Toward the computational design of protein crystals with improved resolution.

Substantial advances have been made in the computational design of protein interfaces over the last 20 years. However, the interfaces targeted by design have typically been stable and high-affinity. Here, we report the development of a generic computational design method to stabilize the weak interactions at crystallographic interfaces. Initially, we analyzed structures reported in the Protein Data Bank to determine whether crystals with more stable interfaces result in higher resolution structures. We found that for 22 variants of a single protein crystallized by a single individual, the Rosetta-calculated `crystal score' correlates with the reported diffraction resolution. We next developed and tested a computational design protocol, seeking to identify point mutations that would improve resolution in a highly stable variant of staphylococcal nuclease (SNase). Using a protocol based on fixed protein backbones, only one of the 11 initial designs crystallized, indicating modeling inaccuracies and forcing us to re-evaluate our strategy. To compensate for slight changes in the local backbone and side-chain environment, we subsequently designed on an ensemble of minimally perturbed protein backbones. Using this strategy, four of the seven designed proteins crystallized. By collecting diffraction data from multiple crystals per design and solving crystal structures, we found that the designed crystals improved the resolution modestly and in unpredictable ways, including altering the crystal space group. Post hoc, in silico analysis of the three observed space groups for SNase showed that the native space group was the lowest scoring for four of six variants (including the wild type), but that resolution did not correlate with crystal score, as it did in the preliminary results. Collectively, our results show that calculated crystal scores can correlate with reported resolution, but that the correlation is absent when the problem is inverted. This outcome suggests that more comprehensive modeling of the crystallographic state is necessary to design high-resolution protein crystals from poorly diffracting crystals.

Dielectric Properties of a Protein Probed by Reversal of a Buried Ion Pair.

Thirty years ago, Hwang and Warshel suggested that a microenvironment preorganized to stabilize an ion pair would be incapable of reorganizing to stabilize the reverse ion pair. The implications were that (1) proteins have a limited capacity to reorganize, even under the influence of strong interactions, such as those present when ionizable groups are buried in the hydrophobic interior of a protein, and (2) the inability of proteins to tolerate the reversal of buried ion pairs demonstrates the limitations inherent to continuum electrostatic models of proteins. Previously we showed that when buried individually in the interior of staphylococcal nuclease, Glu23 and Lys36 have p Ka values near pH 7, but when buried simultaneously, they establish a strong interaction of ∼5 kcal/mol and have p Ka values shifted toward more normal values. Here, using equilibrium thermodynamic measurements, crystal structures, and NMR spectroscopy experiments, we show that although the reversed, individual substitutions-Lys23 and Glu36-also have p Ka values near 7, when buried together, they neither establish a strong interaction nor promote reorganization of their microenvironment. These experiments both confirm Warshel's original hypothesis and expand it by showing that it applies to reorganization, as demonstrated by our artificial ion pairs, as well as to preorganization as is commonly argued for motifs that stabilize naturally occurring ion pairs in polar microenvironments. These data constitute a challenging benchmark useful to test the ability of structure-based algorithms to reproduce the compensation between self-energy, Coulomb and polar interactions in hydrophobic environments of proteins.

Anomalous Properties of Lys Residues Buried in the Hydrophobic Interior of a Protein Revealed with 15N-Detect NMR Spectroscopy.

Ionizable residues buried in hydrophobic environments in proteins are essential for many fundamental biochemical processes. These residues titrate with anomalous pKa values that are challenging to reproduce with structure-based calculations owing to the conformational reorganization coupled to their ionization. Detailed characterization of this conformational reorganization is of interest; unfortunately, the properties of buried Lys residues are difficult to study experimentally. Here we demonstrate the utility of 15N NMR spectroscopy to gain insight into the protonation state, state of hydration and conformational dynamics of the Nζ amino group of buried Lys residues. The experiments were applied to five variants of staphylococcal nuclease, with internal Lys residues that titrate with pKa values ranging from 6.2 to 8.1. Direct detection of buried Lys residues with these NMR spectroscopy methods will enable correlation between thermodynamic and structural data as well as unprecedented examination of how conformational transitions coupled to their ionization affect their pKa values.

