24 2. THE KINETICS OF ENZYME REACTIONS 



identical to the Michaelis-Menten Eq. 2-7 but the constants have different 

 values: 



ICi + k,_2 -\- ks 



(2-15) 



Ki(k2 + k-2 ~r fCs) 



Reactions of this type cannot be distinguished from the Michaelis-Menten 

 type by the usual steady-state kinetics and may be more common than 

 supposed. It may be noted that as ^3 becomes larger, K,,^ more closely 

 approaches (A'_i-f A•o)/^•|; also if ^•_2^ ^2 ^^^^ the enzyme complex is mainly 

 ES, even though k^ is small, K,,^ becomes the substrate constant K^. Peller 

 and Alberty (1959) have presented a steady-state treatment of the kinetics 

 followed by enzyme systems in which an indefinite number of intermediary 

 complexes occur between a single substrate entering the reaction and a 

 single product being formed. Reiner (1959, p. 46) has thoroughly analyzed 

 a reversible enzyme system in which two intermediary complexes occur. In 

 most cases, the number of such intermediary complexes is not known and 

 it is very difficult to interpret K^,^ or to determine the values of the rate 

 constants. 



Assumption That the Over-All Reaction Is Irreversible 



The Michaelis-Menten treatment assumes that the breakdown of the ES 

 complex to the products is irreversible; that is, that the reverse reaction 

 whereby an EP complex would be formed does not occur. Enzymes, however, 

 are known to catalyze reactions in both directions. From the practical 

 standpoint, if the measurements are made early in the reaction before the 

 concentration of products has risen or if the products are removed from 

 the reaction as they are formed, this assumption of irreversibility is probably 

 valid. For the situation where the reverse reaction is important, Haldane 

 (1930) derived appropriate extensions to the Michaelis-Menten theory. If 

 one assumes the reaction sequence: 



S + E ^ ES ^ EP ;:± E + P (2-17) 



h/ 1 A. fC 3 



the rates of the forward and backward reactions will be given by typical 

 Michaelis equations and the over-all rate by: 



VJS)K, - F,(P)A;„ ^2.18) 



K,„K, + (S)K., + (P)A',„ 

 where F,„ and 7^ are the maximal rates for the forward and backward reac- 



