574 12. RATES OF INHIBITION 



develops. Tissue preparations usually respond to a substance more rapidly 

 when it reaches the cells in the blood supply or perfusion fluid than when it 

 is applied externally in a bath. Thus octyltrimethylammonium ion at 

 2 raM produced half-paralysis of gastrocnemius muscle in 0.3 min when 

 perfused into the muscle but it required 14 min when the drug was added 

 to the medium in which the muscle was suspended (Ing and Wright, 1931). 

 Diffusion barriers can thus play an important role in kinetics. The major 

 factor is not the absolute rate of penetration into the cells or tissue but 

 the diffusion rate relative to the rate of reaction of the inhibitor with the 

 enzyme. 



It is difficult from kinetic measurements alone to determine if the rate 

 at which a substance affects an intracellular component depends primarily 

 on the rate of penetration of the substance into the cell or on the associa- 

 tion rate for the formation of the complex. The uptake of dyes by cells 

 has been studied thoroughly and has been found to follow monomolecular 

 kinetics in most cases. Thus Irwin (1925) found that cresyl blue entered 

 the vacuole of Nitella according to such kinetics and assumed that the 

 dye combined with something inside the cell; however, the kinetics could 

 be accounted for satisfactorily on the basis of diffusion. The simple diffusion 



of a substance into a cell: 



I 

 I 

 I 

 k 



I 

 I 

 I 



is expressed by the differential equation: 



^ = k[{h) - (I,)] (12-74) 



(it 



which may be integrated to: 



(I.) = (Ij(l - e-«) (12-75) 



On the other hand, the reaction of the substance within the cell may be 



represented as: 



k 

 I + E ^ El 



for which the differential equation: 

 d{EI) 



dt 



A;(I)(E) - A-/^,(E1) (12-76) 



may be written, where K^ is the inhibition constant if the process leads to 

 enzyme inhibition. 



