Tracer and Mother solute flow past a binding site. Equilibrium upset by an added pulse of mother solute, dislodging tracer.

Description

One compartment model of mother solute C and tracer labeled C, called Tr,
with slow binding to a binding ligand B os constant total, Btotal, and 
which does not leave the flowing region..Volume V is constant. Total 
concentration of binding ligand, Btotal = unbound B and the complex CB.
Tracer and mother substance flow in and out. Concn of unbound ligand is 
determined by the concns of mother and tracer analytes relative to the 
Kd mM, which is the dissociation constant for ligand-solute binding.
  The purpose of this model is to demonstrate that when the concn of 
mother substance is raised, tracer that has been attached to a binding 
ligand is driven off and washed out. The function generator fgen_1 is 
set up to provide a constant infusion of mother substance at 1 mM to 
which an additional 1-second pulse is added at t = 6 seconds. The tracer 
infusion is constant at 1 nM through to 12 seconds. The concentrations and
the Kd are chosen ao that the pulse of mother solute suddenly reduces the 
amount of free ligand, and competes with the tracer that is already 
attached, causing a transient release of tracer and a sudden diminution
in the total amount of tracer present in the mixing chamber. An external 
detector would give a signal proportional to Tr + TrB, the total tracer 
present.
  At 12 seconds a 2 second pulse of additional tracer is added, but if 
at a tracer level it has no effect on the mother substance binding. 
Explore the influence of making this pulse large by changing "p2amplitude" 
for Pulse 2 in fgen_2. 
 

Constants:
	Btotal = total concentration of binding ligand, mmol/ml
	V = Volume of compartment, ml
	kon = binding rate, 1/mmol*sec
	koff = off rate, 1/sec 

Variables:
	C(t) = Concentration of mother analyte, mmol/ml
	Tr(t) = Concentration of tracer analyte, nmol/ml
	CB(t) = Concentration of bound mother analyte with ligand B, mmol/ml
	TrB(t) = Concentration of bound tracer with ligand B, nmol/ml
 free Ligand [B] = [Btotal]- [CB]-[TrB]

Equations

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.