MITOCHONDRIA, CELLS, AND TISSUES 575 



This may be integrated to: 



(EI) = [^^^^t (1 - e-^-['i'+*^]'} (12-77) 



(1) + A-, 



Thus the rate of accumulation of the inhibitor in the cell follows the same 

 kinetics in each case, although the constants, of course, have quite differ- 

 ent meanings. 



Three different situations may be postulated: (1) the inhibitor enters 

 into the cell much more slowly than it combines with the enzyme so that 

 (I,) during the development of the inhibition is essentially zero and the 

 rate of the inhibition is dependent primarily on the penetration process; 

 (2) the inhibitor enters the cell much more rapidly than it combines with 

 the enzyme so that (Ij) is approximately equal to (Iq) during the process, 

 the rate of inhibition depending on the reaction with the enzyme; and (3) 

 the rates of entrance and association with the enzyme are comparable so 

 that (I() is less than (I^) but is appreciable, the kinetics being complex. It 

 is interesting that in the first case (1): 



""^^ «I.) (12-78) 



' dt 



where k is a membrane permeability constant, and since i = (EI)/(E,) that: 



di 

 dt 



(12-79) 



when the affinity of the enzyme for the inhibitor is high. Here the inhibi- 

 tion increases linearly with time providing (I^) remains constant. It may 

 be shown that the simultaneous differential equations expressing the general 

 case where the penetration and association rates are comparable (3) are: 



di 



— = A-,(I,) - ^•[(I,) + K,]k; (12-80) 



"^^^'■^ = A-(U -f k,K,i{E^ - a,)[k + A-,(E,)(1 - ^•)] (12-81) 



dt 



where k is a permeability constant and k^ is the forward rate constant for 

 the formation of the EI complex.* 



* It would be relatively easy and perhaps rewarding to test such kinetics on arti- 

 ficial systems wherein an enzyme is contained within a synthetic membrane and the 

 inhibitor is added to the external medium. The permeability of the membrane to the 

 inhibitor and the rate of reaction of the inhibitor with the enzyme could be determined 

 separately. The resulting behavior in the total system could be progressively applied 

 to inhibition within cells as more accurate data become available. 



