54 3. KINETICS OF ENZYME INHIBITION 



reversal can occur over periods of a few minutes and true equilibrium states 

 cannot be achieved. Irreversible inhibitors are not necessarily character- 

 ized by very low K^'s, since k^ may be small and comparable to k_i. Most 

 irreversible inhibitors react chemically with the enzyme, e.g., the ary- 

 lation of amino groups with dinitrophenyl derivatives, the alkylation of 

 thiol groups with iodoacetate, and the phosphorylation of serine residues 

 with the phosphorofluoridates. Most irreversible inhibitors progressively in- 

 hibit an enzyme to completion if there is sufficient total inhibitor to react 

 with all the enzyme groups (including other reactive groups that may be 

 present in the preparation); the exceptions would be those inhibitors where 

 ki and k_i are both small, since partial inhibition only may be achieved at 

 equilibrium. The kinetics of irreversible inhibition are thus relatively simple 

 since the inhibition increases with time as the active enzyme concentration 

 is reduced. In fact, if the disappearance of active enzyme can be written as 

 —d(E)ldt = ^•i(E)(I), integration leads to an expression for the enzyme 

 concentration at any time, namely (E) = (EQ)e~^'i'^" where (Eq) is the 

 initial concentration. The inhibited enzyme rate thus is v^ = -yg"^'!'^'' and 

 the fractional inhibition i = 1— p-^i'i". The reversal of inhibition by va- 

 rious means and the kinetics involved will be discussed in some detail in 

 Chapter 13. 



The usual formulations of inhibition kinetics apply only to reversible in- 

 hibitors where reaction 3-1 is assumed to reach equilibrium. In many 

 investigations the data have been analyzed without adequate proof that 

 equilibrium was reached under the experimental conditions. A comparison 

 of several inhibitors on an enzyme using a constant experimental interval, 

 a common procedure, may signify little, especially if the interval is short 

 and the inhibitors are of different types, since some may not have reached 

 equilibrium with the enzyme. 



COMPETITIVE AND NONCOMPETITIVE INHIBITORS 



A favorite classification of inhibitors is into competitive and noncompet- 

 itive types and it is necessary to consider the meaning of this distinction 

 before presenting the kinetic equations. The usual meaning attached to 

 competitive inhibition is that the inhibitor reacts reversibly with a site on 

 the enzyme and thereby prevents combination of that component of the 

 enzyme reaction that normally forms a complex at that site; thus an in- 

 hibitor may be competitive with substrate, coenzyme, or activator. In a 

 competitive situation there are two complexes with the enzyme, ES and EI 

 (assuming competition with substrate), one enzymatically active and the 

 other inactive. The rate will depend as usual on the concentration of ES 

 and the formation of EI will reduce this concentration. The relative con- 

 centrations of ES and EI depend on two factors — the relative concentra- 



