Two sequential, first-order enzymatic reactions S <--> P with substrates binding to enzymes, and reversible product formation. Reactions facilitated by a single enzyme, Xanthine Oxidase.

Description

 Bidirectional fluxes Hx <--> Xa <--> Ua facilitated 
 by a single enzyme, Xanthine Oxidase (EC# 1.7.3.2), in a hyperoxic medium at pH 8,
 so it is oxidative. The equations are standard reactions, forward and backward, so 
 the concentration changes are driven by the NET flux through each reaction. The
 enzyme is assumed to bind only 1 substrate at a time, so all three of Hx, Xa and Ua 
 compete for the single site.

 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.

 A conservation test is provided by:
 Uacons = Hx0 + Xa0 + Ua0 - Hx - Xa - EHx - EXa; 
 where the Test is that Uacons should = Ua.

Equations

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.