Measurement of pK_a Values from the pH Dependence of Thermodynamic Stability.

The pK_a values of internal ionizable groups are usually highly sensitive to protein conformation. In the unfolded ensemble (U), the side chains of all ionizable groups are hydrated and the pK_a values are mostly normal. In the folded state (F), the pK_a values of internal groups will vary depending on their location and on the polarity and polarizability of their microenvironments. In highly polar or polarizable internal microenvironments, the pK_a values will tend to be like those in water, but in microenvironments that are less polar or polarizable, the pK_a values will shift in the direction that favors the neutral state. In general, the pK_a values of internal groups in proteins are shifted relative to the normal pK_a values in water. This coupling between pK_a and protein conformation is responsible for the pH dependence of thermodynamic stability (): [1]where is the contribution of a single ionizable group to stability, z is the charge of the ionizable side chain, and and are pK_a values of the ionizable group in the F and U ensembles. Eq. 1 shows that and must be different if ionizable group i is to make a net contribution to protein stability at any pH value. It also shows that the stability of a protein changes by 1.36 kcal/mol (298 K) for every unit pK_a difference between and .

The thermodynamic stability of the Δ+PHS variant of SNase used for these studies is relatively invariant between pH 5 and 10 and declines rapidly in the acidic and basic limits (Fig. 1 A and C). (Δ+PHS is the stabilized form of SNase used as the reference protein in these studies.) The introduction of a buried Lys with a depressed pK_a leads to a steep dependence of stability between pH 5 and 10 (Fig. 1 A and C). If the Lys side chain does not alter the pK_a values of any of the other ionizable side chains of the protein, the difference in the pH dependence of stability () between the reference and variant protein can be attributed to the shift in the pK_a of the introduced Lys residue (Fig. 1B). This pK_a value can be determined by fitting the vs. pH profile with this relationship (2, 4, 7): [2]where is the pH-dependent difference in stability between a reference protein and a variant with one internal Lys, and is the free energy difference between the reference protein and the variant under conditions of pH where the internal Lys is neutral. The validity of measurement of pK_a values of internal groups by analysis of vs. pH profiles has been corroborated previously by independent measurements with other equilibrium thermodynamic methods (2, 4–6), including NMR spectroscopy (3, 18).

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Fig. 1.

Measurement of pK_a values through linkage analysis of the pH dependence of thermodynamic stability. (A) Thermodynamic stability () of reference protein (Δ+PHS nuclease) (○) and its L125K variant (●) measured by GdnHCl denaturation monitored by Trp fluorescence. The line is from a simulation and it is only meant to guide the eye. (B) Difference in thermodynamic stability of Δ+PHS and the L125K variant (variant–reference). The line describes the fit of Eq. 2 to the data. The pK_a of Lys-125 in folded () and denatured () states are indicated. (C) Thermodynamic stability of Δ+PHS nuclease (○) and of its T62K variant (●) measured by GdnHCl denaturation monitored by Trp fluorescence. The line is from a simulation and it is only meant to guide the eye. (D) Difference in thermodynamic stability of Δ+PHS and the T62K variant (variant–reference). The line describes the fit of Eq. 3 to the data. The pK_a values relevant to Lys-62 ( and ) and the phenomenological pK_a values ( and ) of other ionizable side chain(s) affected by Lys-62 are indicated.

When the internal Lys residue affects the pK_a of one or more ionizable groups, either directly through Coulomb interactions or indirectly by affecting the protein’s conformation, the vs. pH profile is more complex and may exhibit more than one distinct region of pH dependence (Fig. 1D). In this case, the observed pH dependence of relative stability can be described phenomenologically with this relationship: [3]where and represent the pK_a of the internal Lys residue, and and represent the apparent pK_a of an ionizable group (or more than one) that is perturbed by the presence of the internal Lys.

In 15 of the 25 Lys-containing variants, the vs. pH curve was governed by the substantial depression in the pK_a of the internal Lys without any apparent contributions from shifts in the pK_a of other ionizable groups (Fig. 1 A and B and Fig. S1). These cases were analyzed with Eq. 2. For 10 variants (Lys-23, Lys-34, Lys-36, Lys-41, Lys-62, Lys-90, Lys-103, Lys-72, Lys-104, and Lys-109) the vs. pH profiles showed clear evidence of contributions from one or more ionizable group whose pK_a was affected by the ionization of the internal Lys (Fig. 1 C and D and Fig S1). These cases were analyzed using Eq. 3, and the higher of the two pK_a values resolved with Eq. 3 was assumed to represent the pK_a of the internal Lys.

pK_a Values of 25 Internal Lys Residues.

