First-order reversible enzymatic reaction with binding of either substrate or product to enzyme and allows thermodynamic equilibrium. Uses two methods, the enzyme binding and
This model represents the enzymatic conversion of a single substrate, S, to a single product, P. First is binding of the solute to the enzyme, E, forming the substrate-enzyme complex, ES. The binding is followed by a reaction-release event, which yields the product and releases free enzyme. The model parameters can be adjusted to fit Michaelis-Menten conditions (Substrate concentrations high compared to enzyme; on/off reaction fast compared to forward reaction rate) and Briggs-Haldane conditions where the on-rate is low but not over a wide range of conditions. A second part of the program is given for the same enzyme concentrations and kinetics constants but now expressed as "reversible Michaelis Menten Equations. Comparisons are odious, 'tis said. This one reveals the inaccuracy of the MM approximation for a reversible reaction when Kp >> Ks: Run the loops; these are set up to decrease Etot by 10-fold per loop, and to increase both k1 and k_2 by 10-fold so that the apparent forward and backward Vmax's are unchanged. The result is that successive reductions of Etot results in a better and better approximation of the true kinetics to the MM-kinetics, as expected, because the fundamental assumption of the MM kinetics is that S >> Etot. However, as the reaction proceeds toward equilibrium (here Kp/Ks = 5000 = P(equil)/S(equil), the MM expression cannot be correct. The MM expression contains contradictory assumptions, namely that k1 and k_1 are fast compared to k2 (for the S -> P reaction), and that k2 and k_2 are fast compared to k_1. Therefore the MM fails when P > 0.3*S0 in this progress experiment.
The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.
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Bassingthwaighte JB.: Enzymes and Metabolic Reactions, Chapter 10 in "Transport and Reactions in Biological Systems", Pages 7-8
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.