SPONTANEOUS REACTIVATION OF INHIBITED ENZYMES 



629 



from which: 



Since ko is so small: 



(I) 



(I) + [{Tc_, + lc,)j{Tc,)] 

 (I) 



(I) + K, 



(13-40) 



(13-41) 



which is the expression for noncompetitive inhibition. If the substrate is 

 present during the development of the inhibition, it will slow down the rate 

 at which the maximal inhibition is reached and may decrease the maximal 

 inhibition if it can compete significantly with the inhibitor. In those instan- 

 ces where A'o is significant, Eq. 13-40 should be used and the inhibition 

 will no longer relate directly to the inhibition constant, K ^. The shape of 

 the total curve giving the time course of the inhibition will depend also on 

 the amount of inhibitor present; if (I,) = (E,) the curve will have a sharp 

 maximal peak whereas if (I,) ^ (E^), the curve will show a plateau since 

 the inhibition will not begin to decrease until there is no more inhibitor 

 to replace that reacted on the enzyme. 



A more accurate reaction sequence for the phosphorylation or carbamy- 

 lation of enzymes might be written as: 



E 



^1 A-j 



I — EI -^ 



EX 



X 



(13-42) 



where EI is the initial complex of the inhibitor with the enzyme, EX is 

 the chemically inactivated enzyme (X representing the inhibitor group 

 remaining on the enzyme), and X' is the inhibitor group after it has been 

 dissociated from the enzyme and perhaps chemically modified (as in a 

 hydrolytic reaction). From the differential equation representing the change 

 in EX concentration: 



rf(EX) 

 dt 



^:,(EI) - ^3(EX) 



(13-43) 



the conservation equation, (E^) = (E) + (EI) + (EX), and the equili- 

 brium, Ki^ = (E)(1) /(EI), the rate of change of (EX) may be determined: 



d(EX) 



A-.,(E,)(I) 



(EX) 



dt (I) + K 



In the steady state, d(KK)jclt = so that: 



(EX,., = *-''E'' 



A-3 + 



UD 



(I) + K, 



k, + k,[l + KJiD] 



(13-44) 



(13-45) 



