Simple model for temperature control of glycolytic oscillations

Postnikov, Eugene B.; Verveyko, Darya V.; Verisokin, Andrey Yu.

doi:10.1103/physreve.83.062901

Cited by 9 publications

(11 citation statements)

References 17 publications

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“…( 11) are considered as k 1 = k 2 = 1 and k 3 = 2. As both theoretical [47] and experimental [48] evidence regarding temperature dependence of glycolysis oscillation are available, one should stick to a constant temperature assumption. A constant temperature assumption implies heat diffuses much faster than the intermediate species of the reaction-diffusion model.…”

Section: Resultsmentioning

confidence: 99%

Nonequilibrium thermodynamics of glycolytic traveling wave: Benjamin-Feir instability

Kumar,

Gangopadhyay

2021

Preprint

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Evolution of the nonequilibrium thermodynamic entities corresponding to dynamics of the Hopf instabilities and traveling waves at a nonequilibrium steady state of a spatially extended glycolysis model is assessed here by implementing an analytically tractable scheme incorporating complex Ginzberg-Landau equation(CGLE). In the presence of self and cross diffusion, a more general amplitude equation exploiting the multiscale Krylov-Bogoliubov averaging method serves as an essential tool to reveal the various dynamical instability criteria, specially Benjamin-Feir(BF) instability, to estimate the corresponding nonlinear dispersion relation of the traveling wave pattern. The critical control parameter, wavenumber selection criteria, and magnitude of the complex amplitude for traveling waves are modified by self-and cross-diffusion coefficients within the oscillatory regime, and their variabilities are exhibited against the amplitude equation. Unlike the traveling waves, a low amplitude broad region appears for the Hopf instability in the concentration dynamics as the system phase passes through minima during its variation with the control parameter. The total entropy production rate of the uniform Hopf oscillation and glycolysis wave not only qualitatively reflects the global dynamics of concentrations of intermediate species but almost quantitatively. Despite the crucial role of diffusion in generating and shaping the traveling waves, the diffusive part of the entropy production rate has a negligible contribution to the system's total entropy production rate. The Hopf instability shows a more complex and colossal change in the energy profile of the open nonlinear system than so in the traveling waves. A detailed analysis of BF instability shows a contrary nature of the semigrand Gibbs free energy with discrete and continuous wavenumbers for the traveling wave. We hope the Hopf and traveling wave pattern around the BF instability in terms of energetics and dissipation would open up new applications of such dynamical phenomena.

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Section: Resultsmentioning

confidence: 99%

Nonequilibrium thermodynamics of glycolytic traveling wave: Benjamin-Feir instability

Kumar,

Gangopadhyay

2021

Preprint

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“…The first term of the perturbation solution by (19) is the solution of the fol-Open Journal of Biophysics lowing equation:…”

Section: Discussionmentioning

confidence: 99%

“…Temperature is a trivial driving parameter of glycolysis [16] [17]. It was widely investigated experimentally [18] and explained theoretically too [19] as further-developed Selkov's model. Two factors were introduced for this study: a constant α for positive feedback catalytic effect and a β(T) for temperature dependence.…”

Section: Methodsmentioning

confidence: 99%

Similarities of Modulation by Temperature and by Electric Field

Vincze¹,

Szász²

2018

OJBIPHY

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Glycolytic oscillation is one of the first observed and described nonlinear phenomena in living objects. Our recent paper points out the similarity of the temperature and outer electric field to influence this oscillation. The electric field is absorbed and changes the molecules. Similarly to the effect of heating, molecules have various structural, dynamical and chemical changes promoted by electric field. The changes sometimes happen without increasing the temperature. Temperature, as the average energy of the included particles, has various kinds of "waste" energy used to heat up the particles which do not participate in the desired changes. The inaccuracy of the effects of temperature growth in local molecular changes could be remarkably high and could be corrected by the well-applied electric field absorption.

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“…This type of bi-rhythmic oscillator is not known in the literature. For γ = δ = 0, case-II gives the maximum number of limit cycles 4, but amplitude equation (17) says that it has at most three non-zero roots of distinct magnitudes and the zero root has multiplicity three. The bi-rhythmic parameter zone and the phase space plot for γ = δ = 0 are given in Fig.…”

Section: Another Generalization Of Van Der Pol System: Three Stable Limit Cyclesmentioning

confidence: 99%

Systematic designing of bi-rhythmic and tri-rhythmic models in families of Van der Pol and Rayleigh oscillators

Saha

Gangopadhyay

Ray

2020

Communications in Nonlinear Science and Numerical Simulation

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Van der Pol and Rayleigh oscillators are two traditional paradigms of nonlinear dynamics. They can be subsumed into a general form of Liénard-Levinson-Smith(LLS) system. Based on a recipe for finding out maximum number of limit cycles possible for a class of LLS oscillator, we propose here a scheme for systematic designing of generalised Rayleigh and Van der Pol families of oscillators with a desired number of multiple limit cycles. Numerical simulations are explicitly carried out for systematic search of the parameter space for birhythmic and tri-rhythmic systems and their higher order variants.

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Simple model for temperature control of glycolytic oscillations

Cited by 9 publications

References 17 publications

Nonequilibrium thermodynamics of glycolytic traveling wave: Benjamin-Feir instability

Nonequilibrium thermodynamics of glycolytic traveling wave: Benjamin-Feir instability

Similarities of Modulation by Temperature and by Electric Field

Systematic designing of bi-rhythmic and tri-rhythmic models in families of Van der Pol and Rayleigh oscillators

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