576 



12. RATES OF INHIBITION 



The most important treatment of diffusion-limited kinetics for the present 

 purpose is that of Roughton (1960). Equations were developed by Roughton 

 for the diffusion of a substance from medium I through a membrane into 

 medium 11, in which the substance diffuses and is immobilized rapidly and 

 irreversibly on a finite number of sites. This model would correspond rea- 

 sonably well to certain situations in which an inhibitor is bound tightly to 

 intracellular components (including the enzyme attacked) following pen- 

 etration of the plasma membrane. The behavior in such systems depends 

 on spatial factors and the treatment was applied to flat layers, cylinders, 

 and spheres. If the membrane between the media is very thin, the effect 

 of the membrane on the time required for a given per cent uptake in me- 

 dium II is linearly related to the ratio of the permeabilities in medium II 

 and in the membrane. This would imply that under these conditions, the 

 rate of the reaction with the sites would be proportional to the membrane 

 permeability. 



(B) The pH of the extracellular medium. Since many inhibitors are weak 

 acid or bases, the rate of inhibition may depend on the pH of the external 

 medium because the undissociated and ionic forms penetrate the membrane 

 at different rates. For a simple acidic inhibitor where HI penetrates into 

 the cell but I~ does not: 



d{l, 



dt 



A^„,[(H1,-,) - (HI,)] 



(12-82) 



where A'jjj is the permeability constant for the undissociated form HI. 

 The total concentration of the inhibitor in both forms inside the cell is 

 (I,),. The concentration of HI will depend on the pH, both outside and in- 

 side the cell, and thus Eq. 12-82 may be rewritten as: 



d(hh 

 dt 



— ^'hi 



!lo). 



(I.) 



1 + A'„/(H,^ 



1 + KJiU,^) 



(12-83) 



where K^, is the acid dissociation constant of the inliiljitor. The rate of 

 inhibition may thus depend on the intracellular pH as well as that of the 

 external medium. If the ionized form I~ also penetrates into the cell: 



d(h 



dt 



+ k,- 



do). 



1 + A'J(H,+) 



ao)t 



a.)t 



1 + /la/(H, 

 (I.). 



(12-84) 



1 + (H,-)//i„ 1 + (H,+)/A^„ J 

 where I'l- is the permeability constant for the ionic species. The usual ex- 



