Realistic modeling of the denatured states of proteins allows accurate calculations of the pH dependence of protein stability

Contribution of single tryptophan residues to the fluorescence and stability of ribonuclease Sa

Ribonuclease Sa (RNase Sa) contains no tryptophan (Trp) residues. We have added single Trp residues to RNase Sa at sites where Trp is found in four other microbial ribonucleases, yielding the following variants of RNase Sa: Y52W, Y55W, T76W, and Y81W. We have determined crystal structures of T76W and Y81W at 1.1 and 1.0 A resolution, respectively. We have studied the fluorescence properties and stabilities of the four variants and compared them to wild-type RNase Sa and the other ribonucleases on which they were based. Our results should help others in selecting sites for adding Trp residues to proteins. The most interesting findings are: 1), Y52W is 2.9 kcal/mol less stable than RNase Sa and the fluorescence intensity emission maximum is blue-shifted to 309 nm. Only a Trp in azurin is blue-shifted to a greater extent (308 nm). This blue shift is considerably greater than observed for Trp71 in barnase, the Trp on which Y52W is based. 2), Y55W is 2.1 kcal/mol less stable than RNase Sa and the tryptophan fluorescence is almost completely quenched. In contrast, Trp59 in RNase T1, on which Y55W is based, has a 10-fold greater fluorescence emission intensity. 3), T76W is 0.7 kcal/mol more stable than RNase Sa, indicating that the Trp side chain has more favorable interactions with the protein than the threonine side chain. The fluorescence properties of folded Y76W are similar to those of the unfolded protein, showing that the tryptophan side chain in the folded protein is largely exposed to solvent. This is confirmed by the crystal structure of the T76W which shows that the side chain of the Trp is only approximately 7% buried. 4), Y81W is 0.4 kcal/mol less stable than RNase Sa. Based on the crystal structure of Y81W, the side chain of the Trp is 87% buried. Although all of the Trp side chains in the variants contribute to the unusual positive circular dichroism band observed near 235 nm for RNase Sa, the contribution is greatest for Y81W.

Inverse Electrostatic Effect: Electrostatic Repulsion in the Unfolded State Stabilizes a Leucine Zipper,

The pH-dependent stability of a protein is strongly affected by electrostatic interactions between ionizable residues in the folded as well as unfolded state. Here we characterize the individual contributions of charged Glu and His residues to stability and determine the NMR structure of the designed, heterodimeric leucine zipper AB consisting of an acidic A chain and a basic B chain. Thermodynamic parameters are compared with those of the homologous leucine zipper AB(SS) in which the A and B chains are disulfide-linked. NMR structures of AB based on (1)H NMR data collected at 600 MHz converge, and formation of the same six interchain salt bridges found previously in disulfide-linked AB(SS) [Marti, D. N., and Bosshard, H. R. (2003) J. Mol. Biol. 330, 621-637] is indicated. While the structures of AB and AB(SS) are very similar, their pH-dependent relative stabilities are strikingly different. The stability of AB peaks at pH approximately 4.5 and is higher at pH 8 than at pH 2. In contrast, AB(SS) is most stable at acidic pH where no interhelical salt bridges are formed. The different energetic contributions of charged Glu and His residues to stability of the two coiled coil structures were evaluated from pK(a) shifts induced by folding. The six charged Glu residues involved in salt bridges stabilize leucine zipper AB by 4.5 kJ/mol yet destabilize disulfide-linked AB(SS) by -1.1 kJ/mol. Two non-ion-paired Glu charges destabilize AB by only -1.8 kJ/mol but AB(SS) by -5.6 kJ/mol. The higher relative stability of AB at neutral pH is not caused by more favorable electrostatic interactions in the folded leucine zipper. It is due mainly to unfavorable electrostatic interactions in the unfolded A and B chains and may therefore be called an inverse electrostatic effect. This study illustrates the importance of residual interactions in the unfolded state and how the energetics of the unfolded state affect the stability of the folded protein.

