Two solutes, A and B, reversibly react to form C. A + B <---> C reaches equilibrium at the ratio A*B/C = Kd.
Pseudo-equilibria are often assumed in reaction processes, and if efficient to compute, can save much computation time and avoid using the on- and off- rate constants of the reaction. This is interesting since the "ratio" A*B/C progresses with time becoming Kd if t.max is long enough, while the implicit solution gives ratio = Kd immediately. The implicit solution solves Mass conservation from initial concentrations Definition of chemical equilibrium Change from initial concentrations same for ssA and ssB and fails to be compiled if any one of the three equations is omitted.
Comparison of Ordinary Differential Equation model with implicit and analytic solutions.
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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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.