## Abstract

It is now generally accepted that the equilibrium between oxygen (or carbon monoxide) and mammalian haemoglobin is expressible in terms of four intermediate reactions $Hb_{4}+\text{O}_{2}$$\rightleftharpoons $ $Hb_{4}\text{O}_{2}$ $\text{(equilibrium constant}$ $K_{1})$, $Hb_{4}\text{O}_{2}+\text{O}_{2}$\rightleftharpoons $Hb_{4}\text{O}_{4}(K_{2})$,$Hb_{4}\text{O}_{4}+\text{O}_{2}$\rightleftharpoons $Hb_{4}\text{O}_{6}(K_{3})$ and $Hb_{4}\text{O}_{6}+\text{O}_{2}$\rightleftharpoons $Hb_{4}\text{O}_{8}(K_{4})$, as Adair first suggested about 30 years ago. Hitherto, experimental data on the oxyhaemoglobin dissociation curve have not been precise enough to permit the direct determination of the equilibrium constants, $K_{1}$ $\text{to}$ $K_{4}$, of the intermediate reactions. Recently, however, the accuracy of the observations at the top and at the bottom ends of the dissociation curve has been improved about 10-fold, i.e. to within $\pm 0.05\%$ saturation. From such measurements--together with 2- to 3-fold more accurate data over the main part of the curve--it has now proved possible to evaluate directly, by standard statistical procedure, the values of $K_{1}$ $(\pm $ $ca$. 5%), $K_{2}$ $(\pm $ $ca$. 25%), $K_{3}$ $(\pm $ $ca$. 33%) $\text{and}$ $K_{4}$ ($\pm $ $ca$. $13.7\%$) for sheep haemoglobin solutions at alkaline pH (9.1). Unfortunately, it is not yet feasible to extend the attack fully to haemoglobin solutions at neutral pH, since the method for obtaining highly accurate data at the top of the dissociation curve breaks down at this pH. For 3 to 4% solutions of sheep haemoglobin at pH 9.1, $K_{1}$, $K_{2}$ $\text{and}$ $K_{3}$ are found to be of the same order, whereas $K_{4}$ is from 10 to 20 times greater, thus pointing to some marked internal change in the sheep haemoglobin molecule after three molecules of oxygen have combined therewith. From the effect of temperature on $K_{1}$ $\text{and}$ $K_{4}$, values are derived for the heats of all the intermediate reactions and for the entropies, $\Delta S_{1}$ and $\Delta S_{4}$, of the first and last of the intermediate reactions. There are appreciable differences between the heats of the intermediate reactions, contrary to the old view that these heats are all equal. Preliminary, but very rough, data are also given on the effect of pH and dilution. In the discussion it is shown that the new and more accurate data on the dissociation curve are incompatible with previous special theories of the oxygen-haemoglobin equilibrium, which had been based on, and checked by, conventional but less accurate experimental data. Wyman's recent symmetry theory is a striking example in the latter category and hence is given detailed consideration. The kinetic implications of the higher value of $K_{4}$ are briefly considered. It appears that the responsibility therefore is about equally borne by the relative increase in $k_{4}^{\prime}$, the velocity constant of the combination $Hb_{4}\text{O}_{6}$+ $\text{O}_{2}$ $\rightarrow $ $Hb_{4}\text{O}_{8}$, and by the relative decrease in $k_{4}$, the velocity constant of the dissociation $Hb_{4}\text{O}_{8}$\rightarrow $Hb_{4}\text{O}_{6}+\text{O}_{2}$.