Two_Enzyme_Reversible

This model simulates the competitive binding of two different enzymes which result in a similar product.

Model number: 0132

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Description

This model represents the enzymatic conversion of a single substrate, S, to a single product, P by two competing enzymes. First a binding of the solute to an enzyme, E1 or E2, is achieved, which forms a substrate-enzyme complex, ES1 or ES2. 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
$\mathrm{ \qquad \qquad \qquad \qquad \qquad E_1 \qquad \begin{array}{c} k_{11} \\ \longrightarrow \\ \longleftarrow \\ k_{-11} \end{array} \qquad E_1S \qquad \begin{array}{c} k_{21} \\ \longrightarrow \\ \longleftarrow \\ k_{-21} \end{array} \qquad E_1 \\ S \quad + \quad \begin{array}{c} \nearrow \\ \searrow \end{array} \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad \begin{array}{c} \searrow \\ \nearrow \end{array} \quad + \quad P \\ \qquad \qquad \qquad \qquad \qquad E_2 \qquad \begin{array}{c} k_{12} \\ \longrightarrow \\ \longleftarrow \\ k_{-12} \end{array} \qquad E_2S \qquad \begin{array}{c} k_{22} \\ \longrightarrow \\ \longleftarrow \\ k_{-22} \end{array} \qquad E_2}$
where k₁₁ is the forward binding rate of S to E₁, k_-11 is the backwards reaction rate of E₁S dissociating to E₁ and S, k₂₁ is the forward reaction rate of E₁S forming E₁ and P, k_-21 is the reverse reaction rate of E₁ and P producing E₁S, k₁₂ is the forward binding rate of S to E₂, k_-12 is the backwards reaction rate of E₂S dissociating to E₂ and S, k₂₂ is the forward reaction rate of E₂S forming E₂ and P, and k_-22 is the reverse reaction rate of E₂ and P producing E₂S.

Equations

This reaction is governed by a system of four ODEs which describe the concentrations of the substrate, enzyme complex for enzyme 1 and enzyme 2 and product. The fifth and sixth equations to close the system are given by specifying the total amount of enzyme 1, E_1tot, and enzyme 2, E_2tot present which must be conserved. The initial conditions specify that all of the substrate and no complex or product are present at time t=0. The system of equations are:

$\frac{dS}{dt} = k_{-11} \ast E_1S \quad - \quad k_{11} \ast S \ast E_1 + k_{-12} \ast E_2S \quad - \quad k_{12} \ast S \ast E_2 \\ \frac{dE_1S}{dt} = k_{11} \ast S \ast E_1 \quad - \quad k_{-11} \ast E_1S \quad - \quad k_{21} \ast E_1S \quad + \quad k_{-21} \ast E_1 \ast P \\ \frac{dE_2S}{dt} = k_{12} \ast S \ast E_2 \quad - \quad k_{-12} \ast E_2S \quad - \quad k_{22} \ast E_2S \quad + \quad k_{-22} \ast E_2 \ast P \\ \frac{dP}{dt} = k_{21} \ast E_1S \quad - \quad k_{-21} \ast E_1 \ast P + k_{22} \ast E_2S \quad - \quad k_{-22} \ast E_2 \ast P\\ E_1 = E_{1 \rm tot} \quad - \quad E_1S \\ E_1 = E_{2 \rm tot} \quad - \quad E_2S$
The backward reaction rates in this model are determined from the equilibrium dissociation rates of S and P binding to the enzymes and are given by:
$K_{s1} = \frac{k_{-11}}{k_{11}} \\ K_{p1} = \frac{k_{21}}{k_{-21}} \\ K_{s2} = \frac{k_{-12}}{k_{12}} \\ K_{p2} = \frac{k_{22}}{k_{-22}}$
where K_s1 is the equilibrium dissociation rate of S binding to E₁, K_p1 of P binding to E₁, K_s2 of S binding to E₂ and K_p2 of P binding to E₂.

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References

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

Related Models

Key Terms

Enzymatic Reaction, Competitive Binding, reversible reaction, two enzyme

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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, 2:24 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.