RESERVAL IN CELLS AND WHOLE ANIMALS 647 



When the inhibitor reacts with and is inactivated by a substance in the 

 body, and the inhibited enzyme is not reactivated: 



E + I ^ EI (13-75) 



I + A 4 Q (13-76) 

 The rates of change of (E) and (I) may be expressed as: 



d(^)ldt = - k,ma) (13-77) 



diDldt = - A-i(E)(I) - A:3(I)(A) (13-78) 

 Dividing these equations, one obtains: 



and integrating: 



-^ ^ 1 + i^ (13-79) 



d(E) /ki(E) 



(I) = ih) - ^^ hi -^^ - (E,) + (E) (13-80) 



fci (Ml) 



where (I,) and (E^) represent the initial or total concentrations of inhibitor 

 and enzyme. When (I^) ^ (E,): 



(I) = (I,) In — -— (13-81) 



After all of the inhibitor has reacted and (I) = 0: 



(I,, = i^ 1„ <^ (13-82) 



where (E),„,„ is the final and minimal enzyme concentration reached. If 

 we now require that this minimal enzyme concentration be lethal to the 

 organism, the initial concentration of the inhibitor required to kill is 

 given by: 



(I), = IfL In -*L (13-83) 



ki (E)l 



where (E)^ is the concentration to which the enzyme must drop for a lethal 

 action. In terms of the enzyme inhibition required for a lethal action: 



^2(A) , 



(I)l = -~^ hi 

 ki 



1 -^r 



(13-84) 



