Severinghaus' Equation for O2 binding to hemoglobin

## Description

Both the Severinghaus and Hill Equations assume instantaneous equilibrative binding of oxygen to Hb. The Severinghaus expression is empirical but fits the experimental data better than the Hill expression, particularly for pO2's < 30 mmHg. Severinghaus provides a second equation to calculate pO2 from observed SHb: ln(pO2) = 0.385*ln(SHb^(-1)- 1)^(-1) + 3.32 - (72*SHb)^(-1) - Shb^6/6. The parameter values were obtained by an optimization to fit experimental data. To evaluate the accuracy of the calculation, he plotted the percent difference between calculated and observed values over the range of saturations, that is the residuals. AV Hill's empirical description of the hemoglobin-oxygen dissociation curve was based on data before the van Slyke apparatus for measuring the content of O2 in blood equilibrated with air at known PO2 and PCO2 was developed. The simplicity of the equation led to its wide utility, even though it is too low at saturations below 30% (a region not often visited physiologically). Other models, Adair's, Severinghaus', etc. offer improvements over Hill's two parameter power law relationship. Antonini and Brunori (1971) and Frauenfelder (Austin et al 1975; Mourant et al 1993) showed that the rebinding of O2 to Hb involved a family of rate constants (including a fractal scaling region) and that the reaction was complete in less than 50 msec in free solution. If there is delay due to diffusion or a membrane barrier, then the reaction is slowed.In a related program "HbO.Hill.slow" we apply a trick, surrounding the Hb with a barrier to allow accounting for slow rates of association and dissociation, and which gives a fairly realistic sccounting for O2 exchange across RBC membranes. VERIFICATION: 1. Changes of step size make no difference since solution is analytic. VALIDATION: The Severinghouse Equation fits his carefully acquired data better than does the Hill equation.

## 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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Severinghaus JW: Simple, accurate equations for human blood O2 dissociation computations. J. Appl. Physiol. 46(3) 599-602, 1979. Antonini E and Brunori M: Hemoglobin and Myoglobin in their Reactions with Ligands. Amsterdam: North Holland, 1971, 436 pp. Van Slyke DD and Neill JM: The determination of gases in blood and other solutions by vacuum extraction and manometric measurement I.. J Biol Chem 61: 523-573, 1924. Austin RH, Beeson KW, Eisenstein L, Frauenfelder H, and Gunsalus IC: Dynamics of ligand binding to myoglobin. Biochemistry 14: 5355-5375, 1975. Mourant JR, Braunstein DP, Chu K, Frauenfelder H, Nienhaus GU, Ormos P, and Young RD: Ligand binding to heme proteins: II. Transitions in th heme pocket of myoglobin. Biophys J 65: 1496-1507, 1993. Hill AV: The diffusion of oxygen and lactic acid through tissues. Proc R Soc Lond (Biol) 104: 39-96, 1928. Hill AV: The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. J Physiol 40: iv-vii, 1910 Adair GS: The hemoglobin system. VI. The oxygen dissociation curve of hemoglobin. J Biol Chem 63: 529-545, 1925. 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.

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**Model development and archiving support at https://www.imagwiki.nibib.nih.gov/physiome provided by the following grants:** NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.