On the pH dependence of protein stability

This paper treats the free energy contribution of ionizable groups to protein stability. A method is presented for the calculation of the pH dependence of the denaturation free energy of a protein, which yields results that can be compared directly to experiment. The first step in the treatment is the determination of the average charges of all the ionizable groups in both the folded and unfolded protein. An expression due to Tanford then relates the pH dependence of the unfolding free energy to the difference in net charge between the two states. In order to determine absolute rather than relative unfolding free energies, it is necessary to calculate the total contribution of ionizable groups to protein stability at some reference pH. This is accomplished through a statistical mechanical treatment similar to the one used previously in the calculation of pKas. The treatment itself is rigorous but it suffers from uncertainties in the pKa calculations. Nevertheless, the overall shape of experimentally observed plots of denaturation free energy as a function of pH are reasonably well reproduced by the calculations. A number of general conclusions that arise from the analysis are: (1) knowledge of titration curves and/or effective pKa values of ionizable groups in proteins is sufficient to calculate the pH dependence of the denaturation free energy with respect to some reference pH value. However, in order to calculate the absolute contribution of ionizable groups to protein stability, it is necessary to also know the intrinsic pKa of each group. This is defined as the pKa of a group in a hypothetical state of the protein where all other groups are neutral. (2) Due to desolvation effects, ionizable groups destabilize proteins, although the effect is strongly dependent on pH. There are however, strongly stabilizing pairwise Coulombic interactions on the surface of proteins. (3) Plots of stability versus pH should not be interpreted in terms of a group whose pKa corresponds to the titration midpoint, but rather to a group with different pKas (that correspond approximately to the titration end points) in each state. (4) Any residual structure in the GuHCl-denatured state of proteins appears to have little effect on the pH dependence of stability. (5) pH-dependent unfolding, for example to the "molten globule" state, appears due to individual groups with anomalous pKas whose locations on the protein surface may determine the nature of the unfolded state.