42 2. THE KINETICS OF ENZYME REACTIONS 



/i 7 = Ki\KnK_2 ~r K,\knKf, 



-'i 10 ^ K^kiki 



Kii = k_ik_Jc_i + k_ik_3k^2 + k^ik.sk^ 



adapted from Dixon and Webb (1958, p. 99). This expression is presented 

 here complete to emphasize the complexity of the general treatment of 

 what is, probably, the most common reaction mechanism. It is clear why 

 the majority of ^„/s determined from simple reciprocal plots bear no ne- 

 cessary relationship to dissociation constants. Of course, many assumptions 

 and simplifications may be introduced, but agreement of the resulting equa- 

 tion with the experimental data does not prove the particular mechanism 

 assumed. One of the most common assumptions is that the concentrations 

 of the complexes are determined by the usual equilibria, in which case the 

 rate equation reduces to: 



. = F. ^-^^ (2-60) 



"^ (A)(B) + ^3'(A) + K,'{B) + K,K,' 



where K^ = (E)(A)/(EA), Kj,' = (EB)(A)/(EAB) and K^' = (EA)(B)/ 

 (EAB), this applying to cases where binding of one substrate alters the 

 binding of the second substrate. If the binding is independent (K)^' = Kj^ 

 and K^ = K^), the following rate equation is obtained and this has been 

 frequently applied to enzymic transfer reactions: 



, . F ^-^^ (2-61) 



" [(A) + X,] [(B) + XJ 



It is seen from the reciprocal equation: 



1 _ 1 



1+^1+ ^' 



(B) VJA) 



1 + 



(B) 



(2-62) 



that if \jv is plotted against 1/(A), both the intercept and the slope will 

 be changed by the factor 1-f ^^/(B) compared to the case where A is the 

 only substrate; thus the determined ii,,, is dependent on the concentration 

 of the other substrate or coenzyme. However, by varying both (A) and (B), 

 it is possible to determine the constants; for example, as (B) increases, the 

 Ky„ for A will decrease and will approach Kp^. 



The most complete analysis of the kinetics of reactions involving coen- 

 zymes has been given by Alberty (1958). Following Dalziel (1957), he showed 

 that all enzyme reactions in which two substrates (or a substrate and a 



