874 16. SPECIFICITY or inhibition 



Inhibition of Ii on Eg: in = -^r- — ^--^ — (16-9) 



(li) + A,„ 



Inhibition of I, on E,: i,^ = -^j^- — ~ — (16-10) 



(li) + Ki^^ 



Inhibition of la on Ej: tji = ~z ^-— — (16-11) 



Inhibition of Ij on E3: I'as = ^^.^t ^^ — (16-12) 



(la) + Ae33 



Inhibition of I, and L on E,: ^^,, = ^^'".^^^i. tf^'",^^'l^ .t T d^-lS) 



where the first subscripts refer to the inhibitor and the last subscripts to 

 the enzyme. This applies to noncompetitive inhibition but the results will 

 be applicable in principle to competitive inhibition as well. To facilitate 

 discussion and interpretation we shall assume the following values for the 

 inhibition constants: K, = 0.3 mM; K, = 3 mM; K: = 1 mM; K^ = 



'11 _ '12 _ '21 _ '23 



5 m.M. The results are not readily plotted in two dimensions and thus the 

 general behavior of the system is shown in Table 16-2, where the inhibitions 

 produced by each inhibitor alone and by them acting together have been 

 calculated. The specificities, as defined by Eq. 16-1, are also shown. It may 

 be noted first that certain combinations of the two inhibitors will produce 

 a greater inhibition on E^ compared to the single inhibitors, with no increase 

 in the inhibitions on Eg and Eg. In other words, the specificity may be in- 

 creased significantly. It is also evident that high concentrations of each 

 inhibitor when they are used together will decrease the specificity in the 

 sense that both E2 and E3 may be strongly inhibited. It is of some impor- 

 tance, therefore, to inquire into optimal concentrations for inhibitor com- 

 binations. The best concentrations to be used will depend in any case on 

 what type of effect is desired. Three general situations may be visualized: 

 (rt) it is desired to inhibit E^ to a certain degree with minimal inhibitions 

 on E., and E3, {h) it is desired to inhibit E^ maximally with certain limits 

 placed on the inhibitions of E2 and Eg, or (0) it is desired to achieve the 

 maximal specificity. 



If it is required to inhibit E^ to the extent of i-^^i^ rearrangement of 

 Eq. 16-13 gives the relationship between (IJ and (L). 



