Fast–slow variable analysis of the transition to mixed‐mode oscillations and chaos in the peroxidase reaction

An examination of the complex oscillations and chaotic behavior observed in a model of the peroxidase‐catalyzed oxidation of NADH is made via numerical simulation and a fast/slow variable analysis. The NADH is considered to be a slowly varying species, compared to oxygen and the two key free‐radical intermediates in the mechanism. By considering NADH to be a parameter which modulates the dynamics of a reduced model composed of the remaining fast variables, the origin of the complex oscillations is elucidated. Possibilities for the origin of the observed chaotic behavior are also suggested by this approach. The observation of birhythmicity and metastable chaos in this system may also be related to the two inherent time scales in the kinetics.

[1]  Lars Folke Olsen,et al.  BISTABILITY, OSCILLATION, AND CHAOS IN AN ENZYME REACTION , 1979 .

[2]  Baltazar D. Aguda,et al.  Bistability in chemical reaction networks: Theory and application to the peroxidase–oxidase reaction , 1987 .

[3]  K. Showalter,et al.  Period lengthening and associated bifurcations in a two‐variable, flow Oregonator , 1988 .

[4]  William H. Press,et al.  Numerical recipes , 1990 .

[5]  A. Goldbeter,et al.  From simple to complex oscillatory behaviour: analysis of bursting in a multiply regulated biochemical system. , 1987, Journal of theoretical biology.

[6]  Jensen,et al.  Renormalization, unstable manifolds, and the fractal structure of mode locking. , 1985, Physical review letters.

[7]  Baltazar D. Aguda,et al.  Multiple steady states, complex oscillations, and the devil’s staircase in the peroxidase–oxidase reaction , 1987 .

[8]  I. Yamazaki,et al.  Sustained Oscillations in a Lactoperoxidase, NADPH and O2 System , 1969, Nature.

[9]  I. Yamazaki,et al.  Oscillatory oxidations of reduced pyridine nucleotide by peroxidase. , 1965, Biochemical and biophysical research communications.

[10]  Celso Grebogi,et al.  Super persistent chaotic transients , 1985, Ergodic Theory and Dynamical Systems.

[11]  Irving R. Epstein,et al.  Systematic design of chemical oscillators. Part 13. Complex periodic and aperiodic oscillation in the chlorite-thiosulfate reaction , 1982 .

[12]  L. Olsen,et al.  Oscillatory kinetics of the peroxidase-oxidase reaction in an open system. Experimental and theoretical studies. , 1978, Biochimica et biophysica acta.

[13]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[14]  L. Olsen,et al.  Chaos in an enzyme reaction , 1977, Nature.

[15]  Harry L. Swinney,et al.  Complex periodic oscillations and Farey arithmetic in the Belousov–Zhabotinskii reaction , 1986 .

[16]  Françoise Argoul,et al.  From quasiperiodicity to chaos in the Belousov–Zhabotinskii reaction. I. Experiment , 1987 .

[17]  J. Doyne Farmer,et al.  Mode locking, the Belousov-Zhabotinsky reaction, and one-dimensional mappings , 1986 .