Feedback_Inhibition

This model shows an enzymatic reaction in which the product acts as an inhibitor to reduce the reaction progress.

Model number: 0139

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Description

    In this reaction, we start with an enzyme and substrate along with a product. 
    The enzyme and substrate bond, however, since the reaction goes to equilibrium,
    the product also bonds with the substrate forming an inhibitor to the formation of pure product.

$\frac{dS}{dt} \quad = \quad k_{-1} \ast ES \quad + \quad k_{-3} \ast SP \quad - \quad k_1 \ast S \ast E \quad - \quad k_3 \ast S \ast P \\ \frac{dES}{dt} \quad = \quad k_1 \ast S \ast E \quad - \quad k_{-1} \ast ES \quad - \quad k_2 \ast ES \quad + \quad k_{-2} \ast E \ast P \\ \frac{dP}{dt} \quad = \quad k_2 \ast ES \quad + \quad k_{-3} \ast SP \quad - \quad k_{-2} \ast E \ast P \quad - \quad k_3 \ast S \ast P \\ \frac{dSP}{dt} \quad = \quad k_3 \ast S \ast P \quad - \quad k_{-3} \ast SP \\ E \quad = \quad E_{\rm tot} \quad - \quad ES$

$K_s \quad = \quad \frac{k_{-1}}{k_1} \\ K_i \quad = \quad \frac{k_{-3}}{k_3} \\ K_p \quad = \quad \frac{k_2}{k_{-2}}$

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References

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

Related Models

Key Terms

Enzyme, Substrate, Product, Inhibitor, enzymatic reactions

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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 08Feb10, 2:28 pm.]

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.