36 2. THE KINETICS OF ENZYME REACTIONS 



determined; however, if 1/v is plotted against 1/(E^), even though the ab- 

 solute enzyme concentrations are not known, both k^ and ^„, may be eval- 

 uated. Inhibition of such systems presents interesting possibilities to be 

 applied to intracellular studies. 



J 



The Enzyme Contains Two Interdependent Active Centers 



An enzyme may possess two active centers that are sufficiently close to- 

 gether so that binding of substrate to one site will affect the properties of 

 the other site, altering either the affinity for the substrate {K^) or the rate 

 of breakdown of the ES complex {k^. The reactions may be written: 



(2-31] 



(2-32) 



where /? characterizes any change in rate of ES breakdown brought about by 

 binding of one substrate molecule. Actually SES could break down with 

 respect to either substrate molecule (forming ES+P or SE-fP) but the 

 rates are identical for each reaction and we assume that the probability of 

 both substrate molecules being involved simultaneously is negligible (i.e., 

 the reaction SES —^ E-f2P is ignored). One can now write: 



(Z(ES) 



Jt 

 (Z(SES) 



dt 



(E,) = (E) + (ES) + (SES) (2-33) 



A;i(S)(E) - A'_i(ES) - A:,(ES) = (2-34) 



A:3(ES)(S) - A:_3(SES) - iSA-2(SES) = (2-35) 



V = /^^(ES) + i3A;2(SES) (2-36) 



From these the following general rate expression may be derived: 



[1 + WS)/g„'](S) 



" = ^" (S) + if,,, + (S)./if./ <'-«" 



where K„^ = {k_]^ + k2)lk-i^ and KJ = {k_^^j3 hi)lk^, these being the Mi- 

 chaelis constants for Eqs. 2-31 and 2-32, respectively. If one now assumes 

 that the ^,„'s are dissociation constants and that KJ = aKg. 



"" '™(S)-f«A^ + «AV/(S) ^ ^ 



where a characterizes any change in K^ induced by the binding of one sub- 



