phone +7 (3412) 91 60 92

Archive of Issues

Russia Yekaterinburg
Section Mathematics
Title The phenomenon of stochastic excitability in the enzymatic reaction model
Author(-s) Bashkirtseva I.A.a, Zaitseva S.S.a
Affiliations Ural Federal Universitya
Abstract We study the influence of noise on the Goldbeter model of the enzymatic reaction, which describes the mechanism of oscillatory synthesis of cyclic adenosine monophosphate in a cell. It is shown that the model is highly sensitive to variations of parameters and initial conditions. The phenomenon of stochastic excitability in a stable equilibrium zone is demonstrated and studied. We show that the noise results in a sharp transition from low-amplitude stochastic oscillations to large-amplitude spike oscillations. For the parametric analysis of this phenomenon, the technique of stochastic sensitivity functions and the method of confidence ellipses are used. We study how the critical value of the noise intensity corresponding to the generation of large-amplitude oscillations depends on the proximity of a control parameter to a bifurcation point. For a detailed analysis of the frequency properties of stochastic oscillations, a statistical analysis of interspike intervals is carried out, and a phenomenon of coherent resonance is found.
Keywords random disturbances, excitability, stochastic sensitivity, confidence ellipses
UDC 517.977
MSC 93E03
DOI 10.20537/vm180101
Received 25 December 2017
Language Russian
Citation Bashkirtseva I.A., Zaitseva S.S. The phenomenon of stochastic excitability in the enzymatic reaction model, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, vol. 28, issue 1, pp. 3-14.
  1. Horsthemke W., Lefever R. Noise-induced transitions, Berlin: Springer, 1984, 322 p.
  2. Anishchenko V.S., Astakhov V.V., Vadivasova T.E., Neiman A.B., Strelkova G.I., Shimanskii-Gaier L. Nelineinye effekty v khaoticheskikh i stokhasticheskikh sistemakh (Nonlinear effects in chaotic and stochastic systems), Izhevsk: Institute of Computer Sciences, 2003, 535 p.
  3. Romanovskii Yu.M., Stepanova N.V., Chernavskii D.S. Matematicheskoe modelirovanie v biofizike (Mathematical modeling in biophysics), Moscow: Nauka, 1975, 304 p.
  4. Kaimachnikov N.P., Sel'kov Ye.Ye. Hysteresis and multiplicity of dynamic states in an open two-substrate enzymatic reaction with substrate depression, Biophysics, 1975, vol. 20, pp. 713-718.
  5. Ivanitskii G.R., Krinskii V.I., Sel'kov E.E. Matematicheskaya biofizika kletki (Mathematical biophysics of the cell), Moscow: Nauka, 1978, 308 p.
  6. Gurel D., Gurel O. Oscillations in chemical reactions, New York: Springer, 1983, 124 p. Translated under the title Kolebatel'nye khimicheskie reaktsii, Moscow: Mir, 1986, 148 p.
  7. Strogatz S.H. Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Boston: Addison-Wesley Publishing Company, 1994.
  8. Bashkirtseva I., Ryashko L. Stochastic sensitivity and variability of glycolytic oscillations in the randomly forced Sel'kov model, The European Physical Journal B, 2017, vol. 90, issue 1, article 17. DOI: 10.1140/epjb/e2016-70674-4
  9. Goldbeter A. Patterns of spatiotemporal organization in an allosteric enzyme model, Proc. Natl. Acad. Sci. USA, 1973, vol. 70, issue 11, pp. 3255-3259. DOI: 10.1073/pnas.70.11.3255
  10. Goldbeter A. Modulation of the adenylate energy charge by sustained metabolic oscillations, FEBS Letters, 1974, vol. 43, no. 3, pp. 327-330. DOI: 10.1016/0014-5793(74)80672-1
  11. Boiteux A., Goldbeter A., Hess B. Control of oscillating glycolysis of yeast by stochastic, periodic, and steady source of substrate: a model and experimental study, Proc. Natl. Acad. Sci. USA, 1975, vol. 72, issue 10, pp. 3829-3833. DOI: 10.1073/pnas.72.10.3829
  12. Goldbeter A., Segel L.A. Unified mechanism for relay and oscillation of cyclic AMP in dictyostelium discoideum, Proc. Natl. Acad. Sci. USA, 1977, vol. 74, issue 4, pp. 1543-1547. DOI: 10.1073/pnas.74.4.1543
  13. Goldbeter A., Martiel J.-L. Birhythmicity in a model for the cyclic AMP signalling system of the slime mold dictyostelium discoideum, FEBS Letters, 1985, vol. 191, no. 1, pp. 149-153. DOI: 10.1016/0014-5793(85)81012-7
  14. Borghans J., Duont G., Goldbeter A. Complex intracellular calcium oscillations: a theoretical exploration of possible mechanisms, Biophysical Chemistry, 1997, vol. 66, issue 1, pp. 25-41. DOI: 10.1016/S0301-4622(97)00010-0
  15. Ya J., Li-Jian Y., Dan W., Quan L., Xuan Z. Noise-induced bursting and coherence resonance in minimal cytosolic $Ca$${2+}$ oscillation model, Chinese Physics Letters, 2004, vol. 21, no. 8, pp. 1666-1669. DOI: 10.1088/0256-307X/21/8/070
  16. Decroly O., Goldbeter A. Birhythmicity, chaos, and other patterns of temporal self-organization in a multiply regulated biochemical system, Proc. Natl. Acad. Sci. USA, 1982, vol. 79, issue 22, pp. 6917-6921. DOI: 10.1073/pnas.79.22.6917
  17. Goldbeter A., Erneux T., Segel L.A. Excitability in the adenylate cyclase reaction in dictyostelium discoideum, FEBS Letters, 1978, vol. 89, no. 2, pp. 237-241. DOI: 10.1016/0014-5793(78)80226-9
  18. Bashkirtseva I., Ryashko L. Noise-induced extinction in Bazykin-Berezovskaya population model, The European Physical Journal B, 2016, vol. 89, issue 7, article 165. DOI: 10.1140/epjb/e2016-70345-6
  19. Ryashko L., Slepukhina E. Noise-induced torus bursting in the stochastic Hindmarsh-Rose neuron model, Physical Review E, 2017, vol. 96, issue 3, 032212. DOI: 10.1103/PhysRevE.96.032212
  20. Venttsel' A.D., Freidlin M.I. Fluktuatsii v dinamicheskikh sistemakh pod deistviem malykh sluchainykh vozmushchenii (Fluctuations in dynamical systems under the action of small random perturbations), Moscow: Nauka, 1979, 424 p.
Full text
Next article >>