Model number

Three substrates converted by two 1st order reversible enzymatic reactions.

fig 1



Two reversible enzyme catalyzed reactions convert A to B and B to C. There are two enzymes, E1 and E2. The intermediate complexes are AE1 and CE2. The "on" rate constants are given and the "off" rate constants are given as the product of the "on" rate constants multiplying dissociation constants.



     Off Rate Equations

e0 ,  e1

e2 ,  e3 .

     Ordinary Differential Equations






     Mass Balance Equations for Enzymes

e9  , and  e10

     Initial Conditions

e11 ,  e12 ,  e13 ,  e14 , and  e15 .


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 JB.: Enzymes and Metabolic Reactions, Chapter 10 in 
    "Transport and Reactions in Biological Systems"
   Lehninger AL. Biochemistry. New York: Worth Publishers, Inc., 1975.
Key terms
Progress curves
reversible reactions
equilibrium dissociation first order enzyme kinetics
Competitive Binding

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.

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.