Carolyn A. Fitch

Experimental pKa 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.

Molecular determinants of the pK(a) values of Asp and Glu residues in staphylococcal nuclease.

Prior computational studies of the acid‐unfolding behavior of staphylococcal nuclease (SNase) suggest that the pKa values of its carboxylic groups are difficult to reproduce with electrostatics calculations with continuum methods. To examine the molecular determinants of the pKa values of carboxylic groups in SNase, the pKa 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 pKa values that are depressed by less than 1.1 units relative to the normal pKa of Asp and Glu in water. Only six residues have pKa values shifted by more than 1.5 units. Asp‐21 has an unusually high pKa of 6.5, which is probably the result of interactions with other carboxylic groups at the active site. The most perturbed pKa values appear to be governed by hydrogen bonding and not by Coulomb interactions. The pKa 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 pKa values; however, no major pH‐sensitive conformational reorganization of the backbone was detected using NMR spectroscopy. Proteins 2009.

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

Histidine pKa 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 1H‐NMR spectroscopy. Energies of interaction between pairs of charges (ΔGij) were obtained from the shifts in pKa 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 ΔGij when static structures were used and when the protein interior was treated empirically with a dielectric constant of 20. The ΔGij when rij ≤ 10 Å were exaggerated slightly in the calculations. Coulombs 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 ΔGij 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 (rij) ≈5 Å interacted with ΔGij ≈ 0.6 kcal/mole in 0.01 M KCl, but ΔGij decayed to ≤0.10 kcal/mole when rij = 20 Å. In 0.10 M KCl, ΔGij ≈ 0.10 kcal/mole when rij = 10 Å. In 1.5 M KCl, only short‐range interactions with rij ≤ 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.

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.

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.

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.

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. Proteins 2006.

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 pKa values of ionizable groups must be known and their molecular determinants must be understood. Structure‐based calculations of electrostatic energies and pKa values are necessary for this purpose. This unit describes protocols for pKa 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 pKa values. Applied judiciously, these methods can contribute useful and novel insight into properties of surface ionizable groups in proteins.