Single enzyme irreversible Michaelis-Menten Eqs for Hx->Xa->Ua: Progress curves for xanthine oxidase reactions to oxidize hypoxanthine, Hx, to xanthine, Xa, to uric acid, Ua, and invokes inhibition by second product.(Data and equations from Escribano 1988).
Unidirectional fluxes Hx to Xa to Ua are facilitated by a single enzyme, Xanthine Oxidase (EC# 184.108.40.206), in a hyperoxic medium at pH 8, so it is oxidative. Equations are Michaelis-Menten. The strategy is to have two models operating simultaneously, the first one to fit the data of Fig 4 (Hx->xa->Ua) Escribano88, and the second to fit the data of Fig 5(Xa->Ua). Both models use the identical parameters, The optimizer minimizes the RMS error for five (5) data curves at once, thereby providing an overall best estimate of the parameters. This strategy maximizes the ratio of data to parameters and narrows the confidence limits on the parameters. The inhibitory action of Ua was found by Escribano et al (1988) in a set of inital velocity experiments, showing an apparent Ki, they report, of 178 uM, but no data were provided. As an exercise, set up this model to show a set of initial consumptions of Xa at varied background levels of Ua. Alternatively, add a new variable for tracer Ua to be produced from tracer Xa and show initial rates of production of tracer Ua.
The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.
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Bassingthwaighte James B., Chinn Tamara Meiko, Re-examining Michaelis-Menten enzyme kinetics for xanthine oxidase, Adv Physiol Educ 37: 37-48, 2013 Escribano, J., Garcia-Canovas, F., and Garcia-Carmona,F. A kinetic study of hypoxanthine oxidation by milk xanthine oxidase. Biochem. J. 254: 829-833, 1988. Michaelis L and Menten ML. Die Kinetik der Invertinwirkung. Biochem Z 49: 333-369, 1913.
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