KINETICS OF COMPLEX ENZYME REACTION TYPES 43 



coenzyme) participate, whatever the order or mechanism of complex for- 

 mation, follow rate expressions of the general type: 



= 9^0 + -T-rr + TFTT + 



« (A) (B) (A)(B) 



where (A) and (B) are the concentrations of the two substrates and the 9?'s 

 are parameters which involve the rate constants and can be determined by 

 the proper methods of plotting. This equation is equivalent to: 



,r (A)(B) 



-Fu + <P2{A) + <fAB) + gPo(A)(B) 

 with which the above expressions are seen to correspond. 



The Solvent Participates in the Reaction 



The role of water in enzyme reactions is frequently ignored. However, 

 without directly entering into the reaction, water can contribute to the value 

 of the Michaelis constant or substrate constant. The enzyme active center 

 and the substrate may be hydrated and reaction between them to form the 

 ES complex may involve displacement of water, according to the following 

 equation: 



E-W + S-W ;^ ES + W-W (2-63) 



The substrate constant, therefore, does not relate only to the affinity of 

 the enzyme for the substrate but includes the relative affinities of both 

 for water, as pointed out by Laurence (1955). 



In hydrolytic reactions, water is one of the substrates but terms for it 

 are usually omitted from the kinetic equations because its concentration is 

 generally constant and very high. From Eq. 2-61, if B is water it is seen that 

 the usual Michaelis-Menten expression is obtained sinc« (H2O) ^ -K^HoO ^^ 

 an E-H.2O complex exists. It is generally not known if a site exists on the 

 enzyme for the binding of the water that enters hydrolytic reactions. It 

 is known that the rate with /?-fructofuranosidase is a function of the water 

 concentration when this is altered by high concentrations of sucrose or al- 

 cohol (Nelson and Schubert, 1928) and a water-site on urease has been 

 postulated to explain the inhibition by excess substrate (Laidler and Hoare, 

 1949). Two active centers were assumed to occur on urease, one for urea 

 and one for water, and reaction occurs when the ternary complex is formed; 

 however, urea can also compete with the water for the water-site, although 

 such a complex is catalytically inactive. The rate expression derived for 

 this situation was: 



kKdE.m ,. (S) ^_^^ 



K,K, + {K, + A%)(S) 4- (S)^ " (S) + K„, 4- (S)V(A\ + A%) 



