Perturbations of Simple Oscillations and Complex Dynamics in the Peroxidase−Oxidase Reaction Using Magnetic Fields

Amplification of weak magnetic field effects on oscillating reactions

We explore the possibility that chemical feedback and autocatalysis in oscillating chemical reactions could amplify weak magnetic field effects on the rate constant of one of the constituent reactions, assumed to proceed via a radical pair mechanism. Using the Brusselator model oscillator, we find that the amplitude of limit cycle oscillations in the concentrations of reaction intermediates can be extraordinarily sensitive to minute changes in the rate constant of the initiation step. The relevance of such amplification to biological effects of 50/60 Hz electromagnetic fields is discussed.

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.

Upper bound on the biological effects of 50/60 Hz magnetic fields mediated by radical pairs

Prolonged exposure to weak (~1 μT) extremely-low-frequency (ELF, 50/60 Hz) magnetic fields has been associated with an increased risk of childhood leukaemia. One of the few biophysical mechanisms that might account for this link involves short-lived chemical reaction intermediates known as radical pairs. In this report, we use spin dynamics simulations to derive an upper bound of 10 parts per million on the effect of a 1 μT ELF magnetic field on the yield of a radical pair reaction. By comparing this figure with the corresponding effects of changes in the strength of the Earth’s magnetic field, we conclude that if exposure to such weak 50/60 Hz magnetic fields has any effect on human biology, and results from a radical pair mechanism, then the risk should be no greater than travelling a few kilometres towards or away from the geomagnetic north or south pole.

Quantum mechanical model for the anticarcinogenic effect of extremely-low-frequency electromagnetic fields on early chemical hepatocarcinogenesis

Using the conventional Haberkorn approach, it is evaluated the recombination of the radical pair (RP) singlet spin state to study theoretically the cytoprotective effect of an extremely-low-frequency electromagnetic field (ELF-EMF) on early stages of hepatic cancer chemically induced in rats. The proposal is that ELF-EMF modulates the interconversion rate of singlet and triplet spin states of the RP populations modifying the products from the metabolization of carcinogens. Previously, we found that the daily treatment with ELF-EMF 120 Hz inhibited the number and area of preneoplastic lesions in chemical carcinogenesis. The singlet spin population is evaluated diagonalizing the spin density matrix through the Lanczos method in a radical pair mechanism (RPM). Using four values of the interchange energy, we have studied the variations over the singlet population. The low magnetic field effect as a test of the influence over the enzymatic chemical reaction is evaluated calculating the quantum yield. Through a bootstrap technique the range is found for the singlet decay rate for the process. Applying the quantum measurements concept, we addressed the impact toward hepatic cells. The result contributes to improving our understanding of the chemical carcinogenesis process affected by charged particles that damage the DNA.

Biofilm effects on the peroxidase-oxidase reaction

In experiments on the kinetics of the peroxidase-oxidase oscillatory reaction in pH 5.l acetate buffer, biofilms form in less than 48 h on the quartz reactor surface. The nominally homogeneous peroxidase system shows dynamical changes in response to this biofilm growth, partially explaining subtle differences among dynamics observed over time and between laboratories. Kinetics data and model computations are correlated with micrographs of biofilm formation. It is evident that bare quartz also interacts with reaction species, so that the surface area-to-volume ratio is an important parameter on which observed dynamics depend.

Specific external forcing of spatiotemporal dynamics in reaction-diffusion systems

Self-organization behavior and in particular pattern forming spatiotemporal dynamics play an important role in far from equilibrium chemical and biochemical systems. Specific external forcing and control of self-organizing processes might be of great benefit in various applications ranging from technical systems to modern biomedical research. We demonstrate that in a cellular chemotaxis system modeled by one-dimensional reaction-diffusion equations particular forms of spatiotemporal dynamics can be induced and stabilized by controlling spatially distributed influx patterns of a chemical species as a function of time. In our model study we show that a propagating wave with certain shape and velocity and static symmetrical and asymmetrical patterns can be forced and manipulated by numerically computing open-loop optimal influx controls.

