the rapidly expanding literature on chaos in discrete model systems described by difference equations has been published by May. Rössler, on the other hand, has discussed a few published works on systems of differential equations with chaotic solutions, and he has proposed a three-component chemical model system which he argues has chaotic solutions [figure see text]. The argument is based on a theorem by Li and Yorke. Here we report the finding of chaotic behaviour as an experimental result in an enzyme system (peroxidase). Like Rössler we base our identification of chaos on the theorem by Li and Yorke.