276 VI. HEMOGLOBIN 



By a mathematical argument, Wyman and Ingalls (3130) have been able 

 to develop equations expressing the interrelationship between the equilibria 

 of oxidation-reduction, combination with oxygen, and dissociation of proton.s. 

 For the hemoglobin-oxyhemoglobin system, they obtained the equation: 



log (l/p.) - ^^ 

 4 



• (K^ + H+) . . . (K, + H+) - 

 .(K; + H+) . . . (K- + H+)J 



+ constant 



where p is the oxygen pressure, x the ratio Hb02/Hb, Ki . . . Ky the disso- 

 ciation constants for ionization of protons from ionizable groups I . . . g 

 assumed to be present in oxyhemoglobin, and K' . . . K' the corresponding 

 constants for hemoglobin. 



For the hemogl(>{3in-hemi"globin system, they obtained a similar equation 

 from the data of Taylor and Hastings: 



lo2 

 16.63 £', 



4 L (k; + h+) . . . (k; + H+) J 



+ constant 



'// 



where Ez is the redox potential of the system when z =Hi/Hb, and K',' . . . K 

 and K| . . . K^ dissociation constants as defined above for ionizable groups 

 in hem/globin and hemoglobin, respectively. 



These two equations can, if necessary, be combined to give a third equation 

 which relates Ez and px to the dissociation constants of the ionizable groups 

 in hemoglobin a'^d oxyhemoglobin, respectively. 



We have referred in Section 3.2.2. to the expression of the difference in 

 base bound between oxyhemoglobin and hemoglobin in terms of the shifting 

 the pK values of two imidazole groups (988) and to the description of the 

 difference in base bound between hem/globin and oxyhemoglobin solely in 

 terms of the pK dissociation of proton from the heme {3136). The substitu- 

 tion of these pK values in the above equation gave a reasonable fit of the data 

 for the variation of the half-saturation pressure with pH and for the variation 

 of the oxidation-reduction potential with pH. By slight adjustment of the 

 numerical values given to the pK values they were able to improve their 

 equation further. The latter values, at 25° C. and /x of 0.16 are: 



The success with which they were able to describe the data can be seen 

 from the curves in Figure 10. It should be noted that, while these deductions 

 have been used to support the hypothesis that the "hemaffine" groups are 

 histidine imidazoles, the derivation is essentially a formal one and is not 

 necessarily dependent on this. 



Further w^ork is needed before Wyman's treatment can be extended 

 to cover the effect variations in pH will have on the s^'stems which 



