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

## 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.

## Equations

#### 4 state transporter between two compartments with flow in the first compartment:

where*Surf* is the surface area of the membrane, *Flow* is the inflow and outflow from compartment 1, *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 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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- Information on SBML conversion in JSim

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Please cite https://www.imagwiki.nibib.nih.gov/physiome 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.

**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.