Mixed-mode oscillations in a homogeneous <b>
                     <i>p</i>
                  </b>H-oscillatory chemical reaction system

Bakeš, D.; Schreiberová, Lenka; Schreiber, Igor; Hauser, M.

doi:10.1063/1.2779857

Cited by 28 publications

(21 citation statements)

References 56 publications

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“…Another example of a biochemical oscillator that can display complex behavior in vitro is the peroxidase-oxidase reaction [4]. In this system, the peroxidase enzyme catalyzes oxidization of a substrate e.g.…”

Section: Introductionmentioning

confidence: 99%

Kinetics of the urea–urease clock reaction with urease immobilized in hydrogel beads

Bubanja

Bánsági

Taylor

2017

Reac Kinet Mech Cat

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Feedback driven by enzyme catalyzed reactions occurs widely in biology and has been well characterized in single celled organisms such as yeast. There are still few examples of robust enzyme oscillators in vitro that might be used to study nonlinear dynamical behavior. One of the simplest is the urea-urease reaction that displays autocatalysis driven by the increase in pH accompanying the production of ammonia. A clock reaction was obtained from low to high pH in batch reactor and bistability and oscillations were reported in a continuous flow rector. However, the oscillations were found to be irreproducible and one contributing factor may be the lack of stability of the enzyme in solution at room temperature. Here, we investigated the effect of immobilizing urease in thiol-poly(ethylene glycol) acrylate (PEGDA) hydrogel beads, prepared using emulsion polymerization, on the ureaurease reaction. The resultant mm-sized beads were found to reproduce the pH clock and, under the conditions employed here, the stability of the enzyme was increased from hours to days.

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Section: Introductionmentioning

confidence: 99%

Kinetics of the urea–urease clock reaction with urease immobilized in hydrogel beads

Bubanja

Bánsági

Taylor

2017

Reac Kinet Mech Cat

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“…The interest devoted to the study of folded singularities is due to the fact that the occurrence of relaxation and canard cycles is underlain by the passage of system trajectory near these particular points [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. This important result was established for the first time by Benoît et al [2] while studying relaxation oscillations in the van der Pol oscillator (vdPO) subjected to constant forcing.…”

Section: Introductionmentioning

confidence: 95%

Quasi-static transient and mixed mode oscillations induced by fractional derivatives effect on the slow flow near folded singularity

2014

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This paper aims at offering an insight into the dynamical behaviors of incommensurate fractionalorder singularly perturbed van der Pol oscillators subjected to constant forcing, especially when the forcing is close to Andronov-Hopf bifurcation points. These bifurcation points are predicted thanks to the theorem on stability of incommensurate fractionalorder systems, as functions of the forcing and fractional derivative orders. When the forcing is chosen near Andronov-Hopf bifurcation, the dynamics of fractional-order systems show a static-looking transient regime whose length increases exponentially with the closeness to the bifurcation point. This peculiar phenomenon is not common in numerical simulation of dynamical systems. We show that this quasi-static transient behavior is due to the combine action of the slow passage effect at folded saddle-node singularity and fractional derivation memory effect on the slow flow around this singularity; this forces the system to remain for a long time in the vicinity of its equilibrium point, though unstable. The system frees oneself from this quasi-static transient state by spiraling before entering relaxation oscillation. Such a situation results in mixed mode oscillations in the oscillatory regime. One obtains mixed mode oscillations from a very simple system: A two-variable system subjected to constant forcing.

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“…Complex behaviour should be expected, as we are dealing with a high-dimensional dynamical system. (Chaotic and bursting dynamics have been recorded experimentally in this system [19,33].) At these low feed concentrations of reactants, the small specific reaction heat is absorbed by and lost to the system, which remains nearly isothermal.…”

Section: Characterization Of the Thp Oscillatormentioning

confidence: 99%

The life story of hydrogen peroxide II: a periodic pH and thermochemical drive for the RNA world

Ball

Brindley

2015

J. R. Soc. Interface.

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It is now accepted that primordial non-cellular RNA communities must have been subject to a periodic drive in order to replicate and prosper. We have proposed the oxidation of thiosulfate by hydrogen peroxide as this drive. This reaction system behaves as (i) a thermochemical and (ii) a pH oscillator, and in this work, we unify (i) and (ii) for the first time. We report thermally selfconsistent, dynamical simulations in which the system transitions smoothly from nearly isothermal pH to fully developed thermo-pH oscillatory regimes. We use this oscillator to drive simulated replication of a 39-bp RNA species. Production of replicated duplex under thermo-pH drive was significantly enhanced compared with that under purely thermochemical drive, effectively allowing longer strands to replicate. Longer strands are fitter, with more potential to evolve enzyme activity and resist degradation. We affirm that concern over the alleged toxicity of hydrogen peroxide to life is largely misplaced in the current context, we survey its occurrence in the solar system to motivate its inclusion as a biosignature in the search for life on other worlds and highlight that pH oscillations in a spatially extended, bounded system manifest as the fundamental driving force of life: a proton gradient.

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Mixed-mode oscillations in a homogeneous p H-oscillatory chemical reaction system

Cited by 28 publications

References 56 publications

Kinetics of the urea–urease clock reaction with urease immobilized in hydrogel beads

Kinetics of the urea–urease clock reaction with urease immobilized in hydrogel beads

Quasi-static transient and mixed mode oscillations induced by fractional derivatives effect on the slow flow near folded singularity

The life story of hydrogen peroxide II: a periodic pH and thermochemical drive for the RNA world

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