Observations of the Effect of Anionic, Cationic, Neutral, and Zwitterionic Surfactants on the Belousov−Zhabotinsky Reaction

In this paper we report the experimental observations of the effects of various surfactants on the oscillations of the ferroin-catalyzed Belousov-Zhabotinsky (BZ) reaction. The oscillations are followed by observing the change in absorbance at 510 nm due to ferroin in a well-stirred closed BZ reacting system. We have used sodium dodecyl sulfate (SDS) as the anionic surfactant, cetyl trimethylammonium bromide (CTAB) as the cationic surfactant, Triton X-100 as the neutral surfactant, and 3-[(3-cholamidopropyl)dimethylammonio)]-1-propanesulfonate (CHAPS) as the zwitterionic surfactant. In general, we observed that there is a change in the oscillation behavior in the presence of each of these surfactants above their critical micellar concentrations. For different surfactants, the time-dependent evolution of the oscillations is found to be characteristic of the surfactant. The results of our study suggest that the evolution of oscillations is most regular in the presence of micelles of SDS.

Rapporteur's report: sources and interaction mechanisms

This, the first session of the Workshop, focussed on sources of exposure to and interaction mechanisms of intense static magnetic fields. The four presentations dealt with (1) the magnetic fields produced by diagnostic magnetic resonance imaging systems; (2) the ways in which static magnetic fields can interact with matter, in particular human tissue; (3) the effects of magnetic fields on enzyme reaction rates; and (4) working practices for high-field magnet development.

Mechanism of protection of peroxidase activity by oscillatory dynamics

The peroxidase-oxidase reaction is known to involve reactive oxygen species as intermediates. These intermediates inactivate many types of biomolecules, including peroxidase itself. Previously, we have shown that oscillatory dynamics in the peroxidase-oxidase reaction seem to protect the enzyme from inactivation. It was suggested that this is due to a lower average concentration of reactive oxygen species in the oscillatory state compared to the steady state. Here, we studied the peroxidase-oxidase reaction with either 4-hydroxybenzoic acid or melatonin as cofactors. We show that the protective effect of oscillatory dynamics is present in both cases. We also found that the enzyme degradation depends on the concentration of the cofactor and on the pH of the reaction mixture. We simulated the oscillatory behaviour, including the oscillation/steady state bistability observed experimentally, using a detailed reaction scheme. The computational results confirm the hypothesis that protection is due to lower average concentrations of superoxide radical during oscillations. They also show that the shape of the oscillations changes with increasing cofactor concentration resulting in a further decrease in the average concentration of radicals. We therefore hypothesize that the protective effect of oscillatory dynamics is a general effect in this system.

Mechanism of melatonin-induced oscillations in the peroxidase-oxidase reaction

Melatonin induces oscillations in the peroxidase-oxidase (PO) reaction catalyzed by horseradish peroxidase. We present here studies of the effect of pH, enzyme concentration, and concentration of melatonin on the oscillation frequency. We also present a mechanistic model to explain the experimentally observed changes in oscillation frequency. Using the data obtained here we are able to predict that oscillations will also occur in the PO reaction catalyzed by myeloperoxidase. Myeloperoxidase is an important protein in activated neutrophils and we provide evidence that the oscillations of NAD(P)H, superoxide and hydrogen peroxide in these cells may involve this enzyme. Thus, our experimental system can be considered a model system for the nonrespiratory oxygen metabolism in activated neutrophils and other similar cells participating in the defence against invading pathogens.

Simulations of temperature sensitivity of the peroxidase-oxidase oscillator

The influence of temperature on the oscillatory kinetics of the peroxidase-oxidase reaction was studied theoretically. Assuming Q(10)=2 for elementary reactions, the effect of multiplying the rate constants of the model by factors between 0.5 and 2 (corresponding to a 10 degrees C decrease and increase, respectively, of temperature) was investigated. First, the individual rate constants were successively multiplied by 0.5 or 2 while all other rate constants were kept unchanged. This resulted in either a longer or a shorter period, depending on the rate constant being changed. Multiplication by 0.5 or by 2 generally resulted in opposite effects on the period length. However, the absolute value of this deviation differed. Also, the dynamics changed when halving the dimerization rate of NAD* as well as when doubling the rate constant for the reduction of ferric peroxidase by NAD*. Next, simulations were performed multiplying all rate constants by one and the same factor, which increased progressively from 0.5 to 2. Intervals were found corresponding to temperature dependency, compensation, and over-compensation, respectively.