The consequences of interactive noise for understanding the dynamics of complex biochemical systems

Dynamical Systems

Volumn 11, Issue 2, 1996, Pages 135-148

  Liu, Junli ^a   Crawford, John W ^a   Viola, Roberto ^a  

^a SCOTTISH CROP RESEARCH INSTITUTE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); BIOCHEMISTRY; LARGE SCALE SYSTEMS; MATHEMATICAL MODELS; METABOLITES; OSCILLATIONS; SPURIOUS SIGNAL NOISE;

COMPLEX BIOCHEMICAL SYSTEMS; ENZYMATIC REACTIONS; HOPF BIFURCATION; INTERACTIVE NOISE;

DYNAMICS;

EID: 0030169058     PISSN: 14689367     EISSN: None     Source Type: Journal    
DOI: 10.1080/02681119608806221     Document Type: Article

References (25)

1. Carnal, N. W. and Black, C. C. (1983) Phosphofructokinase activities in photosynthetic organisms: the occurrence of pyrophosphate: fructose-6-phosphate phosphotransferase in plants and algae. Plant Physiology 71, 150-155.
2. Dechert, G. and Schneider, F. W. (1994) Shifting and switching between chemical steady states through electrode processes. Journal of Physical Chemistry 98, 3927-3929.
3. Decroly, O. and Goldbetter, A. (1982) Birhythmicity, chaos and other patterns of temporal self-organization in a multiply regulated biochemical system. Proceedings of the National Academy of Sciences of the USA 79, 6917-6921.
4. Epstein, I. R. (1995) The consequences of imperfect mixing in autocatalytic chemical and biological systems. Nature 374, 321-327.
5. Gray, G., Nicolis, G., Baras, F., Borckmans, P. and Scott, S. K. (eds) (1990) Spatial Inhomogeneities and Transient Behaviour in Chemical Kinetics (Manchester University Press, Manchester).
6. Györgyi, L. and Field, R. J. (1989) Aperiodicity resulting from 2-cycle coupling in the Belousov-Zhabotinskii reaction. 3. Analysis of a model of the effect of spatial inhomogenieties at the input ports of a continuous-flow stirred tank reactor. Journal of Chemical Physics 91, 6131-6141.
7. Györgyi, L., Rempe, S. L. and Field, R. J. (1991) A novel model for the simulation of chaos in low-flow-rate CSTR experiments with the Belousov-Zhabotinskii reaction - a chemical mechanism for 2 frequency oscillations. Journal of Physical Chemistry 95, 3159-3165.
8. Harding, R. H. and Ross, J. (1988) Symptoms of chaos in observed oscillations near a bifurcation with noise. Journal of Chemical Physics 89, 4743-4751.
9. Hess, B. and Plesser, T. (1979) Temporal and spatial order in biochemical systems. Annals of the New York Academy of Sciences 316, 203-213.
10. 2 reaction. Journal of the Chemical Society, Faraday Transactions 86, 3701-3705.
11. Kruel, Th.-M., Freund, A. and Schneider, F. W. (1990) The effects of interactive noise on the driven Brusselator model. Journal of Chemical Physics 93, 416-427.
12. Kruel, Th.-M., Eiswirth, M. and Schneider, F. W. (1993) Computation of Lyapunov spectra: effects of interactive noise and application to a chemical oscillator. Physica D 63, 117-137.
13. Liu, J. and Crawford, J. W. (1996) Stability of an autocatalytic system under noise perturbations and its dependence on attraction basin. Proceedings of the Royal Society of London, Series A (in press).
14. Liu, J. and Scott, S. K. (1991) Hysteresis and complex oscillations of the uncatalysed Belousov-Zhabotinskii reaction in a stirred flow reactor. Journal of the Chemical Society, Faraday Transactions 87, 2135-2240.
15. Liu, J., Crawford, J. and Viola, R. (1995a) Chaos, coexistence of attractors and fractal basin boundaries of attraction in a model system coupling activation and inhibition in parallel. Dynamics and Stability of Systems 10, 111-124.
16. Liu, J., Crawford, J. and Viola, R. (1995b) An interpretation of the dynamical role of fructose 6-p, 1-phosphotransferase in higher plant cell metabolism using nonlinear dynamical analysis. Proceedings of the Royal Society of London, Series B (in press).
17. Markus, M. and Hess, B. (1984) Transitions between oscillatory modes in a glycolytic model system. Proceedings of the National Academy of Sciences of the USA 81, 4394-4398.
18. Roux, J. C., De Kepper, P. and Boissonade, J. J. (1983) Experimental evidence of nucleation induced transition in a bistable chemical system. Physics Letters 97A, L168-L170.
19. Sabularse, D. C. and Anderson, R. L. (1981a) Inorganic pyrophosphate: D-fructose-6-phosphate 1-phosphotransferase in mung beans and its activation by D-fructose 1, 6-bisphosphate and D-glucosel,6-bisphosphate. Biochemical and Biophysical Research Communications 100, 1423-1429.
20. Sabularse, D. C. and Anderson, R. L. (1981b) D-fructose 2,6-biphosphate: a naturally occurring activator for inorganic pyrophosphate: D-fructose-6-phosphate 1-phosphotransferase in plants. Biochemical and Biophysical Research Communications 103, 848-855.
21. Schimansky-Geier, L. and Zulicke, Ch. (1990) Harmonic noise. Zeitschrift für Physik B - Condensed Matter 79, 451-460.
22. Schneider, F. W. and Munster, A. F. (1991) Chemical oscillations, chaos, and fluctuations in flow reactors. Journal of Physical Chemistry 95, 2130-2138.
23. Steinmetz, C. G. and Larter, R. (1991) The quasi-periodic route to chaos in a model of the peroxidase oxidase reaction. Journal of Chemical Physics 94, 1388-1396.
24. Stitt, M. (1990) Fructose-2,6-bisphosphate as a regulatory molecule in plants. Annual Review of Plant Physiology and Plant Molecular Biology 41, 153-185.
25. Zeyer, K.-P., Munster, A. F. and Schneider, F. W. (1995) Quasiperiodic forcing of a chemical reaction: experiments and calculations. Journal of Physical Chemistry 99, 13173-13180.