Hill Equation for O2 binding binding to hemoglobin
The Hill Equation assumes instantaneous equilibrative binding of oxygen to Hb, but if there is delay due to diffusion or a membrane barrier, then the reaction is slowed. 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 the the reaction was complete in less than 50 msec. 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. 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 this two parameter power law relationship.
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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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