Pauling's equation 265 



These will be discussed later. The most important step was, however, 

 the recognition that interaction might take place between the hemes. 



5.1.5. Pauling's Equation. In 1935, Pauling (2123) reinvestigated 

 the problem and, by making certain simple assumptions, developed 

 an equation which contained only two constants and which was 

 able to describe the equilibrium satisfactorily. While Adair did not 

 assume that the hemes were arranged in any particular way, Pauling 

 considered certain steric arrangements, in one of which the hemes 

 were assumed to lie at the corners of a square. He gave a quantitative 

 meaning to Adair's conception of interaction between the hemes by 

 assuming that this took place between oxygen molecules along the 

 sides of the square so that the free energy of addition of ox^'gen to a 

 heme, RT In K, is diminished by an amount RT \n a by the presence 

 of an adjacent oxygen atom. If a second oxygen combined with the 

 heme diagonally opposite to one which held an oxygen atom, no 

 interaction is assumed to occur. The number of possible intermediates 

 on this basis is: 



O O 



D a a n :n :u 



where a double line indicates interaction along the sides of the square. 

 If account is taken of the number of ways the oxygen molecules can 

 be arranged on the four hemes, the relative proportion of the six types 

 is given by: 



1 : 4Kp : 4aKV : 2KV : ia'^K^p^ : a'K'p* 



The oxygen saturation is then expressed by: 



_ Kp + (2a + 1)KV + Sa^K^p' + a'K'p* 



y 



1 + 4K/; + (4a + ^)K'p^ + 4a2K»/J=' + a^K'p' 



Pauling assumed that the equilibrium constant, K, was dependent 

 on the p\\ of the solution, but that the interaction constant was 

 independent of pH. He concluded from a study of the data of 

 Ferry and Green {7I^7) that each heme was as.sociated with two acid 

 groups, of p\i 7.9 in hemoglol)in rather than with one "oxylabile" 

 group as previous investigators had assumed (llJi.<^,l 15^). By assum- 

 ing an interaction constant /3, which described the effect of o.xygenation 



