442 9. INHIBITION IN CELLS AND TISSUES 



When correction for the endogenous factor is made, it is usually done 

 in the manner just described, that is by determining the relative effects of 

 adding substrate in the absence and presence of the inhibitor. This may 

 not be justified in some instances. It has been assumed, for example, that 

 the addition of substrate does not alter the endogenous rate, so that the 

 exogenous and endogenous rates are additive, but many instances where 

 this is not true can be conceived. It is, however, very difficult to determine 

 if a change in endogenous rate does occur, unless the endogenous reaction 

 is so different from the exogenous one that they can be measured separately 

 by some means. 



Relations between Endogenous and Exogenous Metabolism 



Let us now consider in more detail the possible effects that an added 

 substrate may have. There are four cases which must be analyzed. 



Case 1: one enzyme and one substrate (the same enzyme and the same sub- 

 strate are responsible for both endogenous and exogenous rates). 



S, + E ;=^ ES, -> E + P 

 S +E;=tES ^E + P 



(The subscript e will be used to designate whatever is endogenous; in this 

 case, S^ and S are the same substrate but the former occurs with the en- 

 zyme and the latter is added.) The endogenous rate will be v^ = 7(S^)/ 

 [(S^) + £",„] and the rate after the substrate is added will be v = F[(SJ + 

 (S)]/[(S^) -f- (S) -f ^„J. If no endogenous reaction were occurring, the rate 

 due to the added substrate would be 7(S)/[(S) + ^„,], which is clearly not 



V - V,. 



Case 2: one enzyme and two substrates (the endogenous substrate is 

 different from that added). 



Se + E ^ ES, ^ E + P 

 S' + E ^ ES' ^ E + P 



The individual rates would be given by the usual Michaelis-Menten expres- 

 sions but the actual rate when S' is added will be: 



^^(^^) ^-^ /-^^'^ , .- (9-1) 



(SJ + ^1 + {K,IK,) (S') (S') +K, + (K.JK,) (SJ 



Here also the rates are not additive because the two substrates may be 

 considered as competing for the same enzyme. 



