Progress3.Enz

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

Model number: 0268

Run Model:

(Java model applet may take 10-20 seconds to load.)

Description

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.

Equations

Off Rate Equations

${\it k_{offA}}={\it k_{onA}}\cdot {\it KA}$ , ${\it k_{offBE_1}}={\it k_{onBE_1}}\cdot {\it KB_1}$
${\it k_{offBE_2}}={\it k_{onBE_2}}\cdot {\it KB_2}$ , ${\it k_{offC}}={\it k_{onC}}\cdot {\it KC}$ .

Ordinary Differential Equations

${\frac {d}{dt}}A=-{\it k_{onA}}\cdot A \cdot {\it E_1}+{\it k_{offA}}\cdot {\it AE_1}$

${\frac {d}{dt}}{\it AE_1}= {\it k_{onA}}\cdot A \cdot{\it E_1}-{\it k_{offA}}\cdot {\it AE_1} +{\it k_{onBE_1}}\cdot B \cdot {\it E_1}- {\it k_{offBE_1}}\cdot {\it AE_1}$

${\frac {d}{dt}}B=-{\it k_{onBE_1}}\cdot B \cdot {\it E_1}+{\it k_{offBE_1}}\cdot {\it AE_1}-{\it k_{onBE_2}}\cdot B \cdot {\it E_2}+{ \it k_{offBE_2}}\cdot {\it CE_2}$

${\frac {d}{dt}}{\it CE_2}={\it k_{onBE_2}}\cdot B \cdot {\it E_2}-{\it k_{offBE_2}}\cdot {\it CE_2} +{\it k_{onC}}\cdot C \cdot {\it E_2 }-{\it k_{offC}}\cdot {\it CE_2}$

${\frac {d}{dt}}C=-{\it k_{onC}}\cdot C \cdot {\it E_2}+{\it k_{offC}}\,{\it CE_2}$

Mass Balance Equations for Enzymes

${\it E_1}={\it E_{1tot}}-{\it AE_1}$ , and ${\it E_2}={\it E_{2tot}}-{\it CE_2}$ .

Initial Conditions

${\it A} \left( 0 \right) ={\it A_0}$ , ${\it AE_1} \left( 0 \right) ={\it AE_{10}}$ , ${\it B} \left( 0 \right) ={\it B_0}$ , ${\it CE_2} \left( 0 \right) ={\it CE_{20}}$ , and ${\it C} \left( 0 \right) ={\it C_0}$ .

The equations for this model may also 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 project file

References

    Bassingthwaighte JB.: Enzymes and Metabolic Reactions, Chapter 10 in 
    "Transport and Reactions in Biological Systems"
    
   Lehninger AL. Biochemistry. New York: Worth Publishers, Inc., 1975.

Related Models

Single Compartment Models:

Two Compartment Models:

N>2 Compartment Models:

Osmotic Exchange:

Pharmacology:

Key Terms

Progress curves, reversible reactions, equilibrium dissociation first order enzyme kinetics, Competitive Binding, tutorial

Model Feedback

We welcome comments and feedback for this model. Please use the button below to send comments:

Model History

Get Model history in CVS.

Acknowledgements

Please cite www.physiome.org 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 09Feb10, 10:11 am.]

Model development and archiving support at physiome.org provided by the following grants: 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.