Effect of backbone cyclization on protein folding stability: chain entropies of both the unfolded and the folded states are restricted

Circular versions of a large number of proteins have been designed by connecting the N and C termini via peptide linkers. A motivation for these designs is the assumed enhancement in folding stability, because backbone cyclization reduces the chain entropy of the unfolded state. Here, it is recognized that backbone cyclization also reduces the chain entropy of a flexible peptide linker in the folded state. Specifically, the end-to-end distance of the linker is restricted to fluctuations around the average displacement between the N and C termini of the folded protein. The balance of the chain-entropy reductions in the folded and unfolded states is used to predict the change in the unfolding free energy, deltadeltaG(cycl), by backbone cyclization. Predicted values of deltadeltaG(cycl) are in quantitative agreement with results of a careful study on cyclizing the 34 residue PIN1 WW domain by linkers with two to seen residues. The experimental results of an optimal linker length l=4 and a maximum stabilization of 1.7 kcal/mol are reproduced. Calculations of deltadeltaG(cycl) for a broad selection of circular proteins suggest that the stabilizing effect of backbone cyclization is modest, reflecting entropy reductions in both the unfolded and the folded states.     

Protein folding and binding in confined spaces and in crowded solutions

Simple theoretical models are presented to illustrate the effects of spatial confinement and macromolecular crowding on the equilibria and rates of protein folding and binding. Confinement is expected to significantly stabilize the folded state, but for crowding only a marginal effect on protein stability is expected. In confinement the unfolded chain is restricted to a cage but in crowding the unfolded chain may explore different interstitial voids. Because confinement and crowding eliminate the more expanded conformations of the unfolded state, folding from the compact unfolded state is expected to speed up. Crowding will shift the binding equilibrium of proteins toward the bound state. The significant slowing down in protein diffusion by crowding, perhaps beneficial for chaperonin action, could result in a decrease in protein binding rates.     

Effects of pH, salt, and macromolecular crowding on the stability of FK506-binding protein: an integrated experimental and theoretical study

Environmental variables can exert significant influences on the folding stability of a protein, and elucidating these influences provides insight on the determinants of protein stability. Here, experimental data on the stability of FKBP12 are reported for the effects of three environmental variables: pH, salt, and macromolecular crowding. In the pH range of 5-9, contribution to the pH dependence of the unfolding free energy from residual charge-charge interactions in the unfolded state was found to be negligible. The negligible contribution was attributed to the lack of sequentially nearest neighboring charged residues around groups that titrate in the pH range. KCl lowered the stability of FKBP12 and the E31Q/D32N double mutant at small salt concentrations but raised stability after approximately 0.5 M salt. Such a turnover behavior was accounted for by the balance of two opposing types of protein-salt interactions: the Debye-Hückel type, modeling the response of the ions to protein charges, favors the unfolded state while the Kirkwood type, accounting for the disadvantage of the ions moving toward the low-dielectric protein cavity from the bulk solvent, disfavors the unfolded state. Ficoll 70 as a crowding agent was found to have a modest effect on protein stability, in qualitative agreement with a simple model suggesting that the folded and unfolded states are nearly equally adversely affected by macromolecular crowding. For any environmental variable, it is the balance of its effects on the folded and unfolded states that determines the outcome on the folding stability.     

pK(a) values for the unfolded state under native conditions explain the pH-dependent stability of PGB1

Understanding the role of electrostatics in protein stability requires knowledge of these interactions in both the folded and unfolded states. Electrostatic interactions can be probed experimentally by characterizing ionization equilibria of titrating groups, parameterized as pK_a values. However, pK_a values of the unfolded state are rarely accessible under native conditions, where the unfolded state has a very low population. Here, we report pK_a values under nondenaturing conditions for two unfolded fragments of the protein G B1 domain that mimic the unfolded state of the intact protein. pK_a values were determined for carboxyl groups by monitoring their pH-dependent ¹³C chemical shifts. Monte Carlo simulations using a Gaussian chain model provide corrections for changes in electrostatic interactions that arise from fragmentation of the protein. Most pK_a values for the unfolded state agree well with model values, but some residues show significant perturbations that can be rationalized by local electrostatic interactions. The pH-dependent stability was calculated from the experimental pK_a values of the folded and unfolded states and compared to experimental stability data. The use of experimental pK_a values for the unfolded state results in significantly improved agreement with experimental data, as compared to calculations based on model data alone.     

