Control and Dissipation in Oscillatory Chemical Engines

Richter, Péter; Rehmus, Paul; Ross, John

doi:10.1143/ptp.66.385

Cited by 83 publications

(52 citation statements)

References 6 publications

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“…However, if the fixed external period after the bifurcation is outside the entrainment band (see ref. 17), then the value of the ATP͞ADP ratio is decreased. The result for the one-variable case is shown in Fig.…”

Section: Results Of Computationsmentioning

confidence: 99%

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Advantages of external periodic events to the evolution of biochemical oscillatory reactions

Tsuchiya

Ross

2003

Proc. Natl. Acad. Sci. U.S.A.

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We compare, by calculations on a simple model of glycolysis, the evolutionary development of oscillatory reaction mechanisms in the presence and absence of external periodic events, such as an oscillatory or constant influx of glucose in an open reaction system. The chosen model has autonomous oscillations for given choices of the parameters of the feedback loops responsible for the oscillations, and for a given range of the total adenylate pool concentration. We change first one, then two of the parameters, so that there are no autonomous oscillations, and then vary these parameters with a genetic algorithm method in which the parameters are represented by binary strings that evolve by selection, crossover, and mutations; the optimization goal is the attainment of a high ATP͞ADP concentration ratio in the system. This goal is taken to provide evolutionary advantages and is shown to be achieved more quickly in the presence of external periodic events, rather than constant influx of glucose. The results suggest the possibility of the enhanced evolutionary development of oscillatory biological reactions at shores where waves impinge on rocks and bring nutrients periodically. Measurements have shown that animals and plants grow more rapidly in the presence of such wave action than in its absence.

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Section: Results Of Computationsmentioning

confidence: 99%

“…A variation of dissipation, both increases and decreases, with the frequency of an external perturbation on an oscillatory reaction within entrainment bands was reported in ref. 17. We are considering time scales of the order of minutes, not circadian time scales.…”

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confidence: 99%

Advantages of external periodic events to the evolution of biochemical oscillatory reactions

Tsuchiya

Ross

2003

Proc. Natl. Acad. Sci. U.S.A.

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“…The free enzyme E (PFK1), itself, is inactive but becomes active in the complex form EP γ after combination with γ product molecules. Richter et al 17 have proposed the following three reversible kinetic steps (2.1 to 2.3), based on Sel'kov model, known as the reversible Sel'kov model,…”

Section: The Modelmentioning

confidence: 99%

“…[9][10][11][12][13] AE derivation for the Swift-Hohenberg model 14 has been widely used for a qualitative description of the convective structures originated from Benard-Marangoni instability or non-Boussinesq Benard convection. 15,16 In this paper, we have derived the AE for the reversible Sel'kov model 17,18 a kinetic model of glycolytic 19,20 D-R system, in which the steady state from the reaction kinetics is required to be obtained by the analytical solution of a cubic equation using Cardon's method, 21 which is rather complicated. For such a D-R model, 17,18 we have attempted to derive the AE, which interprets the stability of various forms of Turing patterns as well as the structural transitions between them.…”

Section: Introductionmentioning

confidence: 99%

“…15,16 In this paper, we have derived the AE for the reversible Sel'kov model 17,18 a kinetic model of glycolytic 19,20 D-R system, in which the steady state from the reaction kinetics is required to be obtained by the analytical solution of a cubic equation using Cardon's method, 21 which is rather complicated. For such a D-R model, 17,18 we have attempted to derive the AE, which interprets the stability of various forms of Turing patterns as well as the structural transitions between them. In a recent paper, 22 we have made a preliminary report of this derivation, but could not present in detail, particularly the nonlinear analysis and the amplitude equation derivation steps after incorporating the two solvability conditions -this has been accomplished in this manuscript.…”

Section: Introductionmentioning

confidence: 99%

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Amplitude equation for a diffusion-reaction system: The reversible Sel'kov model

Dutt

2012

AIP Advances

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For a model glycolytic diffusion-reaction system, an amplitude equation has been derived in the framework of a weakly nonlinear theory. The linear stability analysis of this amplitude equation interprets the structural transitions and stability of various forms of Turing structures. This amplitude equation also conforms to the expectation that time-invariant amplitudes in Turing structures are independent of complexing reaction with the activator species, whereas complexing reaction strongly influences Hopf-wave bifurcation.

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