The dynamic and steady-state behaviors of two open substrate cycles sharing a common interconversion enzyme are investigated in a homogeneous flow-through reactor. Lactate dehydrogenase (LDH) converts pyruvate and NADH into lactate and NAD, respectively. In turn, NAD (+ formate) is recycled into NADH (+ CO 2 ) by formate dehydrogenase (FDH), and in the presence of the oxidized form of 2-(hydroxymethyl)-6-methoxy-1,4-benzoquinone (Q), lactate is reoxidized into pyruvate (+ Q red ) by flavocytochrome b 2 (FCytb 2 ). When operating under thermodynamically open conditions by a continuous supply of pyruvate, quinone, NADH, and formate, this multienzyme system can exhibit multiple steady states under the form of dynamic hysteresis when using, among others, the pyruvate input concentration as the control parameter. This nonlinear behavior results from the strong inhibition of LDH exerted by its substrate pyruvate. The numerical predictions of a simple mathematical model, taking into account the coupling between the actual enzyme rate equations and mass transfers, agree both quantitatively and qualitatively with the observed experiments.
The dynamic and steady-state behaviors of three coupled substrate cycles sharing interconversion enzymes are investigated in a homogeneous flow-through reactor (CSTR). Lactate dehydrogenase (LDH) converts pyruvate (Prv) and NADH into lactate (Lac) and NAD, respectively. In turn, NAD [and glucose 6-phosphate (Glc6P)] is recycled into NADH (and gluconolactone 6-phosphate) by glucose 6-phosphate dehydrogenase, and in the presence of ferricyanide (Ferri), Lac is reoxidized into Prv [and ferrocyanide (Ferro)]. Finally, Ferro is reoxidized in turn by a reticulated vitreous carbon (RVC) electrode poised at a controlled potential in a three-electrode configuration. Under thermodynamically open conditions with a constant supply of Prv, Ferri, NADH, and Glc6P, this multienzyme system exhibits irreversible transitions between alternative stable steady states (bistability without hysteresis) when the electrochemical rate of ferrocyanide recycling is varied. This nonlinear behavior results from the strong inhibition of LDH exerted by its substrate Prv. In the absence of an electrochemically driven recycling of ferrocyanide, only reversible bistability (dynamic hysteresis) may be observed [Simonet et al. J. Phys. Chem. 1996, 100, 19148]. The numerical predictions of a simple mathematical model taking into account the coupling between the actual enzyme rate equations, mass transfers, and electrochemical recycling agree both qualitatively and quantitatively with the observed experiments.
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