812 15. EFFECTS OF VARIOUS FACTORS ON INHIBITION 



centration is raised to 20% and then declines. The breakdown of the ES 

 complex to inorganic phosphate, ADP, and free enzyme can be visualized 

 as two separate reactions: the splitting off of a negatively charged phosphate 

 from the negatively charged ATP molecule, and the release of the negatively 

 charged ADP from a positively charged active center. The rate of the for- 

 mer reaction would presumably be increased by a low dielectric constant 

 and the rate of the latter reaction decreased. The observed increase in k^ 

 might, therefore, be attributed to the effect on phosphate splitting. 



Laidler and Ethier used these data to obtain the electrostatic and non- 

 electrostatic contributions to the entropy change in the formation of the 

 ES complex and to the activation entropy for the breakdown of the complex. 

 Since the Michaelis constant here appears to be the true substrate constant, 

 Kg, its variation with the dielectric constant provides direct information 

 on the affinity between the enzyme and the substrate. They found that AS^^ 

 = 25 e.u. and from the total entropy change, AS = 49 e.u., the nonelectro- 

 static contribution, ASnf,g — 24 e.u. Thus the electrostatic and nonelectro- 

 static contributions were approximately equal. Now, the calculation of 

 ASgg involves an expression proportional to {dDldT)jD^. Laidler and Ethier 

 used bulk dielectric constants and the question arises, as it always does, 

 as to the validity of this. Since we do not know the separation distance 

 between the enzyme and the substrate, it is impossible to estimate exactly 

 the microscopic dielectric constant that is applicable. However, if one as- 

 sumes a separation of around 7 A, which would compare roughly with other 

 ion-ion interactions, the microscopic dielectric constant would be about 

 one-half the bulk dielectric constant; likewise, (W/dT would be about one- 

 half that for the bulk dielectric constant. Under these assumptions, AS^g 

 would be calculated to be about twice the value obtained by Laidler and 

 Ethier, namely 50 e.u., which would imply that the total entropy change 

 for the formation of the ES complex would be entirely electrostatic. This 

 might actually be more reasonable considering the highly charged nature 

 of ATP and the low binding energies of adenosine and AMP. This large 

 entropy change would perhaps be associated with a marked release of 

 water of hydration. A change in the local configuration of the enzyme 

 must also be considered. In any event, this example illustrates some of 

 the difficulties inherent in the quantitative interpretation of dielectric 

 studies. 



(c) Papain. The effects of methanol on the hydrolysis of benzoyl-L-arginin- 

 amide by papain are shown in Table 15-4 (Smith et al., 1955; Stockell and 

 Smith, 1957). As the methanol concentration is increased, iiC,„ becomes 

 larger and ko is relatively unchanged. Since plots of log K„^ or log k2 against 

 1/Z) are not linear and since an opposite effect on K„, was anticipated, in 

 the earlier report it was concluded that the methanol reacted with the pa- 

 pain active site by hydrogen bonding and interfered with the binding of 



