RATES OF INHIBITION OF PURE ENZYMES 



565 



which may be integrated to give: 



^■ = 1 _ e-i-id)^ 



(12-56) 



It is evident that the development of inhibition is independent of the inac- 

 tivation reaction since the formation of X from EI is of no consequence. 

 The com'se of the inhibition is plotted in curve 5 of Fig. 12-20 for an arbi- 

 trarily chosen set of conditions. 



TIME 



Fig. 12-20. Variation of the inhibition with time in various systems in which inac- 

 tivation occurs. K^ = 1 milf, (I) = 5 mil/, k^ = 1, and ^-3 = 10-^. Curve 1, E and EI 

 unstable (irreversible); curve 2, E and EI unstable (reversible); curve 3, no inactivation; 

 curve 4, E stable and EI— >X (reversible); curve 5. E stable and EI^X (irreversible). 



When the dissociation reaction of the EI complex must be included, the 

 situation is much more complex. We now have: 



*i "-'3 



E -f 1 — EI ^ X 



for which two differential equations may be written: 

 dijdt = A-,(I)(1 - - A-,A', ■(£!)/(£,)] 



dm)idt = A-,(i)(E,)(i - - m)a\K, + 1-.. 



(12-57) 



(12-58) 



(12-59) 



