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.     

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.     

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.     

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.     

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.     

A shorter peptide model from staphylococcal nuclease for the folding-unfolding equilibrium of a beta-hairpin shows that unfolded state has significant contribution from compact conformational states

It is important to understand the conformational features of the unfolded state in equilibrium with folded state under physiological conditions. In this paper, we consider a short peptide model LMYKGQPM from staphylococcal nuclease to model the conformational equilibrium between a hairpin conformation and its unfolded state using molecular dynamics simulation under NVT conditions at 300K using GROMOS96 force field. The free energy landscape has overall funnel-like shape with hairpin conformations sampling the minima. The "unfolded" state has a higher free energy of approximately 12kJ/mol with respect to native hairpin minimum and occupies a plateau region. We find that the unfolded state has significant contributions from compact conformations. Many of these conformations have hairpin-like topology. Further, these compact conformational forms are stabilized by hydrophobic interactions. Conversion between native and non-native hairpins occurs via unfolded states. Frequent conversions between folded and unfolded hairpins are observed with single exponential kinetics. We compare our results with the emerging picture of unfolded state from both experimental and theoretical studies.     

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.     

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.     

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.     

Stochastic simulation of structural properties of natively unfolded and denatured proteins

A new simulation strategy based on a stochastic process has been developed and tested to study the structural properties of the unfolded state of proteins at the atomistic level. The procedure combines a generation algorithm to produce representative uncorrelated atomistic microstructures and an original relaxation method to minimize repulsive non-bonded interactions. Using this methodology, a set of 14 unfolded proteins, including seven natively unfolded proteins as well as seven "classical" proteins experimentally described in denaturation conditions, has been investigated. Comparisons between the calculated and available experimental values of several properties, at hydrodynamic and atomic level, used to describe the unfolded state, such as the radius of gyration, the maximum length, the hydrodynamic radius, the diffusion coefficient, the sedimentation coefficient, and the NMR chemical shifts, reflect a very good agreement. Furthermore, our results indicate that the relationship between the radius of gyration and the hydrodynamic radius deviates from the Zimm's theory of polymer dynamics for random coils, as was recently observed using single-molecule fluorescent methods. Simulations reveal that the interactions between atoms separated by three chemical bonds (1-4 interactions) play a crucial role in the generation process, suggesting that the unfolded state is essentially governed by bonding and short-range non-bonding interactions.     

Highly perturbed pKa values in the unfolded state of hen egg white lysozyme

The majority of pK_a values in protein unfolded states are close to the amino acid model pK_a values, thus reflecting the weak intramolecular interactions present in the unfolded ensemble of most proteins. We have carried out thermal denaturation measurements on the WT and eight mutants of HEWL from pH 1.5 to pH 11.0 to examine the unfolded state pK_a values and the pH dependence of protein stability for this enzyme. The availability of accurate pK_a values for the folded state of HEWL and separate measurements of mutant-induced effects on the folded state pK_a values, allows us to estimate the pK_a values of seven acidic residues in the unfolded state of HEWL. Asp-48 and Asp-66 display pK_a values of 2.9 and 3.1 in our analysis, thus representing the most depressed unfolded state pK_a values observed to date. We observe a strong correlation between the folded state pK_a values and the unfolded state pK_a values of HEWL, thus suggesting that the unfolded state of HEWL possesses a large degree of native state characteristics.     

A folding model of α-lactalbumin deduced from the three-state denaturation mechanism

It has been shown that α-lactalbumin undergoes a three-state denaturation, involving a helical intermediate state, on treatment with guanidine hydrochloride. The unfolding of the protein and the characteristics of the intermediate state are examined by means of circular dichroism, difference spectra and pH-jump measurements to investigate the temperature dependence and kinetic properties of the unfolding and refolding, the pH dependence of the transition between the intermediate and the fully unfolded states, and the effect of disulphide bond reduction on the stabilization of the intermediate.The results show that the long-range specific interactions such as specific electrostatic interactions and disulphide linkages are not important for stabilizing the intermediate, and that the transition between the intermediate and the fully unfolded states is extremely rapid (a relaxation time of less than one millisecond) and may correspond to the helix-coil transition of a polypeptide backbone. On the other hand, the activation parameters of the transition between the native and the intermediate states have suggested that the final stabilization by charge-pair interactions is preceded by hydrophobic interactions in the process of going from the intermediate to the native state.The mechanism of folding of the protein is discussed, and the folding process from the fully unfolded to the native state is apparently divided into at least three main steps: (1) the formation of incipient helical structures dictated by local interactions; (2) the packing of the helical segments accompanied with hydrophobic interactions; (3) the final stabilization by the electrostatic interactions. The relevance to the current theoretical results on protein folding is also discussed.     

