Three steady state situation in an open chemical reaction system. I

Geiseler, W.; Follner, H.

doi:10.1016/0301-4622(77)87001-4

Cited by 78 publications

(19 citation statements)

References 11 publications

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“…Bistability has previously been shown to occur in a number of chemical or biochemical systems, both experimentally (Degn, 1968;Naparstek et al, 1974;Geiseler and Föllner, 1977;Eschrich et al, 1980;Ganapathisubramanian and Showalter, 1983;Frenzel et al, 1995) and in theoretical models (Edelstein, 1970;Babloyantz and Nicolis, 1972;Boiteux et al, 1980;Lisman, 1985;Goldbeter and Moran, 1987;Hervagault and Canu, 1987;Gray and Scott, 1994). The phenomenon is due to the nonlinearity of kinetic equations.…”

Section: Discussionmentioning

confidence: 97%

Bistability in the Isocitrate Dehydrogenase Reaction: An Experimentally Based Theoretical Study

Guidi

Carlier

Goldbeter

1998

Biophysical Journal

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The enzyme isocitrate dehydrogenase (IDH, EC 1.1.1.42) can exhibit activation by one of its products, NADPH. This activation is competitively inhibited by the substrate NADP+, whereas NADPH competes with NADP+ for the catalytic site. Experimental observations briefly presented here have shown that if IDH is coupled to another enzyme, diaphorase (EC 1.8.1.4), which transforms NADPH into NADP+, the system can attain either one of two stable states, corresponding to a low and a high NADPH concentration. The evolution toward either one of these stable states depends on the time of addition of diaphorase to the medium containing IDH and its substrate NADP+. We present a theoretical and numerical analysis of a model for the IDH-diaphorase bienzymatic system, based on the regulatory properties of IDH. The results confirm the occurrence of bistability for parameter values derived from the experiments. Depending on the total concentration of NADP+ plus NADPH and the concentration of IDH, the system can either admit a single steady state or display bistability. We obtain an expression for the critical time t*, before which diaphorase addition leads to the lower steady state and after which addition of the enzyme leads to the upper steady state of NADPH. The analysis is extended to the case where the second substrate of IDH, isocitrate, is consumed in the course of the reaction without being regenerated. Bistability occurs only as a transient phenomenon in these conditions.

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Section: Discussionmentioning

confidence: 97%

Bistability in the Isocitrate Dehydrogenase Reaction: An Experimentally Based Theoretical Study

Guidi

Carlier

Goldbeter

1998

Biophysical Journal

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“…Instead, the trap hypothesis identifies substrate inhibition, an inherent and well-studied feature of some enzymes that can, in response to pathogenic triggers, unmask metabolic bistability. Bistability is a phenomenon unique to nonlinear dynamics that has been studied for decades [23,24,58,59]. The essential fact of bistability is that it is possible for a bistable system to be driven into an alternative (e.g., pathological) steady-state and be maintained in that chronic disease state long after the trigger is removed and without requiring a chronic infection or chronic exposure to a toxin .…”

Section: Discussionmentioning

confidence: 99%

The IDO Metabolic Trap Hypothesis for the Etiology of ME/CFS

Kashi

Davis

Phair³

2019

Diagnostics

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Myalgic encephalomyelitis/chronic fatigue syndrome (ME/CFS) is a debilitating noncommunicable disease brandishing an enormous worldwide disease burden with some evidence of inherited genetic risk. Absence of measurable changes in patients’ standard blood work has necessitated ad hoc symptom-driven therapies and a dearth of mechanistic hypotheses regarding its etiology and possible cure. A new hypothesis, the indolamine-2,3-dioxygenase (IDO) metabolic trap, was developed and formulated as a mathematical model. The historical occurrence of ME/CFS outbreaks is a singular feature of the disease and implies that any predisposing genetic mutation must be common. A database search for common damaging mutations in human enzymes produces 208 hits, including IDO2 with four such mutations. Non-functional IDO2, combined with well-established substrate inhibition of IDO1 and kinetic asymmetry of the large neutral amino acid transporter, LAT1, yielded a mathematical model of tryptophan metabolism that displays both physiological and pathological steady-states. Escape from the pathological one requires an exogenous perturbation. This model also identifies a critical point in cytosolic tryptophan abundance beyond which descent into the pathological steady-state is inevitable. If, however, means can be discovered to return cytosolic tryptophan below the critical point, return to the normal physiological steady-state is assured. Testing this hypothesis for any cell type requires only labelled tryptophan, a means to measure cytosolic tryptophan and kynurenine, and the standard tools of tracer kinetics.

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“…Field and Noyes were able to construct a simplified mathematical model [11], now known as the Oregonator, which exhibits oscillatory limit cycles. The model also successfully describes the fascinating features of the complex phenomena seen in the BZ reaction, both temporal, such as excitability [12,13], bistability [14], stirring effects [15,16], quasiperiodicity, and chaos [17,18], and spatial, including traveling waves [19], target and spiral patterns [20,21], scroll rings [22], and their orientation dynamics in advective fields [23]. In our study, we will, in particular review the evidence supporting the presence of long range correlation in this reaction.…”

Section: Long Range Correlations Have Been Found In a Widementioning

confidence: 99%

Long Range Correlations in Chemical Oscillations

Chowdhury¹,

Lahiri²,

Iyengar³

et al. 2016

JCSE

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Abstract:The purpose of the present study is to determine whether a long range correlation is present in BZ (Belousov-Zhabotinskii) reaction and how this correlation varies with the change in concentration of the solution. To explore the dynamics of the system with change in concentration, phase space plot and power spectrum are studied. Hurst exponent is estimated using lo g log plot and R/S technique. We discuss the results which uncover how the system changes from an excitable steady state to a limit cycle.

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Three steady state situation in an open chemical reaction system. I

Cited by 78 publications

References 11 publications

Bistability in the Isocitrate Dehydrogenase Reaction: An Experimentally Based Theoretical Study

Bistability in the Isocitrate Dehydrogenase Reaction: An Experimentally Based Theoretical Study

The IDO Metabolic Trap Hypothesis for the Etiology of ME/CFS

Long Range Correlations in Chemical Oscillations

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