92 3. KINETICS OF ENZYME INHIBITION 



w = 2; it is simple to extend this treatment to higher vahies of n. The 

 most general pattern of reactions is the following: 



, E + P 



E EIS ^ (3-82) 



^' EI ^' ELS 



a^ EL ^s 



If noncompetitive inhibition is assumed (no effect on substrate binding), 

 the following rate expression is obtained, using specific concentrations for 

 convenience: 



Vi = 



(S') + 1 



1 + ^H') 



1 + (I') + lariai 



(3-83) 



where a is the factor expressing the change in inhibitor binding due to the 

 attachment of the first inhibitor molecule and /5 represents the reduction 

 in k produced by the binding of one molecule of inhibitor. The inhibition is 

 then given by: 



. (1 - m') + [aria] 



1 + (D + [Uria] 



(3-84) 



Various special cases dependent upon the values of a and /? will now be 

 considered. When /? = the binding of the first inhibitor molecule prevents 

 the breakdown of the substrate, but the inhibition is greater than in the 

 case where only one inhibitor molecule combines because there are in addi- 

 tion to EI and EIS the complexes EI2 and EI2S, which further reduce the 

 concentration of active centers. The inhibition is given by: 



^- ^''^ + [(^')^/«l ^ = (3-85) 



1 + c) + [uricc] 



If a is very low (second inhibitor molecule bound more tightly than first), 

 the inhibition will increase and approach a situation where aK^ is the 

 dominant constant: 



(I)^ 



(1)2 + aKi^ 



P = 0, a low (3-86) 



which is as close as the inhibition will come to Eq. 3-8L although aK,^ 

 is quite different from K/. If a is very high (second inhibitor molecule 

 bound less tightly than the first), the equation reduces to the usual one 

 for noncompetitive inhibition: 



i = TpT^ /3 = 0, « high (3-87) 



