Simplified methods for pK_a and acid pH-dependent stability estimation in proteins: Removing dielectric and counterion boundaries

Abstract

Much computational research aimed at understanding ionizable group interactions in proteins has focused on numerical solutions of the Poisson–Boltzmann (PB) equation, incorporating protein exclusion zones for solvent and counterions in a continuum model. Poor agreement with measured pK_as and pH-dependent stabilities for a (protein, solvent) relative dielectric boundary of (4,80) has lead to the adoption of an intermediate (20,80) boundary. It is now shown that a simple Debye–Hückel (DH) calculation, removing both the low dielectric and counterion exclusion regions associated with protein, is equally effective in general pK_a calculations. However, a broad-based discrepancy to measured pH-dependent stabilities is maintained in the absence of ionizable group interactions in the unfolded state. A simple model is introduced for these interactions, with a significantly improved match to experiment that suggests a potential utility in predicting and analyzing the acid pH-dependence of protein stability. The methods are applied to the relative pH-dependent stabilities of the pore-forming domains of colicins A and N. The results relate generally to the well-known preponderance of surface ionizable groups with solvent-mediated interactions. Although numerical PB solutions do not currently have a significant advantage for overall pK_a estimations, development based on consideration of microscopic solvation energetics in tandem with the continuum model could combine the large ΔpK_as of a subset of ionizable groups with the overall robustness of the DH model.