Facilitating Transporter for 2 competing solutes including binding steps. Shows countertransport facilitation/inhibition Enymatic conversion in V2.

Description

This model is a six state transporter model for 2 solutes in competition.
Two solute species compete for the transporter site on either side of a
membrane between two mixing chambers. In chamber 2 A is reacted to form B
in an enzymatic reaction approximated by a Michaelis Menten expression, 
and without any accounting for binding of substrate or product to the 
enzyme. When the rates of conformational state change for transmembrane 
flipping of TA and TB are high compared to that for uncomplexed transporter T,
then the model behaves much like an obligatory countertransporter, exchanging
B for A across the membrane;

MODEL VERIFICATION: Total Mass is conserved: Substrate in solution is
totalled as SubstrateV, and substrate bound to transporter as SubstrateM, 
for membrane bound. Total transporter conservation is forced through the
equation for T2. 
 
 WARNING: An additional thermodynamic constraint is not included in the model.  
 For a passive transporter, the transport rate constants should satisfy
 the following constraints:
 kTA12*kT21*konA1*koffA2
 ------------------------ = 1    (1)  see TestA
 kTA21*kT12*koffA1*konA2
 kTB12*kT21*konB1*koffB2
 ------------------------ = 1    (2)  see TestB
 kTB21*kT12*koffB1*konB2
 These constraints ensure that the model runs to equlibrium 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 a energy source, which is not explicitly modeled here.

Equations

     Ordinary Differential Equations

     Transporter Mass Conservation

     Substrate Mass Conservation Check

WARNING: Thermodynamic constraint are not included in the model. For a passive transporter, the transport rate constants should satisfy the following constraints:

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.