640 13. REVERSAL OF INHIBITION 



and the other the rate of change of the free inhibitor concentration: 



^ ' A-_i(E,)^ ~ — ^ (E,)(l - 0(1) - A-(I) (13-63) 



dt ' A', 



It may be easily seen that the rate of reversal will be less than that for 

 EI dissociation in the absence of free inhibitor because (I) will always 

 have a significant value. The reversal curves will have a form intermediate 

 between the exponential dissociation type and the sigmoid destruction 

 type (i.e., between curve C in Fig. 13-1 and the curves in Fig. 13-13). 



Destruction of the Inhibitor by the Inhibited Enzyme 



A kinetic equation for this situation was derived by Goldstein (1944) 

 in connection with the reversal of serum cholinesterase inhibited with phy- 

 sostigmine. Expressing his equation in termes of inhibition rather than 

 activity: 



-r + In 



I - i 1 - i 



^-^^'^ t (13-64) 



A, 



where A'., is the rate constant for the dissociation of the EI complex, as in 

 reaction 13-38. Experimental data for the destruction of the inhibitor will 

 provide the means of determining A-2(E^)/iL j. If (E,) and K, are known, which 

 is seldom the case, h.^ may be obtained, or A;.2 may be determined by methods 

 such as have been worked out for ordinary substrate reactions (Huennekens, 

 1953, p. 583). Physostigmine is destroyed slowly by serum cholinesterase 

 and the above equation fits the data obtained by Ellis et aL, (1943) with 

 k^{'Eif)IKi = 1.4 as pointed out by Goldstein, from whom Fig. 13-14 is 

 taken. Curve B corresponds to the experimental data and curves A and C 

 were plotted for other initial inhibitions. The curves are again all of the 

 same configuration and the most rapid decrease in the inhibition occurs 

 now at i = 0.33. 



Destruction of the Inhibitor by an Enzyme Other Than the One Inhibited 

 The reactions that occur in this situation are: 



EJ — El + 1 (13-65) 



^■. 



1 + E^ 4 E J 4 E^ + Q (13-66) 



k_, 



where E^ is the inhibited enzyme and E2 is the enzyme catalyzing the 



