264 6. INTERACTIONS OF INHIBITORS WITH ENZYMES 



When a substrate or inhibitor approaches the enzyme surface it will modify 

 the charge distribution if it possesses ionic groups; a positively-charged 

 inhibitor will create a region of relative negativity on the enzyme and the 

 attraction will be increased. One might think of the enzyme as being polar- 

 ized or of the ionic inhibitor evoking image forces (as in the adsorption 

 of ions on metal or ionic surfaces). An inhibitor bound to an enzyme site 

 will experience forces of attraction arising from the fluctuating charges 

 on the surface vicinal to the site (Kirkwood, 1955). The potential energy 

 involved will depend on 1/cZ^ where d is the distance from the interacting 

 ion to the fluctuating ions and, since the forces are electrostatic, will depend 

 on the ionic strength (Kirkwood, 1954, p. 4). Hill (1956) has considered 

 such interactions on a quantitative basis and pointed out that the increased 

 stability would be opposed by the entropy changes. In any event, the dis- 

 tortion of the normal charge distribution by the inhibitor introduces a 

 small energy term into the total interaction. This effect is closely related 

 to the alteration in proton affinity of acidic or basic groups induced by the 

 proximity of an ion and the resultant change in p^^; this aspect will be 

 considered in more detail in Chapter 14. 



INHIBITION CONSTANTS AND INTERACTION ENERGY 



The various types of interactions and energy contributions involved in 

 the binding of inhibitors to enzymes have now been discussed. We shall 

 next relate the interaction energy to the experimentally determined inhi- 

 bition constant K,. If K^ is known, it is possible to calculate the over-all 

 change in free energy attending the binding of an inhibitor to the enzyme 

 from the equation: 



AF = RT\nKi (6-91) 



which at 37. 5° may be written as: 



AF = 1.422 log K, kcal/mole (6-92) 



The interaction energy values discussed in the previous sections generally 

 refer to the free energy changes in the process of bringing the interacting 

 molecules from infinite distance to the equilibrium separation d^. The 

 changes in free energy, enthalpy, and entropy are related by the equation: 



AF = AH - TAS (6-93) 



The relative contributions of AH and TAS to the free energy change depend 

 on the nature of the interaction and the medium in which it occurs. It is 

 possible to determine experimentally both AH and AS and these often 

 give useful information with respect to the reaction mechanism. 