Only 6 of the 25 variants with internal Lys residues (Lys-20, Lys-37, Lys-38, Lys-58, Lys-118, and Lys-132) had vs. pH profiles that were independent of pH, implying that the internal Lys residues had near normal pK_a≥10 (Table 1, Fig. 2, and Table S1). Most of these Lys residues are in loops and at the ends of elements of secondary structure (Fig. 2B), where fraying might lead to the exposure of the putatively buried group to water. Alternatively, the Lys residues with normal pK_a values are buried but sampling highly dynamic, polar or hydrated microenvironments, as has been shown previously for Lys-38 (3, 18).

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Fig. 2.

pK_a values of Lys at 25 internal positions. (A) pK_a values. White bars identify groups that do not exhibit a detectable shift in pK_a value. Colors are only meant to separate arbitrarily small, medium, and large shifts in pK_a values (B) Distribution of internal Lys residues in the structure of Δ+PHS nuclease [PDB ID code 3BDC (35)], color-coded according to the magnitude of the shift in pK_a relative to the normal value of 10.4 for Lys in water, as represented in A.

Nineteen of the 25 internal Lys residues exhibited shifted pK_a values depressed below the normal pK_a of 10.4 for Lys in water (Table 1 and Fig. 2A). These pK_a shifts are consistent with the few known pK_a values measured for naturally occurring internal Lys residues (19). In fact, the data show that simply by virtue of being internal, the internal Lys residues in SNase achieved pK_a values comparable to those of naturally occurring internal Lys involved in H⁺-activated processes (19). Some of the pK_a values for Lys in SNase were depressed by more than 5 units and constitute some of the largest shifts in pK_a ever measured. The depression of pK_a values of basic residues implies that the neutral form of the side chain is favored, consistent with the Lys side chains being buried in at least a partially dehydrated form, and in microenvironments that are less polar and polarizable than water. The buried nature of some of the ionizable side chains engineered to be internal is being corroborated by crystal structures of many of the variants. Thus far, in over 25 structures of variants of SNase with Lys, Glu, or Asp at some of the 25 internal positions [the coordinates of these structures have been deposited in the Protein Data Bank (PDB) and released in advance of publication], criteria of solvent-accessible surface area and depth of burial have shown that the ionizable side chains in the neutral state are internal and sequestered from contact with bulk water.

The Gibbs free energy required to create positive charge inside SNase varied between 1.5 and 6.9 kcal/mol ( in Table 1), depending on the location of the internal ionizable group. These energies are comparable to the energies required to create negative charge inside SNase (12). The importance of these free energies is twofold. First, they demonstrate the remarkable ability of proteins to stabilize charge in their hydrophobic interior. Second, they describe the range of the minimum thermodynamic stability required for proteins to stay at least partially folded when internal basic groups become charged as part of their natural cycle of biological function. This has important implications for the evolution of enzymes and of other proteins that depend on internal ionizable groups for their biological function. It suggests that enzymes might have evolved by the random introduction of ionizable groups in the core of highly stable proteins, without the need of specialized microenvironments to stabilize the internal ionizable groups. Similarly, it has implications for the engineering of novel active sites in proteins where, in addition to fulfilling the requirements for the desired chemical reaction, the thermodynamic stability of the protein scaffold has to be sufficiently high to tolerate the presence and ionization of the internal residues at the active site. In fact, the combined observations that internal ionizable groups in highly stable proteins are well tolerated when they are charged, and that their pK_a values fall naturally into the range required for function simply by virtue of being internal, suggests that the engineering of artificial enzymes might be simpler than currently thought.

Apparent Dielectric Constants in the Protein Interior.

