276 



6. INTERACTIONS OF INHIBITORS WITH ENZYMES 



haptens, interactions (1), (2), and (3) may be assumed to remain constant, 

 so that differences in binding energy may be attributed to interactions of 

 the group X with the protein, specifically that part of the protein adjacent 

 to the — N=N— group in the normal antigen-antibody reaction. Let us 

 first consider the binding energy difference due only to dispersion forces 

 between the group X and the protein. The displacement of water originally 

 adjacent to both hapten and antibody must also be considered. Further- 

 more, the substitution of the group X on the benzene ring replaces a hy- 

 drogen atom, the interaction of which must be included. The reactions may 

 now be written: 



Unsubstituted hapten: H(W) + A(W) ^ HA + W 

 Substituted hapten: X(W) + A(W) ^ XA + W 



where H is phenylarsonate, X is X-phenylarsonate. A is antibody, and W 

 represents an unspecified number of water molecules. The dispersion energy 

 changes for the reactions are given by: 



'Pb = f>E-A + fw-w - Vb-w - "Pa-w 

 fx = 'Px-A + "Pw-w - fx-w - 'Pa-w 

 and the difference in dispersion energy is: 



^(Pdisv = (Px - Vh = "Px-A - "Px-w - "Pb-a + Vn-w 

 From Eq. 6-69 the individual dispersion terms may be written as: 



Vx-A = -18.7 V^^AA^/ 



Vb-a = - 18.7 V^ R^RAld/ 

 'Pb-w - - 18.7 «\/^4 RbK^^^' 



(6-113) 

 (6-114) 



(6-115) 



leading to: 



18.7 



\/Z, R.,R^ - n\/ Z,R^R^~\/ Z,R^R^ + n\/ Z.RgR,, 



(6-116) 



where Z^ = VZ^^Z^^, Z, - VZ^^Z^,, Z., = VZ^^Z^, Z^ ^VZj^Z^,, n = the 

 number of water molecules adjacent to hapten group, and where the equi- 

 librium distance d^ is assumed to be the same for each interaction. From 

 the molar refractions, electron numbers and van der Waals' radii of the 



