Model number

Single enzyme reversible Michaelis-Menten Eqs for Hx->Xa->Ua, that is, two reactions on one enzyme. Data are progress curves for xanthine oxidase reactions to oxidize hypoxanthine, Hx, to xanthine, Xa, to uric acid, Ua, without inhibition by product.(Data from Escribano 1988).


 Bidirectional fluxes Hx <--> Xa <--> Ua facilitated 
 by a single enzyme, Xanthine Oxidase (EC#, in a hyperoxic medium at pH 8,
 so it is oxidative. The equations are Michaelis-Menten, forward and backward, so 
 the concentration changes are driven by the NET flux through each reaction.

 The optimization strategy is to have two models
 operating simultaneously, the first one to fit the data of Fig 4 (Hx->xa->Ua) of
 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.

Download JSim model project file


Help running a JSim model.

 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.

 Hofmeyr J-HS and Cornish-Bowden A. The reversible Hill equation:  
 How to incorporate cooperative  enzymes into metabolic models. 
 Comput Appl Biosci 13: 377-385, 1997.

 Houston M, Estevez M, Chumley P, Aslan M, Marklund S, Parks D, and Freeman BA. 
 Binding of Xanthine Oxidase to vascular endothelium. Kinetic characterization 
 and oxidative impairment of nitric oxide-dependent signaling. 
 J Biol Chem  274: 4985-4994, 1999.

 Michaelis L and Menten ML. Die Kinetik der Invertinwirkung.
 Biochem Z 49: 333-369, 1913.
Key terms
purine nucleosides
xanthine oxidase
simple Michaelis-Menten equations
double reaction
serial reactions
progress curves
bovine milk
uric acid
saturable binding

Please cite https://www.imagwiki.nibib.nih.gov/physiome in any publication for which this software is used and send one reprint to the address given below:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

Model development and archiving support at https://www.imagwiki.nibib.nih.gov/physiome provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.