50 CHARLES TANFORD [3 



a particular kind of group on the molecule. This quantity is an effective 

 pK for the hydrogen ion dissociation of the kind of group being considered, 

 and, at constant ionic strength and temperature, it would be a constant 

 quantity independent of net charge if there were no interaction between 

 the many acidic and basic sites present on a protein or simple polyelectro- 

 lyte molecule. Such interaction does in fact exist, however, as a result of 

 ordinary Coulombic forces between electrostatic charges. 



Consider first a globular protein in its compact impenetrable configura- 

 tion, or any other large molecule in which the distances between sites and 

 the penetrability by solvent do not change during the course of titration. 

 Then each proton added to the molecule will provide a repulsive force for 

 all subsequent protons, and each proton removed will have the opposite 

 eff'ect. Thus pH— loga/(l— a) will decrease with increasing net positive 

 charge and increase with increasing net negative charge.^*^ The effect will 

 be greatest at low ionic strengths, but for impenetrable configurations will 

 persist to high ionic strengths. The resulting behavior is illustrated by 

 Fig. 5, which is obtained from the titration of carboxyl groups of ribonu- 

 clease,''^ a protein known from viscosity measurements to remain compact 



10.6 



10.4 



1^ 

 "0 I 



§ 10.2 



a 



10.0 



9.8 



2 -2 -4 -6 -8 



CHARGE 



Fig. 4. Logarithmic plot for titration of the free phenolic groups of ribonuclease (Tan- 

 ford, Hauenstein and Rands^^). 



and impenetrable throughout the pH range under consideration, and by 

 Fig. 4, obtained from the titration of the three surface phenolic groups of 

 the same protein. ^^ 



For simple flexible polyelectrolytes the effect of Coulombic interaction is 

 quite different. The first few protons added or removed exert the expected 

 effect. But each increment of net charge results, as we have seen, in a greater 

 extension of the molecular domain and this in turn leads to an increase in 



