338 7. INHIBITION IN MULTIENZYME SYSTEMS 



PARTIALLY AND COMPLETELY REVERSIBLE MONOLINEAR 



CHAINS 



Either the first, the second, or both steps in a two-enzyme chain may be 

 reversible. For the system: 



F F 



A;^B->C (7-13) 



the rates of the individual reactions are given by: 



F,^_,(A) - F_,A'„(B) 



KaK_, + K_,{k) + A'a(B) 



V^(S,) 



(B) + K, 



(7-14) 

 (7-15) 



where the negative sign of a subscript refers to the reverse reaction from 

 B -> A. Solution of these equations gives a quadratic expression for (B); 

 from (B) the rate of formation of C may be calculated using Eq. 7-15. 



Ka{V_, + V,)(QY + [VJi.,K, + V,K_,{A.) -f V ^,K,K, - F,A'_,(A)](B) 



- V,K_,K,{X) = (7-16) 



The reduction in (B) and the steady-state rate as the reverse reaction in- 

 creases is shown in Fig. 7-11. Such a system will more often be in a steady 

 state, compared to a similar irreversible system, because a slow second 

 reaction, by increasing (B), will slow down the first reaction. 



Noncompetitive inhibition of Eg will have a different effect on the over- 

 all system compared to the irreversible system 7-1. As Fg is decreased, 

 the rate of formation of C will be reduced (Fig. 7-12) more readily because 

 the increase in (B) will slow down the over-all forward rate of reaction 1. 

 The sensitivity of the system to inhibition will depend on the initial level 

 of Fa; when it is high relative to F^, the inhibition on C formation will be 

 slight, but when it is lower than F^ the inhibition may be appreciable. 

 The buffer capacity of this partially reversible system is thus less than that 

 of the irreversible chain. 



The system: 



El Eg 

 A^B;i±C (7-17) 



under the conditions specified [that (C) is kept constant by some diffusion 

 process] does not behave differently to inhibition compared to the irreversi- 

 ble chain because the reverse reaction remains constant. However, it is 

 more difficult to maintain the steady state since tlie over-all forward rate 



