SUBSTRATE INHIBITION 117 



molecules bound) or occurs by a different mechanism. The peak of the 

 rate curve is defined by the various constants as follows: 



Substrate concentration for maximal rate: (So') = v a^y (4-4) 



Maximal rate attained: Vo — V^ . (4-5) 



1 +ljp + lly + {2l\/aM 



The value of (Sq') is obtained by differentiating Eq. 4-2 and setting dvjdiS') 

 = 0, and the peak rate in obtained by substituting this value in Eq. 4.2. 

 The usual formulation for this type of inhibition has been somewhat 

 different from that given above. The treatment given originally by Hal- 

 dane (1930, p. 84) and generally followed by others (Dixon and Webb, 

 1958, p. 81) assumes that a second substrate molecule is bound to the ES 

 complex to inactivate: 



k 

 E+S — ES^E+P 



ES + S — ESa 

 by which it is meant that the following reactions occur: 



E + P 



\^ ^/V^^, (4-6) 



E 



^S 



This differs basically from the previous treatment in that inactive com- 

 plexes of the enzyme with single substrate molecules are ignored and the 

 only inactive species is ESg. The rate equation is given by: 



V = V ^^ = V ^- (4-7) 



- 1 + (S') + (S')V« " 1 + 1/(S') + (S')/a ^ 



where the constant a corresponds to its previous meaning, representing 

 the interference of one substrate molecule on the binding of the second. 

 Since this equation is of the same general form as Eq. 4-2, it is impossible 

 experimentally to distinguish between them and curves of similar form 

 are predicted. The basic difference in these treatments is that Haldane's 

 expresses the effect of the formation of ES2 only while the present formu- 

 lation involves also the inactive ES complexes. In some respects, it de- 

 pends on the choice of a normal baseline for the uninhibited system, but on 

 the other hand the interpretation of the determined constants will depend 

 on the pattern of reactions assumed. 



