40 2. THE KINETICS OF ENZYME REACTIONS 



(a) Only One Substrate Forms a Complex With the Enzyme. When B 

 reacts directly with the EA complex to form the products immediately, 

 one may write: 



E + A ^ EA (2-47) 



EA + b4e+C+D (2-48) 



The rate equation is found to be: 



'^^^'^^^^^^^ ^F.-, j^^^^L, , (2-49) 



(A) + [k_, + h{B)]lk, (A) + K^+ ihlk.HB) 



where F^; is the maximal rate with respect to A and K^^ is the dissociation 

 constant of the EA complex. The expression is similar to the classic Mi- 

 chaelis-Menten formulation but both the maximal rate and the Michaelis 

 constant now depend on the concentration of B. Since the reciprocal equa- 

 tion is: 



11 1 



V = YjBf ^ t;:('a)" 



(B) "^ k. 



(2-50) 



plots of Ijv against 1/(A) at different concentrations of B will often allow 

 evaluation of the constants. 



If one of the products forms a complex with the enzyme, there are two 

 binary complexes involved and the reactions may be written as: 



(2-51) 



(2-52) 



(2-53) 



The steps wherein products are formed are written in the forward direction 

 only because we are considering initial rates before the products have ac- 

 cumulated sufficiently to make the back reactions significant. The rate 

 equation is found to be: 



. ^ F. ^^15) (2-54) 



(A) +K^+ K-{B) + K"{A){B) 



where V„, = k^iE/), K^ = k_^jk^, K' = kjk-^, and K" = k^jk.^. This is iden- 

 tical to Eq. 2-49 except for the additional term for (A)(B) in the denomina- 

 tor, which alters the intercept but not the slope in the reciprocal plots. 



