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Journal ArticleDOI

Instabilities and oscillations in ‘‘The Reversible Oregonator Model’’: A thermodynamic approach to calculate the excess entropy production (δmP) and the corresponding antisymmetric function (δmΠ)

15 May 1985-Journal of Chemical Physics (American Institute of Physics)-Vol. 82, Iss: 10, pp 4678-4682

AbstractNear equilibrium thermodynamic analysis of the reversible ‘‘Oregonator kinetic model’’ has been done using the entropy production technique of Prigogine in the range of the validity of the Onsager relations. Expressions for the excess entropy production (δmP) and the corresponding antisymmetric function (δmΠ) have been derived in terms of the rate constants of the steps, the concentrations of the reactants and products, steady state concentrations of the intermediates, and the coefficients of the real and imaginary parts of the complex differentials δX, δY, and δZ, which represent, respectively, the fluctuations from the steady state concentrations of the intermediates X, Y, and Z. Factors destabilizing the steady states have been determined and steps other than autocatalytic and cross catalytic are also found to be involved.

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Citations
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Journal ArticleDOI
Abstract: Thermodynamic analysis of the reversible Selkov model (a simple kinetic model describing glycolytic oscillations) has been done by an entropy production technique of Prigogine and it is shown that only the autocatalytic step can destabilize the steady state in this model. It is derived that at thermodynamic equilibrium, the product δS δP is always a positive quantity which appears to be a Chatelier‐like principle for local concentration fluctuation applicable to the autocatalytic step S ⇄ P of this model.

6 citations

Journal ArticleDOI
Abstract: Field expanded the five step Oregonator model of the oscillatory Belousov–Zhabotinskii reaction by introducing reversibility into the various steps. The present work involves the calculation of entropy flow (φ[S]) and entropy production (P[S]) in a specially designed reversible Oregonator. Entropy flow due to thermostatic temperature control and the osmotic transport of the reactants (A,B) and product (P) into and out of the reactor has been considered. Entropy production (e.p.) due to mixing of the reactants and product, diffusion of the intermediates (X, Y, and Z), and most importantly the chemical reactions has been considered. An attempt has been made to calculate the e.p. of the model using the results obtained by Field by numerical integration of the appropriate stiff kinetic differential equations. The following new results are obtained: (a) Limit cycle traces of e.p. against concentration of the oscillatory intermediates have been constructed. (b) The model resides on the low e.p. branch for about...

4 citations

Journal ArticleDOI
Abstract: Concentration oscillations are ubiquitous phenomenon in biochemical systems. The present paper considers the simple nonlinear chemical feedback model for standard glycolytic route with prototype autocatalytic steps. Quadratic S + P ⇄ 2P. Cubic S + 2P ⇄ 3P. We couple these steps to get the mixed quadratic-cubic model but remarkable array of complex behavior and oscillatory patterns as expected on coupling is surprisingly missing. The observation is in conformity with natural glycolytic alternatives like the Entner-Doudoroff (ED), and phosphoketolase pathways found in Archaea – Thermoproteustenax and other prokaryotes. The fundamental and the practical implications of our findings are thoroughly discussed with pilot calculations and numerical simulations supported via non-linear dynamic analysis. A basic kinetic scheme is suggested for natural glycolytic alternative, ED pathway with its comparison and contrast to other standard routes for glucose metabolism. A key outcome of the study is the phenomenon of oscillator death for the coupled network. A discussion on the thermodynamic aspect of entropy production rate for the model networks are also presented for a comparison.

1 citations

Journal ArticleDOI
Abstract: Oscillation is ubiquitous and important in both bio-engineering and biosystems. We here analyze the features of oscillation in a well-studied biochemical model of glycolysis with autocatalytic kinetic step. This Selkov model is followed deterministically using mass action kinetics. We explore the sensitivity analysis technique to assess degree of susceptibility of the system with respect to different input parameters for a thorough understanding of the merit of individual parameters controlling the core dynamics. Emphasis is concentrated on the system’s biological response via oscillation, bracketing the range of perturbation allowed to the kinetic parameters. An interesting observation is the switchover of the dynamics from non-oscillating to damping followed by stable sustained undulation with one or two controlling kinetic parameters which are quite appealing. The result may be illuminating in understanding the dynamics behind oscillations in biochemical systems in general. A key outcome of the study is the prioritization of most sensitive parameter for the network model controlling the dynamical features via scatterplot analysis.

References
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Journal ArticleDOI
Abstract: The chemical mechanism of Field, Koros, and Noyes for the oscillatory Belousov reaction has been generalized by a model composed of five steps involving three independent chemical intermediates. The behavior of the resulting differential equations has been examined numerically, and it has been shown that the system traces a stable closed trajectory in three dimensional phase space. The same trajectory is attained from other phase points and even from the point corresponding to steady state solution of the differential equations. The model appears to exhibit limit cycle behavior. By stiffly coupling the concentrations of two of the intermediates, the limit cycle model can be simplified to a system described by two independent variables; this coupled system is amenable to analysis by theoretical techniques already developed for such systems.

1,116 citations

Journal ArticleDOI
Abstract: That chemical reactions can exhibit all of the interesting and well known behavior of nonlinear oscillators is shown by collecting the scattered results in the literature for a simple reaction mechanism, supplementing them with some new results, and analyzing the behavior of the single chemical oscillator using the method of isoclines. Furthermore, two oscillators coupled in series illustrate the phenomena of synchronization, multiply periodic and almost‐periodic oscillations, and subharmonic resonance. Finally the reaction mechanism is modified to a form which is biochemically realistic and still behaves similarly to the original scheme.

185 citations

Book ChapterDOI
14 Mar 2007

93 citations