F. J. W. ROUGHTON 



2 Hb and 95 per cent 2 Hb. It is of interest that the experimental data 

 for crystalline horse haemoglobin and diluted sheep haemoglobin agree 

 closely when the respective scales of 2 pressure are suitably adjusted. 

 F Another set of ratios put forward by Roughton 2 also give a good 

 fit {Figure IF). In this case 



K x = 0-408, K X K 2 = 0.031, K X K 2 K Z = 0-0022, K t K 2 K 3 K^ = 0-0195. 



G, //and /. For many years Hill's equation j>/100 =Kx n /(l+Kx") 

 has been used for empiric description of the dissociation curve, n being 

 usually taken to be between 2 and 3 for mammalian blood. The 

 equation lost its theoretical basis 25 years ago, when the molecule of 

 haemoglobin was shown to contain 4 atoms of iron. Figure 2G, H and / 

 show that the discrepancy between the calculated and experimental 

 results, alike for n = 2-0, 2-5 and 30, much exceeds experimental 

 error. It is impossible to get a good fit whatever value of n be chosen. 

 It is questionable therefore whether the continued use of Hill's equation, 

 even for empiric purposes, is justifiable. 



The present position may now be summarized. With more accurate 

 data, especially at the top and the bottom of the dissociation curve, 

 than those mostly used in previous tests, it has been shown that some 

 of the equations which have appeared in the literature must be dis- 

 carded. There still, however, remain several rather widely varying sets 

 of intermediate constants, all of which give an almost equally satis- 

 factory fit between calculated and observed results. At present we have 

 no grounds for choosing between them, nor can we be sure there are 

 not many other sets of constants which would give as good a fit. All 

 we can be at all sure of, at present, is the range within which A^ and 

 K X K 2 K Z K^ must lie. Numerical trial and error when applied to the 

 data of Table I show that K x must lie between 0-2 and 0-6, and once 

 it is fixed there is little choice in the range of values that may be 

 assigned to K X K 2 K Z K X . There still remains, however, considerable 

 liberty in regard to K X K 2 and K^KJK^. The only way that suggests 

 itself at present, of cutting the Gordian knot caused by such a large 

 number of arbitrary constants, is to work out to a finish the very accurate 

 study of the extreme bottom of the curve (which should give K x inde- 

 pendently) and the extreme top of the curve (which should give K^ 

 independently). This suggestion was put forward by Forbes and 

 Roughton 2 and is now being carried out in our laboratory, with Dr W. 

 Paul. With two of the unknown constants independently settled, it 

 should then be feasible to fix the remaining two and thus get a decisive 

 test of agreement between calculation and experiment. Such procedure 

 should be applied to haemoglobin under as wide a variation of con- 

 ditions as possible, e.g. of species, pH, salt content, etc, since all too 



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