COMBIXATION WITH MOLECULES OF INHIBITORS 91 



actually K- = K^^K^.^-.-Km oi% if each molecule is bound equally, K- = 

 K^l. Before presenting a general treatment of this problem, it will be well 

 to examine the ways in which enzymes can bind several inhibitor molecules. 

 Several possible situations may be distinguished and the inhibition ki- 

 netics are in general different for each. In the following, R represents an 

 active center while B is a nonenzymic or nonfunctional binding site. 



(I) The enzyme possesses two or more active centers on each molecule 



A. The centers are independent: in this case the inhibition kinetics are iden- 

 tical to those developed previously, since (E^) refers to the concentration 

 of active centers and not to enzyme molecules, 



ER„ + wl ^ ER„I„ Ki same for each group 



B. The centers have equal intrinsic affinities for the inhibitor but interact 

 so that binding of each inhibitor molecule influences the binding of other 

 molecules to adjacent sites. 



ER„ + wl;;^ ER„I„ Ki, uKi, fiKi ... for successive bindings 



C. The centers have different intrinsic affinities for the inhibitor. 



ER'R" ... R„ + nl;=i ER'IR"! ... RJ K/, K/' ... for each site 



(II) The enzyme possesses functional centers and nonfunctional binding sites 



Only a certain fraction of the bound inhibitor exerts an inhibitory action. 

 In this case there is no effect by the nonfunctional group binding on 

 the inhibition unless the system is in zone B or C and thus this binding 

 contributes to the reduction of free inhibitor concentration. 



R RI Ki for functional group 



/ / 



E +(n + l)I;:±E 



\ \ 



B„ B„I„ K^, for nonfunctional group 



(III) Each active center binds more than one inhibitor molecule 



ER -f nl :^ ERI„ Ki may be the same for each molecule of 



inhibitor or different if interaction occurs 



There are thus three situations [(I) B, (I) C, and (III)] which require ex- 

 tension of the previous formulation. 



Each Active Center Binds More Than One Inhibitor Molecule 



Inasmuch as binding of three or more inhibitor molecules to an active 

 center is relatively rare, attention will be given to the situation where 



