PH-Dependent pKa Values in Proteins—A Theoretical Analysis of Protonation Energies with Practical Consequences for Enzymatic Reactions

Abstract

Because of their central importance for understanding enzymatic mechanisms, pK(a) values are of great interest in biochemical research. It is common practice to determine pK(a) values of amino acid residues in proteins from NMR or FTIR titration curves by determining the pH at which the protonation probability is 50%. The pH dependence of the free energy required to protonate this residue is then determined from the linear relationship DeltaG(prot) = RT ln 10 (pH-pK(a)), where R is the gas constant and T the absolute temperature. However, this approach neglects that there can be important electrostatic interactions in the proteins that can shift the protonation energy. Even if the titration curves seem to have a standard sigmoidal shape, the protonation energy of an individual site in a protein may depend nonlinearly on pH. To account for this nonlinear dependence, we show that it is required to introduce pK(a) values for individual sites in proteins that depend on pH. Two different definitions are discussed. One definition is based on a rearranged Henderson-Hasselbalch equation, and the other definition is based on an equation that was used by Tanford and Roxby to approximate titration curves of proteins. In the limiting case of weak interactions, the two definitions lead to nearly the same pK(a) value. We discuss how these two differently defined pK(a) values are related to the free energy change required to protonate a site. Using individual site pK(a) values, we demonstrate on simple model systems that the interactions between protonatable residues in proteins can help to maintain the energy required to protonate a site in the protein nearly constant over a wide pH range. We show with the example of RNase T1 that such a mechanism to keep the protonation energy constant is used in enzymes. The pH dependence of pK(a) values may be an important concept in enzyme catalysis. Neglecting this concept, important features of enzymes may be missed, and the enzymatic mechanism may not be fully understood.