488 



10. EFFECTS OF MORE THAN ONE INHIBITOR 



TWO INHIBITORS ACTING ON A SINGLE ENZYME 



When two inhibitors and a substrate react with an enzyme, it is necessary 

 to consider all the possible interactions between the components of the 

 system. The situations conceivably range from the case in which all the 

 reactants bind at the active site and completely interfere with the attach- 

 ment of each other to the enzyme, so that only the complexes ES, EI^, 

 and EIo are present, to the case in which all the reactants are capable of 

 binding to the enzyme independently, so that in addition to the above com- 

 plexes, ESIi, ESI2, EI^Ij, and ESI^Ig also occur. The kinetics will thus de- 

 pend primarily on the type of inhibition — competitive, noncompetitive, 

 uncompetitive, etc. — exerted by each inhibitor. A semigeneralized treat- 

 ment of single enzyme multiple inhibition will now be presented, the 

 ES complex being considered for simplicity to be the only active form 

 capable of forming the product. The following reaction scheme may 

 be written: 



aK 



EIJ2S 



(10-1] 



for which the conservation equation takes the form 



(E, 



(E) + (ES) + (ET,) + (EI2) + (EIiS) + (EI^S) + (EIJ^) + (EIJ^S). 



Assuming that Vj = A:(ES), the rate of the inhibited reaction may be ex- 

 pressed as: 



F„,(S)' 



1 + (I.)' + (I.)' + ^^^^^^^ + (S)' 



: , di)' , (I2)' , (ii)'(i.)' 



ocf^Y 



(10-2) 



where specific concentrations have been used for convenience. The constants 

 a, /?, and y, giving the degrees of alteration of the binding of each component 

 brought about by the presence of the other components on the enzyme, 

 may be assigned various values depending on the type of inhibition occur- 

 ring. Taking into consideration only competitive and noncompetitive in- 

 hibition, one would expect four situations to be most common. 