Shifts in the pK_a values of internal groups relative to the normal pK_a values of ionizable groups in water are proportional to the Gibbs free energy required to create charge inside a protein. The magnitude of these free energies are determined by the ability of the protein to respond to the presence of charge, which is precisely the property of proteins that determines the energetics of all biological processes governed by internal ionizable groups, and the property that needs to be understood in molecular detail. To gain preliminary insight into these properties the shifts in pK_a values of internal Lys residues in SNase (Table 1) were analyzed using a simple Born formalism that assumes that the pK_a is determined exclusively by the difference in the self-energy of the charged Lys in water and in an environment with apparent dielectric constant (ε_app): [4]where pK_a,ref is the reference pK_a = 10.4 for Lys in water, r_cav = 2 Å describes the cavity radius of the ionizable moiety of Lys, r_prot = 12 Å is the radius of the sphere that crudely approximates the size of SNase, and κ is the Debye–Hückel parameter. ε_H2O = 78.5 was used to describe the dielectric properties of water. The apparent dielectric constants (ε_app) determined with this expression are not true dielectric constants. They represent a parameter that captures contributions to the pK_a value that are not treated explicitly in the simple model represented by Eq. 4. A variety of continuum and microscopic methods are being used in other laboratories to examine the character of the dielectric processes reflected in the pK_a values we have measured. For a more sophisticated treatment of this problem, beyond the scope of this study, see, for example, the study by Muegge et al. (20). The analysis with Eq. 4 is simply meant to demonstrate that throughout the protein, the internal Lys residues report high apparent polarizabilities comparable to those of materials with dielectric constants of 8 and higher (Table 1), which are considerably higher than the values of 2 to 4 measured with dry protein powders (21, 22). It has been suggested that the analysis of ΔpK_a values with Eq. 4 invariably leads to high apparent dielectric constants because it ignores dielectric saturation for the ionizable group in water (23); however, rigorous microscopic simulations of dielectric constants based on calculation of macroscopic electric fields and polarizability have demonstrated that the microscopic dielectric constant inside proteins can be high (20, 24). This is fully consistent with our interpretation of the magnitude of protein dielectric effects reflected in ΔpK_a values. The general conclusions of the analysis with Eq. 4, demonstrating that the internal Lys residues report high apparent dielectric constants, are robust and also fully consistent with the conclusions from more sophisticated continuum electrostatics methods that take factors other than self-energies into account (2–6).

Structural Consequences of Ionization of Internal Lys Residues.

A protein can respond to the ionization of an internal group in a variety of ways. If the buried side chain is located in a polar or polarizable microenvironment, its charge can be stabilized without the protein undergoing any significant structural reorganization. If the protein can access an alternative folded conformation in which the charge is stabilized better, perhaps through interaction with internal water molecules or with bulk water, the ionization of the protein will trigger a subglobal structural change. In an extreme case the ionization of the internal group will unfold the protein globally.

To examine the possibility of structural changes coupled to the ionization of internal Lys residues, pH titrations monitored by intrinsic Trp fluorescence (Fig. 3A) and far-UV CD at 222 nm (Fig. 3B) were performed in the range of pH where the internal Lys residues become ionized. The titrations showed that most of the variants were fully folded under conditions of pH where the internal Lys were charged. Despite being small, SNase appears to be remarkably resilient toward the ionization of internal Lys residues. NMR spectroscopy is currently being used to try to detect conformational reorganization below the level of detection of optical spectroscopic methods

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Fig. 3.

Conformational consequences of ionization of Lys residues at 25 internal positions. (A) pH titrations of Δ+PHS nuclease (black circle) and of variants with internal Lys (red, blue, and gray circles) residues monitored by Trp-fluorescence, as described previously (12). Variants that exhibit partial (blue circles) or global (red circles) unfolding concomitant with ionization of the internal Lys are labeled. (B) pH titrations of Δ+PHS nuclease (black circle) and of variants with internal Lys (red, blue, and gray circles) residues monitored by far-UV CD at 222 nm. Variants that exhibit partial (blue circles) or global (red circles) unfolding concomitant with ionization of the internal Lys are labeled. (C) Location of Lys residues that trigger local (blue spheres) or global (red spheres) structural changes upon ionization, mapped on the structure of Δ+PHS [PDB ID code 3BDC (35)].

The pK_a of 5.3 for Lys-92 is within the actual global, acid unfolding titration monitored by Trp fluorescence or CD spectroscopy, which have pH midpoints of 5.0 and 4.8, respectively (Table 1). This is the only protein for which this is true; the I92K variant is the only one that is globally unfolded by the ionization of the internal Lys. Lys-92 is also the Lys with the most depressed pK_a of all the internal lysines (pK_a = 5.3). Similarly, the ionization of Glu-92 also triggered global unfolding (14). The large shifts in the pK_a of Glu-92 and Lys-92 suggest that the polarity and polarizability of the region of the protein where these side chains are embedded is relatively low. This is consistent with crystal structures showing that their side chains are buried deeply in the main hydrophobic core (25). Interestingly, despite being buried deeply, in the crystal structure of the I92K variant (PDB ID code 1TT2) obtained with crystals grown under conditions of pH where Lys-92 should be neutral, the side chain of Lys-92 occupies two alternative conformations. The side chain of Glu-92 (PDB ID code 1TQ0) is hydrated by internal water molecules (15–17, 25). Conformational heterogeneity and water penetration are two factors that could help stabilize the internal groups in their charged state, but apparently in the case of the I92K and I92E variants the stabilization gained is not enough to prevent global unfolding when Lys-92 or Glu-93 are charged.