Local Backbone Flexibility as a Determinant of the Apparent pKa Values of Buried Ionizable Groups in Proteins.

Ionizable groups buried in the hydrophobic interior of proteins are essential for energy transduction. These groups can have highly anomalous pKa values that reflect the incompatibility between charges and dehydrated environments. A systematic study of pKa values of buried ionizable groups in staphylococcal nuclease (SNase) suggests that these pKa values are determined in part by conformational reorganization of the protein. Lys-66 is one of the most deeply buried residues in SNase. We show that its apparent pKa of 5.7 reflects the average of the pKa values of Lys-66 in different conformational states of the protein. In the fully folded state, Lys-66 is deeply buried in the hydrophobic core of SNase and must titrate with a pKa of ≪5.7. In other states, the side chain of Lys-66 is fully solvent-exposed and has a normal pKa of ≈10.4. We show that the pKa of Lys-66 can be shifted from 5.7 toward a more normal value of 7.1 via the insertion of flanking Gly residues at positions 64 and 67 to promote an "open" conformation of SNase. Crystal structures and nuclear magnetic resonance spectroscopy show that in these Gly-containing variants Lys-66 can access bulk water as a consequence of overwinding of the C-terminal end of helix 1. These data illustrate that the apparent pKa values of buried groups in proteins are governed in part by the difference in free energy between different conformational states of the protein and by differences in the pKa values of the buried groups in the different conformations.

Charges in Hydrophobic Environments: A Strategy for Identifying Alternative States in Proteins.

In the V23E variant of staphylococcal nuclease, Glu-23 has a pKa of 7.5. At low pH, Glu-23 is neutral and buried in the hydrophobic interior of the protein. Crystal structures and NMR spectroscopy experiments show that when Glu-23 becomes charged, the protein switches into an open state in which strands ß1 and ß2 separate from the ß-barrel; the remaining structure is unaffected. In the open state the hydrophobic interior of the protein is exposed to bulk water, allowing Glu-23 to become hydrated. This illustrates several key aspects of protein electrostatics: (1) The apparent pKa of an internal ionizable group can reflect the average of the very different pKa values (open ≈4.5, closed ≫7.5) sampled in the different conformational states. (2) The high apparent dielectric constant reported by the pKa value of internal ionizable group reflects conformational reorganization. (3) The apparent pKa of internal groups can be governed by large conformational changes. (4) A single charge buried in the hydrophobic interior of a protein is sufficient to convert what might have been a transient, partially unfolded state into the dominant state in solution. This suggests a general strategy for examining inaccessible regions of the folding landscape and for engineering conformational switches driven by small changes in pH. These data also constitute a benchmark for stringent testing of the ability of computational algorithms to predict pKa values of internal residues and to reproduce pH-driven conformational transitions of proteins.

Conformational Reorganization Coupled to the Ionization of Internal Lys Residues in Proteins.

Ionizable groups buried in the hydrophobic interior of proteins are essential for energy transduction and catalysis. Because the protein interior is usually neither as polar nor as polarizable as water, these groups tend to have anomalous pKa values, and their ionization tends to be coupled to conformational reorganization. To elucidate mechanisms of energy transduction in proteins, it is necessary to understand the structural determinants of the pKa values of these buried groups, including the range and character of the conformational reorganization that the ionization of these buried groups can elicit. The L25K and L125K variants of staphylococcal nuclease (SNase) were used to characterize the diverse types of structural reorganization that can be promoted by the ionization of buried groups. NMR relaxation dispersion and ZZ-exchange experiments were used to identify the locations and measure the time scales and extent of pH-dependent conformational exchange in these two proteins. The buried Lys-25 and Lys-125 residues titrate with pKa of 6.3 and 6.2, respectively. The L25K protein fluctuates between the native state and an ensemble of locally unfolded states on the 400 µs to 7 ms time scale. On the 100 to 500 ms time scale the native state exchanges with a subglobally unfolded state in which the ß-barrel is partially reorganized. The equilibrium between the native state and this alternative state is highly pH dependent; at pH values below the pKa of Lys-25 the state with the partially reorganized ß-barrel is the dominant state. In contrast, the L125K protein only exhibited pH-independent fluctuation in the microsecond to millisecond time scale in the region near Lys-125. The study illustrates how diverse and how localized the coupling between conformational reorganization and ionization of buried groups can be. The pH-sensitive exchange between the fully native and subglobally or locally unfolded states in time scales well into hundreds of milliseconds will challenge all computational methods for structure-based calculations of pKa values.