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

Computational techniques based on continuum electrostatics treatments have been successful in predicting and interpreting the pKa values of ionizable amino acids in folded proteins. Despite this progress, efforts to reproduce the pH-dependence of protein stability have met with only limited success: agreement with experimental results has been only qualitative. It has been argued previously that the most likely reason for discrepancies is the presence of residual electrostatic interactions in the unfolded state, which cause pKa values to be shifted from their model compound values. Here we show that by constructing atomistic models of the unfolded state with a simple molecular mechanics protocol that uses the native state as a starting point, much improved reproduction of pH effects on protein stability can be obtained. In contrast, when a fully extended model of the unfolded state is used, no such improvement is obtained, a result that suggests that local interactions with residues nearby in the sequence are not sufficient to properly account for the pKa shifts in the unfolded state. In comparison to model compound values, the pKa values of acidic residues in "native-like" unfolded states are typically found to be shifted downwards by approximately 0.3 pH unit, in good agreement with the average downward shift deduced from experimental measurements. Given its success in the present situation, the protocol employed here for developing simple models of the unfolded state may prove useful in other computer simulation applications.     

Dimensions,energetics, and denaturant effects of the protein unstructured state

Determining the energetics of the unfolded state of a protein is essential for understanding the folding mechanics of ordered proteins and the structure–function relation of intrinsically disordered proteins. Here, we adopt a coil‐globule transition theory to develop a general scheme to extract interaction and free energy information from single‐molecule fluorescence resonance energy transfer spectroscopy. By combining protein stability data, we have determined the free energy difference between the native state and the maximally collapsed denatured state in a number of systems, providing insight on the specific/nonspecific interactions in protein folding. Both the transfer and binding models of the denaturant effects are demonstrated to account for the revealed linear dependence of inter‐residue interactions on the denaturant concentration, and are thus compatible under the coil‐globule transition theory to further determine the dimension and free energy of the conformational ensemble of the unfolded state. The scaling behaviors and the effective θ‐state are also discussed.     

Electrostatic contributions to the stability of the GCN4 leucine zipper structure

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

Role of the charge-charge interactions in defining stability and halophilicity of the CspB proteins

Charge-charge interactions on the surface of native proteins are important for protein stability and can be computationally redesigned in a rational way to modulate protein stability. Such computational effort led to an engineered protein, CspB-TB that has the same core as the mesophilic cold shock protein CspB-Bs from Bacillus subtilis, but optimized distribution of charge-charge interactions on the surface. The CspB-TB protein shows an increase in the transition temperature by 20 degrees C relative to the unfolding temperature of CspB-Bs. The CspB-TB and CspB-Bs protein pair offers a unique opportunity to further explore the energetics of charge-charge interactions as the substitutions at the same sequence positions are done in largely similar structural but different electrostatic environments. In particular we addressed two questions. What is the contribution of charge-charge interactions in the unfolded state to the protein stability and how amino acid substitutions modulate the effect of increase in ionic strength on protein stability (i.e. protein halophilicity). To this end, we experimentally measured the stabilities of over 100 variants of CspB-TB and CspB-Bs proteins with substitutions at charged residues. We also performed computational modeling of these protein variants. Analysis of the experimental and computational data allowed us to conclude that the charge-charge interactions in the unfolded state of two model proteins CspB-Bs and CspB-TB are not very significant and computational models that are based only on the native state structure can adequately, i.e. qualitatively (stabilizing versus destabilizing) and semi-quantitatively (relative rank order), predict the effects of surface charge neutralization or reversal on protein stability. We also show that the effect of ionic strength on protein stability (protein halophilicity) appears to be mainly due to the screening of the long-range charge-charge interactions.     

SQ/TQ cluster domains: concentrated ATM/ATR kinase phosphorylation site regions in DNA-damage-response proteins

ATM/ATR-like protein kinases play central roles in the maintenance of genome stability and phosphorylate numerous substrates in response to DNA damage, preferentially on SQ or TQ motifs. ATM/ATR substrates often contain several closely spaced SQ/TQ motifs in regions that have been termed SQ/TQ cluster domains (SCDs). SCDs are now considered a structural hallmark of DNA-damage-response proteins. Mutational analyses of a number of SCD-containing proteins indicate that multisite phosphorylation of SQ/TQ motifs is required for normal DNA-damage responses, most commonly by mediating protein-protein interactions in the formation of DNA-damage-induced complexes. SCD sequences are highly diverse and these domains may be largely unfolded in their native state rather than adopting a common three-dimensional fold. Structural disorder of SCDs could be advantageous for efficient phosphorylation by ATM/ATR kinases and also enable them to be molded into distinct conformations to facilitate flexible interactions with multiple binding partners.     

Protein folding in confined and crowded environments

Confinement and crowding are two major factors that can potentially impact protein folding in cellular environments. Theories based on considerations of excluded volumes predict disparate effects on protein folding stability for confinement and crowding: confinement can stabilize proteins by over 10k_BT but crowding has a very modest effect on stability. On the other hand, confinement and crowding are both predicted to favor conformations of the unfolded state which are compact, and consequently may increase the folding rate. These predictions are largely borne out by experimental studies of protein folding under confined and crowded conditions in the test tube. Protein folding in cellular environments is further complicated by interactions with surrounding surfaces and other factors. Concerted theoretical modeling and test-tube and in vivo experiments promise to elucidate the complexity of protein folding in cellular environments.     

