# Transp1sol.Comp2

Models a two compartment, 1 solute, T1-T2 (facilitated 4-state transporter. Includes binding steps and transmembrane flip rates for free and occupied transporters.

Model number: 0007

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## Description

The model is a saturable four state transporter with a binding site on both sides of the membrane for 1 solute in a two compartment model. The binding site undergoes a conformational change, flipping from side 1 to side 2 and back again when it is empty (T1<->T2) or filled (TA1<->TA2).

## Equations

#### 4 state transporter between two compartments without flow

where

*Surf* is the surface area of the membrane,

*V _{1}* is the volume of compartment 1,

*V*is the volume of compartment 2,

_{2}*K*and

_{dA1}*K*are equilibrium dissociation constants,

_{dA2}*k*and

_{onA1}*k*are the on rate constants,

_{onA2}*k*and

_{offA1}*k*are the off rate constants,

_{offA2}*KT*is the flip rate for the empty transporter from side 1 to side 2,

_{12}*KT*is the flip rate for the empty transporter from side 2 to side 1,

_{21}*KTA*is the flip rate for the filled transporter from side 1 to side 2, and

_{12}*KTA*is the flip rate for the filled transporter from side 2 to side 1.

_{21}** WARNING**: An additional thermodynamic constraint is not included in the
model.
For a passive transporter, the transport rate constants should satisfy
the following constraint:

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.

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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

Master Two Compartment Transporter Model (includes all cases):

Transporter models from Compartment Tutorial (mostly passive exchange):- Compartmental
- Comp2Exchange: 2 compartments, no flow, 1 solute, 2 sided passive transporter
- Comp2FlowExchange: 2 compartments, with flow, 1 solute, 2 sided passive transporter
- Comp2ExchangeReaction: 2 compartments, no flow, 2 solutes, 2 sided passive transporter
- Comp2FlowExchangeReaction: 2 compartments, with flow, 2 solutes, 2 sided passive transporter
- Comp2FlowMMExchangeReaction: 2 compartments, with flow, 2 solutes, 4 single 1 sided Michaelis-Menten transporters
- Distributed
- BTEX20: 2 distributed regions (PDE), with flow, 1 solute, 2 sided passive transporter
- CTEX20: 2 distributed regions (serially connected ODEs), with flow, 1 solute, 2 sided passive transporter
- CTEX20b: 2 distributed regions (serially connected ODEs), with flow, 1 solute, 2 sided passive and 1 sided Michaelis-Menten transporter

- No Flow
- TranspMM1sidedComp2: 2 compartments, no flow, 1 solute, 1 sided MM transporter
- TranspMM.2sided.Comp2: 2 compartments, no flow, 1 solute, both 1 sided and 2 sided MM transporters
- With Flow

- 1 solute
- Transp1sol.Comp2: 2 compartments, no flow, 1 solute, T1-T2 transporter
- Transp1sol.Comp2F: 2 compartments, with flow, 1 solute, T1-T2 transporter
- Two solutes
- Transp2sol.Comp2: 2 compartments, no flow, 2 solutes, competitive T1-T2 transporter
- Transp2sol.Comp2: 2 compartments, with flow, 2 solutes, competitive T1-T2 transporter
- Transp2sol.Distrib2F: 2 regions with flow, 2 solutes, both T1-T2 and passive transporters, Michaelis-Menten enzymatic reaction, Counter-Transport Faciliation

## Key Terms

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## Model History

Get Model history in CVS.## Acknowledgements

Please cite **www.physiome.org** 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, 3:04 pm.]

**Model development and archiving support at
physiome.org 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.