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# HbCoop

Oxygen binding to hemoglobin at 4 cooperative sites. alp > 1 for pos cooperativity, alp < 1 for neg coop.

Model number: 0030

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## Description

```   Hemoglobin, a protein with 4 interdependent binding sites, can become
saturated with oxygen, i.e all of its binding sites can be occupied at high
concentrations. The fractional saturation is calculated here by a cooperative
scheme by which there is a constant ratio of increases in affinity as each site
is filled in succession. The cooperativity factor "alp" is >1 for positive
cooperativity, and < 1 for anticooperativity.
The results are compared with the result using a Hill equation with a
Hill coefficient of 2.7. The value is chosen because the Hill equation
with nH (Hill coefficient 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 are, at varying concentrations, 4 sites available to fill. When
one is filled, only 3 remain, reducing the odds from 4 to 3, and so on. The actual O2
carriage 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 other cooperativity models wherein the filling of
the first and successive sites causes (by cooperativity = positive feedback through
molecular conformational rearrangement) successively higher affinities. The ratio, "alp"
is not necessarily constant. For example the Adair eqautions are equivalent  to
having "alp as a variable.

```

## 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.

## References

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

Dash RK and Bassingthwaighte JB. Erratum to: Blood HbO2 and HbCO2 dissociation curves at
varied O2, CO2, pH, 2,3-DPG and Temperature Levels. Ann Biomed Eng 38(4): 1683-1701, 2010.

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.

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.

```

## Key Terms

hemoglobin, oxygen, carbon dioxide, saturation, Haldane, Bohr, acidity, pH, blood gases, Hill equation, solubility, cooperativity, Data