Quantitative understanding of the energy transfer between fluorescent proteins connected via flexible peptide linkers

The fusion of different protein domains via peptide linkers is a powerful, modular approach to obtain proteins with new functions. A detailed understanding of the conformational behavior of peptide linkers is important for applications such as fluorescence resonance energy transfer (FRET)-based sensor proteins and multidomain proteins involved in multivalent interactions. To investigate the conformational behavior of flexible glycine- and serine-containing peptide linkers, we constructed a series of fusion proteins of enhanced cyan and yellow fluorescent proteins (ECFP-linker-EYFP) in which the linker length was systematically varied by incorporating between 1 and 9 GGSGGS repeats. As expected, both steady-state and time-resolved fluorescence measurements showed a decrease in energy transfer with increasing linker length. The amount of energy transfer observed in these fusion proteins can be quantitatively understood by simple models that describe the flexible linker as a worm-like chain with a persistence length of 4.5 A or a Gaussian chain with a characteristic ratio of 2.3. The implications of our results for understanding the properties of FRET-based sensors and other fusion proteins with Gly/Ser linkers are discussed.     

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.     

Kinetic consequences of native state optimization of surface-exposed electrostatic interactions in the Fyn SH3 domain

Optimization of surface exposed charge-charge interactions in the native state has emerged as an effective means to enhance protein stability; but the effect of electrostatic interactions on the kinetics of protein folding is not well understood. To investigate the kinetic consequences of surface charge optimization, we characterized the folding kinetics of a Fyn SH3 domain variant containing five amino acid substitutions that was computationally designed to optimize surface charge-charge interactions. Our results demonstrate that this optimized Fyn SH3 domain is stabilized primarily through an eight-fold acceleration in the folding rate. Analyses of the constituent single amino acid substitutions indicate that the effects of optimization of charge-charge interactions on folding rate are additive. This is in contrast to the trend seen in folded state stability, and suggests that electrostatic interactions are less specific in the transition state compared to the folded state. Simulations of the transition state using a coarse-grained chain model show that native electrostatic contacts are weakly formed, thereby making the transition state conducive to nonspecific, or even nonnative, electrostatic interactions. Because folding from the unfolded state to the folding transition state for small proteins is accompanied by an increase in charge density, nonspecific electrostatic interactions, that is, generic charge density effects can have a significant contribution to the kinetics of protein folding. Thus, the interpretation of the effects of amino acid substitutions at surface charged positions may be complicated and consideration of only native-state interactions may fail to provide an adequate picture.     

Charge effects on folded and unfolded proteins

We develop a theory for the effects of charge on the stabilization of globular proteins. The folding process is modeled as occurring through a fictitious intermediate state along a two-part thermodynamic pathway in which the molecule (i) increases its density and then (ii) rearranges its ionic groups to the protein surface. The equilibrium for the binding of protons in salt solutions is assumed to be driven by the electrical potential due to the charge distribution, in addition to the intrinsic binding affinity and bulk proton concentration. The potential is calculated for inside and outside a porous sphere model of the protein using the Poisson-Boltzmann relation, wherein the interior dielectric constant is taken to be a linear function of the chain density. The model predicts the slope of the titration curves for native myoglobin in agreement with experiments by Breslow and Gurd (1962). From the similar experiments on the unfolded state, and from the experiments of Privalov et al. (1986) on the intrinsic viscosity of the unfolded molecules, the theory shows that the unfolded state has a much higher density than a chain in a theta solvent and that the density increases with ionic strength. In addition, from the free energy of proton binding to the protein, we also calculate the electrostatic contributions to protein stability, a major contribution deriving from changes in ionization. We consider the example of the stability of myoglobin as a function of pH, ionic strength, and ionic groups buried in the native protein structure. We show that although maximum stability of most proteins should occur at their isoelectric point, the burial of nontitratable groups should lead to maximum stabilities at pH values other than the isoelectric point.     

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.     

Effects of urea and guanidine · HCl on the folding and unfolding of pancreatic trypsin inhibitor

