# 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.

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## 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.

## Related Models

- Detailed Dash 2010 Blood HbO2 and HbCO2 Dissociation Curves (Model #0149)
- HbO Hill slow binding (#0036)
- HbO.Hill (#0028)
- Hb Independent (#0029)
- Hb Cooperative (#0030)
- HbO.Adair (#0031)
- HbO.Severinghaus (#0027)
- Total Blood oxygen content (#0034)
- Compare HbO binding models. (#0035)

## Key Terms

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## Model History

Get Model history in CVS.## Acknowledgements

Please cite **www.physiome.org** in any publication for which this software is used and send one reprint to the address given below:

The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

[This page was last modified 02Nov16, 3:56 pm.]

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