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HbIndep

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

Model number: 0029

Description

     A protein with 4 independent binding sites, can be 
  saturated with a ligand, i.e all of its binding sites can be occupied at high 
  concentrations. The fractional saturation 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 straightforward, based on the equation for single site binding, modified
  in recognition that there at very concentrations 4 sites available to fill, then when
  one is filled, only 3 remain, reducing the odds from 4 to 3, and so on. The generic 
  substrate is represented here by O2 and the binding site by Hb. The binding
  depends on the relative abundances of HbO, HbO2, etc, and the fact that there
  is twice as much O2 on HbO2 as on HbO, etc. The sum of the products of the relative 
  concentrations times the O2s being carried in each form is divided by 4*HbO4, the 
  maximum that can be carried.
     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.

Equations

Hill AV: The diffusion of oxygen and lactic acid through tissues. 
Proc R Soc Lond (Biol) 104: 39-96, 1928.

Adair GS: The hemoglobin system.  VI.  The oxygen dissociation curve of 
hemoglobin. J Biol Chem 63: 529-545, 1925.

Hill AV: The possible effects of the aggregation of the molecules of haemoglobin on its
dissociation curves. J Physiol 40: iv-vii, 1910

Hill R: Oxygen dissociation curves of muscle hemoglobin. Proc Roy Soc Lond B
120: 472-480, 1936.

Keener J and Sneyd J: Mathematical Physiology. New York, NY: 
Springer-Verlag, 1998, 766 pp.

 Roughton FJW, Deland EC, Kernohan JC, and Severinghaus JW: Some recent studies of the
oxyhemoglobin dissociation curve of human blood under physiological conditions and the
fitting of the Adair equation to the standard curve. In: Oxygen Affinity of Hemoglobin and
Red Cell Acid Base Status. Proceedings of the Alfred Benzon Symposium IV Held at the
Premises of the Royal Danish Academy of Sciences and Letters, Copenhagen 17-22 May,
1971, edited by Rorth M and Astrup P. Copenhagen: Munksgaard, 1972, p. 73-81.

Winslow RM, Swenberg M-L, Berger RL, Shrager RI, Luzzana M, Samaja M,and
Rossi-Bernardi L: Oxygen equilibrium curve of normal human blood and its evaluation by
Adair's equation. J Biol Chem 252: 2331-2337, 1977.