388 



7. INHIBITION IN MULTIENZYME SYSTEMS 



induce a complex pattern of response when the metabolic system involved 

 is composed of multiple interdependent reactions. 



Although enzyme systems are much more complex, the simple formu- 

 lation for first-order kinetics (Denbigh et al., 1948) is useful in expressing 

 these complex changes in mathematical form After perturbation of the 

 system, the concentration of any intermediate may be written as: 



(B) = (B)o + aie-^i' + a,e-'^^~' + ... + a„e- 



/inf 



(7-75) 



where (B)o is the initial steady-state concentration The constants, /?i ... /?„, 

 depend only on the kinetic parameters of the enzymes but a^ .. «„ may 

 depend in addition on the intermediate concentration. Each exponential 

 term gives the effect of one component of the system on (B). The as may 



TIME ► 



Fig. 7-41. Illustration of overshoot (curve 

 A), fluctuation (curve B), and false start 

 (curve C) following inhibition in a multi- 

 enzyme system. (X) represents the con- 

 centration of any intermediate. 



be either positive or negative depending on whether the effect is to increase 

 or decrease (B). Various combinations of values of the as and /5's will 

 give all the possible types of overshoot, false start, and fluctuation. When 

 multienzyme systems are more rigorously characterized, the evaluation 

 of these parameters, or the more complex ones resulting from enzyme 

 kinetics, may be worthwhile but at the present would be premature. 



