KINETICS OF COMPLEX ENZYME REACTION TYPES 39 



a K^ = a K,{K,) = KJK^, the value of \/aK^^ will give only a mean 

 value for the dissociation constant. In the case of two independent sites with 

 different parameters, where: 



+ ,c^. T. (2-42) 



(S) + A% (S) + aK, 



a plot of 1/v against 1/(S) will give a similarly shaped curve but the slope 

 will approach zero near the \jv axis and approach [al{\-{-a)^ {KJV^^) at 

 low values of (S) where the curve for interacting sites would have a slope 

 of KJV„^. It is evident that the complexities become greater if more than 

 two interacting active centers occur on the enzyme. 



Two Different Substrates Are Involved in the Reaction 



One of the most serious limitations of the Michaelis-Menten theory is 

 that it assumes only one substrate enters into the reaction, whereas the 

 majority of enzyme reactions involve two or more substrates. The common 

 reactions involving two substrates fall into three categories: 



A + B ;^ AB (2-4.3) 



A + B ^ A + C (2-44) 



A + B ;z^ (' + D (2-45) 



but kinetically they may all be treated in a similar manner. Reaction 2-43 

 represents an addition reaction; reaction 2-44 represents the situation where 

 an activator is necessary; and reaction 2-45 represents transfer of groups 

 between substrates. Most enzyme reactions are probably of type 2-45 

 inasmuch as this includes all reactions of group transfer: 



A-X + B^A + B-X (2-46) 



where X may be hydrogen atoms as in oxidation-reduction, or chemical 

 groups as in transmethylation, transamination, or transacylation, or that 

 part of the substrate that is transferred to the hydroxyl group of water in 

 hydrolytic reactions. It has been estimated that such transfer reactions may 

 include over 90% of all enzyme reactions (Dixon and Webb, 1958, p. 184). 

 All two-substrate reactions may he divided into two general categories: in 

 the first, only one of the substrates forms an ES complex with the enzyme 

 and the second substrate reacts directly with this, whereas in the second, 

 both substrates form complexes with the enzyme and, these being adjacent, 

 formation of the products occurs within this ternary complex. 



