HEMOGLOBIN EQUILIBRIA 



269 



of Pauling's equation, since in spite of doubts as to its generality it 

 is a convenient expression and a suitable form in which to deal with 

 the problem of the sigmoid dissociation curve. 



5.1.7. Relation between n and a. In an extremely interesting analysis, 

 Coryell (498) has succeeded in relating Hill's equation to Pauling's equation 

 and has thereby facilitated the application of the heme-heme interaction to 

 a number of systems which are generally described in terms of the former 

 equation. The value of n may be rigorously defined by the equation: 



n = 



8 \ogR 

 8 log K;; 



where R = y/{l —.'/)• Pauling's equation may be cast into a form where R 

 is a function of a, K, and p. When R = 1, it can be shown that K;; = l/oc 

 and the relation: 



4a* + 2Sa^ + 28a- -f 4a 



4a- -j- 4a 



a* + Ua^ + SSa- + 12a + 1 a^ + 6a + 1 



may be derived by partial differentiation. The relation between n and a is 

 expressed graphically in the curve shown in Figure 8. The value of n repre- 

 sents the slope of the tangent to the curve obtained by plotting log R against 

 log p when /? = 1. This value, when substituted in Hill's equation is able 

 to describe the dissociation curve of Ferry and Green with reasonable accuracy 

 between 10 and 90% saturation. 



500 



1000 1500 

 RTlna 



2000 



Fig. 8. Relation between n and a (after Coryell, .'t9f<). 



In consideration of Keilins data on the equilibrium l)etween hem/globin 

 and hydrogen sulfide, Coryell finds that the slope of the plot of log HiSH/Hi 

 against log (HoS), n = 1.84, corresponds to a value of a of 4.1 or to a heme- 

 heme interaction of 840 cal. per mole. Similar treatment of the hem/globin- 

 hemiglobin hydroxide equilibrium as a function of /»H shows that n = \ and 

 that heme-heme interaction is absent. 