Evolutionarily Conserved Pattern of Interactions in a Protein Revealed by Local Thermal Expansion Properties.

The way in which the network of intramolecular interactions determines the cooperative folding and conformational dynamics of a protein remains poorly understood. High-pressure NMR spectroscopy is uniquely suited to examine this problem because it combines the site-specific resolution of the NMR experiments with the local character of pressure perturbations. Here we report on the temperature dependence of the site-specific volumetric properties of various forms of staphylococcal nuclease (SNase), including three variants with engineered internal cavities, as measured with high-pressure NMR spectroscopy. The strong temperature dependence of pressure-induced unfolding arises from poorly understood differences in thermal expansion between the folded and unfolded states. A significant inverse correlation was observed between the global thermal expansion of the folded proteins and the number of strong intramolecular hydrogen bonds, as determined by the temperature coefficient of the backbone amide chemical shifts. Comparison of the identity of these strong H-bonds with the co-evolution of pairs of residues in the SNase protein family suggests that the architecture of the interactions detected in the NMR experiments could be linked to a functional aspect of the protein. Moreover, the temperature dependence of the residue-specific volume changes of unfolding yielded residue-specific differences in expansivity and revealed how mutations impact intramolecular interaction patterns. These results show that intramolecular interactions in the folded states of proteins impose constraints against thermal expansion and that, hence, knowledge of site-specific thermal expansivity offers insight into the patterns of strong intramolecular interactions and other local determinants of protein stability, cooperativity, and potentially also of function.

pH dependence of conformational fluctuations of the protein backbone.

Proton binding equilibria (pK(a) values) of ionizable groups in proteins are exquisitely sensitive to their microenvironments. Apparent pK(a) values measured for individual ionizable residues with NMR spectroscopy are actually population-weighted averages of the pK(a) in different conformational microstates. NMR spectroscopy experiments with staphylococcal nuclease were used to test the hypothesis that pK(a) values of surface Glu and Asp residues are affected by pH-sensitive fluctuations of the backbone between folded and locally unfolded conformations. (15)N spin relaxation studies showed that as the pH decreases from the neutral into the acidic range the amplitudes of backbone fluctuations in the ps-ns timescale increase near carboxylic residues. Hydrogen exchange experiments suggested that backbone conformational fluctuations promoted by decreasing pH also reflect slower local or sub-global unfolding near carboxylic groups. This study has implications for structure-based pKa calculations: (1) The timescale of the backbone's response to ionization events in proteins can range from ps to ms, and even longer; (2) pH-sensitive fluctuations of the backbone can be localized to both the segment the ionizable residue is attached to or the one that occludes the ionizable group; (3) Structural perturbations are not necessarily propagated through Coulomb interactions; instead, local fluctuations appear to be coupled through the co-operativity inherent to elements of secondary structure and to networks of hydrogen bonds. These results are consistent with the idea that local conformational fluctuations and stabilities are important determinants of apparent pK(a) values of ionizable residues in proteins.

Structural and thermodynamic consequences of burial of an artificial ion pair in the hydrophobic interior of a protein.

