Types of Oscillations in Chemical Reactions

Using the mean-Ðeld reactionÈdi †usion equations and Monte Carlo (MC) technique, we simulate oscillatory glycolytic kinetics in 3D spherical or 2D circular cells. The model employed takes into account the glucose supply to the cell via the cell membrane and a few elementary reaction steps running inside the cell. The model parameters are chosen so that the typical size of oscillatory patterns is comparable with the cell size. In the mean-Ðeld approximation, the oscillations are periodic and may occur with large amplitude. In contrast, the MC kinetics are appreciably irregular and the amplitude of oscillations is smaller in the latter case. Both these e †ects are connected with deviation of the metabolite distribution in the cell from the symmetrical one due to Ñuctuations. The spatiotemporal patterns obtained in our MC simulations are qualitatively similar to those observed recently in neutrophils.

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“…( 5) and ( 6) by and (ii) drop the Ðrst term in the N P (t), right-hand part of eqn. (6). Thus, we have…”

Section: Reaction-di †Usion Equationsmentioning

confidence: 93%

Simulations of oscillatory glycolytic patterns in cells

Zhdanov

Kasemo

2001

Phys. Chem. Chem. Phys.

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“…and Gurel (1983) and Razón and Schmitz (1987)). Enzyme reactions are commonly observed to display these regimes as well as hysteresis.…”

Section: Overdesignmentioning

confidence: 97%

Nonlinear analysis in process design. Why overdesign to avoid complex nonlinearities?

Seider¹,

Brengel²,

Provost³

et al. 1990

Ind. Eng. Chem. Res.

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“…The spatiotemporal phenomena in glycolysis were discovered and widely studied in experiments. [1][2][3][4][5][6] The theoretical investigation of glycolytic oscillation processes in yeast cells by local mathematical models using ordinary differential equations was initiated by Higgins 7 and Sel'kov 8 and continued by many researchers (see, e.g., Gurel and Gurel and Goldbeter 9,10 and references therein).…”

Section: Introductionmentioning

confidence: 99%

Selkov glycolytic model with diffusion: Patterns, multistability, and stochastic transitions

Bashkirtseva

Панкратов

2022

Math Methods in App Sciences

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We consider a distributed variant of the Selkov mathematical model of glycolysis with diffusion and stochastic disturbances. The Turing instability zone, in which nonhomogeneous patterns are formed, is determined parametrically. Diversity of waveform spatial structures with different number of peaks is described and studied depending on the diffusion coefficients. The coexistence of various patterns of different waveforms and amplitudes is demonstrated. The quantitative analysis of the pattern formation from the random initial states is carried out using statistics and harmonic coefficients. Multistage noise-induced transitions between coexisting spatial structures are discussed.

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Types of Oscillations in Chemical Reactions

Cited by 6 publications

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Simulations of oscillatory glycolytic patterns in cells

Simulations of oscillatory glycolytic patterns in cells

Nonlinear analysis in process design. Why overdesign to avoid complex nonlinearities?

Selkov glycolytic model with diffusion: Patterns, multistability, and stochastic transitions

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