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# One_Enzyme_Reversible

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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## Description

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
$\large \mathrm{ S + E \qquad \begin{array}{c} k_1 \\ \longrightarrow \\ \longleftarrow \\ k_{-1} \end{array} \qquad ES \qquad \begin{array}{c} k_2 \\ \longrightarrow \\ \longleftarrow \\ k_{-2} \end{array} \qquad P + E}$
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.

## Equations

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:
$\large E = E_{\rm tot} \quad - \quad ES \\ \frac{dS}{dt} = k_{-1}\ast ES \quad - \quad k_1\ast S\ast E \\ \frac{dES}{dt} = k_1*S*E \quad - \quad k_{-1}*ES \quad - \quad k_2*ES \quad + \quad k_{-2}*E*P \\ \frac{dP}{dt} = k_2*ES \quad - \quad k_{-2}*E*P$
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:
$\large K_s = \frac{k_{-1}}{k_1}\\ K_p = \frac{k_2}{k_{-2}}$
where Ks is the equilibrium dissociation rate of S binding to E and Kp of p binding to E.

## References

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



## Key Terms

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

## 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.