An artificial charge pair buried in the hydrophobic core of staphylococcal nuclease was engineered by making the V23E and L36K substitutions. Buried individually, Glu-23 and Lys-36 both titrate with pKa values near 7. When buried together their pKa values appear to be normal. The ionizable moieties of the buried Glu-Lys pair are 2.6 Å apart. The interaction between them at pH 7 is worth 5 kcal/mol. Despite this strong interaction, the buried Glu-Lys pair destabilizes the protein significantly because the apparent Coulomb interaction is sufficient to offset the dehydration of only one of the two buried charges. Save for minor reorganization of dipoles and water penetration consistent with the relatively high dielectric constant reported by the buried ion pair, there is no evidence that the presence of two charges in the hydrophobic interior of the protein induces any significant structural reorganization. The successful engineering of an artificial ion pair in a highly hydrophobic environment suggests that buried Glu-Lys pairs in dehydrated environments can be charged and that it is possible to engineer charge clusters that loosely resemble catalytic sites in a scaffold protein with high thermodynamic stability, without the need for specialized structural adaptations.

Protein dielectric constants determined from NMR chemical shift perturbations.

Understanding the connection between protein structure and function requires a quantitative understanding of electrostatic effects. Structure-based electrostatic calculations are essential for this purpose, but their use has been limited by a long-standing discussion on which value to use for the dielectric constants (ε(eff) and ε(p)) required in Coulombic and Poisson-Boltzmann models. The currently used values for ε(eff) and ε(p) are essentially empirical parameters calibrated against thermodynamic properties that are indirect measurements of protein electric fields. We determine optimal values for ε(eff) and ε(p) by measuring protein electric fields in solution using direct detection of NMR chemical shift perturbations (CSPs). We measured CSPs in 14 proteins to get a broad and general characterization of electric fields. Coulomb's law reproduces the measured CSPs optimally with a protein dielectric constant (ε(eff)) from 3 to 13, with an optimal value across all proteins of 6.5. However, when the water-protein interface is treated with finite difference Poisson-Boltzmann calculations, the optimal protein dielectric constant (ε(p)) ranged from 2 to 5 with an optimum of 3. It is striking how similar this value is to the dielectric constant of 2-4 measured for protein powders and how different it is from the ε(p) of 6-20 used in models based on the Poisson-Boltzmann equation when calculating thermodynamic parameters. Because the value of ε(p) = 3 is obtained by analysis of NMR chemical shift perturbations instead of thermodynamic parameters such as pK(a) values, it is likely to describe only the electric field and thus represent a more general, intrinsic, and transferable ε(p) common to most folded proteins.

Probing the physical determinants of thermal expansion of folded proteins.

The magnitude and sign of the volume change upon protein unfolding are strongly dependent on temperature. This temperature dependence reflects differences in the thermal expansivity of the folded and unfolded states. The factors that determine protein molar expansivities and the large differences in thermal expansivity for proteins of similar molar volume are not well understood. Model compound studies have suggested that a major contribution is made by differences in the molar volume of water molecules as they transfer from the protein surface to the bulk upon heating. The expansion of internal solvent-excluded voids upon heating is another possible contributing factor. Here, the contribution from hydration density to the molar thermal expansivity of a protein was examined by comparing bovine pancreatic trypsin inhibitor and variants with alanine substitutions at or near the protein-water interface. Variants of two of these proteins with an additional mutation that unfolded them under native conditions were also examined. A modest decrease in thermal expansivity was observed in both the folded and unfolded states for the alanine variants compared with the parent protein, revealing that large changes can be made to the external polarity of a protein without causing large ensuing changes in thermal expansivity. This modest effect is not surprising, given the small molar volume of the alanine residue. Contributions of the expansion of the internal void volume were probed by measuring the thermal expansion for cavity-containing variants of a highly stable form of staphylococcal nuclease. Significantly larger (2-3-fold) molar expansivities were found for these cavity-containing proteins relative to the reference protein. Taken together, these results suggest that a key determinant of the thermal expansivities of folded proteins lies in the expansion of internal solvent-excluded voids.

The high dielectric constant of staphylococcal nuclease is encoded in its structural architecture.

