376 7. INHIBITION IN MULTIENZYME SYSTEMS 



require only 3.9 X 10~^^ sec for a molecule to go 100 A on the average. Even 

 if the molecule had to bounce around within the cavity many times before it 

 collided appropriately with the active site, an extremely short time would 

 be necessary and such could not iiossibly exert a limiting action on the 

 rate. 



However, most instances of transfer involve diffusion through the aque- 

 ous medium and this requires displacement of water molecules, many 

 collisions, and a nonlinear path. The time required for a mean displace- 

 ment, d, of a diffusing molecule is given by the approximate equation, 

 t = d^l2D, where D is the diffusion coefficient and applies to a unit con- 

 centration gradient. We may take D= 1x10"^ cm-/sec for a molecule 

 of molecular weight of 100. Actually a good deal of variation in D occurs 

 between molecules of the same molecular weight, because hydration of ionic 

 groups or hydrogen bonding to the solvent water may slow diffusion sig- 

 nificantly. Since the diffusion coefficient varies inversely with the cube 

 root of the molecular weight, approximate values for D may be assigned 

 for any size molecule. It is also evident that the shape of a molecule will 

 be a modifying factor in the rate of diffusion. Since here we are interested 

 only in rough values for comparative purposes, the values assigned D 

 in Table 7-1 are adequate and correspond well with experimental results. 

 The table gives the times required for molecules of various sizes to diffuse 

 over the distances indicated. These figures may be compared with the times 

 required to catalyze the reaction of one molecule in a multi-enzyme system. 

 The turnover numbers of enzymes vary over a wide range but for many 

 important enzymes occurring in sequences (such as those in glycolysis, 



Table 7-1 

 Transit Times of Molecules Diefusing through Aqueous Medium " 



" The transit times given are the average intervals in msec required for spherical 

 molecules of the molecular weight indicated to diffuse the distances shown in the left- 

 hand column. The figures are only approximate and give merely the general order of 

 magnitude to be expected. 



