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Cardiac Physiome Society workshop: November 6-9, 2017 , Toronto


Facilitating Transporter for 2 competing solutes including binding steps. Shows countertransport facilitation/inhibition Enymatic conversion in V2.

Model number: 0010

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This model is a six state transporter model for 2 solutes in competition.
Two solute species compete for the transporter site on either side of a
membrane between two mixing chambers. In chamber 2 A is reacted to form B
in an enzymatic reaction approximated by a Michaelis Menten expression, 
and without any accounting for binding of substrate or product to the 
enzyme. When the rates of conformational state change for transmembrane 
flipping of TA and TB are high compared to that for uncomplexed transporter T,
then the model behaves much like an obligatory countertransporter, exchanging
B for A across the membrane;

MODEL VERIFICATION: Total Mass is conserved: Substrate in solution is
totalled as SubstrateV, and substrate bound to transporter as SubstrateM, 
for membrane bound. Total transporter conservation is forced through the
equation for T2. 
 WARNING: An additional thermodynamic constraint is not included in the model.  
 For a passive transporter, the transport rate constants should satisfy
 the following constraints:
 ------------------------ = 1    (1)  see TestA
 ------------------------ = 1    (2)  see TestB
 These constraints ensure that the model runs to equlibrium at steady-state.
 If these ratios deviate from 1, the model will run to a steady-state
 net concentration gradient.  This would be the case if the transporter
 is coupled to a energy source, which is not explicitly modeled here.



     Ordinary Differential Equations


     Transporter Mass Conservation


     Substrate Mass Conservation Check

WARNING: Thermodynamic constraint are not included in the model. For a passive transporter, the transport rate constants should satisfy the following constraints:

The equations for this model may also 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.

Download JSim project file


 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.

 Foster DM and Jacquez JA. An analysis of the adequacy of the asymmetric carrier model for sugar 
 transport. Biochim Biophys Acta 436: 210-221, 1976. 

Related Models

Master Two Compartment Transporter Model (includes all cases): Transporter models from Compartment Tutorial (mostly passive exchange): Two Compartment Michaelis-Menten (MM) Transporter Models: Two Compartment 2-sided Facilitated Transporter (T1-T2) Models:

Key Terms

Two solutes, competing solutes, enzymatic reaction, transmembrane flip, countertransporter, six state transporter, tutorial, Transp2sol, two compartment

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Model History

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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.

[This page was last modified 02Nov16, 3:07 pm.]

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