EXTRANEOUS BINDING AND IMPURITIES 855 



acids, heavy metal ions, or polysaccharides). With the increasingly exten- 

 sive use of more potent inhibitors, this problem becomes of greater sig- 

 nificance, and it is necessary to look into the quantitative asi)ects and the 

 means to detect such binding. 



For a system containing n different extraneous binding sites or sub- 

 stances, the conservation equation for the inhibitor in a mutual depletion 

 system may be written as: 



(I)e = K, —^ + i(E), + ri(PJ, + ... + •/■„(?„), (15-120) 



\ — % 



where (Py); is the total concentration of the yth type of binding site and 

 Tj is the fraction of the jth site bound to the inhibitor, i.e., r, = (P^I)/(Pj);. 

 In comparison with Eq. 3-32, the first term is the concentration of the 

 free inhibitor, the second term the concentration of inhibitor bound to the 

 enzyme active site, and the other terms the concentrations of inhibitor 

 bound to the various extraneous sites. In zone C, where the concentration 

 of the free inhibitor is negligible, the situation is fairly simple, since: 



(I), r,(P,), + ... 4- r„(P„), nRioix 

 (15-121) 



(E), (E), 



The inhibition will be reduced by the amount indicated in the second term. 

 Let us now assume that the total concentration of each of the extraneous 

 binding sites is related to the total enzyme concentration by equations such 

 as (Pj)^ = 'Pj(Ei)t, so that: 



^ = T^r - '^'P^ - - - ^-Vn (15-122) 



The effect of the extraneous binding sites on the zone C inhibition will 

 thus depend on (1) the number of different types of binding sites, (2) the 

 concentrations of these sites relative to the enzyme, and (3) the afiinities 

 of the sites for the inhibitor as reflected in the r values. 



These relationships are i^articularly important in the deductions made 

 from the studies of pseudoirreversible or titration-type inhibitors, since 

 in these the enzyme concentration is assumed to be proportional to the am- 

 mount or concentration of the inhibitor, i.e., (E)^ = (1)^/^ (see Chapter 3). 

 In the presence of extraneous binding sites: 



(E), = -. — (15-123) 



^ + nPl + ... + rnVn 



In any specified condition, (E), is still proportional to (I),, but when one 

 is determining the relative enzyme concentrations in different prepara- 

 tions or tissues, the term r-^^p-^^ + ... -f r,j:),j may not be constant, i.e., 

 some tissues will have more extraneous binding sites than others and the 