Conferring thermostability to mesophilic proteins through optimized electrostatic surfaces

Recently, there have been several experimental reports of proteins displaying appreciable stability gains through mutation of one or two amino acid residues. Here, we employ a simple theoretical model to quickly screen mutant structures for increased thermostability through optimization of the protein's electrostatic surface. Our results are able to reproduce the experimental observation that elimination of like-charge repulsions and creation of opposite-charge attractions on the protein surface is an efficient method to confer thermostability to a mesophilic protein. Using Poisson-Boltzmann electrostatics, we calculate relative protein stabilities for the exhaustive surface mutagenesis of the cold shock, RNase T1, and CheY proteins. Comparison with 25 experimentally characterized cold shock protein mutants reveals an average correlation of 0.86. The model is also quantitatively accurate when reproducing the experimental D49A and D49H mutant stabilities of RNase T1. This work represents the first comprehensive in silico screening of mutant candidates likely to confer thermostability to mesophilic proteins through optimization of surface electrostatics. Systematic single mutant, followed by double mutant, screening yields a limited number of mutant structures displaying significant stability gains suitable for subsequent experimental characterization.

Numerical calculations of the pH of maximal protein stability. The effect of the sequence composition and three-dimensional structure

A large number of proteins, found experimentally to have different optimum pH of maximal stability, were studied to reveal the basic principles of their preference for a particular pH. The pH-dependent free energy of folding was modeled numerically as a function of pH as well as the net charge of the protein. The optimum pH was determined in the numerical calculations as the pH of the minimum free energy of folding. The experimental data for the pH of maximal stability (experimental optimum pH) was reproducible (rmsd = 0.73). It was shown that the optimum pH results from two factors - amino acid composition and the organization of the titratable groups with the 3D structure. It was demonstrated that the optimum pH and isoelectric point could be quite different. In many cases, the optimum pH was found at a pH corresponding to a large net charge of the protein. At the same time, there was a tendency for proteins having acidic optimum pHs to have a base/acid ratio smaller than one and vice versa. The correlation between the optimum pH and base/acid ratio is significant if only buried groups are taken into account. It was shown that a protein that provides a favorable electrostatic environment for acids and disfavors the bases tends to have high optimum pH and vice versa.

Polymer Models of Protein Stability, Folding, and Interactions

The unfolded state and flexible linkers in the folded structure play essential roles in protein stability and folding and protein-protein interactions. Intrinsic to these roles is the fact that unfolded proteins and flexible linkers sample many different conformations. Polymer models may capture this and complement experiments in elucidating the contributions of the unfolded state and flexible linkers. Here I review what can be predicted from these models and how well these predictions match experiments. For example, Gaussian chain models give quantitatively reasonable predictions of the effects of residual charge-charge interactions in the unfolded state and qualitatively reasonable results for the effects of spatial confinement and macromolecular crowding on protein stability. A wormlike chain model has met with success in quantifying the effects of flexible linkers in binding affinity enhancement and in regulatory switches. In future developments, more realistic models may emerge from molecular dynamics simulations, and these models will guide experiments to advance our understanding of the unfolded state and flexible linkers.

Folding of Cu, Zn Superoxide Dismutase and Familial Amyotrophic Lateral Sclerosis

Cu, Zn superoxide dismutase (SOD1) has been implicated in the familial form of the neurodegenerative disease amyotrophic lateral sclerosis (ALS). It has been suggested that mutant mediated SOD1 misfolding/aggregation is an integral part of the pathology of ALS. We study the folding thermodynamics and kinetics of SOD1 using a hybrid molecular dynamics approach. We reproduce the experimentally observed SOD1 folding thermodynamics and find that the residues which contribute the most to SOD1 thermal stability are also crucial for apparent two-state folding kinetics. Surprisingly, we find that these residues are located on the surface of the protein and not in the hydrophobic core. Mutations in some of the identified residues are found in patients with the disease. We argue that the identified residues may play an important role in aggregation. To further characterize the folding of SOD1, we study the role of cysteine residues in folding and find that non-native disulfide bond formation may significantly alter SOD1 folding dynamics and aggregation propensity.

The pH dependence of stability of the activation helix and the catalytic site of GART

We have predicted the free energy of unfolding for the pH-dependent helix-coil transition of the activation helix of GART using continuum electrostatic calculations and structural modeling. We have assigned the contributions of each element of secondary structure and of each ionizable residue, within and in the vicinity of the activation helix, to the stability of several fragments of GART that participate in the formation of the catalytic site. We demonstrate that the interaction of His121-His132 contributes 2.2 kcal/mol to the ionization free energy between pH 0 and approximately 6. We also show that the ionization state of a network of five histidines, His108, His119, His121, His132 and His137, and two aspartic acids Asp141 and Asp144, contributes approximately 12 kcal/mol to the stability of the catalytic site of GART, out of a total stability of 16 kcal/mol of the whole enzyme. These interactions are important for the formation of the catalytic site of GART.

