» 



TITRATION CURVES OF PROTEINS 27 



The logarithmic expression of dissociation constants as pK. values is con- 

 venient, and has been extended beyond the field of acidic and basic dis- 

 sociations. In any equilibrium involving equiraolecular ratios of the reactants 

 and product, we may write: 



A -\- B^ AB 



whence by a process similar to the above: 



p(A) = pK + log— ^ — 

 I — a 



where a is the degree of dissociation of the product AB. At 50% dissociation, 

 the pK is the logarithm of the reciprocal of the concentration of either 

 reactant. Where the equilibrium is more complicated, pK has this same 

 meaning for each step if the association is stepwise. This use of the term 

 pK should be carefully distinguished from that discussed above, although 

 the two are analogous. 



7.1.2. Titration Curves. If salts are assumed to be completely 

 dissociated, equation 1 may be written in the form: 



pH = pK„ + logfe!il (4) 



[acid J 



expressing the relationship between the pH and the extent of stoichio- 

 metric neutralization of the acid. It must be emphasized that this 

 equation is only approximate, owing to the limitation imposed by 

 the above assumption; further, the acid cannot be assumed to be 

 completely undissociated, and a curve of pH against degree of 

 neutralization drawn by means of this equation will deviate from an 

 experimental curve more with strong acids than with weak. How- 

 ever, over the middle portion of the curves, the correspondence is 

 usually good with weak acids so that the pK value may be found 

 from an experimental titration curve. The titration curve is sigmoid, 

 with the pK at the i)oint of inflexion. 



7.1.3. Titration Curves of Proteins. Proteins contain a large 

 number of groups capable of acidic or basic dissociation, so that 

 titration of a protein solution with an acid or alkali is possible. 

 By plotting the number of equivalents of reagent added against the 

 pH, it is possible to determine the number of dissociable groups 

 with plci values within a given pH range. For a detailed treatment, 

 the reader is referred to the work of Cohn and Edsall, and papers of 

 Wyman, Theorell, and other workers. It has been found possible to 

 identify, in each pH range, dissociable groups belonging to various 

 amino acid residues. 



