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

Abstract

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.

Exploring Emergent Properties in Enzymatic Reaction Networks: Design and Control of Dynamic Functional Systems

“…Oscillations occur during the horseradish peroxidase (HRP)-catalyzed oxidation of NADH (reduced nicotinamide adenine dinucleotide) by oxygen in the presence of additives such as methylene blue and 2,4-dichlorophenol in a semibatch stirred reactor with an influx of NADH and diffusion of oxygen from a gas mixture and no outlet as shown in Figure d3. The PO reaction has a complex mechanism comprising multiple redox and coordination forms of the heme cofactor of HRP and very rich dynamics that include normal, period-doubled, and mixed-mode oscillations, quasi-periodicity, and chaos, shown in Figure e5 and e6. , It is hypothesized that many more new dynamic states of the PO reaction are still to be discovered using experimental parameter combinations that go beyond the current regimes, with the pH being an especially important control parameter . We refer the reader to more specialized literature for further details. , …”

“…The PO reaction has a complex mechanism comprising multiple redox and coordination forms of the heme cofactor of HRP and very rich dynamics that include normal, period-doubled, and mixed-mode oscillations, quasi-periodicity, and chaos, shown in Figure e5 and e6. , It is hypothesized that many more new dynamic states of the PO reaction are still to be discovered using experimental parameter combinations that go beyond the current regimes, with the pH being an especially important control parameter . We refer the reader to more specialized literature for further details. , …”