Marcus J. B. Hauser

Mixed-mode oscillations and homoclinic chaos in an enzyme reaction

We have studied mixed-mode oscillations (MMO) in the peroxidase–oxidase reaction at pH 6.3 and its dynamic behaviour as the stationary concentration of reduced nicotinamide adenine dinucleotide (NADH) is changed. At low NADH concentration, simple periodic relaxation oscillations of large amplitude are observed. As the concentration of NADH is increased, MMOs arise. They start with a simple 11 state where one oscillation with large amplitude is followed by one oscillation of small amplitude. Further increase in NADH results in 1i patterns where one large amplitude oscillation is followed by i small amplitude oscillations. The individual MMO states lose stability through period doubling sequences leading to narrow chaotic regions. These are followed by period-added regimes of MMOs. The period adding sequence of MMOs culminates in a broad region of homoclinic chaos. The experimental results are compared with numerical simulations of a detailed model of the reaction.

Desynchronisation of Glycolytic Oscillations in Yeast Cell Populations

Glycolytic oscillations of intact yeast cells of the strain Saccharomyces carlsbergensis were investigated at both the levels of cell populations and of individual cells. Individual cells showed glycolytic oscillations even at very low cell densities (e.g. 1.0105 cells/ml). By contrast, the collective behaviour on the population level was cell density-dependent: at high cell densities it is oscillatory, but below the threshold density of 1.0106 cells/ml the collective dynamics becomes quiescent. We demonstrate that the transition in the collective dynamics is caused by the desynchronisation of the oscillations of individual cells. This is characteristic for a Kuramoto transition. Spatially resolved measurements at low cell densities revealed that even cells that adhere to their neighbours oscillated with their own, independent frequencies and phases.

Oscillatory dynamics protect enzymes and possibly cells against toxic substances

We have used the oscillating peroxidase-oxidase (PO) reaction as a model system to study how oscillatory dynamics may affect the influence of toxic reaction intermediates on enzyme stability. In the peroxidase-oxidase reaction reactive intermediates, such as hydrogen peroxide, superoxide, and hydroxyl radical are formed. Such intermediates inactivate many cellular macromolecules such as proteins and nucleic acids. These reaction intermediates also react with peroxidase itself to form an inactive enzyme. The fact that the PO reaction shows bistability between an oscillatory and a steady state gives us a unique possibility to compare such inactivation when the system is in one of these two states. We show that inactivation of peroxidase is slower when the system is in an oscillatory state, and using numerical simulations we provide evidence that oscillatory dynamics lower the average concentration of the reactive intermediates.

Coupled chaotic states and apparent noise in experiment and model

We present an experimental and model study of the effect of mass coupling of two similar chaotic states in the Belousov–Zhabotinskii (BZ) reaction. At high coupling strengths the coupled chaotic states become synchronized as shown by a high correlation coefficient. When the coupling strength is decreased, the coupled system passes through a symmetry–breaking transition from synchronized to asynchroneous chaos. At the transition point the direct experimental evaluation of the maximum Lyapunov exponent of the single chaotic system is possible from the coupling strength. At very low coupling strengths the correlation approaches zero. The differences and sums of the two chaotic time series in each reactor are also investigated. At high and moderate coupling strengths, the differences and the sums are verified to be deterministically chaotic on the basis of their fractal dimensionalities, for example. However, for weakly coupled (and uncoupled) chaotic states our analysis with state‐of‐the‐art methods shows th...

Inhomogeneous precipitation patterns in a chemical wave

Abstract Inhomogeneous BaSO 4 -precipitation patterns are observed in the travelling wave generated in the bistable chlorite-thioureabarium chloride reaction system. At the wave-front SO 2− 4 is formed and detected as BaSO 4 which precipitates inhomogeneously in the region behind the front. These inhomogeneous patterns can be attributed to the formation of dense crystals in the upper solution layer which induce complex three-dimensional convective, and reaction-diffusive motions. The wave propagates with rapid variations in velocity. The inhomogeneous precipitation patterns are annihilated upon a sharp deceleration of the wave.

Mixed-mode oscillations in a homogeneous pH-oscillatory chemical reaction system.

We examine experimentally a chemical system in a flow-through stirred reactor, which is known to provide large-amplitude oscillations of the pH value. By systematic variation of the flow rate, we find that the system displays hysteresis between a steady state and oscillations, and more interestingly, a transition to chaos involving mixed-mode oscillations. The basic pattern of the measured pH in the mixed-mode regime includes a large-scale peak followed by a series of oscillations on a much smaller scale, which are usually highly irregular and of variable duration. The bifurcation diagram shows that chaos sets in via a period-doubling route observed on the large-amplitude scale, but simultaneously small-amplitude oscillations are involved. Beyond the apparent accumulation of period doubling bifurcations, a mixed-mode regime with irregular oscillations on both scales is observed, occasionally interrupted by windows of periodicity. As the flow rate is further increased, chaos turns into quasiperiodicity and later to a simple small-amplitude periodic regime. Dynamics of selected typical regimes were examined with the tools of nonlinear time-series analysis, which include phase space reconstruction of an attractor and calculation of the maximal Lyapunov exponent. The analysis points to deterministic chaos, which appears via a period doubling route from below and via a route involving quasiperiodicity from above, when the flow rate is varied.

