INHIBITION CONSTANTS AND INTERACTION ENERGY 267 



The entropy change from the liberation of water in ionic interactions 

 may be quite large. In the reaction of the "HOgAs— cp— NHCO— cp— 

 CONH— cp— AsO^H" hapten with antibody, it was calculated that the 

 AS for association (with loss of translational and rotational freedom) 

 would be approximately — 100 cal/ mole /degree. Thus the AS for water 

 liberation would be + 122 cal/mole/degree. Since the melting of ice in- 

 volves an entropy change of AS = + 5 cal mole degree, it was concluded 

 that around 24 molecules were displaced (Epstein et al., 1956). In the reac- 

 tion of ATP with myosin ATPase the calculations showed that the elec- 

 trostatic interactions contributed only part of the entropy change (Laidler 

 and Ethier, 1953). It is possible that the remainder was due to the struc- 

 tural changes in the myosin which are known to occur on reaction with 

 ATP. The negative values of AS found for nonionic enzyme interactions 

 have their origin mainly in the association of enzyme and substrate, but 

 it is possible that here there is also a small entropy term for the dis- 

 placement of water. 



The importance of water and entropy in protein interactions is indicated 

 by the fact that the formation of the mercury dimer of seralbumin (Kirk- 

 wood, 1954, p. 16) and the combination of trypsin with soybean trypsin 

 inhibitor (Sturtevant, 1954, p. 17) both show a negligible change in enthalpy. 

 Yet there are large negative changes in free energy which must mean that 

 AS is positive and that water molecules must be displaced from between 

 the interacting protein molecules. 



Relation of Inhibition to Interaction Energy 



Since K, = e'^^-^^, the relation between fractional inhibition and the 

 interaction energy may be written as: 



^ ^ (6-102) 



(I) + xe-'P/RT 



where x depends on the type of inhibition and on the value of a, the factor 

 by which the binding of inhibitor is changed in the presence of bound sub- 

 strate (see Eq. 3-21); for noncompetitive inhibition x = 1 and for com- 

 petitive y = 1 -r [(S) /KJ. Equation 6-102 is plotted in Fig. 6-15 to show 

 the nature of the dependence of inhibition on the interaction energy. In the 

 midrange of the curves, the inhibition is quite sensitive to small changes 

 in the interaction energy; a change in AF of 0.25 kcal/mole will increase 

 or decrease the inhibition by 10%. When a series of related inhibitors is 

 tested at the same concentration, the relative interaction energies may be 

 read off the appropriate curve. 



