GENERAL CONSIDERATIONS OF MULTIENZYME SYSTEMS 373 



Transit Time 



Dixon (1949, p. 15; Dixon and Webb, 1958. p. 566) has pointed out that 

 in multienzyme systems there may be a factor additional to the rates of 

 the component enzymes that may play a role in determining the over-all 

 rate, namely the diffusion of an intermediate from one enzyme to the next. 

 The transit time is the average time required for the diffusion between 

 enzymes to occur. If an irreversible monolinear chain is in a steady state, 

 this implies that the rates of the diffusion processes are identical with the 

 rate of the initial step. If diffusion is slower than this rate, intermediates 

 may progressively accumulate and the rate of formation of the product 

 may be less than the rate of utilization of the initial substrate, in which 

 case the diffusion may be said to be limiting. When diffusion is limiting, 

 the response of the system to inhibition may be different than when the 

 rate is determined by an enzyme reaction. Diffusion is apt to be more im- 

 portant in compartmentalized systems and this wiU be discussed in the 

 following section. 



The transit time will depend on (1) the distance over which diffusion 

 takes place, (2) the diffusion constant of the intermediate, which is related 

 to its molecular size and shape, and (3) the presence of any barriers to dif- 

 fusion between the enzymes. The modifications in the kinetics of multi- 

 enzyme systems introduced by a diffusion process will depend on the struc- 

 tural properties, that is, the spatial relations of the enzymes. In hetero- 

 geneous catalysis, the problem is usually one of diffusion of the reactant 

 from the body of the solution to a surface containing the active sites; the 

 kinetics of diffusion and of diffusion-limited catalysis have been formulated 

 for various types of systems (Lee, 1953, p. 125; Moelwyn-Hughes, 1957, 

 p. 1167; Crank, 1956). 



Let us first consider the simple situation where a substance. B. diffuses 

 from a plane, at which the concentration of B remains constant, to another 

 plane at which B is adsorbed and reacted catalyticaUy (Fig. 7-37). The 

 rate at which the substance arrives at the active sites is given by: 



4r ^ ^ [(B), - (B),] (7-58) 



where a is the area of the planes under consideration, D is the diffusion 

 coefficient, (B)i is the concentration at the first plane and (B)2 is the con- 

 centration at the catalytic plane. The rate at which B is reacted if the 

 mechanism is enzjinic is: 



dB aFf,(B)2 



dt (B), + K, 



(7-59) 



since the rate will also be proportional to the area over which the reaction 

 occurs. In the steady state, these two rates must be equal, and (6)2 may be 



