IRREVERSIBLE MONOLINEAR CHAINS 



331 



rate of reaction 2 in the presence of the inhibitor, V^j, = (1 — i)V2, and we 

 apply Eq. 7-3: 



(B), F,[(A) + K,] - (A)Fi 



(B) (1 -i)V,[{A) +A^] -(A)Fi 



(7-4) 



where (B)^ is the concentration of B in the inhibited system, and it is this 

 equation that is plotted in Fig. 7-6. Since the denominator on the right 

 side must be greater than zero if the numerator is positive and less than 

 zero if the numerator is negative, the maximal inhibition allowable for the 

 system to remain in a steady state is: 



1 - 



F. 



(A) 



(A) + K, 



(7-5) 



One of the most important general properties of multienzyme systems 

 may be illustrated with this simple sequence. The inhibition of the rate of 

 formation of product, in this case d{Q)jdt, will often be less than the inhibi- 

 tion of the single enzyme affected. In some cases, reaction 2 must be almost 

 completely blocked before reduction of d{C)ldt is observed. This ability to 

 resist inhibition might be thought of as the buffer capacity of the system 

 against inhibition. It depends for one thing on the capacity of the system 

 for (B) to increase until reaction 2 again becomes as rapid as reaction 1, 

 or at least to increase to a level saturating E2. Since the uninhibited steady 

 state f/(C)/c/^= Fi(A)/[(A) -f Z^] and the inhibited diQIdt^V^, = (1 - 

 i)V2, if (B) can rise to saturate Eg, the inhibition exerted on the formation 

 of C is given by: 



It = 1 - (1 - ^) 



F, 



(A) + K, 



(A) 



(7-6) 



Plotting if against i gives a straight line with a slope of F2[(A) -f ^J/Fi(A), 

 as shown in Fig. 7-7 for the systems plotted in Fig. 7-6. This form of plotting 

 shows particularly well the buffering capacity of the system. If ViJV^ 

 is much greater than ten in the system assumed, a steady state would 

 not exist previous to inhibition and if will always equal i. A third manner 

 of plotting such phenomena is shown in Fig. 7-8, where ?', is related to the 

 inhibitor concentration. In systems with adequate buffer capacity, no 

 effect will be noted on the formation of C until a critical concentration of 

 inhibitor is reached, at which point the inhibition will increase rapidly. 

 The buffer capacity of a system, as defined by dijdi(, is the change in the 

 inhibition of a single enzyme necessary to produce the change di^ in the 

 inhibition of product formation. For the two-step monolinear chain, the 

 buffer capacity may be obtained from Eq. 7-6: 



di 

 dit 



F. 



(A) 

 (A) + K, 



Vst 



F. 



(7-7) 



