116 4. SUBSTRATE INHIBITION AND PRODUCT INHIBITION 



complex is not formed and no decrease in rate is found at high substrate 

 concentrations. 



When a = CO the rate may be less if the complexes with single groups 

 are formed. In the curves shown, the rate in 2 is always less than in 1 

 because of the formation of the inactive complexes 



S 



E and E 



\ \ 



S 



Practically such inhibition would not be recognized since the reciprocal 

 plot of l/v against 1/(S) will be linear as in the uninhibited situation and 

 the apparent maximal rate determined from the intercept will be related 

 to the true F,„ as follows: 



1 



1 + (1/^) + (1/y) 



(4-3) 



However, the slope of the reciprocal plot is KJV„^ so that the use of F„/ 

 will introduce an error in the determination of K,. The apparent ^5 will 

 actually be a mixed dissociation constant. Thus wdien complete competi- 

 tive substrate inhibition occurs, it will not be recognized. The phenomenon 

 termed substrate inhibition will be observed only when there is completely 

 noncompetitive inhibition or mixed inhibition, i.e., when a = 1 or some 

 finite value. There has been some confusion in terminology inasmuch as 

 typical substrate inhibition (where the rate decreases at high substrate 

 concentrations) has been called competitive (Dixon and Webb, 1958, p. 83) 

 whereas by the usual criteria it is noncompetitive since the binding of the 

 second substrate molecule is not prevented but the rate of substrate break- 

 down is reduced to zero. 



In Figs. 4-2 and 4-3 the constants /? and y have been assigned arbitrary 

 values of 5, indicating symmetrical binding and a reduction in affinity 

 compared to the active complex. It may be noted that if the binding energy 

 of the substrate to each single group is half that for the total binding in 

 the active complex, /? = 7 = l/V Kg. For K, = 10"^ M, as in the figures, 

 it is seen that /5 = 7 = 31.6 and the inhibition would be less marked than 

 shown. Theoretically these constants may have any values from less than 

 unity to infinity and, of course, will differ when the binding sites are dis- 

 similar. 



When the rate is plotted against pS, as in Fig. 4-3, substrate inhibition 

 of the type here considered is always represented by symmetrical bell- 

 shaped curves. Distortion of the symmetry indicates either that the in- 

 hibition is more complex than assumed here (e.g., more than two substrate 



