Preferences help
enabled [disable] Abstract
Number of results
2014 | 69 |
Article title

A cycle of enzymatic reactions with some properties of neuronal circuits

Title variants
Languages of publication
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.
Physical description
22 - 05 - 2015
  • Malarczyk, E. (1989) Transformations of phenolic acids by Nocardia. Acta Microbiol. Polon. 38, 45-53.
  • 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
YADDA identifier
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.