This page will look better in a graphical browser that supports web standards, but is accessible to any browser or internet device.

Served by Samwise.

# Transp1sol.Comp2F

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

Model number: 0008

 Run Model: Help running a JSim model.
Java runtime required. Web browser must support Java Applets.
(JSim model applet may take 10-20 seconds to load.)

## 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:

$\large {\it SoV_1}={\frac {{\it Surf}}{{\it V_1}}} \,\,\,\,\,\,\, {\it SoV_2}={\frac {{\it Surf}}{{\it V_2}}}$

$\large {\it K_{dA_1}}={\frac {{\it k_{offA_1}}}{{\it k_{onA_1}}}} \,\,\,\,\,\,\, {\it K_{dA_2}}={\frac {{\it k_{offA_2}}}{{\it k_{onA_2}}}}$

$\large {\frac {d}{dt}}{\it A_1} \left( t \right) =\, {\frac {{\it Flow}\, \left( {\it A_{in}}-{\it A_1} \right) }{{\it V_1}}}\,+ {\it k_{offA_1}}\cdot {\it TA_1}\cdot { \it SoV_1}-{\it k_{onA_1}}\cdot {\it A_1}\cdot {\it T_1}\cdot {\it SoV_1}$

$\large {\frac {d}{dt}}{\it A_2} \left( t \right) =\, {\it k_{offA_2}}\cdot {\it TA_2}\cdot { \it SoV_2}-{\it k_{onA_2}}\cdot {\it A_2}\cdot {\it T_2}\cdot {\it SoV_2}$

$\large {\frac {d}{dt}}{\it T_1} \left( t \right) =-{\it k_{onA_1}}\cdot {\it A_1} \left( t \right) \cdot {\it T_1} \left( t \right) +{\it k_{offA_1}}\cdot {\it TA_1} \left( t \right) -{\it kT_{12}}\cdot {\it T_1} \left( t \right) +{\it kT_{21}}\cdot {\it T_2} \left( t \right)$

$\large {\frac {d}{dt}}{\it T_2} \left( t \right) =-{\it k_{onA_2}}\cdot {\it A_2} \left( t \right) \cdot {\it T_2} \left( t \right) +{\it k_{offA_2}}\cdot {\it TA_2} \left( t \right) +{\it kT_{12}}\cdot {\it T_1} \left( t \right) -{\it kT_{21}}\cdot {\it T_2} \left( t \right)$

$\large {\frac {d}{dt}}{\it TA_1} \left( t \right) =\,{\it k_{onA_1}}\cdot {\it A_1} \left( t \right) \cdot {\it T_1} \left( t \right) -{\it k_{offA_1}}\cdot {\it TA_1} \left( t \right) -{\it kTA_{12}}\cdot {\it TA_1} \left( t \right) +{\it kTA_{21}}\cdot {\it TA_2} \left( t \right)$

$\large {\frac {d}{dt}}{\it TA_2} \left( t \right) =\,{\it k_{onA_2}}\cdot {\it A_2} \left( t \right) \cdot {\it T_2} \left( t \right) -{\it k_{offA_2}}\cdot {\it TA_2} \left( t \right) +{\it kTA_{12}}\cdot {\it TA_1} \left( t \right) -{\it kTA_{21}}\cdot {\it TA_2} \left( t \right)$

where
Surf is the surface area of the membrane,
Flow is the inflow and outflow from compartment 1,
V1 is the volume of compartment 1,
V2 is the volume of compartment 2,
KdA1 and KdA2 are equilibrium dissociation constants,
konA1 and konA2 are the on rate constants,
koffA1 and koffA2 are the off rate constants,
KT12 is the flip rate for the empty transporter from side 1 to side 2,
KT21 is the flip rate for the empty transporter from side 2 to side 1,
KTA12 is the flip rate for the filled transporter from side 1 to side 2,   and
KTA21 is the flip rate for the filled transporter from side 2 to side 1.

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

$\large {\frac {{\it kTA_{12}}\cdot {\it kT_{21}}\cdot {\it k_{onA_1}}\cdot {\it k_{offA_2}}} {{\it kTA_{21} }\cdot {\it kT_{12}}\cdot {\it k_{offA_1}}\cdot {\it k_{onA_2}}}}=1$

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.

## References

None.

## Related Models

Master Two Compartment Transporter Model (includes all cases):

Transporter models from Compartment Tutorial (mostly passive exchange): Two Compartment Michaelis-Menten (MM) Transporter Models: Two Compartment 2-sided Facilitated Transporter (T1-T2) Models:

## Key Terms

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