Electrostatic interactions in leucine zippers: thermodynamic analysis of the contributions of Glu and His residues and the effect of mutating salt bridges

Electrostatic interactions play a complex role in stabilizing proteins. Here, we present a rigorous thermodynamic analysis of the contribution of individual Glu and His residues to the relative pH-dependent stability of the designed disulfide-linked leucine zipper AB(SS). The contribution of an ionized side-chain to the pH-dependent stability is related to the shift of the pK(a) induced by folding of the coiled coil structure. pK(a)(F) values of ten Glu and two His side-chains in folded AB(SS) and the corresponding pK(a)(U) values in unfolded peptides with partial sequences of AB(SS) were determined by 1H NMR spectroscopy: of four Glu residues not involved in ion pairing, two are destabilizing (-5.6 kJ mol(-1)) and two are interacting with the positive alpha-helix dipoles and are thus stabilizing (+3.8 kJ mol(-1)) in charged form. The two His residues positioned in the C-terminal moiety of AB(SS) interact with the negative alpha-helix dipoles resulting in net stabilization of the coiled coil conformation carrying charged His (-2.6 kJ mol(-1)). Of the six Glu residues involved in inter-helical salt bridges, three are destabilizing and three are stabilizing in charged form, the net contribution of salt-bridged Glu side-chains being destabilizing (-1.1 kJ mol(-1)). The sum of the individual contributions of protonated Glu and His to the higher stability of AB(SS) at acidic pH (-5.4 kJ mol(-1)) agrees with the difference in stability determined by thermal unfolding at pH 8 and pH 2 (-5.3 kJ mol(-1)). To confirm salt bridge formation, the positive charge of the basic partner residue of one stabilizing and one destabilizing Glu was removed by isosteric mutations (Lys-->norleucine, Arg-->norvaline). Both mutations destabilize the coiled coil conformation at neutral pH and increase the pK(a) of the formerly ion-paired Glu side-chain, verifying the formation of a salt bridge even in the case where a charged side-chain is destabilizing. Because removing charges by a double mutation cycle mainly discloses the immediate charge-charge effect, mutational analysis tends to overestimate the overall energetic contribution of salt bridges to protein stability.

Energetic evidence for formation of a pH-dependent hydrophobic cluster in the denatured state of Thermus thermophilus ribonuclease H

NMR studies on the denatured states of proteins indicate that residual structure often resides predominantly in hydrophobic clusters. Such hydrophobic cluster formation implies burial of apolar surface and, consequently, is expected to cause a decrease in heat capacity. We report here that, in the case of ribonuclease H from the thermophile Thermus thermophilus, a sharp decrease in denatured-state heat capacity occurs at about pH 3.8; this result points to the formation of hydrophobic clusters triggered by the protonation of several (about four) carboxylic acid groups, and indicates that the burial of apolar surface is favored by the less hydrophilic character of the uncharged forms of Asp and Glu side-chains. The process is not accompanied by large changes in optically active structure, but appears to be highly cooperative, as indicated by the sharpness of the pH-induced transition in the heat capacity. This acid-induced hydrophobic burial in denatured T.thermophilus ribonuclease H is clearly reflected in the pH dependence of the denaturation temperature (i.e. an abrupt change of slope at about pH 3.8 is seen in the plot of denaturation temperature versus pH), supporting a role for such denatured-state hydrophobic clusters in protein stability. The finding of cooperative protonation of several groups coupled to surface burial in denatured T.thermophilus ribonuclease H emphasizes the potential complexity of denatured-state electrostatics and advises caution when attempting to predict denatured-state properties on the basis of simple electrostatic models. Finally, our results suggest a higher propensity for hydrophobic cluster formation in the denatured state of T.thermophilus ribonuclease H as compared with that of its mesophilic counterpart from Escherichia coli.

