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

## 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

where k_{11} is the forward binding rate of S to E_{1}, k_{-11} is the backwards reaction rate of E_{1}S dissociating to E_{1} and S, k_{21} is the forward reaction rate of E_{1}S forming E_{1} and P, k_{-21} is the reverse reaction rate of E_{1} and P producing E_{1}S, k_{12} is the forward binding rate of S to E_{2}, k_{-12} is the backwards reaction rate of E_{2}S dissociating to E_{2} and S, k_{22} is the forward reaction rate of E_{2}S forming E_{2} and P, and k_{-22} is the reverse reaction rate of E_{2} and P producing E_{2}S.

## 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:

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:

where K_{s1} is the equilibrium dissociation rate of S binding to E_{1}, K_{p1} of P binding to E_{1}, K_{s2} of S binding to E_{2} and K_{p2} of P binding to E_{2}.

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

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

Please cite https://www.imagwiki.nibib.nih.gov/physiome 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 https://www.imagwiki.nibib.nih.gov/physiome 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.