The origin of pH-dependent changes in m-values for the denaturant-induced unfolding of proteins

Denaturant-induced unfolding is one of the most prevalent means of evaluating the structural stability of proteins and of determining the energetic consequences of mutations or changes in solution conditions. In spite of the widespread use of this approach, controversies and inconsistencies still persist with regard to the interpretation of the results of such studies. For example, most proteins show either a significant increase or a decrease (as much as 100 %) in the denaturant-dependence of the free energy of unfolding (i.e. the m-value) under increasingly acidic conditions. The pH dependence of the m-value is given different interpretations depending on whether the m-values increase or decrease with decreasing pH. In cases where m-values decrease, the decrease is attributed to the presence of an intermediate that becomes transiently stabilized during the unfolding transition at low pH. Cases where m-values increase as pH is lowered are usually interpreted in terms of an increase in the amount of surface area exposed by the denatured state at low pH. We have developed a general thermodynamic model that accounts for both types of behavior in terms of an intermediate that is populated throughout the unfolding transition. The model provides a unified framework for explaining both types of observed behavior, and the validity of the model was tested through the analysis of the pH dependence of m-values of staphylococcal nuclease. According to the model, the observed increase in m-values with decreasing pH is consistent with the existence of an intermediate that is populated during urea and guanidine unfolding. The intermediate becomes less populated during the unfolding transition at lower pH values giving rise to the apparent increase in m-values. These results argue that the prevailing interpretation need not apply to all proteins.

pH dependence of stability of staphylococcal nuclease: evidence of substantial electrostatic interactions in the denatured state

The pH dependence of stability of staphylococcal nuclease was studied with two independent equilibrium thermodynamic approaches. First, by measurement of stability in the pH range 9 to 3.5 by fluorescence-monitored denaturation with urea (Delta), GdnHCl (Delta), and heat (Delta). Second, by numerical integration of H(+) titration curves (Delta) measured potentiometrically under native (100 mM KCl) and unfolding (6.0 M GdnHCl) conditions. The pH dependence of stability described by Delta, Delta, and Delta was comparable but significantly different from the one described by Delta. The decrease in Delta between pH 9 and pH 4 was 4 kcal/mol greater than the decrease in Delta, Delta, and Delta in the same pH range. In 6 M GdnHCl, all the ionizable groups titrated with the pK(a) values of model compounds. Therefore, Delta represents the free energy difference between the native state (N) and an ensemble of unstructured, or expanded, and highly screened conformations. In contrast, the shallower pH dependence of stability described by Delta and by Delta between pH 9 and 5 was consistent with the titration of histidines with depressed, nativelike pK(a) values in the denatured state (D). These depressed pK(a) values likely reflect long-range electrostatic interactions with the other 29 basic groups and are a consequence of the compact character of the D state. The steep change in Delta and Delta at pH < 5 suggests that near pH 5 the structural and thermodynamic character of the D state shifts toward a state in which acidic residues titrate with normal pK(a) values, presumably because the electrostatic interactions with basic residues are lost, maybe as a consequence of an expansion.

Salt effects on ionization equilibria of histidines in myoglobin

The salt dependence of histidine pK(a) values in sperm whale and horse myoglobin and in histidine-containing peptides was measured by (1)H-NMR spectroscopy. Structure-based pK(a) calculations were performed with continuum methods to test their ability to capture the effects of solution conditions on pK(a) values. The measured pK(a) of most histidines, whether in the protein or in model compounds, increased by 0.3 pH units or more between 0.02 M and 1.5 M NaCl. In myoglobin two histidines (His(48) and His(36)) exhibited a shallower dependence than the average, and one (His(113)) showed a steeper dependence. The (1)H-NMR data suggested that the salt dependence of histidine pK(a) values in the protein was determined primarily by the preferential stabilization of the charged form of histidine with increasing salt concentrations rather than by screening of electrostatic interactions. The magnitude and salt dependence of interactions between ionizable groups were exaggerated in pK(a) calculations with the finite-difference Poisson-Boltzmann method applied to a static structure, even when the protein interior was treated with arbitrarily high dielectric constants. Improvements in continuum methods for calculating salt effects on pK(a) values will require explicit consideration of the salt dependence of model compound pK(a) values used for reference in the calculations.

High apparent dielectric constants in the interior of a protein reflect water penetration

A glutamic acid was buried in the hydrophobic core of staphylococcal nuclease by replacement of Val-66. Its pK(a) was measured with equilibrium thermodynamic methods. It was 4.3 units higher than the pK(a) of Glu in water. This increase was comparable to the DeltapK(a) of 4.9 units measured previously for a lysine buried at the same location. According to the Born formalism these DeltapK(a) are energetically equivalent to the transfer of a charged group from water to a medium of dielectric constant of 12. In contrast, the static dielectric constants of dry protein powders range from 2 to 4. In the crystallographic structure of the V66E mutant, a chain of water molecules was seen that hydrates the buried Glu-66 and links it with bulk solvent. The buried water molecules have never previously been detected in >20 structures of nuclease. The structure and the measured energetics constitute compelling and unprecedented experimental evidence that solvent penetration can contribute significantly to the high apparent polarizability inside proteins. To improve structure-based calculations of electrostatic effects with continuum methods, it will be necessary to learn to account quantitatively for the contributions by solvent penetration to dielectric effects in the protein interior.