Arginine: Its pKa value revisited.

Using complementary approaches of potentiometry and NMR spectroscopy, we have determined that the equilibrium acid dissociation constant (pKa value) of the arginine guanidinium group is 13.8 ± 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 pKa value helps explains why arginine side chains in proteins are always predominantly charged, even at pH values as great as 10. The high pKa 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.

Molecular determinants of the pKa values of Asp and Glu residues in staphylococcal nuclease.

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.

Electrostatic effects in a network of polar and ionizable groups in staphylococcal nuclease.

His121 and His124 are embedded in a network of polar and ionizable groups on the surface of staphylococcal nuclease. To examine how membership in a network affects the electrostatic properties of ionizable groups, the tautomeric state and the pK(a) values of these histidines were measured with NMR spectroscopy in the wild-type nuclease and in 13 variants designed to disrupt the network. In the background protein, His121 and His124 titrate with pK(a) values of 5.2 and 5.6, respectively. In the variants, where the network was disrupted, the pK(a) values range from 4.03 to 6.46 for His121, and 5.04 to 5.99 for His124. The largest decrease in a pK(a) was observed when the favorable Coulomb interaction between His121 and Glu75 was eliminated; the largest increase was observed when Tyr91 or Tyr93 was substituted with Ala or Phe. In all variants, the dominant tautomeric state at neutral pH was the N(epsilon2) state. At one level the network behaves as a rigid unit that does not readily reorganize when disrupted: crystal structures of the E75A or E75Q variants show that even when the pivotal Glu75 is removed, the overall configuration of the network was unaffected. On the other hand, a few key hydrogen bonds appear to govern the conformation of the network, and when these bonds are disrupted the network reorganizes. Coulomb interactions within the network report an effective dielectric constant of 20, whereas a dielectric constant of 80 is more consistent with the magnitude of medium to long-range Coulomb interactions in this protein. The data demonstrate that when structures are treated as static, rigid bodies, structure-based pK(a) calculations with continuum electrostatics method are not useful to treat ionizable groups in cases where pK(a) values are governed by short-range polar and Coulomb interactions.

Electrostatic contributions to the stability of the GCN4 leucine zipper structure.

Ion pairs are ubiquitous in X-ray structures of coiled coils, and mutagenesis of charged residues can result in large stability losses. By contrast, pK(a) values determined by NMR in solution often predict only small contributions to stability from charge interactions. To help reconcile these results we used triple-resonance NMR to determine pK(a) values for all groups that ionize between pH 1 and 13 in the 33 residue leucine zipper fragment, GCN4p. In addition to the native state we also determined comprehensive pK(a) values for two models of the GCN4p denatured state: the protein in 6 M urea, and unfolded peptide fragments of the protein in water. Only residues that form ion pairs in multiple X-ray structures of GCN4p gave large pK(a) differences between the native and denatured states. Moreover, electrostatic contributions to stability were not equivalent for oppositely charged partners in ion pairs, suggesting that the interactions between a charge and its environment are as important as those within the ion pair. The pH dependence of protein stability calculated from NMR-derived pK(a) values agreed with the stability profile measured from equilibrium urea-unfolding experiments as a function of pH. The stability profile was also reproduced with structure-based continuum electrostatic calculations, although contributions to stability were overestimated at the extremes of pH. We consider potential sources of errors in the calculations, and how pK(a) predictions could be improved. Our results show that although hydrophobic packing and hydrogen bonding have dominant roles, electrostatic interactions also make significant contributions to the stability of the coiled coil.

Role of flexibility and polarity as determinants of the hydration of internal cavities and pockets in proteins.

Molecular dynamics simulations of Staphylococcal nuclease and of 10 variants with internal polar or ionizable groups were performed to investigate systematically the molecular determinants of hydration of internal cavities and pockets in proteins. In contrast to apolar cavities in rigid carbon structures, such as nanotubes or buckeyballs, internal cavities in proteins that are large enough to house a few water molecules will most likely be dehydrated unless they contain a source of polarity. The water content in the protein interior can be modulated by the flexibility of protein elements that interact with water, which can impart positional disorder to water molecules, or bias the pattern of internal hydration that is stabilized. This might explain differences in the patterns of hydration observed in crystal structures obtained at cryogenic and room temperature conditions. The ability of molecular dynamics simulations to determine the most likely sites of water binding in internal pockets and cavities depends on its efficiency in sampling the hydration of internal sites and alternative protein and water conformations. This can be enhanced significantly by performing multiple molecular dynamics simulations as well as simulations started from different initial hydration states.

Structure-based pKa calculations using continuum electrostatics methods.

Electrostatic free energy is useful for correlating structure with function in proteins in which ionizable groups play essential functional roles. To this end, the pK(a) values of ionizable groups must be known and their molecular determinants must be understood. Structure-based calculations of electrostatic energies and pK(a) values are necessary for this purpose. This unit describes protocols for pK(a) calculations with continuum electrostatics methods based on the numerical solution of the linearized Poisson-Boltzmann equation by the method of finite differences. Critical discussion of key parameters, approximations, and shortcomings of these methods is included. Two protocols are described for calculations with methods modified empirically to maximize agreement between measured and calculated pK(a) values. Applied judiciously, these methods can contribute useful and novel insight into properties of surface ionizable groups in proteins.

High apparent dielectric constant inside a protein reflects structural reorganization coupled to the ionization of an internal Asp.

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.

Molecular mechanisms of pH-driven conformational transitions of proteins: insights from continuum electrostatics calculations of acid unfolding.

