298 6. INTERACTIONS OF INHIBITORS WITH ENZYMES 



possible that some enzyme inhibitions involve similar positions of aromatic 

 rings and hence it is of interest to determine the effect of orientation on 

 interaction energy. 



This problem was considered by de Boer (1936) who compared the dis- 

 persion energy of two benzene rings that were 3.5 A apart when lying in 

 the same plane (A) or lying parallel (B), and found it to be four times 

 greater in position (B). He also constructed distance-energy curves and 

 concluded that 3.5 A would be the equilibrium distance for maximal at- 

 traction; calculations, using the equations derived earlier in this chapter, 

 lead to the somewhat greater distance of 3.7 A for position (B). The dis- 

 persion energy at this latter separation would be about 24.6 kcal/mole. 

 For benzene the heat of fusion is 2.35 kcal/mole and the heat of vapori- 

 zation is 7.37 kcal/mole, so that the heat of sublimation is 9.72 kcal/mole; 

 however, in benzene crystals the rings are not parallel throughout but in- 

 clined at angles in alternate rows and displaced along their axes. The 

 average interaction energy of a molecule with its neighbors in a crystal 

 would be about 19.4 kcal/mole so that the value calculated above is not 

 unreasonable. The high dispersion energies possible with aromatic rings 

 may be important in binding substrates and inhibitors to enzymes, for 

 even at a separation of 5 A the attraction energy may amount to 4 kcal/ 

 mole. 



The polarization of a benzene ring by an ionic group can under certain 

 circumstances give rise to appreciable interaction energy. An amino or 

 carboxylate group on a line perpendicular to the plane of the ring and at 

 the distance of closest approach (3.55 A) would be attracted to the induced 

 ring dipole with an energy of approximately 7 kcal/mole (calculated from 

 Eq. 6-62). However, if water were present and a single hydration layer 

 around the ionic group remained, the energy would drop to only 0.2 kcal/ 

 mole (assuming D — ^). Such ion-induced forces could contribute strongly 

 if the interaction of inhibitor with enzyme protein occurred in a cavity from 

 which water is excluded or if the other forces binding the inhibitor were 

 strong enough to force the water from between the reactants. Needless to 

 say, the attraction between a constellation of protein charges and a poly- 

 cyclic aromatic compound could provide the high affinity sometimes ob- 

 served between derivatives of naphthalene and anthracene with enzymes, 

 if the contours and patterns of the contact surface were satisfactory. 



An excellent example of the energies involved in such interactions is 

 given by Munck et al. (1957), who studied the complexes formed between 

 steroids and adenine nucleotides. These 1:1 complexes were shown to be 

 attributable to dispersion forces acting over the relatively large surfaces 

 of these molecules. The reaction may be written as: 



steroid- W + coenzyme-W —^ steroid-coenzyme + W — W 



