Transp1solComp2

Model number: 0007

A two compartment one solute facilitated transporter kinetic model including binding steps and transmembrane flip rates for free and occupied transporter.

Detailed Description

A two compartment single solute model showing facilitated transport across the membrane between the two compartments. Model accounts for single site binding without competition. The model is a saturable four state transporter with a binding site on either one side of the membrane or the other through a conformational change. The binding site can be empty or filled. The side-to-side flipping of the binding site occurs whether or not the state is filled.

FIGURE: Four state transporter model.
A1 and A2 are solute A in volumes 1 and 2.TA1 is the transporter-solute complex on volume 1 side of membrane and TA2 is the transporter-solute complex on the other side.T1 and T2 are the free transporter when it is not bound to a solute.

Relevant Equations

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

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

${ \frac {d}{dt} A2(t) = k_{\text{\small{off A2}}}TA_{\text{\small{2}}}S_{\text{\small{of V2}}} - k_{\text{\small{on A2}}}A2 T2 S_{\text{\small{of V2}}}$

${ \frac {d}{dt} T1(t) = - k_{\text{\small{on A1}}} A1 T1 + k_{\text{\small{off A1}}} TA_{\text{\small{1}}} - k_{\text{\small{T12}}} T1 + k_{\text{\small{T21}}} T2$

${ \frac {d}{dt} TA_{\text{\small{1}}}(t) = k_{\text{\small{on A1}}} A1 T1 - k_{\text{\small{off A1}}} TA_{\text{\small{1}}} - k_{\text{\small{TA12}}} TA_{\text{\small{1}}} + k_{\text{\small{TA21}}} TA_{\text{\small{2}}}$

${ \frac {d}{dt} TA_{\text{\small{2}}}(t) = k_{\text{\small{on A2}}} A2 T2 - k_{\text{\small{off A2}}} TA_{\text{\small{2}}} + k_{\text{\small{TA12}}} TA_{\text{\small{1}}} - k_{\text{\small{TA21}}} TA_{\text{\small{2}}}$

${ T2 = T_{\text{\small{tot}}} - TA_{\text{\small{1}}} - TA_{\text{\small{2}}} - T1$

${ PS_{\text{\small{c}}} = \frac {PS_{\text{\small{cMAX}}}}{1 + \frac {A1}{K_{\text{\small{dA1}}}}}$

Where V1, V2 are the volumes, in ml, of the two compartments. A1(t), A2(t) are the solute concentration in mM. TA₁(t), TA₂(t) are the surface concentrations of the transporter complex on V1 and V2 sides (in micromoles per cm²) and T1(t), T2(t) are the transporter surface concentrations on V1 and V2 sides respectively (all in micromoles per cm²). PSc(t), PScMAX are the membrane permeability surface area and maximum permeability surface area (both in ml/s). k_onA1, k_onA2, k_offA1, k_offA2 are the on and off binding rates for solute A on V1 and V2 sides of the membrane. Binding rates are in 1/(uM*s).

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 is assumed to be coupled to an energy source, as if it were active transport, and creates a transmembrane concentration gradient. This case, if the transporter is coupled to an energy source, 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, binding constants, single site, noncompetitive binding, four state transporter, tutorial

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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.