Identifying residue-residue clashes in protein hybrids by using a second-order mean-field approach

In this article, a second-order mean-field-based approach is introduced for characterizing the complete set of residue-residue couplings consistent with a given protein structure. This information is subsequently used to classify protein hybrids with respect to their potential to be functional based on the presenceabsence and severity of clashing residue-residue interactions. First, atomistic representations of both the native and denatured states are used to calculate rotamer-backbone, rotamer-intrinsic, and rotamer-rotamer conformational energies. Next, this complete conformational energy table is coupled with a second-order mean-field description to elucidate the probabilities of all possible rotamer-rotamer combinations in a minimum Helmholtz free-energy ensemble. Computational results for the dihydrofolate reductase family reveal correlation in substitution patterns between not only contacting but also distal second-order structural elements. Residue-residue clashes in hybrid proteins are quantified by contrasting the ensemble probabilities of protein hybrids against the ones of the original parental sequences. Good agreement with experimental data is demonstrated by superimposing these clashes against the functional crossover profiles of bidirectional incremental truncation libraries for Escherichia coli and human glycinamide ribonucleotide transformylases.

Site-specific contributions to the pH dependence of protein stability

Understanding protein stability is a significant challenge requiring characterization of interactions within both folded and unfolded states. Of these, electrostatic interactions influence ionization equilibria of acidic and basic groups and diversify their pK(a) values. The pH dependence of the thermodynamic stability (Delta G(FU)) of a protein arises as a consequence of differential pK(a) values between folded and unfolded states. Previous attempts to calculate pH-dependent contributions to stability have been limited by the lack of experimental unfolded state pK(a) values. Using recently developed NMR spectroscopic methods, we have determined residue-specific pK(a) values for a thermodynamically unstable Src homology 3 domain in both states, enabling the calculation of the pH dependence of stability based on simple analytical expressions. The calculated pH stability profile obtained agrees very well with experiment, unlike profiles derived from two current models of electrostatic interactions within unfolded states. Most importantly, per-residue contributions to the pH dependence of Delta G(FU) derived from the data provide insights into specific electrostatic interactions in both the folded and unfolded states and their roles in protein stability. These interactions include a hydrogen bond between the Asp-8 side-chain and the Lys-21 backbone amide group in the folded state, which represents a highly conserved interaction in Src homology 3 domains.

Contribution of surface salt bridges to protein stability: guidelines for protein engineering

The small globular protein, ubiquitin, contains a pair of oppositely charged residues, K11 and E34, that according to the three-dimensional structure are located on the surface of this protein with a spatial orientation characteristic of a salt bridge. We investigated the strength of this salt bridge and its contribution to the global stability of the ubiquitin molecule. Using the "double mutant cycle" analysis, the strength of the pairwise interactions between K11 and E34 was estimated to be favorable by 3.6kJ/mol. Further, the salt bridge of the reverse orientation, i.e. E11/K34, can be formed and is found to have a strength (3.8kJ/mol) similar to that of the K11/E34 pair. However, the global stability of the K11/E34 variant of ubiquitin is 2.2kJ/mol higher than that of the E11/K34 variant. The difference in the contribution of the opposing salt bridge orientations to the overall stability of the ubiquitin molecule is attributed to the difference in the charge-charge interactions between residues forming the salt bridge and the rest of the ionizable groups in this protein. On the basis of these results, we concluded that surface salt bridges are stabilizing, but their contribution to the overall protein stability is strongly context-dependent, with charge-charge interactions being the largest determinant. Analysis of 16 salt bridges from six different proteins, for which detailed experimental data on energetics have been reported, support the conclusions made from the analysis of the salt bridge in ubiquitin. Implications of these findings for engineering proteins with enhanced thermostability are discussed.

Direct test of the Gaussian-chain model for treating residual charge-charge interactions in the unfolded state of proteins

The Gaussian-chain model for treating residual charge-charge interactions was critically tested by recent experimental pK(a) results for individual Asp, Glu, and His residues in the unfolded drkN SH3 domain. Predicted pK(a)'s were in good agreement with experiment. The clustering of Asp and Glu residues along the sequence was suggested to limit pK(a) shifts and contribute to the folding stability by destabilizing the unfolded state.

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.

Residual charge interactions in unfolded staphylococcal nuclease can be explained by the Gaussian-chain model

The discrepancy of the pH dependence of the unfolding free energy for staphylococcal nuclease from what is expected from an idealized model for the unfolded state is accounted for by the recently developed Gaussian-chain model. Residual electrostatic effects in the unfolded state are attributed to nonspecific interactions dominated by charges close along the sequence. The dominance of nonspecific local interactions appears to be supported by some experimental evidence.

