378 



7. INHIBITION IN MULTIENZYME SYSTEMS 



either do or do not restrict diffusion sufficiently to make this a factor in 

 the over-all rate. When diffusion is not limited, d{A)jdt will be the same in 

 each case because the spatial distribution of E^ does not affect the rate, 

 but d{C)ldt is not necessarily the same. Compartmentalization may allow 

 (B) to rise to higher levels than in a homogeneous system and aids main- 

 tenance of the steady state in (II); however, in (III), where B must diffuse 

 between compartments, the situation will not differ from (I). System (II) 

 will thus be more resistant to inhibition of Eg with respect to d{C)ldt. 

 When the membranes suppress diffusion, d(A)jdt may be reduced in (II) 

 and (III), and the reduction of d{C)ldt is apt to be greater in (III). It may 

 be pointed out that the kinetics of such systems are the same as those of 

 the simple diffusion case treated above (Eqs. 7-58 and 7-59) with D replaced 



A C 



^1 



A— B — C 

 E, Ep 



A C 



E| Ep 





ft L 



m 



Fig. 7-38. Illustration of the two basic types of compartmentalization. 



System (I) is homogeneous, system (II) has a single compartment, and 



system (III) has two compartments. 



by a permeability constant. It is evident that inhibition of enzymes in a 

 system where permeability determines the metabolic rate will not produce 

 an effect on this rate until the enzyme activity is reduced sufficiently 

 so that the permeability is no longer the limiting factor. The total number 

 of diffusion steps in a two-enzyme reaction within a cell may thus be large: 

 five for (I), nine for (II) and thirteen for (III). One or more of these steps 

 may be important in the rate of formation of C. 



Hearon (1949 b) and Bierman (1954) have discussed metabolic systems 

 limited by diffusion. Bierman particularly has presented a detailed analy- 

 sis of several types of systems. Unfortunately, the kinetics were derived 

 on the basis of a linear relationship between substrate concentration and 

 rate, and are not applicable generally to metabolic systems. The approx- 

 imation, V = F,„(A), is valid only when (A) is much less than Ky„; an 

 appreciable error is introduced if (A) is greater than Kf^JlO. One may say 

 that the steady-state concentrations of intermediates are usually low in 

 most multienzyme systems, but it is not the concentration only, it being 