The pK(a) values of Lys-66, Glu-66, and Asp-66 buried in the interior of the staphylococcal nuclease Δ+PHS variant were reported to be shifted by as much as 5 pK(a) units from their normal values. Reproducing the pK(a) of these buried ionizable residues using continuum electrostatic calculations required the use of a high protein dielectric constant of 10 or higher. The apparent high dielectric constant has been rationalized as a consequence of a local structural reorganization or increased fluctuations in the microenvironment of the mutation site (Chimenti, M. S., et al. J. Mol. Biol. 2011, 405, 361-377). We have calculated the dielectric constant of Δ+PHS and the Lys-66, Asp-66, and Glu-66 mutants from first principles using the Kirkwood-Fröhlich equation and discovered that staphylococcal nuclease has a naturally high dielectric constant ranging from 20 to 30. This high dielectric constant does not change significantly with the mutation of residue 66 or with the ionization of the mutated residues. Calculation of the spatial dependence of the dielectric constant for the microenvironment of residue-66 produces a value of about 10, which matches well with the apparent dielectric constant needed to reproduce pK(a) values from continuum electrostatic calculations. Our results suggest an alternative explanation that the high dielectric constant of staphylococcal nuclease is a property resulting from the intrinsic backbone fluctuations originating from its structural architecture.

Structural plasticity of staphylococcal nuclease probed by perturbation with pressure and pH.

The ionization of internal groups in proteins can trigger conformational change. Despite this being the structural basis of most biological energy transduction, these processes are poorly understood. Small angle X-ray scattering (SAXS) and nuclear magnetic resonance (NMR) spectroscopy experiments at ambient and high hydrostatic pressure were used to examine how the presence and ionization of Lys-66, buried in the hydrophobic core of a stabilized variant of staphylococcal nuclease, affect conformation and dynamics. NMR spectroscopy at atmospheric pressure showed previously that the neutral Lys-66 affects slow conformational fluctuations globally, whereas the effects of the charged form are localized to the region immediately surrounding position 66. Ab initio models from SAXS data suggest that when Lys-66 is charged the protein expands, which is consistent with results from NMR spectroscopy. The application of moderate pressure (<2 kbar) at pH values where Lys-66 is normally neutral at ambient pressure left most of the structure unperturbed but produced significant nonlinear changes in chemical shifts in the helix where Lys-66 is located. Above 2 kbar pressure at these pH values the protein with Lys-66 unfolded cooperatively adopting a relatively compact, albeit random structure according to Kratky analysis of the SAXS data. In contrast, at low pH and high pressure the unfolded state of the variant with Lys-66 is more expanded than that of the reference protein. The combined global and local view of the structural reorganization triggered by ionization of the internal Lys-66 reveals more detectable changes than were previously suggested by NMR spectroscopy at ambient pressure.

Structural origins of high apparent dielectric constants experienced by ionizable groups in the hydrophobic core of a protein.

The side chains of Lys66, Asp66, and Glu66 in staphylococcal nuclease are fully buried and surrounded mainly by hydrophobic matter, except for internal water molecules associated with carboxylic oxygen atoms. These ionizable side chains titrate with pK(a) values of 5.7, 8.8, and 8.9, respectively. To reproduce these pK(a) values with continuum electrostatics calculations, we treated the protein with high dielectric constants. We have examined the structural origins of these high apparent dielectric constants by using NMR spectroscopy to characterize the structural response to the ionization of these internal side chains. Substitution of Val66 with Lys66 and Asp66 led to increased conformational fluctuations of the microenvironments surrounding these groups, even under pH conditions where Lys66 and Asp66 are neutral. When Lys66, Asp66, and Glu66 are charged, the proteins remain almost fully folded, but resonances for a few backbone amides adjacent to the internal ionizable residues are broadened. This suggests that the ionization of the internal groups promotes a local increase in dynamics on the intermediate timescale, consistent with either partial unfolding or increased backbone fluctuations of helix 1 near residue 66, or, less likely, with increased fluctuations of the charged side chains at position 66. These experiments confirm that the high apparent dielectric constants reported by internal Lys66, Asp66, and Glu66 reflect localized changes in conformational fluctuations without incurring detectable global structural reorganization. To improve structure-based pK(a) calculations in proteins, we will need to learn how to treat this coupling between ionization of internal groups and local changes in conformational fluctuations explicitly.

Charges in the hydrophobic interior of proteins.