Electrostatic contributions to T4 lysozyme stability: solvent-exposed charges versus semi-buried salt bridges

We carried our Poisson-Boltzmann (PB) calculations for the effects of charge reversal at five exposed sites (K16E, R119E, K135E, K147E, and R154E) and charge neutralization and proton titration of the H31-D70 semi-buried salt bridge on the stability of T4 lysozyme. Instead of the widely used solvent-exclusion (SE) surface, we used the van der Waals (vdW) surface as the boundary between the protein and solvent dielectrics (a protocol established in our earlier study on charge mutations in barnase). By including residual charge-charge interactions in the unfolded state, the five charge reversal mutations were found to have DeltaDeltaG(unfold) from -1.6 to 1.3 kcal/mol. This indicates that the variable effects of charge reversal observed by Matthews and co-workers are not unexpected. The H31N, D70N, and H31N/D70N mutations were found to destabilize the protein by 2.9, 1.3, and 1.6 kcal/mol, and the pK(a) values of H31 and D70 were shifted to 9.4 and 0.6, respectively. These results are in good accord with experimental data of Dahlquist and co-workers. In contrast, if the SE surface were used, the H31N/D70N mutant would be more stable than the wild-type protein by 1.3 kcal/mol. From these and additional results for 27 charge mutations on five other proteins, we conclude that 1) the popular view that electrostatic interactions are generally destabilizing may have been based on overestimated desolvation cost as a result of using the SE surface as the dielectric boundary; and 2) while solvent-exposed charges may not reliably contribute to protein stability, semi-buried salt bridges can provide significant stabilization.

Empirical relationships between protein structure and carboxyl pKa values in proteins

Relationships between protein structure and ionization of carboxyl groups were investigated in 24 proteins of known structure and for which 115 aspartate and 97 glutamate pK(a) values are known. Mean pK(a) values for aspartates and glutamates are < or = 3.4 (+/-1.0) and 4.1 (+/-0.8), respectively. For aspartates, mean pK(a) values are 3.9 (+/-1.0) and 3.1 (+/-0.9) in acidic (pI < 5) and basic (pI > 8) proteins, respectively, while mean pK(a) values for glutamates are approximately 4.2 for acidic and basic proteins. Burial of carboxyl groups leads to dispersion in pK(a) values: pK(a) values for solvent-exposed groups show narrow distributions while values for buried groups range from < 2 to 6.7. Calculated electrostatic potentials at the carboxyl groups show modest correlations with experimental pK(a) values and these correlations are not improved by including simple surface-area-based terms to account for the effects of desolvation. Mean aspartate pK(a) values decrease with increasing numbers of hydrogen bonds but this is not observed at glutamates. Only 10 pK(a) values are > 5.5 and most are found in active sites or ligand-binding sites. These carboxyl groups are buried and usually accept no more than one hydrogen bond. Aspartates and glutamates at the N-termini of helices have mean pK(a) values of 2.8 (+/-0.5) and 3.4 (+/-0.6), respectively, about 0.6 units less than the overall mean values.

Modeling of denatured state for calculation of the electrostatic contribution to protein stability

Existing models of the denatured state of proteins consider only one possible spatial distribution of protein charges and therefore are applicable to a limited number of cases. In this article, a more general framework for the modeling of the denatured state is proposed. It is based on the assumption that the titratable groups of an unfolded protein can adopt a quasi-random distribution restricted by the protein sequence. The model was applied for the calculations of electrostatic interactions in two proteins, barnase and N-terminal domain of the ribosomal protein L9. The calculated free energy of denaturation, DeltaG(pH), reproduces the experimental data better than the commonly used null approximation (NA). It was shown that the seemingly good agreement with experimental data obtained by NA originates from the compensatory effect between the pairwise electrostatic interactions and the desolvation energy of the individual sites. It was also found that the ionization properties of denatured proteins are influenced by the protein sequence.