Four variants (V66K, N100K, V104K, and L125K) showed pH-dependent changes in optical properties coincident with the ionization of the internal Lys residue (Fig. 3 A and B). These are considered cases where the ionization of the internal Lys led to partial or subglobal unfolding because the pK_a values fall within the predenaturational transition, far from the main, global acid unfolding transition. These instances of partial unfolding are subtle and are defined as partial unfolding only because they seem to be independent of the main, global acid unfolding transition, which can be observed at pH values below the pK_a of the internal Lys. These cases are of special interest because they identify situations where the high apparent polarizability clearly reflects conformational reorganization coupled to the ionization of the internal group. The structural nature of the partial unfolding is not known, but it is currently under study with NMR spectroscopy. In the case of ionizable residues at position 66, which have been studied in detail, CD spectroscopy measurements show that the ionization of the internal Lys with a pK_a near 5.7 leads to the apparent loss of approximately one turn of α-helix (4, 26). NMR spectroscopy experiments show that the structural changes are localized to the region of the protein where the side chain of residue 66 is found; the rest of the protein is intact (27). Cases where the ionization of an internal group is coupled to subglobal structural reorganization will be particularly useful for calibration of structure-based electrostatics calculations designed to reproduce conformational changes coupled to changes in pH, and also to examine excited states in the folding energy landscape of proteins (26, 28).

The probability of populating intermediates between the fully folded and the fully denatured states increases as the stability of the native state decreases. Therefore, the likelihood that the ionization of an internal Lys triggers conformational reorganization is governed by the stability of the native state near the pH where ionization occurs. The stability of the protein in the range of pH where the Lys residues ionize ( in Table 1) is determined by two factors. One is the loss of stability related to the substitution of the internal position with neutral Lys. This is a pH-independent term that accounts for all differences in conformational entropy and noncovalent interactions of the original side chain and the Lys side chain. The stability of the Lys-substituted proteins at high pH, near the normal pK_a of Lys, provides an estimate of the cost of substituting with neutral Lys (12, 13). The second factor that destabilizes the Lys-containing variants is the shift in pK_a proper. At pH values below the normal pK_a of Lys in water, the stability of a variant containing a lysine with a highly depressed pK_a value decreases by 1.36 kcal/mol (298 K) for every unit shift in the pK_a (Fig. 1 A and B). Consequently, larger shifts in pK_a act to decrease protein stability and promote global or partial unfolding in the range of pH where the internal lysine becomes charged. The variants where structural reorganization was observed concomitant with ionization of the internal Lys (V66K, I92K, N100K, V104K, and L125K) had global stabilities of 3.8 kcal/mol or less at the pH where the groups titrate (Table 1 and Table S1). By this criterion, the L25K and V99K variants, and maybe even the F34K variant, should have also exhibited reorganization concomitant with ionization of the internal Lys, but this was not evident in the titrations monitored with CD or Trp-fluorescence spectroscopy.

Coulomb Interactions Between Internal and Surface Ionizable Groups.

The stability profiles (Fig. S1) of 10 Lys-containing variants (Lys-23, Lys-34, Lys-36, Lys-41, Lys-62, Lys-72, Lys-90, Lys-103, Lys-104, and Lys-109) were analyzed with Eq. 3, which assumes that the pK_a of at least one other ionizable group was affected by the ionization of the internal Lys (e.g., Lys-62 in Fig. 1 C and D). In these cases, the pH dependence of above pH ∼ 6 was attributed solely to the titration of the introduced Lys side chain. The pH dependence and the sign of the slope of below pH ∼ 6 implies that the pK_a of one or more histidine or carboxylic groups is coupled to the titration of the internal Lys either through Coulomb interactions or by the effect of the substitution with Lys on conformation or dynamics of the protein. Given that the conformation of most Lys-containing variants is unaffected by the titration of the internal Lys, it is reasonable to propose that the apparent interactions between internal Lys residues and surface carboxylic groups are governed by Coulomb effects.

