p-AMINOBENZOIC ACID 509 



the molecular form to the ionized form is 4.85, which means that the ion 

 is approximately 10 4 - 85 times as active as the corresponding molecular 

 form. This seems to be somewhat high when the activities of nonionizing 

 analogues are compared to similar ionizing forms. 



The inductive constants of Branch and Calvin for various radicals are, 

 according to Bell and Roblin, 204 a linear function of the pK a values of 

 the corresponding sulfanilamides with the radicals substituted in the N 1 

 position. 



J* = -1.33 p#„+ 13.88 



With these three equations, the activity of a sulfonamide could be 

 determined from the ionization constant. In Figure 7, theoretical activi- 

 ties for the ionic and molecular forms at pH 7 are plotted against pK a 

 and compared with the experimental activities. The point of maximum 

 activity occurs at a pK a value of 6.7, which agrees very well with the 

 experimentally determined maximum activity. The pK a of the most active 

 sulfonamide varies with the pH, since the fraction ionized changes for 

 the various sulfonamides with changes in pH. 



The theoretical considerations applicable to the data with one organism, 

 Escherichia coli in this instance, are not necessarily applicable to other 

 organisms, since the combining power of the sulfonamide group may not 

 in all cases be the limiting factor for interaction with the enzyme, and 

 the enzyme may in itself differ to some extent from organism to organism. 



Correlation With Ionization Constant. With the assumptions (1) that 

 only the sulfonamide ion combines with the enzyme; (2) that a constant 

 quantity of enzyme must be combined with the sulfonamide for inhibi- 

 tion of growth of Escherichia coli to occur; (3) that the dissociation 

 constant for the enzyme-sulfonamide ion complex is a function of the 

 ionization constant of the sulfonamide; and (4) that a maximum exists 

 for the activity of sulfonamides correlated with ionization constant, an 

 equation derived from the equilibrium constants by Klotz 205 indicates 

 that at this maximum, the logarithm of the dissociation constant of the 

 enzyme-sulfonamide ion complex is a linear function of the logarithm of 

 the ionization constant of the sulfonamide. Thus, 



dlnK p [H+] 

 dlnKa K° a + [H+] J 



where K p represents the dissociation constant of the enzyme-sulfonamide 

 complex, K is the ionization constant of the sulfonamide, and K° is the 



r ' a 'a 



ionization constant of the most effective sulfonamide at the hydrogen 

 ion concentration, [H + ]. Since the ratio of d In K p to d In K a is con- 



