Model number

This model simulates a single enzyme reaction which occurs inside a vesicle where the substrate and product diffuse across the vesicle boundary on each end of the reaction.


This model represents the enzymatic conversion of a single substrate, S, to a single product, P, inside a vesicle such as an endoplasmic reticulum, across a cell membrane or inside an organelle such as a lysosome. First the solute must permeate across the permeable boundary and then it binds to the enzyme forming a substrate-enzyme complex. This is followed by a reaction-release step which yields the product and the enzyme and then diffusion of the product out of the vesicle into the surrounding volume. The reaction inside the vesicle is given as follows:


where P and S are defined previously, E represents the enzyme, ES the substrate-enzyme complex, 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 the reverse reaction rate of E and P producing ES. The permeability across the vesicle boundary are represented by PVs and PVp for the substrate and product respectively. The diagram shown below gives the entire reaction including diffusion across the vesicle boundaries.

   | VolOut                                                                |
   |             o-------------------------------------------o             |
   |             | VolIn                                     |             |
   |             |                                           |             |
   |         PVs |               k1-->       k2-->           | PVp         |
   |  Sout <-----|-----> S + E <------> ES <-------> P <-----|-----> Pout  |
   |             | PVs          <--k_1      <--k_2       PVp |             |
   |             |                                           |             |
   |             |                                           |             |
   |             o-------------------------------------------o             |
   |                                                                       |


This reaction is governed by a system of five ODEs which describe the concentrations of the substrate and product both inside and outside the vesicle and the concentration of the complex, ES, inside the vesicle. The sixth 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 is outside the vesicle 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 binding to E and P binding to E and are given by:


where Ks is the equilibrium dissociation rate of S binding to E and Kp of p binding to E.

Download JSim model project file
   Bassingthwaighte JB.: Enzymes and Metabolic Reactions, Chapter 10 in 
   "Transport and Reactions in Biological Systems", Pages 30-32
Key terms
Transport Physiology
Chemical Reaction Enzymes
Enzymatic Reactions
Single Enzyme
Michaelis-Menten Kinetics
Cell Membrane

Please cite 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 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.