Model for slow ligand binding to 4 independent non-cooperative, identical, sites without reaction.

Description

     A protein with 4 independent binding sites, without cooperatively, can be empty or fully
  saturated with a ligand, i.e., all of its binding sites can be occupied at high 
  concentrations. The fractional saturation is calculated here by three similar means,
  and compared with the result using a Hill coefficient of 2.7. The value is chosen 
  because the Hill equation with nH = 2.7 fits oxyhemoglobin saturation curves well.
 
    The math is based on the equation for single site binding, modified
  in recognition that there are 4 sites available to fill, and when
  one is filled, only 3 remain, reducing the odds from 4 to 3, and so on. The generic 
  substrate is represented here by the liganding molecule O2 and the 4- binding site protein 
  by Hb. Fully occupied oxyhemoglobin is Hb(O2)_4. In the model, the notation HbO = Hb(O2)_1, 
  HbO2 = Hb(O2)_2, etc. At any given ligand concentration all 5 forms of Hb may exist: Hb, HbO, 
  HbO2, HbO3, and HbO4.  The sum of the products of the relative concentrations of each of 
  these times the # of ligands being carried in each form is divided by 4 gives the fractional 
  saturation, SHb.
 
     This model serves as a basis of cooperativity models wherein the filling of the
  first and successive sites causes (by cooperativity = positive feedback through
  molecular conformational rearrangement) successively higher affinities. See Hbcoop.proj, #30.

Figure: Fraction of bound hemoglobin:

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.