294 6. INTERACTIONS OF INHIBITORS WITH ENZYMES 



the cationic group, that is capable of interacting with the nonpolar part 

 of the inhibitors. Essentially the same is observed in the cp — (CH2),,— COO" 

 series; when the benzene ring is at the pro])er distance from the —COO" 

 group, the interaction is maximal. In the indole-(CH2)rt— C00~ series the 

 benzene ring is already at near optimal distance in indole acetate and 

 further interposition of — CHj— groups only decreases the binding energy. 

 Comparing phenylacetate with propionate, the benzene ring is bound more 

 tightly than a methyl group by 1.82 kcal/mole. This is a reasonable value 

 as calculation of the dispersion energy of a benzene ring interacting on 

 one side with a protein surface leads to 2.35 kcal/mole (the experimental 

 value from cholinesterase is 2.1 kcal/mole), and the methyl group disper- 

 sion energy amounts to approximately 0.3 kcal/mole for side-on inter- 

 action with the protein (see Table 6-19). 



The phenyl group would seem to be bound by 1.66 kcal/mole more tightly 

 than the cyclohexyl group, comparing the respective propionates. The 

 latter will probably be at a somewhat greater distance from the protein, 

 due to the noni>lanar hydrogen atoms, and this could well account for the 

 difference. If the half-thickness of the benzene ring is taken as 1.85 A 

 (Table 6-9), the cyclohexane ring can be calculated to be 2.19 A; the molar 

 refractions are Ri^nz = -5-1 ^^^^ J^cycio = 27.0 ml/mole. Using these val- 

 ues, it is found that the phenyl group should be bound 0.88 kcal/mole 

 more tightly; if these rings fit into a slit or cavity, this value would be ap- 

 proximately doubled and would be of the same order of magnitude as the 

 experimental difference. The ring certainly must be oriented properly 

 because cis- and ^m/?s-cinnamate do not inhibit, the double bond here 

 restricting the rotation of the ring and holding it at an angle. 



Binding of ATP to ATPase 



Laidler and Etliier (1953) determined the entropy change on binding 

 of ATP to muscle ATPase by varying the dielectric constant of the medium 

 with methanol and dioxane, using an equation similar to 6-95, and found 

 a values of 25 cal/mole/degree for the ion-ion contribution. From Eq. 

 6-98, the value of the interaction distance is thus given by d^ — O.lbz-^z^. 

 If this procedure is valid, it is evident that multiple charges are involved; 

 if two phosphate groups interact with two cationic groups on the enzyme, 

 the (If. would be 3.0 A and if three groups on each interactant were involved, 

 d^ would be 6.75 A. The data are only approximate because the bulk di- 

 electric constant was assumed and the ion atmosphere was ignored; taking 

 these into account, it would seem most likely that only two ionic groups 

 are involved in the binding, or possibly even two phosphate groups and 

 one cationic enzyme group. 



Knowledge of substrate and inhibition constants for ATP, ADP, and AMP 

 would provide some information on these electrostatic forces, but these 



