TranspMM.1sided.Comp2

Model number: 0014

A two compartment one-sided Michaelis-Menten transporter.

Detailed Description

Compartmental models are based on mass balance equations. The compartment has a volume, V, and a time-varying concentration of a substance, C(t). An underlying assumption of compartmental models is that the material in the compartment is instantaneously well mixed.

This is a stirred tank model for facilitated exchange between two instantly mixed chambers. It is a closed model, with volumes V1 and V2 for each compartment, time dependent concentrations A1(t) and A2(t) respectively, and an exchange coefficient PS. G2(t) is for Gulosity, the first order consumption of the solute in V2. This model is assuming instantaneous solute binding to a transporter of Michaelis-Menten type, with only a single site available from on side of the membrane. The focus is on solute A. Fluxes are set from the cis side: A1 determines the fractional saturation, PS/PS_max.

Relevant Equations

${\frac {d}{dt}A1(t) = \frac {-PS(A1-A2)}{V1}$

${\frac {d}{dt}A2(t) = \frac {PS(A1-A2)}{V2} - \frac {G2 A2}{V2}$

${ PS = \frac {V_{\text{\small{max}}}}{K_{\text{\small{m}}} + A1} = \frac {PS_{\text{\small{max}}}}{1 + \frac {A1}{K_{\text{\small{m}}}}}$

Where V1 and V2 are the volumes of the two compartments, A1 and A2 are the concentrations respectively, V_max is the max flux at 100% saturation, K_m is the equilibrium dissociation constant, G2 is the gulosity of V2, and PS (Permeability-Surface area product) is the single sided exchange rate between the compartments.

Download File

Run JSim Model

Press the “Run Applet” button to bring up the model in a separate window.

References

Klingenberg M. Membrane protein oligomeric structure and transport function. Nature 290: 449-454, 1981.

Stein WD. The Movement of Molecules across Cell Membranes. New York: Academic Press, 1967.

Stein WD. Transport and Diffusion across Cell Membranes. Orlando, Florida: Academic Press Inc., 1986.

Wilbrandt W and Rosenberg T. The concept of carrier transport and its corollaries in pharmacology. Pharmacol Rev 13: 109-183, 1961.

Schwartz LM, Bukowski TR, Ploger JD, and Bassingthwaighte JB. Endothelial adenosin transporter characterization in perfused guinea pig hearts. Am J Physiol Heart Circ Physiol 279: H1502-H1511, 2000.

Related Models

Return to Transporter

Key Terms

Compartmental Model, Flow and Exchange, Mixing Chamber, Permeability, PS/F, Washout, Inflow-Outflow opreator.ISF, Parenchymal Cell.

JSim Tutorial

Click here to go to a JSim tutorial webpage, with an introduction to the JSim GUI, detailed usage instructions, and an accompaying video.

Model Feedback

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

Model History

Get Model history in CVS.

Copyright (C) 1999-2009 University of Washington. From the National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061. Academic use is unrestricted. Software may be copied so long as this copyright notice is included. This software was developed with support from NIH grant HL073598. Please cite this grant in any publication for which this software is used and send one reprint to the address given above.

Model development and archiving support at physiome.org provided by the following grants: 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.