THE DISSOCIATION CURVE OF HEMOGLOBIN 105 



Taking first that in which the oxygen molecules join one by one, if 

 each oxygen molecule is entirely uninfluenced by its fellows and 

 so far away from them as to be quite independent, the curve which 

 represents each of the four constituent reactions will be a rectangular 

 hyperbola and the curve which represents the whole four will be 

 a hyperbola also. Written after the notation introduced by A. V. 

 Hill(i), if X be the oxygen pressure, y the percentage of the whole 

 haemoglobin which is oxyhsemoglobin and K the equilibrium constant, 



y _ ^^ 

 TOO^ 1 + Kx' 



If on the other hand the intermediate oxides are so unstable as to 

 be incapable of persisting, the reaction would be represented by the 

 equation 



y _ Kx^ 

 100~ 1 + Kx^' 



The curve which represents the last equation is not a hyperbola, but 

 one with a large inflection. (See fig. 31.) 



As Adair has pointed out, if we are not prepared to make either 

 the assumption that the oxygen molecules are quite independent 

 on the one hand, or, on the other, that their union is absolutely 

 dependent upon one another, but that each oxygen atom, as it joins, 

 reduces the affinity of the whole molecule for the next, we could 

 assume a curve with some degree of inflection but intermediate 

 between those given in Fig. 31. As a matter of experience, curves 

 of this kind have usually been obtained when dilute haemoglobin 

 has been equilibrated long enough with carbon monoxide for the 

 purpose. But although much pains have been spent on this reaction 

 it may be doubted whether any finality has been reached as yet. 

 As so often occurs when haemoglobin is the object of investigation 

 we seem to be "between the devil and the deep sea." Clearly a 

 dilute solution of haemoglobin is in theory the proper one to study; 

 on the other hand all experience shows that such a solution is ex- 

 tremely labile. Douglas, Haldane and Haldane(2) emphasised the 

 ease with which haemoglobin is destroyed when shaken in dilute 

 solution, and recommended the addition of ammonia in small quanti- 

 ties. Undoubtedly in slightly alkaline solution the globin shows much 

 less tendency to coagulate than in neutral ones, nevertheless at best 

 the haemoglobin is not very stable. It is the opinion of Roughton, 

 who has great experience on this particular point, that haemoglobin 



