TWO INHIBITORS ACTING ON A MONOLINEAR CHAIN 499 



apy was suggested by Potter and extended by Skipper and associates 

 (1954). No treatment of the kinetics of such situations has been made. 

 Let us consider inhibition to be exerted on each enzyme of the simplest 

 monolinear enzyme chain: 



E, E, 



A-^B->C (lU-21) 



A single inhibitor acting on E^ alone will depress the steady-state rate of 

 formation of C to the same degree as it inhibits reaction 1, while a single 

 inhibitor acting on E2 alone will not depress the formation of C unless the 

 system is removed from a steady state, in which case d{C)ldt will be equal 

 to the rate of reaction 2 (see page 323). For convenience we shall assume 

 that Ii acts specifically on E^ and L, on E2. If (IJ is such that reaction 1 

 is inhibited 50%, d{C)idt is also inhibited 50%; when I2 is added, no further 

 inhibition of d(C)jdt will occur unless the steady state is lost, in which case 

 the over-all inhibition would be no different from that in the presence of 

 I2 alone. Thus in this simple system no greater inhibition is achieved by a 

 combination of the two inhibitors. However, the transition time between 

 steady states may be different if reaction 1 is inhibited simultaneously with 

 reaction 2. Even if Ij is competitive. I^ wiU produce the same inhibition 

 with I2 as it will alone as long as the steady state is maintained. However, 

 when the physical state of the system prevents sufficient rise in (B) to 

 compensate for the inhibition of reaction 2 (as when B diffuses out of a 

 compartment), addition of I^ may decrease (B) and furtiier inhibition can 

 occur. 



If reaction 1 is reversible, inhibition of d{C):dt will be produced with 

 both Ij and I2 alone and a combination of the two inhil)itors will inhibit 

 more strongly than a single inhibitor although less than the sum of the 

 individual inhibitions. This is due to the effect of (B) on the reverse reaction 

 (page 338). In chains of more than two enzymes, the same principles would 

 be demonstrated. Thus in the sequence: 



1^1 ^2 -^3 ^4 5 



A-> B^ C^D->F^ G (10-22) 



d(G)ldt will depend on the rate of reaction 1 if the system is in a steady 

 state and on the slowest reaction if it is not. Inhibition of E4 to the point 

 where d{G);dt is reduced makes reaction 4 the limiting reaction; inhibition 

 then on another enzyme would affect diG)ldt only when the reaction cata- 

 lyzed by that enzyme approaches the limiting rate, and in this case the 

 over-all inhibition would be the same whether the inhibitor acting on E4 

 were present or not. Thus multiple inhibition in simple monolinear chains 

 would seem generally to be incapable of producing an effect much greater 

 than a single inhibitor and a marked potentiation of inhibition would be 

 out of the question. 



