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2014 | 69 |

Article title

A cycle of enzymatic reactions with some properties of neuronal circuits

Content

Title variants

Languages of publication

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.

Keywords

Year

Volume

69

Physical description

Dates

published
2014
online
22 - 05 - 2015

Contributors

References

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  • 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.
  • 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.
  • 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.
  • Sielewiesiuk, J. and Malarczyk, E. (2002) A cycle of enzymatic reactions that behaves as a neuronal circuit. J. Theor. Biol. 214, 255-262.
  • 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.
  • Dunin-Barkovsky, V.L. (1970) The oscillation of activity level in simple closed neurone chains. Biophysics 15, 374-378 (in Russian).
  • Goodwin, B.C. (1966) An entrainment model for timed enzyme syntheses in bacteria. Nature 209, 479-481.
  • Hastings, S., Tyson, J. and Webster, D. (1977) Existence of periodic solutions for negative feedback cellular control systems. J. Differential Equations 25, 39-64.
  • Tyson, J.J. (1975) On the existence of oscillatory solutions in negative feedback cellular control processes. J. Math. Biol. 1, 311-315.
  • Tyson, J.J. (1979) Periodic enzyme synthesis: reconsideration of the theory of oscillatory repression. J. Theor. Biol. 80, 27-38.
  • 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).
  • Romanovsky, Yu.M., Stepanova, N.V. and Chernavsky, D.S. (1975) Mathematical Modelling in Biophysics, Nauka, Moscow.

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.ojs-doi-10_17951_aaa_2014_69_81
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