Facilitating Transporter for 2 competing solutes including binding steps. Shows countertransport facilitation/inhibition Enymatic conversion in V2.
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: kTA12*kT21*konA1*koffA2 ------------------------ = 1 (1) see TestA kTA21*kT12*koffA1*konA2 kTB12*kT21*konB1*koffB2 ------------------------ = 1 (2) see TestB kTB21*kT12*koffB1*konB2 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 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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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.
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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.