72 



3. KINETICS OF ENZYME INHIBITION 



cholinesterase with the very potent inhibitor Nu 683. Equation 3-32 may 

 be written as: 



(I,)3„ = K, + 0.5(E,) (3-43) 



where (I/)5o is the inhibitor concentration producing 50% inhibition. If 

 various dihitions of the enzyme are tested and the activities expressed in 

 f.1 moles of substrate per minute, the activities will be equivalent to the 

 turnover number (TN)x(E^), so that: 



(I,),o =K,+ ^ TN(E,) 



(3-44) 



A plot of (1^)50 against the relative activity of the enzyme will give a straight 

 line with a slope of 0.5/TN and (1^)50 intercept of Ki, from which (E^) and 

 (E/) may be evaluated. Such methods may be applied to any enzyme 

 providing an inhibitor potent enough to place the system in zone B is 

 available. Competitive inhibitors may be used if their rate of displacement 

 from the enzyme is slow and readings are made soon after addition of sub- 

 strate to the inhibited system. Theoretical plots for the two methods are 

 presented in Figs. 3-12 and 3-13. 



Competitive Inhibition in Mutual Depletion Systems 



When the substrate and inhibitor compete for binding to the active site, 

 the general equation, corresponding to 3-33, will be more complex: 



(E/) 



(3-45) 



where (E/) = {Ei)IKg and (E/) = (£,)/£";, the specific concentrations of 

 the enzyme with respect to substrate and inhibitor. This expression applies 

 to the situation where the system is in zone B with respect to both substrate 

 and inhibitor. Equation 3-45 is related to the equation derived by Goldstein 

 (1944) but here is expressed in terms of fractional inhibition rather than 

 fractional activity. 



The general equation given by Goldstein is: 



(I 



') = [{(S') - a(E/)} 1—^ - 1] + [1 -- «ll + ,.,, ^ ,^ J 



(E/) (3-46) 