Cyclosis-mediated transfer of H2O2 elicited by localized illumination of Chara cells and its relevance to the formation of pH bands

Cytoplasmic streaming occurs in most plant cells and is vitally important for large cells as a means of long-distance intracellular transport of metabolites and messengers. In internodal cells of characean algae, cyclosis participates in formation of light-dependent patterns of surface pH and photosynthetic activity, but lateral transport of regulatory metabolites has not been visualized yet. Hydrogen peroxide, being a signaling molecule and a stress factor, is known to accumulate under excessive irradiance. This study was aimed to examine whether H2O2 produced in chloroplasts under high light conditions is released into streaming fluid and transported downstream by cytoplasmic flow. To this end, internodes of Chara corallina were loaded with the fluorogenic probe dihydrodichlorofluorescein diacetate and illuminated locally by a narrow light beam through a thin optic fiber. Fluorescence of dihydrodichlorofluorescein (DCF), produced upon oxidation of the probe by H2O2, was measured within and around the illuminated cell region. In cells exhibiting active streaming, H2O2 first accumulated in the illuminated region and then entered into the streaming cytoplasm, giving rise to the expansion of DCF fluorescence downstream of the illuminated area. Inhibition of cyclosis by cytochalasin B prevented the spreading of DCF fluorescence along the internode. The results suggest that H2O2 released from chloroplasts under high light is transported along the cell with the cytoplasmic flow. It is proposed that the shift of cytoplasmic redox poise and light-induced elevation of cytoplasmic pH facilitate the opening of H+/OH−-permeable channels in the plasma membrane.

Functional organization of the vascular network of Physarum polycephalum

The plasmodium of the slime mould Physarum polycephalum forms a transportation network of veins, in which protoplasm is transported due to peristaltic pumping. This network forms a planar, weighted, undirected graph that, for the first time, can be extracted automatically from photographs or movies. Thus, data from real transportation networks have now become available for the investigation of network properties. We determine the local drag of the vein segments and use these data to calculate the transport efficiency. We unravel which veins form the backbone of the transportation network by using a centrality measure from graph theory. The principal vein segments lie on relatively ample cycles of veins, and the most important segments are those that belong simultaneously to two of these principal cycles. Each principal cycle contains a series of smaller cycles of veins of lower transport efficiency, thus reflecting the hierarchical and self-similar structure of the transportation network. Finally, we calculate accessibility maps that show how easily different nodes of the network may be reached from a given reference node.

Excitation-induced dynamics of external pH pattern in Chara corallina cells and its dependence on external calcium concentration

The influence of cell excitation and external calcium level on the dynamics of light-induced pH bands along the length of Chara corallina cells is studied in the present paper. Generation of an action potential (AP) transiently quenched these pH patterns, which was more pronounced at 0.05-0.1 mM Ca2+ than at higher concentrations of Ca2+ (0.6-2 mM) in the medium. After transient smoothing of the pH bands, some alkaline peaks reemerged at slightly shifted positions in media with low Ca2+ concentrations, while at high Ca2+ concentrations, the alkaline spots reappeared exactly at their initial positions. This Ca2+ dependency has been revealed by both digital imaging and pH microelectrodes. The stabilizing effect of external Ca2+ on the locations of recovering alkaline peaks is supposedly due to formation of a physically heterogeneous environment around the cell owing to precipitation of CaCO3 in the alkaline zones at high Ca2+ during illumination. The elevation of local pH by dissolving CaCO3 facilitates the reappearance of alkaline spots at their initial locations after temporal suppression caused by cell excitation. At low Ca2+ concentrations, when the solubility product of CaCO3 is not attained, the alkaline peaks are not stabilized by CaCO3 dissolution and may appear at random locations.

Feedback loops for Shil'nikov chaos: The peroxidase-oxidase reaction.

Special structures in a chemical reaction network can give rise to bistability, oscillations, and chaos. It has been shown recently [A. Sensse and M. Eiswirth, J. Chem. Phys. 122, 044516 (2005)] that the introduction of an additional species in a supplementary feedback loop to a minimal autocatalytic oscillator gives rise to chaotic dynamics in a certain range of parameters, independent of the particular realization of the additional loop. This provides a possibility to decide if chaos may occur just by analyzing the network structure of an existing model. Here, we apply this concept to analyze the complex dynamics in several essential subsystems of the peroxidase-oxidase reaction system. The aim of the present paper is to determine the nature of the occurring chaos and its location in the parameter space by numerical bifurcation analysis and simulations.