The acid unfolding of staphylococcal nuclease (SNase) is very cooperative (Whitten and García-Moreno, Biochemistry 2000;39:14292-14304). As many as seven hydrogen ions (H+) are bound preferentially by the acid-unfolded state relative to the native (N) state in the pH range 3.2-3.9. To investigate the mechanism of acid unfolding, structure-based pKa calculations were performed with a variety of continuum electrostatic methods. The calculations reproduced successfully the H+ binding properties of the N state between pH 5 and 9, but they systematically overestimated the number of H+ bound upon acid unfolding. The calculated pKa values of all carboxylic residues in the N state were more depressed than they should be. The discrepancy between the observed and the calculated H+ uptake upon acid unfolding was not improved by using high protein dielectric constants, structures relaxed with molecular dynamics, or other empirical modifications implemented previously by others to maximize agreement between measured and calculated pKa values. This suggests an important role for conformational fluctuations of the backbone as important determinants of pKa values of carboxylic groups. Because no global or subglobal conformational changes have been observed previously for SNase under acidic conditions above the acid-unfolding region, these fluctuations must be local. The acid unfolding of SNase does not seem to involve the disruption of the N state by accruement of intramolecular repulsive interactions, nor the protonation of key ion paired carboxylic residues. It is more consistent with modest contributions from many H+ binding groups, with an important role for local conformational fluctuations in the coupling between H+ binding and the global structural transition.

Changes in stability upon charge reversal and neutralization substitution in staphylococcal nuclease are dominated by favorable electrostatic effects.

Single site mutations that reverse or neutralize a surface charge were made at 22 ionizable residues in staphylococcal nuclease. Unfolding free energies were obtained by guanidine hydrochloride denaturation. These data, in conjunction with previously obtained stabilities of the corresponding alanine mutants, unequivocally show that the dominant contribution to stability for virtually all of the wild-type side chains examined is the electrostatic effect associated with each residue's charged group. With only a few exceptions, these charges stabilize the native state, with an average loss of 0.5 kcal/mol of stability upon neutralization of a charge. When the charge is reversed, the average destabilization is doubled. Structure-based calculations of electrostatic free energy with the continuum method based on the finite difference solution to the linearized Poisson-Boltzmann equation reproduce the observed energetics when the polarizability in the protein interior is represented with a dielectric constant of 20. However, in some cases, large differences are found, giving insight into possible areas for improvement of the calculations. In particular, it appears that the assumptions made in the calculations about the absence of electrostatic interactions in the denatured state and the energetic consequences of dynamic fluctuations in the native state will have to be further explored.

Experimental pK(a) values of buried residues: analysis with continuum methods and role of water penetration.

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.

Distance dependence and salt sensitivity of pairwise, coulombic interactions in a protein.

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 (DeltaG(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 DeltaG(ij) when static structures were used and when the protein interior was treated empirically with a dielectric constant of 20. The DeltaG(ij) when r(ij) < or = 10 A 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 DeltaG(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)) approximately 5 A interacted with DeltaG(ij) approximately 0.6 kcal/mole in 0.01 M KCl, but DeltaG(ij) decayed to < or =0.10 kcal/mole when r(ij) = 20 A. In 0.10 M KCl, DeltaG(ij) approximately 0.10 kcal/mole when r(ij) = 10 A. In 1.5 M KCl, only short-range interactions with r(ij) < or = 5 A persisted. Although at physiological ionic strengths the interactions between charges separated by more than 10 A are extremely weak, in situations where charge imbalance exists many weak interactions can cumulatively produce substantial effects.

Electrostatic effects in highly charged proteins: salt sensitivity of pKa values of histidines in staphylococcal nuclease.

The pK(a) values of most histidines in small peptides and in myoglobin increase on average by 0.30 unit between 0.02 and 1.5 M NaCl [Kao et al. (2000) Biophys. J. 79, 1637]. The DeltapK(a) values reflect primarily the ionic strength dependence of the solvation energy; screening of Coulombic interactions contributes only in a minor way. This implies that Coulombic interactions are weak, or that attractive and repulsive contributions to the pK(a) values are balanced. To distinguish experimentally between these two possibilities, and to further characterize the magnitude and salt sensitivity of surface electrostatic interactions in proteins, the salt dependence of pK(a) values of histidines in staphylococcal nuclease was measured by (1)H NMR spectroscopy. Three of the four histidines titrated with significantly depressed pK(a) values, and the salt sensitivity of all histidine pK(a) values was substantial. In three cases, the pK(a) values increased by a full unit between 0.01 and 1.5 M KCl. Anion-specific effects were found; the pK(a) values measured under equivalent ionic strengths in SCN(-) and SO(4)(2-) were higher than in Cl(-); the order of the sensitivity of pK(a) values to anions was SCN(-) > Cl(-) > SO(4)(2-). Structure-based pK(a) calculations with continuum methods were performed to interpret the measured effects structurally and to test their ability to capture the experimental behavior. Calculations in which the protein interior was treated empirically with a dielectric constant of 20 reproduced the pK(a) values and their dependence on the concentration of Cl(-). According to the calculations, the pK(a) values are depressed because of unfavorable self-energies and repulsive Coulombic interactions. Their striking salt sensitivity reflects screening of weak, repulsive, Coulombic interactions among charges separated by more than 10 A. Long-range Coulombic interactions on the surfaces of proteins are weak, but they can add up to produce substantial electrostatic effects when positive and negative charges are not balanced.