136 



4. SUBSTRATE INHIBITION AND PRODUCT INHIBITION 



The most general situation in which there are two binding sites for the 

 substrate can be represented as follows: 



ES C 

 E + P 



E S 

 \ / 



E -^ :n -' ^ 



lES 



SES 



/ \ 

 E I 



\ / 



A 



K, 





El 



IE 



SEI 



lEI 



lES 



(4-30) 



where the two binding sites are indicated on either side of the enzyme in 

 the complexes to the right. The Greek letters are the factors by which either 

 Kg or K^ must be multiplied for the designated reactions. Such a situation 

 is not too unlikely in competitive inhibition by a substance structurally 

 related to the substrate and able to combine similarly with the enzyme 

 sites. The generalized rate equation may be written as: 



V 



fi a 



■(!') 



1 



yfiQ 



+ 



1 



yaji 



1 



'W) 



l+d') 



71 p 



+ - 





+- 



ujiia 

 (4-31) 

 The equation may be simplified by setting the constants for the reactions 

 that are to be excluded equal to infinity. 



The effects of different degrees of substrate inhiljition on the inhibition 

 produced by a competitive inhibitor are shown in Fig. 4-13. When the 



1000 



(I) 



Fig. 4-13. Competitive inhibition of enzymes exhibiting substrate inhibition (Eq. 



4-27). Cm-ve 1: (S') = 3, a = oo; curve 1': (S') = \0, a = oo. Curve 2: (S') = 3, 



a = 10; curve 2': (S') = 10, a = 10. Curve 3: (S') = 3, a ^ 3; curve 3': (S') = 10, 



a = 3. Curve 4: (S') = 3, a = 1; curve 4': (S') = 10, a = 1. 



