114 4. SUBSTRATE INHIBITION AND PRODUCT INHIBITION 



and isolation of the inhibitor was carried out and a number of possible 

 products tested for inhibitory activity. This is not true substrate inhibi- 

 tion but could easily be mistaken for it. If one is bent on demonstrating 

 substrate inhibition, it might be well to bear in mind the possibility of 

 an inhibitory product or intermediate, and to study carefully the rate of 

 development of the inhibition. 



Inhibition by Partial Attachment to Substrate Sites (Type A) 



A general treatment of the kinetics, assuming that the substrate must 

 bind at two points for reaction, will be presented and various special cases 

 will then be considered as simplifications in this formulation. The reaction 

 scheme may be represented as: 



/ -v. 7 



E + P 



(4-1) 



where /? and y represent the changes in binding constant when the sub- 

 strate is bound by only one group and a is the interaction constant indi- 

 cating the effect the first bound substrate molecule has on the binding of 

 the second. It is assumed that reaction occurs only when the substrate is 

 bound by both groups. The general rate equation for this situation is: 



-■ ^^ ^^'> (4-2) 



"* 1 + (S') [1 + i/i? + 1/r] -1- (S')V«^y 



where F,„ is the maximal rate that would be attained if the substrate did 

 not bind to the single groups. Specific concentrations are used because it 

 is somewhat easier to examine the effects of variation in the constants a, 

 /5, and y. The constants /? and y will generally be greater than unity since 

 the substrate will probably be bound less tightly to one group than to two; 

 « will also usually be greater than unity because the two binding groups 

 will be reasonably close on the enzyme surface and interaction between 

 simultaneously bound substrate molecules may be quite marked. 



The variation in rate with substrate concentration is plotted in Figs. 4-2 

 and 4-3 for different values of a. When a = 1 (noncompetitive inhibition 

 by substrate) and the ESg complex is readily formed, the inhibition is 

 most marked. As a increases, substrate inhibition becomes less and less 

 evident until a = co (competitive inhibition by substrate) when the ESg 