The effects of ionic strength on protein stability: the cold shock protein family

Continuum electrostatic models are used to examine in detail the mechanism of protein stabilization and destabilization due to salt near physiological concentrations. Three wild-type cold shock proteins taken from mesophilic, thermophilic, and hyperthermophilic bacteria are studied using these methods. The model is validated by comparison with experimental data collected for these proteins. In addition, a number of single point mutants and three designed sequences are examined. The results from this study demonstrate that the sensitivity of protein stability toward salt is correlated with thermostability in the cold shock protein family. The calculations indicate that the mesophile is stabilized by the presence of salt while the thermophile and hyperthermophile are destabilized. A decomposition of the salt influence at a residue level permits identification of regions of the protein sequences that contribute toward the observed salt-dependent stability. This model is used to rationalize the effect of various point mutations with regard to sensitivity toward salt. Finally, it is demonstrated that designed cold shock protein variants exhibit electrostatic properties similar to the natural thermophilic and hyperthermophilic proteins.

Measurement of side-chain carboxyl pK(a) values of glutamate and aspartate residues in an unfolded protein by multinuclear NMR spectroscopy

A triple-resonance NMR pulse scheme is presented for measuring aspartic and glutamic acid side-chain pK(a) values in unfolded protein states where chemical shift overlap is limiting. The experiment correlates side-chain carboxyl carbon chemical shifts of these residues with the backbone amide proton chemical shift of the following residue. The methodology is applied to an (15)N, (13)C labeled sample of the N-terminal SH3 domain of the Drosophila protein drk, which exists in equilibrium between folded (F(exch)) and unfolded (U(exch)) states under nondenaturing conditions. Residue-specific pK(a) values of side-chain carboxyl groups are presented for the first time for an unfolded protein (drk U(exch) state), determined from a pH titration. Results indicate that deviations from pK(a) values measured for model compounds are likely due to local effects, while long-range electrostatic interactions appear to be of minor importance for this protein.

Residual electrostatic effects in the unfolded state of the N-terminal domain of L9 can be attributed to nonspecific nonlocal charge-charge interactions

Residual electrostatic interactions in the unfolded state of the N-terminal domain of L9 (NTL9) were found by Kuhlman et al. [(1999) Biochemistry 38, 4896-4903]. These residual interactions are analyzed here by the Gaussian-chain model [Zhou, H.-X. (2002) Proc. Natl. Acad. Sci. U.S.A. 99, 3569-3574]. The original model is made more realistic by replacing "standard" model-compound pK(a) values for ionizable groups by those measured by Kuhlman et al. in peptide fragments of NTL9. The predicted pH dependence of the unfolding free energy is in agreement with experiment over the pH range of 1-7 at ionic strengths of 100 and 750 mM. This indicates that the residual electrostatic effects in the unfolded state of NTL9 can be attributed to nonspecific nonlocal charge-charge interactions.

Measurement of electrostatic interactions in protein folding with the use of protein charge ladders

This paper describes a new method for the measurement of the role of interactions between charged groups on the energetics of protein folding. This method uses capillary electrophoresis (CE) and protein charge ladders (mixtures of protein derivatives that differ incrementally in number of charged groups) to measure, in a single set of electrophoresis experiments, the free energy of unfolding (DeltaG(D-N)) of alpha-lactalbumin (alpha-LA) as a function of net charge. These same data also yield the hydrodynamic radius, R(H), and net charge measured by CE, Z(CE), of the folded and denatured proteins. Alpha-LA unfolds to a compact denatured state under mildly alkaline conditions; a small increase in R(H) (11%, 2 A) coincides with a large increase in Z(CE) (71%, -4 charge units), relative to the folded state. The increase in Z(CE), in turn, predicts a large pH dependence of free energy of unfolding (-22 kJ/mol per unit increase in pH), due to differences in proton binding in the folded and denatured states. The free energy of unfolding correlates with the square of net charge of the members of the charge ladder. The differential dependence of DeltaG(D-N) on net charge for holo-alpha-LA, (partial differential) DeltaG(D-N)/(partial differential)Z = -0.14Z kJ/mol per unit of charge. This dependence of DeltaG(D-N) on net charge is a result of a net electrostatic repulsion among charge groups on the protein. These results, together with data from pH titrations, show that both the effects of electrostatic repulsion and differences in proton binding in the folded and denatured states can play an important role in the pH dependence of this protein; the relative magnitude of these effects varies with pH. The combination of charge ladders and CE is a rapid and efficient tool that measures the contributions of electrostatics to the energetics of protein folding, and the size and charge of proteins as they unfold. All this information is obtained from a single set of electrophoresis experiments.

