Two compartment model with flow, Michaelis-Menten type exchanger, and a reversible reaction in non-flowing compartment converting C to B.
Description
This is a two compartmental (plasma and parenchymal cell (pc) exchange model with flow in the plasma compartment. The compartments are instantaneously well mixed. Substances C and B reversibly convert to each other by a first order process in the parenchymal cell compartment. This model has a Michaelis-Menten (MM) type of transporter of the cell membrane between the capillary plasma and the parenchymal cell, expressed in terms of Km and PSmax, for which the denominators include terms for the solute on both sides of the meembrane, as if the binding site is accessible simultaneously from either side. In this sense the transporter is acting more like a channel that a ferry boat.
Further reading:
Equations
Ordinary Differential Equations
Initial Conditions
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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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Wilfred D Stein. Transport and Diffusion across Cell Membranes, 2nd Ed. Academic Press 1986
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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.