266 VI. HEMOGLOBIN 



on the pK values of the heme-Hnked acid group, he deduced the 

 equation: 



to describe the variation of K with pH where (3 = 4, — log A = 7.94 

 and K' = 0.0035. On these assumptions he was able to show that 

 this equation with two constants could describe the Ferry and Green 

 data very well with K = 0.033 at pH 8.3 and a = 12. 



It is frequently of interest to know the relative concentrations of 

 the intermediates. Coryell, Pauling, and Dodson (500) prepared the 

 diagram shown in Figure 7 from values of K which fit the data of 

 Ferr}' and Green. It must be realized that with different values of 

 K and a, a somewhat different distribution will be found, which can 

 easily be calculated once the values of K and a have been determined 

 for the system. 



Pauling also considered the cases in which each heme interacted 

 with one and with three other hemes, the latter suggesting a tetra- 

 hedral arrangement. Where no interaction occurs, the equilibrium 

 is described by the Hiifner equation. When the hemes interact in 

 pairs, the equation: 



Kp + alx-p^ 



y 



1 + 2Kp + aK2p2 



may be derived (Altschul and Hogness, J^Ji), which may be approxi- 

 mated by the Hill equation when 1 ^ n ^ 2 {2123). This equation 

 should be applicable when the protein molecule splits into two 

 particles.* The equation based on the tetrahedral arrangement of 

 the hemes is able to describe the equilibrium as satisfactorily as the 

 equation based on the square configuration. No use has been made 

 of the derivation, however, on account of the difficulty of reconciling 

 its assumptions with other evidence as to the structure of the molecule. 

 The essentially new feature of Pauling's contribution is the more 

 precise physical meaning it gives to the conception of interaction 

 between the hemes. In addition to this it may be considered an 

 improvement on Adair's equation from an empirical point of view, 

 since it has fewer constants and the labor (and arbitrariness) of 

 fitting a dissociation curve with the equation is considerably lessened. 



* Wjman, in an important communication {31S8a), has produced evidence that in 

 intact hemoglobin as well, intropair interaction is stronger than interpair interaction. 



