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Designing an enzymatic oscillator: Bistability and feedback controlled oscillations with glucose oxidase in a continuous flow stirred tank reactor
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10.1063/1.2378833
/content/aip/journal/jcp/125/19/10.1063/1.2378833
http://aip.metastore.ingenta.com/content/aip/journal/jcp/125/19/10.1063/1.2378833
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Figures

Image of FIG. 1.
FIG. 1.

(a) Bistability in system (15) and (16) at , , , and . Dashes denote unstable steady state. (b) Bistability in a CSTR with influxes of GO, glucose, , and ferricyanide . The volume of the reactor, , is , , , , is varied from , and is varied from , where the subscript 0 denotes input concentrations in the CSTR without reaction.

Image of FIG. 2.
FIG. 2.

Experimental setup. -E, electrode; MS, magnetic stirrer; black bar inside the CSTR is a magnetic stirrer bar; PP1, PP2, and PP3 are peristaltic pumps. Dotted lines are electrical connections. A meter between -E and PC is not shown. In preliminary experiments we used five pumps (two additional syringe pumps) to vary input concentrations of some reactants.

Image of FIG. 3.
FIG. 3.

Reaction of glucose with catalyzed by GO in a batch reactor. (a) experiment with , , 10, (curve 2) 7.5, (curves 3 and 4) 5, (curve 5) 2.5, and [GO] 0.5 and (curve 4) 1. (b) Comparison between experiment (curve 1) and model (C1)–(C3), (C5)–(C11), (C17), and (C18) (curves 2 and 3). For curve 1: , , , and . For curves 2 and 3: (curve 2) and (curve 3), , , , , , , , , , , , , and .

Image of FIG. 4.
FIG. 4.

Experimentally observed oscillations in a CSTR for GO-catalyzed oxidation of glucose by ferricyanide supplemented by a negative feedback, . , , and . (a) , , , and . (b) , , , and . [(c) and (d)] , , , and 4.0 and (d) 3.8.

Image of FIG. 5.
FIG. 5.

Experimental and theoretical dynamic phase diagrams. (a) . Experiment (symbols) in a CSTR. Black rhombs denote oscillations, “+” are high steady state, and “×” are low steady state. Concentrations: , , , , and . Curves 1 and 2 are result of linear stability analysis of Eqs. (32) and (33) with parameters , , , , , , , , , and . Theoretical oscillatory region is between curves 1 and 2; curve 2 is supercritical Hopf bifurcation and curve 1 is subcritical Hopf or saddle bifurcation. (b) . Symbols and parameters as in (a), except , , and . (c) . Symbols and parameters as in (a), except (experiment); 0.0025 and (curves 3 and 4) 0.006 (calculations); curves 2 and 4 show supercritical Hopf bifurcation; curves 1 and 3 show subcritical Hopf or saddle. Oscillatory region lies between curves 1 (3) and 2 (4). (d) Bistability region for experimental system GO-glucose-ferricyanide in a CSTR, Symbols: full circles, bistability between and ; +, low ; , high . and .

Image of FIG. 6.
FIG. 6.

Linear stability analysis of Eqs. (32) and (33) at (curves 1 and 2 in and b) and eqs. (17) and (18) (, curves 3 and 4). Oscillatory regions are between curves 1 and 2 for model (32) and (33) and between curves 3 and 4 for for model (17) and (18). Curve 1 is subcritical Hopf line or saddle, curve 2 is supercritical Hopf bifurcation. Parameters for curves 1 and 2 in (a): , , , , , , , , and . Parameters for curves 3 and 4 in (a) , , and . (b) , , , , , , , , , and .

Image of FIG. 7.
FIG. 7.

(a) Diagram for model (32) and (33). Oscillatory region is between curves 1 and 2. Curve 3 is frequency of oscillations for parametric points that are very close to curve 1. For curve 1, ; for curve 2, . (b) Typical dependence of the frequency (curve 3) and amplitude of pH oscillations for model (32) and (33) at constant . Curves 1 and 2 are the maximum and minimum of oscillations. Parameters: , , , , , , and ; (a) , , and ; (b) , , , and .

Image of FIG. 8.
FIG. 8.

Examples of oscillations in model (32) and (33) at . Parameters: , , , , and ; (a) , , , , 4.1 and (curve 2) 4.05 and ; (b) , 0.0087 and (curve 2) 0.0084, , , , and .

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/content/aip/journal/jcp/125/19/10.1063/1.2378833
2006-11-17
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Designing an enzymatic oscillator: Bistability and feedback controlled oscillations with glucose oxidase in a continuous flow stirred tank reactor
http://aip.metastore.ingenta.com/content/aip/journal/jcp/125/19/10.1063/1.2378833
10.1063/1.2378833
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