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First-order reversible enzymatic reaction with binding of either substrate or product to enzyme and allows thermodynamic equilibrium.

Model number: 0130

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This model represents the enzymatic conversion of a single substrate, S, to a single product, P. First a binding of the solute to the enzyme, E, is achieved, which forms a substrate-enzyme complex, ES. The binding is followed by a reaction-release event, which yields the product and the enzyme. The entire binding-reaction-release sequence may be represented symbolically as

where k1 is the forward binding rate of S to E, k-1 is the backwards reaction rate of ES dissociating to E and S, k2 is the forward reaction rate of ES forming E and P, and k-2 is the reverse reaction rate of E and P producing ES.


This reaction is governed by a system of three ODEs which describe the concentrations of the substrate, enzyme complex and product. The fourth equation to close the system is given by specifying the total amount of enzyme present which must be conserved. The initial conditions given are that all of the substrate and no complex or product are present at time t=0. The system of equations are:

The backward reaction rates in this model are determined from the equilibrium dissociation rates of S binding to E and P binding to E and are given by:

where Ks is the equilibrium dissociation rate of S binding to E and Kp of p binding to E.

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  Bassingthwaighte JB.: Enzymes and Metabolic Reactions, Chapter 10 in "Transport and Reactions 
  in Biological Systems", Pages 7-8	

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Key Terms

Transport Physiology, Chemical Reaction Enzymes, Enzymatic Reaction, Single Enzyme, Reversible, Michaelis-Menten Kinetics, Briggs-Haldane Kinetics RELATED MODELS: PGIsomerase

Model History

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Please cite 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.

[This page was last modified 02Jul12, 2:39 pm.]

Model development and archiving support at 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.