Charges are inherently incompatible with hydrophobic environments. Presumably for this reason, ionizable residues are usually excluded from the hydrophobic interior of proteins and are found instead at the surface, where they can interact with bulk water. Paradoxically, ionizable groups buried in the hydrophobic interior of proteins play essential roles, especially in biological energy transduction. To examine the unusual properties of internal ionizable groups we measured the pK(a) of glutamic acid residues at 25 internal positions in a stable form of staphylococcal nuclease. Two of 25 Glu residues titrated with normal pK(a) near 4.5; the other 23 titrated with elevated pK(a) values ranging from 5.2-9.4, with an average value of 7.7. Trp fluorescence and far-UV circular dichroism were used to monitor the effects of internal charges on conformation. These data demonstrate that although charges buried in proteins are indeed destabilizing, charged side chains can be buried readily in the hydrophobic core of stable proteins without the need for specialized structural adaptations to stabilize them, and without inducing any major conformational reorganization. The apparent dielectric effect experienced by the internal charges is considerably higher than the low dielectric constants of hydrophobic matter used to represent the protein interior in electrostatic continuum models of proteins. The high thermodynamic stability required for proteins to withstand the presence of buried charges suggests a pathway for the evolution of enzymes, and it underscores the need to mind thermodynamic stability in any strategy for engineering novel or altered enzymatic active sites in proteins.

Self-guided Langevin dynamics study of regulatory interactions in NtrC.

Multiple self-guided Langevin dynamics (SGLD) simulations were performed to examine structural and dynamical properties of the receiver domain of nitrogen regulatory protein C (NtrC(r)). SGLD and MD simulations of the phosphorylated active form structure suggest a mostly stable but broad structural ensemble of this protein. The finite difference Poisson-Boltzmann calculations of the pK(a) values of the active site residues suggest an increase in the pK(a) of His-84 on phosphorylation of Asp-54. In SGLD simulations of the phosphorylated active form with charged His-84, the average position of the regulatory helix alpha4 is found closer to the starting structure than in simulations with the neutral His-84. To model the transition pathway, the phosphate group was removed from the simulations. After 7 ns of simulations, the regulatory helix alpha4 was found approximately halfway between positions in the NMR structures of the active and inactive forms. Removal of the phosphate group stimulated loss of helix alpha4, suggesting that the pathway of conformational transition may involve partial unfolding mechanism. The study illustrates the potential utility of the SGLD method in studies of the coupling between ligand binding and conformational transitions.

The pK(a) values of acidic and basic residues buried at the same internal location in a protein are governed by different factors.

The pK(a) values of internal ionizable groups are usually very different from the normal pK(a) values of ionizable groups in water. To examine the molecular determinants of pK(a) values of internal groups, we compared the properties of Lys, Asp, and Glu at internal position 38 in staphylococcal nuclease. Lys38 titrates with a normal or elevated pK(a), whereas Asp38 and Glu38 titrate with elevated pK(a) values of 7.0 and 7.2, respectively. In the structure of the L38K variant, the buried amino group of the Lys38 side chain makes an ion pair with Glu122, whereas in the structure of the L38E variant, the buried carboxyl group of Glu38 interacts with two backbone amides and has several nearby carboxyl oxygen atoms. Previously, we showed that the pK(a) of Lys38 is normal owing to structural reorganization and water penetration concomitant with ionization of the Lys side chain. In contrast, the pK(a) values of Asp38 and Glu38 are perturbed significantly owing to an imbalance between favorable polar interactions and unfavorable contributions from dehydration and from Coulomb interactions with surface carboxylic groups. Their ionization is also coupled to subtle structural reorganization. These results illustrate the complex interplay between local polarity, Coulomb interactions, and structural reorganization as determinants of pK(a) values of internal groups in proteins. This study suggests that improvements to computational methods for pK(a) calculations will require explicit treatment of the conformational reorganization that can occur when internal groups ionize.

Open science grid study of the coupling between conformation and water content in the interior of a protein.