A Gaussian-chain model for treating residual charge-charge interactions in the unfolded state of proteins

Characterization of the unfolded state is essential for understanding the protein folding problem. In the unfolded state, a protein molecule samples vastly different conformations. Here I present a simple theoretical method for treating residual charge-charge interactions in the unfolded state. The method is based on modeling an unfolded protein as a Gaussian chain. After sampling over all conformations, the electrostatic interaction energy between two charged residues (separated by l peptide bonds) is given by W = 332(6/pi)(1/2)[1 - pi(1/2)xexp(x(2))erfc(x)]/epsilond, where d = bl(1/2) + s and x = kappad/6(1/2). In unfolded barnase, the residual interactions lead to downward pK(a) shifts of approximately 0.33 unit, in agreement with experiment. pK(a) shifts in the unfolded state significantly affect pH dependence of protein folding stability, and the predicted effects agree very well with experimental results on barnase and four other proteins. For T4 lysozyme, the charge reversal mutation K147E is found to stabilize the unfolded state even more than the folded state (1.39 vs. 0.46 kcal/mol), leading to the experimentally observed result that the mutation is net destabilizing for the folding. The Gaussian-chain model provides a quantitative characterization of the unfolded state and may prove valuable for elucidating the energetic contributions to the stability of thermophilic proteins and the energy landscape of protein folding.

Model for calculation of electrostatic interactions in unfolded proteins

An approach for the calculation of electrostatic interactions and titration properties of unfolded polypeptide chains (denatured proteins) is proposed. It is based on a simple representation of the denatured proteins as a state with titratable sites distributed on the surface of a sphere, radius of which is assumed to be equal to the radius of gyration, R(g), of an unfolded molecule. Distances between the charges, d, obey constraints arising from the protein sequence. Criteria for evaluation of the parameters R(g) and d were obtained from computer simulations on a polypeptide consisting of 20 identical amino acids (polylysine). The model was applied for calculation of titration curves of denatured barnase and staphylococcal nuclease. It was demonstrated that the approach proposed gives considerably better agreement with the experimental data than the commonly used null approximation. It was also found that titration properties of denatured proteins are slightly, but distinguishably influenced by the amino-acid sequence of the protein.

Native-state conformational dynamics of GART: a regulatory pH-dependent coil-helix transition examined by electrostatic calculations

Glycinamide ribonucleotide transformylase (GART) undergoes a pH-dependent coil-helix transition with pK(a) approximately 7. An alpha-helix is formed at high pH spanning 8 residues of a 21-residue-long loop, comprising the segment Thr120-His121-Arg122-Gln123-Ala124-Leu125-Glu126-Asn127. To understand the electrostatic nature of this loop-helix, called the activation loop-helix, which leads to the formation and stability of the alpha-helix, pK(a) values of all ionizable residues of GART have been calculated, using Poisson-Boltzmann electrostatic calculations and crystallographic data. Crystallographic structures of high and low pH E70A GART have been used in our analysis. Low pK(a) values of 5.3, 5.3, 3.9, 1.7, and 4.7 have been calculated for five functionally important histidines, His108, His119, His121, His132, and His137, respectively, using the high pH E70A GART structure. Ten theoretical single and double mutants of the high pH E70A structure have been constructed to identify pairwise interactions of ionizable residues, which have aided in elucidating the multiplicity of electrostatic interactions of the activation loop-helix, and the impact of the activation helix on the catalytic site. Based on our pK(a) calculations and structural data, we propose that: (1) His121 forms a molecular switch for the coil-helix transition of the activation helix, depending on its protonation state; (2) a strong electrostatic interaction between His132 and His121 is observed, which can be of stabilizing or destabilizing nature for the activation helix, depending on the relative orientation and protonation states of the rings of His121 and His132; (3) electrostatic interactions involving His119 and Arg122 play a role in the stability of the activation helix; and (4) the activation helix contains the helix-promoting sequence Arg122-Gln123-Ala124-Leu125-Glu126, but its alignment relative to the N and C termini of the helix is not optimal, and is possibly of a destabilizing nature. Finally, we provide electrostatic evidence that the formation and closure of the activation helix create a hydrophobic environment for catalytic-site residue His108, to facilitate catalysis.

