Prior computational studies of the acid-unfolding behavior of staphylococcal nuclease (SNase) suggest that the pK(a) values of its carboxylic groups are difficult to reproduce with electrostatics calculations with continuum methods. To examine the molecular determinants of the pK(a) values of carboxylic groups in SNase, the pK(a) values of all 20 Asp and Glu residues were measured with multidimensional and multinuclear NMR spectroscopy in an acid insensitive variant of SNase. The crystal structure of the protein was obtained to describe the microenvironments of the carboxylic groups. Fourteen Asp and Glu residues titrate with relatively normal pK(a) values that are depressed by less than 1.1 units relative to the normal pK(a) of Asp and Glu in water. Only six residues have pK(a) values shifted by more than 1.5 units. Asp-21 has an unusually high pK(a) of 6.5, which is probably the result of interactions with other carboxylic groups at the active site. The most perturbed pK(a) values appear to be governed by hydrogen bonding and not by Coulomb interactions. The pK(a) values calculated with standard continuum electrostatics methods applied to static structures are more depressed than the measured values because Coulomb effects are exaggerated in the calculations. The problems persist even when the protein is treated with the dielectric constant of water. This can be interpreted to imply that structural relaxation is an important determinant of the pK(a) values; however, no major pH-sensitive conformational reorganization of the backbone was detected using NMR spectroscopy.

Lys-66 and Glu-66, buried in the hydrophobic interior of staphylococcal nuclease by mutagenesis, titrate with pK(a) values of 5.7 and 8.8, respectively (Dwyer et al., Biophys. J. 79:1610-1620; García-Moreno E. et al., Biophys. Chem. 64:211-224). Continuum calculations with static structures reproduced the pK(a) values when the protein interior was treated with a dielectric constant (epsilon(in)) of 10. This high apparent polarizability can be rationalized in the case of Glu-66 in terms of internal water molecules, visible in crystallographic structures, hydrogen bonded to Glu-66. The water molecules are absent in structures with Lys-66; the high polarizability cannot be reconciled with the hydrophobic environment surrounding Lys-66. Equilibrium thermodynamic experiments showed that the Lys-66 mutant remained folded and native-like after ionization of the buried lysine. The high polarizability must therefore reflect water penetration, minor local structural rearrangement, or both. When in pK(a) calculations with continuum methods, the internal water molecules were treated explicitly, and allowed to relax in the field of the buried charged group, the pK(a) values of buried residues were reproduced with epsilon(in) in the range 4-5. The calculations show that internal waters can modulate pK(a) values of buried residues effectively, and they support the hypothesis that the buried Lys-66 is in contact with internal waters even though these are not seen crystallographically. When only the one or two innermost water molecules were treated explicitly, epsilon(in) of 5-7 reproduced the pK(a) values. These values of epsilon(in) > 4 imply that some conformational reorganization occurs concomitant with the ionization of the buried groups.

Using complementary approaches of potentiometry and NMR spectroscopy, we have determined that the equilibrium acid dissociation constant (pK a value) of the arginine guanidinium group is 13.8 6 0.1. This is substantially higher than that of~12 often used in structure-based electrostatics calculations and cited in biochemistry textbooks. The revised intrinsic pK a value helps explains why arginine side chains in proteins are always predominantly charged, even at pH values as great as 10. The high pK a value also reinforces the observation that arginine side chains are invariably protonated under physiological conditions of near neutral pH. This occurs even when the guanidinium moiety is buried in a hydrophobic micro-environment, such as that inside a protein or a lipid membrane, thought to be incompatible with the presence of a charged group.

The dielectric properties of proteins are poorly understood and difficult to describe quantitatively. This limits the accuracy of methods for structure-based calculation of electrostatic energies and pK(a) values. The pK(a) values of many internal groups report apparent protein dielectric constants of 10 or higher. These values are substantially higher than the dielectric constants of 2-4 measured experimentally with dry proteins. The structural origins of these high apparent dielectric constants are not well understood. Here we report on structural and equilibrium thermodynamic studies of the effects of pH on the V66D variant of staphylococcal nuclease. In a crystal structure of this protein the neutral side chain of Asp-66 is buried in the hydrophobic core of the protein and hydrated by internal water molecules. Asp-66 titrates with a pK(a) value near 9. A decrease in the far UV-CD signal was observed, concomitant with ionization of this aspartic acid, and consistent with the loss of 1.5 turns of alpha-helix. These data suggest that the protein dielectric constant needed to reproduce the pK(a) value of Asp-66 with continuum electrostatics calculations is high because the dielectric constant has to capture, implicitly, the energetic consequences of the structural reorganization that are not treated explicitly in continuum calculations with static structures.

Histidine pK a values were measured in charge-reversal (K78E, K97E, K127E, and K97E/K127E) and charge-neutralization (E10A, E101A, and R35A) mutants of staphylococcal nuclease (SNase) by 1 H-NMR spectroscopy. Energies of interaction between pairs of charges (⌬G ij ) were obtained from the shifts in pK a values relative to wild-type values. The data describe the distance dependence and salt sensitivity of pairwise coulombic interactions. Calculations with a continuum electrostatics method captured the experimental ⌬G ij when static structures were used and when the protein interior was treated empirically with a dielectric constant of 20. The ⌬G ij when r ij Յ 10 Å were exaggerated slightly in the calculations. Coulomb's law with a dielectric constant near 80 and a Debye-Hückel term to account for screening by the ionic strength reproduced the salt sensitivity and distance dependence of ⌬G ij as well as the structure-based method. In their interactions with each other, surface charges behave as if immersed in water; the Debye length describes realistically the distance where interactions become negligible at a given ionic strength. On average, charges separated by distances (r ij ) ≈5 Å interacted with ⌬G ij ≈ 0.6 kcal/mole in 0.01 M KCl, but ⌬G ij decayed to Յ0.10 kcal/mole when r ij ‫ס‬ 20 Å. In 0.10 M KCl, ⌬G ij ≈ 0.10 kcal/mole when r ij ‫ס‬ 10 Å. In 1.5 M KCl, only short-range interactions with r ij Յ 5 Å persisted. Although at physiological ionic strengths the interactions between charges separated by more than 10 Å are extremely weak, in situations where charge imbalance exists many weak interactions can cumulatively produce substantial effects.Keywords: Electrostatics; Poisson-Boltzmann; determinants of pK a values; salt effects; ionic strength; coulombic interactions; staphylococcal nuclease The structure, stability, and function of many proteins are governed by electrostatics. Therefore, knowledge of the pK a values of ionizable residues and of their molecular determinants is often required to understand the physical basis of stability and function. pK a values can be measured experimentally in small, soluble proteins, but in larger proteins and in membrane proteins they are experimentally inaccessible. In such cases, structure-based pK a calculations are useful for analysis of the relationship between protein structure and function. This approach is only productive if the reliability of the computational methods is established by comparison with experimental data. Here we present an experimental study of the magnitude, distance dependence, and salt sensitivity of the energy of coulombic interaction between pairs of surface charges in staphylococcal nuclease (SNase). The data are used to assess coulombic contributions to pK a values and to test the ability of a continuum method for structure-based pK a calculations to reproduce the experimental data.The validity of physical models for calculation of electrostatic energies in proteins is usually established by comparison of measured and calculate...