154 



5. DETERMINATION OF MECHANISMS AND CONSTANTS 



GENERALIZED EQUATIONS FOR DETERMINATION 

 OF CONSTANTS 



Six types of plotting procedures have been outlined for the specific 

 case of completely competitive inhibition. These may be applied to any 

 mechanism of inhibition and before considering particular situations it 

 will be profitable to indicate a general approach from which most cases 

 of inhibition can be derived. 



Let us assume that in addition to the substrate the enzyme binds other 

 substances X^, X,, ... X„ which may be activators, inhibitors, cofactors, 

 coenzymes, hydrogen ions, or any component of the total reaction. The 

 general expression for the total enzyme concentration is thus: 



(E,) = (E) + (ES) + (EXJ + ... + (EXJ + (EX,S) + ... + (EX„8) (5-8) 



If ES is the only active complex breaking down to the products, this equa- 

 tion may be rewritten in terms of (ES): 



(E,) 



(S) 



(ES) + (ES) + 



+ 



(X,) 



aK, 



+ ... 



A%(X,) 

 (S)Ai 



(XJ 



I'/i, 



+ 



(ES) 



/is(Xj 



(S)/i„ 



(ES) 



(5-9) 



and the rate equation derived from v = A'(ES), in the double-reciprocal 

 (type A) form is given by: 



where a ... v are the interaction constants: 



K, = 



(E)(X,) 

 (EX,) 



aKi 



(ES)(X,) 

 (ESX,) 



etc. 



indicating the effect of each component on the binding of substrate. A plot 

 of \jv against 1/(S) will give a straight line with the characteristics: 



(5-11) 



(5-12) 



Thus the slope is de]iendent on the interaction constants while the inter- 

 cept is not. If the inhibition is partially noncompetitive (or if any other 