Computational grids are a promising resource for modeling complex biochemical processes such as protein folding, penetration of gases or water into proteins, or protein structural rearrangements coupled to ligand binding. We have enabled the molecular dynamics program CHARMM to run on the Open Science Grid. The implementation is general, flexible, easily modifiable for use with other molecular dynamics programs and other grids and automated in terms of job submission, monitoring, and resubmission. The usefulness of grid computing was demonstrated through the study of hydration of the Glu-66 side chain in the interior of protein staphylococcal nuclease. Multiple simulations started with and without two internal water molecules shown crystallographically to be associated with the side chain of Glu-66 yielded two distinct populations of rotameric states of Glu-66 that differed by as much as 20%. This illustrates how internal water molecules can bias protein conformations. Furthermore, there appeared to be a temporal correlation between dehydration of the side chain and conformational transitions of Glu-66. This example demonstrated how difficult it is to get convergence even in the relatively simple case of a side chain oscillating between two conformations. With grid computing, we also benchmarked the self-guided Langevin dynamics method against the Langevin dynamics method traditionally used for temperature control in molecular dynamics simulations and showed that the two methods yield comparable results.

Backbone relaxation coupled to the ionization of internal groups in proteins: a self-guided Langevin dynamics study.

Pathways of structural relaxation triggered by ionization of internal groups in staphylococcal nuclease (SNase) were studied through multiple self-guided Langevin dynamics (SGLD) simulations. Circular dichroism, steady-state Trp fluorescence, and nuclear magnetic resonance spectroscopy have shown previously that variants of SNase with internal Glu, Asp, and Lys at positions 66 or 92, and Arg at position 66, exhibit local reorganization or global unfolding when the internal ionizable group is charged. Except for Arg-66, these internal ionizable groups have unusual pKa values and are neutral at physiological pH. The structural trends observed in the simulations are in general agreement with experimental observations. The I92D variant, which unfolds globally upon ionization of Asp-92, in simulations often exhibits extensive hydration of the protein core, and sometimes also significant perturbations of the beta-barrel. In the crystal structure of the V66R variant, the beta1 strand from the beta-barrel is domain-swapped; in the simulations, the beta1 strand is sometimes partially released. The V66K variant, which in solutions shows reorganization of six residues at the C-terminus of helix alpha1 and perturbations in the beta-barrel structure, exhibits fraying of three residues of helix alpha1 in one simulation, and perturbations and partial unfolding of three beta-strands in a few other simulations. In sharp contrast, very small structural changes were observed in simulations of the wild-type protein. The simulations indicate that charging of internal groups frequently triggers penetration of water into the protein interior. The pKa values of Asp-92 and Arg-66 calculated with continuum methods on SGLD-relaxed structures reached the normal values in most simulations. Detailed analysis of accuracy and performance of SGLD demonstrates that SGLD outperforms LD in sampling of alternative protein conformations without loss of the accuracy and level of detail characteristic of regular LD.

Electrostatic effects in unfolded staphylococcal nuclease.

Structure-based calculations of pKa values and electrostatic free energies of proteins assume that electrostatic effects in the unfolded state are negligible. In light of experimental evidence showing that this assumption is invalid for many proteins, and with increasing awareness that the unfolded state is more structured and compact than previously thought, a detailed examination of electrostatic effects in unfolded proteins is warranted. Here we address this issue with structure-based calculations of electrostatic interactions in unfolded staphylococcal nuclease. The approach involves the generation of ensembles of structures representing the unfolded state, and calculation of Coulomb energies to Boltzmann weight the unfolded state ensembles. Four different structural models of the unfolded state were tested. Experimental proton binding data measured with a variant of nuclease that is unfolded under native conditions were used to establish the validity of the calculations. These calculations suggest that weak Coulomb interactions are an unavoidable property of unfolded proteins. At neutral pH, the interactions are too weak to organize the unfolded state; however, at extreme pH values, where the protein has a significant net charge, the combined action of a large number of weak repulsive interactions can lead to the expansion of the unfolded state. The calculated pKa values of ionizable groups in the unfolded state are similar but not identical to the values in small peptides in water. These studies suggest that the accuracy of structure-based calculations of electrostatic contributions to stability cannot be improved unless electrostatic effects in the unfolded state are calculated explicitly.