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Russia Yekaterinburg
Year
2018
Volume
28
Issue
1
Pages
3-14
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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.
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