GENERAL CONSIDERATIONS OF MULTIENZYME SYSTEMS 381 



brought down to Fg to inhibit reaction 2; the degree of inhibition to reduce 

 Vj just to V2 is then: 



H = 1 1^ 



' 1 



' ^ (A, 



F2 



= 1 (7-64) 



The limiting rate coefficient for reaction 2 may be defined as 72/^1 '^^^^^ ^^6- 

 signated bv Lg- Thus: 



^o = 1 - L, (7-65) 



When iv2 is unity or greater, reaction 2 is not limiting and inhibition of E^ 

 will always depress v^, when Lo is less than unity, a certain amount of in- 

 hibition, ?o- must be exerted on E^ before v.^ is altered, and the smaller 

 L2 is, the greater must this inhibition be. We may next inquire into the 

 inhibition exerted on V2 by any inhibition of i\. The inhibition of i\ is 

 {j and the consequent inhibition of v.^ is io and the relation between them is: 



i, = AJLil (7-66) 



1 - lo 



which can be shown to reduce to: 



U = 1 - ^-f^ (7-67) 



after substitution from Eq. 7-65. The inhibition of V2, or the formation of 

 product C, is thus related quantitatively to the limiting rate coefficient L^. 

 This may be extended to a chain of any number of steps and to primary 

 inhibition of any nonlimiting reaction in that sequence: 



io = l - Lj (7-68) 



i, = 1 - ^^-^ (7-69) 



where j refers to the step that is limiting and k to the step that is acted 

 upon by the inhibitor. Lj would be given by Vjlv;^. In certain cases, Iq 

 might be greater than indicated by Eq. 7-68 because the concentration 

 of the intermediate may not be able to rise to a level saturating the enzyme, 

 so that if) is actually the minimal degree of inhibition that must be exerted 

 before the formation of product is depressed. 



This simple formulation indicates the danger inherent in such statements 

 as "the over-all rate can be depressed only by inhibition on the reaction 

 that is limiting," for it will depend on how great the inhibition is and the 

 degree to which the reaction is limiting, that is, on i^. and Lj. If Lj is not 

 much less than unity, although reaction j is truly limiting the rate of for- 

 mation of the product, inhibition on another enzyme maj^ quite readily 

 depress the over-all rate. Determination of limiting rate coefficients is 



