GENERALIZED KINETICS OF REVERSIBLE INHIBITION 65 



Inhibition Equations in Terms of Specific Concentrations 



The rate of an enzyme reaction does not depend on the substrate concen- 

 tration alone but on the concentration relative to the dissociation constant 

 of the ES complex. This may be seen from rearrangement of the Michaelis 

 equation: 



^ m r.ovrr-. . , = ^ m , c. , . , . (3-26) 



'" (S) + K, '" [(S)/if,] + 1 '" (S') + 1 



where (S') = (S)/^,. (S') was called the " specific concentration " of the 

 substrate by Straus and Goldstein (1943) and is the quantity that deter- 

 mines the rate with respect to substrate. Likewise, the effect of an inhibitor 

 depends on its concentration relative to K^, i.e., on (1)1 K^ which can be de- 

 signated (I'), the specific concentration of inhibitor. The same would also 

 apply to coenzymes and activators, where the specific concentrations (C) 

 and (A') would determine their activity in the enzyme reaction. The inhi- 

 bition equations may be rewritten in terms of specific concentrations: 



P V A■^■^■,■ ■ (D [(S')(l - fi) +{a - fi)] 



Generahzed mhibition: . = (p) ^(g,) ^ ,] + .[(S') 'TT] ^'"'^^ 



Competitive inhibition: i = -r— (3-28) 



Noncompetitive inhibition: i = — (3-29) 



CoupUng inhibition: i = (3-30) 



(-•-) + 1 + [^l\^ )\ 



These equations demonstrate that the degree of inhibition depends only on 

 the specific concentrations for any type. The fundamental reason for the 

 importance of specific concentrations is that the activity of a component 

 in an enzyme reaction depends on the concentration of its complex with 

 the enzyme, and this depends on the component concentration relative to 

 its affinity for the enzyme since (EX)/(E,) = (X')/[(X') + 1]. 



The quantities here designated as specific concentrations are called 

 " relative concentrations " by Dixon and Webb (1958, p. 76). We retain 

 the older term: it is felt that the use of the word " relative " may cause some 

 confusion since it would usually be construed as indicating the concentration 

 relative to another concentration or substance. 



