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2015 | 69 | 1 | 79-91
Article title

A Cycle Of Enzymatic Reactions With Some Properties Of Neuronal Circuits

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EN
Abstracts
EN
A cycle of four methylation and four demethylation reactions with repression or allosteric inhibition of enzymes is considered. The corresponding dynamical system is characterised by two parameters: the sum of reagent concentrations (C) and the ratio of rate constants of forward and backward reactions (k). In a symmetrical case (k=1) the system has a unique equilibrium. At C>4 the equilibrium is unstable and the system has oscillatory solutions. At k essentially different from 1, the system becomes excitable or behaves as a bistable trigger.
Publisher
Year
Volume
69
Issue
1
Pages
79-91
Physical description
Dates
published
1 - 3 - 2015
online
13 - 3 - 2015
References
  • 1. References: Malarczyk, E. (1989) Transformations of phenolic acids by Nocardia. Acta Microbiol. Polon. 38, 45-53.
  • 2. Malarczyk, E. and Kochmańska-Rdest, J. (1990) New aspects of co-regulation of decarboxylation and demethylation activities in Nocardia. Acta Biochim. Polon. 34, 145-148.
  • 3. Malarczyk, E. and Paździoch-Czochra, M. (2000) Multiple respiratory bursts as a response to veratrate stress in Rhodococcus erythropolis. Cell Biol. Int. 24, 515- 527. [Crossref]
  • 4. Paździoch-Czochra, M., Malarczyk, E. and Sielewiesiuk, J. (2003) Relationship of demethylation processes and cell density in cultures of Rhodococcus erythropolis. Cell Biol. Int. 27, 325-336.
  • 5. Sielewiesiuk, J. and Malarczyk, E. (2002) A cycle of enzymatic reactions that behaves as a neuronal circuit. J. Theor. Biol. 214, 255-262.
  • 6. Sielewiesiuk, J., Czubla, A., Malarczyk, E. and Paździoch, M. (1999) Kinetic model for oscillations in a cycle of enzymatic reactions related to methoxyphenol transformation in Rhodococcus erythropolis culture. Cell. Mol. Biol. Lett. 4, 131- 146.
  • 7. Dunin-Barkovsky, V.L. (1970) The oscillation of activity level in simple closed neurone chains. Biophysics 15, 374-378 (in Russian).
  • 8. Goodwin, B.C. (1966) An entrainment model for timed enzyme syntheses in bacteria. Nature 209, 479-481.
  • 9. Hastings, S., Tyson, J. and Webster, D. (1977) Existence of periodic solutions for negative feedback cellular control systems. J. Differential Equations 25, 39-64. [Crossref]
  • 10. Tyson, J.J. (1975) On the existence of oscillatory solutions in negative feedback cellular control processes. J. Math. Biol. 1, 311-315.
  • 11. Tyson, J.J. (1979) Periodic enzyme synthesis: reconsideration of the theory of oscillatory repression. J. Theor. Biol. 80, 27-38.
  • 12. Grigorov, N.L., Poljakova, M.S. and Chernavsky, D.S. (1967) Model investigations of the trigger schemes and the differentiation process. Molecular Biol. 1, 410-418, (in Russian).
  • 13. Romanovsky, Yu.M., Stepanova, N.V. and Chernavsky, D.S. (1975) Mathematical Modelling in Biophysics, Nauka, Moscow.[WoS]
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.-psjd-doi-10_1515_physica-2015-0005
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