Prediction of functionally important residues based solely on the computed energetics of protein structure

Catalytic and other functionally important residues in proteins can often be mutated to yield more stable proteins. Many of these residues are charged residues that are located in electrostatically unfavorable environments. Here it is demonstrated that because continuum electrostatics methods can identify these destabilizing residues, the same methods can also be used to identify functionally important residues in otherwise uncharacterized proteins. To establish this point, detailed calculations are performed on six proteins for which good structural and mutational data are available from experiments. In all cases it is shown that functionally important residues known to be destabilizing experimentally are among the most destabilizing residues found in the calculations. A larger scale analysis performed on 216 different proteins demonstrates the existence of a general relationship between the calculated electrostatic energy of a charged residue and its degree of evolutionary conservation. This relationship becomes obscured when electrostatic energies are calculated using Coulomb's law instead of the more complete continuum electrostatics method. Finally, in a first predictive application of the method, calculations are performed on three proteins whose structures have recently been reported by a structural genomics consortium.

Calculation of ensembles of structures representing the unfolded state of an SH3 domain

The N-terminal SH3 domain of drk (drkN SH3 domain) exists in equilibrium between a folded (F(exch)) and an unfolded (U(exch)) form under non-denaturing conditions. In order to further our previous descriptions of the U(exch) state, we have developed a protocol for calculating ensembles of structures, based on experimental spectroscopic data, which broadly represent the unfolded state. A large number of unfolding trajectories were generated, starting from the folded state structure of the protein, in order to provide a reasonable sampling of the conformational space accessible to this sequence. Unfolded state ensembles have been "calculated" using a newly developed program ENSEMBLE, which optimizes the population weights assigned to each structure based on experimental properties of the U(exch) state. Pseudo-energy terms for nuclear Overhauser effects, J-coupling constants, (13)C chemical shifts, translational diffusion coefficients and tryptophan ring burial based on NMR and fluorescence data have been implemented. The population weight assignment procedure was performed for different starting ensembles. Small numbers of structures (<60) dominate the final ensembles compared to the total number in the starting ensembles, suggesting that the drkN SH3 domain U(exch) state can be described by a limited number of lower-energy conformations. The calculated U(exch) state ensembles are much more compact than a "random coil" chain, with significant native-like residual structure observed. In particular, a sizable population of conformers having the n-src loop and distal beta-hairpin structures exist in the calculated U(exch) state ensembles, and Trp36 is involved in a large number of interactions, both native and non-native.

To charge or not to charge?

The ability to engineer proteins with increased thermostability will profoundly broaden their practical applications. Recent experimental results show that optimization of charge-charge interactions on the surface of proteins can be a useful strategy in the design of thermostable enzymes. Results also indicate a possibility that such optimized interactions provide structural determinants for enhanced stability of proteins from thermophilic organisms. In this article, the general strategy for design of thermostable proteins and perspectives for future studies are discussed.

Macromolecular electrostatics: continuum models and their growing pains

Theoretical understanding of macromolecular electrostatics has advanced substantially over the past year. Continuum models have given promising results for calculating protein-ligand binding free energy differences, as well as pK(a)s and redox properties, particularly with explicit treatment of multiple conformers. Generalized Born and other techniques have led to the first molecular dynamics simulations of proteins and RNA with continuum solvent. Continuum and microscopic descriptions of dielectric relaxation have been critically compared.

Charge-charge interactions influence the denatured state ensemble and contribute to protein stability

Several recent studies have shown that it is possible to increase protein stability by improving electrostatic interactions among charged groups on the surface of the folded protein. However, the stability increases are considerably smaller than predicted by a simple Coulomb's law calculation, and in some cases, a charge reversal on the surface leads to a decrease in stability when an increase was predicted. These results suggest that favorable charge-charge interactions are important in determining the denatured state ensemble, and that the free energy of the denatured state may be decreased more than that of the native state by reversing the charge of a side chain. We suggest that when the hydrophobic and hydrogen bonding interactions that stabilize the folded state are disrupted, the unfolded polypeptide chain rearranges to compact conformations with favorable long-range electrostatic interactions. These charge-charge interactions in the denatured state will reduce the net contribution of electrostatic interactions to protein stability and will help determine the denatured state ensemble. To support this idea, we show that the denatured state ensemble of ribonuclease Sa is considerably more compact at pH 7 where favorable charge-charge interactions are possible than at pH 3, where unfavorable electrostatic repulsion among the positive charges causes an expansion of the denatured state ensemble. Further support is provided by studies of the ionic strength dependence of the stability of charge-reversal mutants of ribonuclease Sa. These results may have important implications for the mechanism of protein folding.