370 



7. INHIBITION IN MULTIENZYME SYSTEMS 



where K^ is the inhibition constant for C on E^. Eqnating i\ and v^, the 

 following quadratic espression for (C) in the steady state is obtained: 



(C)^ + K, 



(A) 





(C) 



VrKcKAM 



(7-57) 



From (C) the steady-state rate may be obtained from Eq. 7-56. Results 

 for an arbitrarily chosen system are shown in Fig. 7-35. The steady-state 

 rate is, of course, less than if no feedback existed, and the fractional re- 

 duction due to feedback is shown in curve 3. However, the feedback helps 



lOOrnM 



CA)- 



FiG. 7-35. Variation of the rate with substrate concentration in a feedback system 

 (7-53). Fi = 2, Fa = 10, Fa = 1, K, = \ mM, K, = 0.3 mM, and K^ = 1 mM. 

 Curve 1: steady-state rate Vg^. Curve 2: rate of reaction 1 assuming no feedback. Curve 

 3: fractional reduction of the rate by feedback. The dashed hne 4 indicates the 

 maximal (A) for a steady state if there is no feedback. 



to maintain the system in a steady state; without the feedback, (A) could 

 not be greater than 1 mM, as indicated by line 4, but with the feedback, 

 (A) can be any value and a steady state may be established. The reason 

 for this is that as (A) increases, (C) increases and exerts more inhibition 

 on Ej so that reaction 1 slows down; an equilibrium is reached when (C) 

 is at that level which will inhibit E^ sufficiently to maintain (C). 



Inhibition of Feedback Systems 



Inhibition of either E^ or E3 will alter the steady-state concentration 

 of C, according to Eq. 7-57, and when the resultant over-all rates are cal- 

 culated it is found that there is relatively little buffer capacity, as shown 



