INTRODUCTION AND THEORETICAL CONSIDERATIONS 451 



under such conditions. Thus, the ratio, R/r is equal [E t ]/[ES] for which 

 an expression can be obtained from equation (12) by dividing by [ES] : 



[E t ] _R_K s .Ks[I] M , [/] m , 



[ES]~ r ~ [SVKAS^^Ks! KX * } 



These equations can be applied with slight modification to (a) en- 

 zymatic reaction in the absence of an inhibitor, (b) competitive inhibition 

 in which the inhibitor combines only with the free enzyme and not with 

 the enzyme-substrate complex and (c) noncompetitive inhibition in 

 which the inhibitor combines with the enzyme-substrate complex and 

 may or may not combine with the free enzyme. 



In the absence of an inhibitor, the [EI] and [ESI] terms> of equation 

 (11) are zero, and the corresponding terms of equation (13) can be 

 omitted to obtain an expression for the velocity of an enzymatic reaction 

 in terms of the concentration of the substrate. 



Hbj+s <14) 



In the case of competitive inhibition, the inhibitor does not combine 

 with the enzyme-substrate complex, so that the [ESI] term of equation 

 (11) and the corresponding term of equation (13) can be omitted. 



1 [K s K b [I]1 1 

 S]\_R " 1 ~ KiRyR 



r [S]\_R ' KjRJ ' R (15) 



For strictly noncompetitive inhibition, the inhibitor combines with both 

 the enzyme and the enzyme-substrate complex; so equation (13) rear- 

 ranged applies: 



1 i[k s K s [I}~] 1 

 r [S}\_R^ KjRyR 



+ mk (16) 



Since the dissociation constants, Kj and K S i may not be identical, the 

 extreme can be represented by a competitive inhibition in which the 

 inhibitor does not combine with the enzyme-substrate complex and by a 

 noncompetitive enzyme-substrate inhibition in which inhibitor does not 

 combine with the free enzyme but combines only with the enzyme- 

 substrate complex. In the latter case, which has been termed "uncompeti- 

 tive" inhibition, 18 the [El] term of equation (11) and the corresponding 

 term of equation (13) can be omitted: 



i = **- + I+_M- (17) 



r R[SVR^RKsi K } 



In order to determine the type of inhibition, the rate of an enzymatic 

 reaction is determined over a wide range of substrate concentrations in 

 the absence of an inhibitor and at two or more concentrations of inhibitor. 