Concentrated solutions of urea and of guanidine · HCl produced a random spectrum of single-disulphide forms of the polypeptide chain of the pancreatic trypsin inhibitor. Guanidine · HCl also unfolded completely, with accompanying interchange of disulphide bonds, the two-disulphide form of this protein in the native-like conformation; urea produced an equilibrium mixture in which one-quarter of the molecules had the native-like conformation and disulphide bonds. The unfolded forms of the protein in the denaturants were very flexible polypeptide chains. The observations suggest that urea and guanidine · HCl are denaturants because they produce essentially equally favourable solvation of all portions of a polypeptide.The energetics of the conformational transitions involved in folding and unfolding of the inhibitor were determined in urea and compared with those observed in its absence. The denaturant lowers the stability of the native, folded inhibitor relative to that of the reduced, unfolded state by 6.5 kilocalories per mole; the greatest part of this apparent free-energy difference was expressed at the two-disulphide stage of folding. The results are consistent with other indications that most of the favourable interactions stabilizing the native conformation of this protein are not encountered until the final stage of folding, when all may occur simultaneously.The unfolded one- and two-disulphide species produced in guanidine · HCl were trapped, and their rearrangement to the normal intermediates followed after removal of the denaturant. The random single-disulphide species, with one exception, reverted very rapidly to the non-random spectrum of intermediates normally observed during folding; this confirms that these species are normally rapidly interconverted and that normal refolding of the reduced protein is not dependent kinetically upon residual stable conformation in the reduced protein. The unfolded two-disulphide species refolded to the native-like conformation more slowly, but appeared to pass through the same intermediates normally observed during refolding from the fully reduced state.     

Beta-turn propensities as paradigms for the analysis of structural motifs to engineer protein stability.

The thermodynamic stability of a protein provides an experimental metric for the relationship of protein sequence and native structure. We have investigated an approach based on an analysis of the structural database for stability engineering of an immunoglobulin variable domain. The most frequently occurring residues in specific positions of beta-turn motifs were predicted to increase the folding stability of mutants that were constructed by site-directed mutagenesis. Even in positions in which different residues are conserved in immunoglobulin sequences, the predictions were confirmed. Frequently, mutants with increased beta-turn propensities display increased folding cooperativities, suggesting pronounced effects on the unfolded state independent of the expected effect on conformational entropy. We conclude that structural motifs with predominantly local interactions can serve as templates with which patterns of sequence preferences can be extracted from the database of protein structures. Such preferences can predict the stability effects of mutations for protein engineering and design.     

Nonnative Electrostatic Interactions Can Modulate Protein Folding: Molecular Dynamics with a Grain of Salt

In recent years, a growing number of protein folding studies have focused on the unfolded state, which is now recognized as playing a major role in the folding process. Some of these studies show that interactions occurring in the unfolded state can significantly affect the stability and kinetics of the protein folding reaction. In this study, we modeled the effect of electrostatic interactions, both native and nonnative, on the folding of three protein systems that underwent selective charge neutralization or reversal or complete charge suppression. In the case of the N-terminal L9 protein domain, our results directly attribute the increase in thermodynamic stability to destabilization of the unfolded ensemble, reaffirming the experimental observations. These results provide a deeper structural insight into the ensemble of the unfolded state and predict a new mutation site for increased protein stability. In the second case, charge reversal mutations of RNase Sa affected protein stability, with the destabilizing mutations being less destabilizing at higher salt concentrations, indicating the formation of charge-charge interactions in the unfolded state. In the N-terminal L9 and RNase Sa systems, changes in electrostatic interactions in the unfolded state that cause an increase in free energy had an overall compaction effect that suggests a decrease in entropy. In the third case, in which we compared the β-lactalbumin and hen egg-white lysozyme protein homologues, we successfully eliminated differences between the folding kinetics of the two systems by suppressing electrostatic interactions, supporting previously reported findings. Our coarse-grained molecular dynamics study not only reproduces experimentally reported findings but also provides a detailed molecular understanding of the elusive unfolded-state ensemble and how charge-charge interactions can modulate the biophysical characteristics of folding.     

Effects of excluded volume upon protein stability in covalently cross-linked proteins with variable linker lengths

To explore the effects of molecular crowding and excluded volume upon protein stability, we used a series of cross-linking reagents with nine different single-cysteine mutants of staphylococcal nuclease to make covalently linked dimers. These cross-linkers ranged in length from 10.5 to 21.3 A, compelling separations which would normally be found only in the most concentrated protein solutions. The stabilities of the dimeric proteins and monomeric controls were determined by guanidine hydrochloride and thermal denaturation. Dimers with short linkers tend to exhibit pronounced three-state denaturation behavior, as opposed to the two-state behavior of the monomeric controls. Increasing linker length leads to less pronounced three-state behavior. The three-state behavior is interpreted in a three-state model where cross-linked native protein dimer, N-N, interconverts in a two-state transition with a dimer where one protein subunit is denatured, N-D. The remaining native protein in turn can denature in another two-state transition to a state, D-D, in which both tethered proteins are denatured. Three-state behavior is best explained by excluded volume effects in the denatured state. For many dimers, linkers longer than 17 A removed most three-state character. This sets a limit on the flexibility and size of the denatured state. Notably, in contradiction to theoretical predictions, these cross-linked dimers were not stabilized. The failure of these predictions is possibly due to neglect of the alteration in hydrophobic exposure that accompanies any significant reduction in the conformational space of the denatured state.