266 6. INTERACTIONS OF INHIBITORS WITH ENZYMES 



Finally, AS may be calculated from Eq. 6-98. The dielectric constant may 

 be varied by employing different mixtures of aqueous medium and a mis- 

 cible organic liquid (such as dioxane or methanol): direct effects of such 

 organic substances on the enzyme or inhibitor must be ruled out. 



Although a beginning has been made in the determination of entropy 

 changes in protein binding and the formation of the enzyme-substrate 

 complex, unfortunately there is little work with enzyme inhibitors (see 

 Chapter 15). However, one may take as typical the entropy of formation 

 of the ES complex (Laidler, 1955 a). Values in the range between — 50 

 and + 50 cal /mole /degree have been found and indeed in some cases the 

 entropy change is the principal driving force in the formation of the complex. 

 Such would be the case in the binding of the hapten "HOgAs— cp— NHCO- 

 cp— CONH— cp— AsOgH" to antibody protein, in which the thermodynamic 

 constants were found to be AF = — 7.4 kcal/mole, AH = — 0.8 kcal/ 

 mole, and AS = 22 cal/mole/degree (Epstein et al., 1956). In the binding of 

 Ca"^"^ ions to seralbumin, there was little effect of temperature on the bind- 

 ing and hence AH was assumed to be zero, in which case AS = — AFjT 

 or around 14 cal/mole/degree (Katz and Klotz, 1953). The binding of 

 Cu++ ions is similar and gave a value of AS — 28 cal/mole/degree (Klotz, 

 1952, p. 427). It is evident that the role of entropy in protein interactions 

 is very important. 



Components of the Entropy Change in Protein Interactions 

 The over-all entropy change in the reaction: 



E -iv^ + I -Wy -» El ~iv, -\- {x + y - z)w (6-101) 



may be considered to be made up of three parts in the general case, [a) The 

 rigidity imposed in the molecules by the formation of the EI complex which 

 would result in a negative AS. (b) Structural modifications in the enzyme 

 or substrate consequent to binding, the J^S for which could be either posi- 

 tive or negative, (c) The liberation of water molecules with an increase in 

 their rotational degrees of freedom resulting in a positive AS. It is proba- 

 ble that the last is the most important contribution in reactions involving 

 ionic groups. In fact when AS is definitely positive, it is evidence that 

 oppositely charged groups are interacting and displacing water of hydra- 

 tion as pointed out by Laidler (1955 a). Enzymes such as pepsin, trypsin, 

 and ATPase (which act on ionic substrates) show a + z]*S for formation 

 of the ES complex, while chymotrypsin and urease (which act on uncharged 

 molecules) show a — AS. Similar -f J*S values are obtained for the ionic 

 interactions of the arsenical hapten with antibody and for Ca"^"^ and Cu"^"^ 

 with seralbumin. 



