SUBSTRATE INHIBITION 



131 



The rate and inhibition equations are quite complex, involving a quadratic 

 expression in the most general situation. However, if it is assumed that 

 (E;) <^ (A;) so that the activator exists mainly in the free and substrate- 

 combined forms, the expression for free activator: 



(A) = 



(S) + K, 



(4-15) 



may be substituted in Eq. 2-69 to give the approximate rate. It would 

 appear, contrary to expectations, that such a mechanism, although it may 

 produce marked inhibition of the rate, cannot lead to a peak in the rate-(S) 

 curves, and hence will not be recognized as typical substrate inhibition. 

 However, if the activation mechanism follows the reaction scheme 2-70, 

 substitution of the value of (A) from Eq. 4-15 leads to an equation of the 

 type: 



(4-16) 



where: 



A + B/(S) -f (S)/C 



1 + 



K. 



B 



C = 



(A,) 



1 + 



1 -f 



^1 



K„ 



(A,) 





and the inhibition will lead to a decreasing rate at high substrate concen- 

 trations. Such inhibition may be distinguished from substrate inhibition 

 of types A and B by varying the concentration of the activator. If the 

 substrate inhibition is removed by increasing the activator concentration 

 to above optimal levels, it is likely that the substrate is complexing with 

 the activator and removing it from the system. This was done in the case 

 of the inhibition of enolase by 2-phosphoglycerate (Westhead and Malm- 

 strom, 1957), where increasing the Mg++ concentration from 1 raM to 

 10 vaM abolished the inhibition. In such systems the buffer may also play 

 a role, inasmuch as it often can complex with the activator and in the pre- 

 sent case a difference was observed between Tris-HCl and phosphate buf- 

 fers. The enolase system is also complicated by activator inhibition: high 

 concentrations of Mg++ reduce the rate and this is independent of the 

 reduction in free substrate concentration. The kinetics for activator in- 

 hibition are worked out in detail by Friedenwald and Maengwyn-Davies 

 (1954, p. 185). Needless to say, the degree of inhibition in type C systems 

 depends on the value of J^,,, relative to K^ and K^, i.e., the relative affinities 

 of activator and substrate for each other and for the enzyme. 



