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.
Bidirectional fluxes Hx <--> Xa <--> Ua facilitated by a single enzyme, Xanthine Oxidase (EC# 22.214.171.124), 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.
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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 Bassingthwaighte JB.: Enzymes and Metabolic Reactions, Chapter 10 in "Transport and Reactions in Biological Systems", Pages 7-8 Escribano J, Garcia-Canovas F, and Garcia-Carmona F. A kinetic study of of hypoxanthine oxidation by milk xanthine oxidase. Biochem J. 254: 829-833, 1988. Schwartz LM, Bukowski TR, Revkin JH, and Bassingthwaighte JB. Cardiac endothelial transport and metabolism of adenosine and inosine. Am J Physiol Heart Circ Physiol 277: H1241-H1251, 1999. Kroll K, Bukowski TR, Schwartz LM, Knoepfler D, and Bassingthwaighte JB. Capillary endothelial transport of uric acid in the guinea pig heart. Am J Physiol Heart Circ Physiol 262: H420-H431, 1992. Kroll K, Bukowski TR, King RB, Chan IS, and Bassingthwaighte JB Enzyme holdup of xanthine in production of uric acid from hypoxanthine endothelial cells in guinea pig heart. FASEB J 7: A890, 1993. Bassingthwaighte JB, Bukowski T, and Kroll K. Capillary transport and metabolism of hypoxanthine, xanthine and uric acid in the guinea pig heart. Am J Physiol Heart Circ Physiol (in prep) 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.
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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.