Transp2sol.Comp2F
Model number: 0011
Facilitating Transporter for 2 competing solutes, including binding steps, with input via Flow. Shows countertransport facilitation/inhibition Enzymatic conversion in V2. Revised from Transp2sol.Comp2 to include flow and washout.
Detailed Description
Transp2sol.Comp2F is a six state transporter model for 2 solutes in competition, input via Flow, with a membrane between two mixing chambers. In V2, A is reacted to form B in an enzymatic reaction approximated by a Michaelis-Menten expression, 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 of uncomplexed transporter T, 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. The Michaelis-Menten reaction is at 50% of maximum at the Km, shown on the JSim PlotPage labled MM.
Assumptions: Compartmental assumptions apply to the solutions on either side of the membrane. These are: instantaneously stirred tank, no concentration gradients, no diffusion limitation for reactants. Also, it is assumed that reactions are first order with fixed rates, not fractal.
Known Bugs: These calculations are subject to numerical round off errors under certain conditions, such as when kdA1/koffA1 >> kTA12/kTA21. This occurs because the net flux (A1:t) is calculated as the difference of two much larger unidirectional fluxes. Calculations of state variables (concentrations) are accurate.
Relevant Equations
Ordinary Differential Equations
 = S_{\text{\small{of V1}}}(k_{\text{\small{off A1}}}T_{\text{\small{A1}}} - k_{\text{\small{on A1}}}A1 T1) + \frac {Flow(A_{\text{\small{in}}} - A1)}{V1})
 = S_{\text{\small{of V2}}}(k_{\text{\small{off A2}}}T_{\text{\small{A2}}} - k_{\text{\small{on A2}}}A2 T2) - \frac {Consump_{\text{\small{A2}}}A2}{V2})
 = S_{\text{\small{of V1}}}(k_{\text{\small{off B1}}}T_{\text{\small{B1}}} - k_{\text{\small{on B1}}}B1 T1) + \frac {Flow(B_{\text{\small{in}}} - B1)}{V1})
 = S_{\text{\small{of V2}}}(k_{\text{\small{off B2}}}T_{\text{\small{B2}}} - k_{\text{\small{on B2}}}B2 T2) + \frac {Consump_{\text{\small{A2}}}A2}{V2})
 = -(k_{\text{\small{on A1}}}A1 + k_{\text{\small{on B1}}}B1)T1 + k_{\text{\small{off A1}}}T_{\text{\small{A1}}} + k_{\text{\small{off B1}}}T_{\text{\small{B1}}} - k_{\text{\small{T12}}}T1 + k_{\text{\small{T21}}}T2)
 = k_{\text{\small{on A1}}}A1 T1 - k_{\text{\small{off A1}}} T_{\text{\small{A1}}} - k_{\text{\small{TA12}}}T_{\text{\small{A1}}} + k_{\text{\small{TA21}}}T_{\text{\small{A2}}})
 = k_{\text{\small{on A2}}}A2 T2 - k_{\text{\small{off A2}}} T_{\text{\small{A2}}} + k_{\text{\small{TA12}}}T_{\text{\small{A1}}} - k_{\text{\small{TA21}}}T_{\text{\small{A2}}})
 = k_{\text{\small{on B1}}}B1 T1 - k_{\text{\small{off B1}}} T_{\text{\small{B1}}} - k_{\text{\small{TB12}}}T_{\text{\small{B1}}} + k_{\text{\small{TB21}}}T_{\text{\small{B2}}})
 = k_{\text{\small{on B2}}}B2 T2 - k_{\text{\small{off B2}}} T_{\text{\small{B2}}} + k_{\text{\small{TB12}}}T_{\text{\small{B1}}} - k_{\text{\small{TB21}}}T_{\text{\small{B2}}})
Mass conservation check for the closed system of V1 and V2
 + V2(A2 + B2))
)
WARNING: An additional thermodynamic constraint is not included in the model. For a passive transporter, the transport rate constants should follow the following constraints.
These constraints ensure that the model runs to equilibrium 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 an energy source, which is not explicitly modeled here.
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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.
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
- Two solute, 2 region, facilitated transport with enzymatic conversion.
- Two solute, 2 region, axially distributed, facilitated transport with enzymatic conversion, and flow.
- A General multi-region tissue exchange model (Gentex model).
Return to Transporter
Key Terms
Two solutes, competing solutes, enzymatic reaction, transmembrane flip, countertransporter, six state transporter, Flow.
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Copyright (C) 1999-2010 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.
WARNING: An additional thermodynamic constraint is not included in the model. For a passive transporter, the transport rate constants should follow the following constraints.
These constraints ensure that the model runs to equilibrium 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 an energy source, which is not explicitly modeled here.
Download File
Run JSim Model
Press the “Run Applet” button to bring up the model in a separate window.
References
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
- Two solute, 2 region, facilitated transport with enzymatic conversion.
- Two solute, 2 region, axially distributed, facilitated transport with enzymatic conversion, and flow.
- A General multi-region tissue exchange model (Gentex model).
Key Terms
Two solutes, competing solutes, enzymatic reaction, transmembrane flip, countertransporter, six state transporter, Flow.
JSim Tutorial
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Model History
Get Model history in CVS.Copyright (C) 1999-2010 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.