Further evidence of Coulomb interactions between internal and surface charges comes from comparison of pK_a values of Glu and Lys residues at the same internal positions (Fig. 4 A and B). At seven positions (38, 39, 58, 103, 104, 109, and 132), the shifts in the pK_a of Glu residues relative to the normal pK_a of 4.5 for Glu in water are greater by nearly one full pK_a unit than the shifts in pK_a values of Lys residues in SNase relative to the normal pK_a of 10.4 of Lys in water (Fig. 4A). These seven positions cluster near the active site of SNase (Fig. 4B), which has a high concentration of acidic residues (Asp-19, Asp-21, Asp-40, and Glu-43, and peripherally Glu-52, Glu-101, Glu-129, and Glu-135). This suggests there are favorable Coulomb interactions between internal Lys residues in the charged state and the cluster of surface acidic residues in this region of the protein, or repulsive interactions between the internal Glu residues and surface negative charges. The observation that, with the exception of these residues clustered near the active site, the shifts in pK_a values of Lys or Glu residues at a given position, relative to normal pK_a values of Lys or Glu in water, are within 1 pK_a unit of each other suggests that polarizability is an important determinant of pK_a values of internal ionizable groups in SNase. The extent to which this polarizability involves conformational reorganization remains to be established with NMR spectroscopy. The fact that in the majority of cases no large conformational reorganization concomitant with ionization of Lys or Glu residues was observed by CD or Trp fluorescence suggests that the reorganization is subtle, beyond the level of detection with optical spectroscopy.

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Fig. 4.

Comparison of pK_a shifts of Glu and Lys at 25 internal positions. (A) Difference in absolute values of shifts in pK_a of Lys and Glu residues at 25 internal positions in SNase, calculated as (|(pK_a,Glu - 4.5)| - |(pK_a,Lys - 10.4)|). This assumes values of 4.5 and 10.4 for the normal pK_a of Glu and Lys in water, respectively. Positive values identify cases where the shifts in the pK_a of a Glu residue at a given position is greater than the shift in the pK_a of a Lys residue. The color code is meant to distinguish groups with small (green) and large (blue) differences in pK_a values. (B) Distribution of the differences in the pK_a values of Lys and Glu residues mapped on the structure of Δ+PHS [PDB ID code 3BDC (35)].

Implications for Structure-Based Energy Calculations.

The preliminary analysis of pK_a shifts with simple continuum models, and strictly in terms of dehydration processes (Eq. 4), suggested that the protein behaves as a material with a relatively high dielectric constant ranging from 8 to 26 (Table 1). The apparent dielectric constants obtained by more sophisticated analysis of some of these variants of SNase with state-of-the-art continuum electrostatics methods were equally high (4, 5), and fully consistent with the results of more rigorous and self-consistent microscopic calculations showing that the microscopic dielectric constants in the protein interior can be high because of local polar microenvironments (20). The magnitudes of the shifts in pK_a values of internal ionizable groups in SNase are consistent with the magnitude of the effects of internal ionizable residues on reduction potentials of myoglobins (29, 30), suggesting that the properties probed by the internal ionizable groups in SNase are general properties of proteins. It remains to be seen if structure-based calculations with microscopic methods or with parameterized macroscopic methods can reproduce the properties of internal ionizable groups. As illustrated by a recent study of the Kemp elimination (31), reproducing the pK_a values of internal groups is difficult because these pK_a values reflect a balance between strong and opposing influences (dehydration vs. electronic polarization, Coulomb interactions with permanent dipoles or surface charges, and interactions with internal water or reaction field of bulk water), each of which is difficult to calculate. The pK_a values can also reflect local or subglobal structural reorganization that maximizes favorable interactions between the internal charge and the protein, or more likely, hydration of the charge; these effects are very difficult to calculate from structure. The fact that a simple analysis of shifts in pK_a values with the primitive Eq. 4 or with sophisticated structure-based methods both show that the internal Lys residues report high apparent dielectric constants suggests that polarizability related to conformational reorganization is one of the most important determinants of the pK_a values of these internal ionizable groups. The flexibility of the Lys side chain was identified previously as a reason for the relatively high apparent dielectric constants reported by these residues (32). Our experimental results imply that accurate calculation of pK_a values of internal ionizable groups in proteins might require prediction of conformational rearrangement and alternative conformations, which is still a daunting challenge (9–11). Our data will allow rigorous and unprecedented benchmarking of computational methods for calculation of electrostatic effects in dehydrated environments such as the interior of proteins and interfaces between proteins.