INTERACTIONS OF HAPTENS WITH ANTIBODIES 279 



Determination of Electrostatic Interactions of Ionic Groups 

 Antibody to p-azophenyltrimethylammoniiim ion 



-N=N-<p-N(CH3)3+ 



was reacted with two haptens that were identical except one contained 

 the trimethylamnioniuni ionic group and the other a neutral tertiary 

 butyl group. 



, /CH3 yCH3 



The former R-X=N-^\- N^CH3 R-N=N-^^\-C^CH3 



was bound more tightly and this difference may be attributed to the elec- 

 trostatic attraction between the positively charged hapten and a negative 

 antibody group. The ratio of the combining constants is 8.0 and hence the 

 binding energy difference is 1.15 kcal/mole (Pressman et al., 1946; Pressman 

 and Siegel, 1953). The distance between charge centers was calculated to 

 be 8 A, leaving approximately 3 A separation between the van der Waals' 

 surfaces of the ionic groups, sufficient space to accomodate a molecule of 

 water. However, since the reaction occurred in a physiological medium, 

 the effect of the ion atmosphere should be taken into- account. Using Eq. 

 6-90, an equilibrium distance d^ between charge centers of 6.35 A is obtained. 

 If the groups interact head-on, 0.6 A must be added to this as the distance 

 from the charge center to the carbon-atom of the carboxylate group, 

 giving 6.95 A as the distance between group centers. The plot of Eq. 6.90 

 is shown in Fig. 6-17 to facilitate such calculations of d^. The distance of 

 closest head-on approach would be 5.32 A, using the van der Waals' radii 

 in Table 6-9; if interaction were along the C— and N— C bond directions, 

 the distance would be 5.10 A, this being the maximal distance when the 

 groups are in contact. There is, however, an energy term that has been 

 omitted; the — N(CH3)3"^ group will attract water molecules more strongly 

 than the —C( 0113)3 group, and some energy may be necessary to displace 

 these. If this displacement energy amounted to only 0.7 kcal/mole, making 

 the true ion-ion interaction energy 1.85 kcal/mole, the calculated separation 

 would be that for head-on contact. It seems likely that these ionic groups 

 interact directly without interposed water molecules. 



A similar determination was made with antibody to p-(/y-azoplienylazo)- 

 benzoate and haptens that were identical except that one had a terminal 

 negatively charged benzoate group and the other a terminal nitrobenzene 

 group; the former was bound very tightly with a Kq = 89 and the latter 

 was bound so weakly that the K^ could not be determined but was less 

 than 0.01. The difference in binding energy is thus at least 5.0 kcal/mole 

 and possibly more. Reference to Fig. 6-17 shows that this indicates a charge 



