Transp1sol.Comp2F

Model number: 0008

A two compartment one solute facilitated transporter model with flow through one compartment. Includes binding steps and transmembrane flip rates for transporter.

Detailed Description

A two compartment, one solute facilitated transporter kinetic model. Flow is modeled through volume V1, with an input concentration of our solute Ain. Binding rates to the transporter are given, as well as flip rates. Flip rates are also given for when nothing is bound to the transporter. This is a saturable four state transporter model. Fluxes linear in TA complex concentrations.

Relevant Equations

${ S_{\text{\small{of V1}}} = \frac {Surf}{V1}, S_{\text{\small{of V2}}} = \frac {Surf}{V2}$

${ \frac {d}{dt} A1(t) = k_{\text{\small{off A1}}}T_{\text{\small{A1}}}S_{\text{\small{of V1}}} - k_{\text{\small{on A1}}}A1 T1 S_{\text{\small{of V1}}} + \frac {Flow(A_{\text{\small{in}}} - A1)}{V1}$

${ \frac {d}{dt} A2(t) = k_{\text{\small{off A2}}}T_{\text{\small{A2}}}S_{\text{\small{of V2}}} - k_{\text{\small{on A2}}}A2 T2 S_{\text{\small{of V2}}}$

${ \frac {d}{dt} T1(t) = - k_{\text{\small{on A1}}} A1 T1 + k_{\text{\small{off A1}}} T_{\text{\small{A1}}} - k_{\text{\small{T12}}} T1 + k_{\text{\small{T21}}} T2$

${ \frac {d}{dt} T_{\text{\small{A1}}}(t) = k_{\text{\small{on A1}}} A1 T1 - k_{\text{\small{off A1}}} T_{\text{\small{A1}}} - k_{\text{\small{TA12}}} T_{\text{\small{A1}}} + k_{\text{\small{TA21}}} T_{\text{\small{A2}}}$

${ \frac {d}{dt} T_{\text{\small{A2}}}(t) = k_{\text{\small{on A2}}} A2 T2 - k_{\text{\small{off A2}}} T_{\text{\small{A2}}} + k_{\text{\small{TA12}}} T_{\text{\small{A1}}} - k_{\text{\small{TA21}}} T_{\text{\small{A2}}}$

${ T2 = T_{\text{\small{tot}}} - T_{\text{\small{A1}}} - T_{\text{\small{A2}}} - T1$

WARNING: An additional thermodynamic constraint is not included in the model. For a passive transporter, the transport rate constants should satisfy the following constraint:

${ \frac {k_{\text{\small{TA12}}} k_{\text{\small{T21}}} k_{\text{\small{on A1}}} k_{\text{\small{off A2}}}}{k_{\text{\small{TA21}}} k_{\text{\small{T12}}} k_{\text{\small{off A1}}} k_{\text{\small{on A2}}}} = 1 = {\text {test}} = \frac {k_{\text{\small{TA12}}} k_{\text{\small{T21}}} k_{\text{\small{dA2}}}}{k_{\text{\small{TA21}}} k_{\text{\small{T12}}} k_{\text{\small{dA1}}}}$

This constraint ensures 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.

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Key Terms

two compartment, facilitated transporter, transmembrane, flow, two region, single transporter, one solute, no competition

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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.