Is the hydrophobic effect stabilizing or destabilizing in proteins? The contribution of disulphide bonds to protein stability

It has been recently concluded that the hydrophobic effect, hitherto regarded as a major driving force in the folding of proteins, destabilizes the folded state relative to the unfolded state. We summarize the properties of the hydrophobic effect obtained from solvent transfer experiments and show that the recent conclusion is an artifact of crosslinking in the unfolded state, caused by disulphide bonds, metals or cofactors. We show that, for the proteins in the data set, crosslinks surprisingly destabilize folded structures entropically, but stabilize them enthalpically to a greater extent. We also calculate non-polar surface areas of these unfolded proteins. These surface areas are decreased by crosslinks. The unfolded state of proteins lacking constraints, such as myoglobin, is well approximated by a mixture of residues containing alpha-helical and beta-sheet dihedral angles. Surface areas of unfolded proteins cannot be obtained by summing the surface areas of individual residues, since this ignores any unavoidable side-chain-side-chain interactions.     

Equilibrium and kinetics of the thermal unfolding of alpha-lactalbumin. The relation to its folding mechanism.

The thermal unfolding of alpha-lactalbumin has been studied by equilibrium measurements of aromatic difference spectra, and by kinetic measurements of the Joule heating temperature-jump. The unfolding at neutral pH is a reversible two-state transition. The equilibrium transition curves are analyzed by the nonlinear squares method, which gives correct values of thermodynamic parameters based on the data in a wide range of temperature. The results are discussed in relation to the previous studies on the unfolding by guanidine hydrochloride or by acid. The thermally unfolded state, a partially unfolded species, is shown to be thermodynamically similar to but not identical with the acid state. The folding pathway deduced from the kinetic results is essentially consistent with the folding model of alpha-lactalbumin proposed previously. Large decreases in entropy and in heat capacity during the reversed activation suggest the packing of the folded segments by hydrophobic interactions, while the forward activation shows a marked temperature dependence, probably caused by the disruption of specific long-range interactions.     

An effective solvent theory connecting the underlying mechanisms of osmolytes and denaturants for protein stability

An all-atom Gō model of Trp-cage protein is simulated using discontinuous molecular dynamics in an explicit minimal solvent, using a single, contact-based interaction energy between protein and solvent particles. An effective denaturant or osmolyte solution can be constructed by making the interaction energy attractive or repulsive. A statistical mechanical equivalence is demonstrated between this effective solvent model and models in which proteins are immersed in solutions consisting of water and osmolytes or denaturants. Analysis of these studies yields the following conclusions: 1), Osmolytes impart extra stability to the protein by reducing the entropy of the unfolded state. 2), Unfolded states in the presence of osmolyte are more collapsed than in water. 3), The folding transition in osmolyte solutions tends to be less cooperative than in water, as determined by the ratio of van 't Hoff to calorimetric enthalpy changes. The decrease in cooperativity arises from an increase in native structure in the unfolded state, and thus a lower thermodynamic barrier at the transition midpoint. 4), Weak denaturants were observed to destabilize small proteins not by lowering the unfolded enthalpy, but primarily by swelling the unfolded state and raising its entropy. However, adding a strong denaturant destabilizes proteins enthalpically. 5), The folding transition in denaturant-containing solutions is more cooperative than in water. 6), Transfer to a concentrated osmolyte solution with purely hard-sphere steric repulsion significantly stabilizes the protein, due to excluded volume interactions not present in the canonical Tanford transfer model. 7), Although a solution with hard-sphere interactions adds a solvation barrier to native contacts, the folding is nevertheless less cooperative for reasons 1–3 above, because a hard-sphere solvent acts as a protecting osmolyte.     

Destabilization of the Escherichia coli RNase H kinetic intermediate: switching between a two-state and three-state folding mechanism

Escherichia coli RNase H folds through a partially folded kinetic intermediate that mirrors a rarely populated, partially unfolded form detectable by native-state hydrogen exchange under equilibrium conditions. Residue 53 is at the interface of two helices known to be structured in this intermediate. Kinetic refolding studies on mutant proteins varying in size and hydrophobicity at residue 53 support a contribution of hydrophobicity to the stabilities of the kinetic intermediate and the transition state. Packing interactions also play a significant role in the stability of these two states, though they play a much larger role in the native-state stability. One dramatic mutation, I53D, results in the conversion from a three-state to a two-state folding mechanism, which is explained most easily through a simple destabilization of the kinetic intermediate such that it is no longer stable with respect to the unfolded state. These results demonstrate that interactions that stabilize an intermediate can accelerate folding if these same interactions are present in the transition state. Our results are consistent with a hierarchical model of folding, where the intermediate consists of native-like interactions, is on-pathway, and is productive for folding.     

Test for cooperativity in the early kinetic intermediate in lysozyme folding

During the folding of many proteins, collapsed globular states are formed prior to the native structure. The role of these states for the folding process has been widely discussed. Comparison with properties of synthetic homo and heteropolymers had suggested that the initial collapse represented a shift of the ensemble of unfolded conformations to more compact states without major energy barriers. We investigated the folding/unfolding transition of a collapsed state, which transiently populates early in lysozyme folding. This state forms within the dead-time of stopped-flow mixing and it has been shown to be significantly more compact and globular than the denaturant-induced unfolded state. We used the GdmCl-dependence of the dead-time signal change to characterize the unfolding transition of the burst phase intermediate. Fluorescence and far-UV CD give identical unfolding curves, arguing for a cooperative two-state folding/unfolding transition between unfolded and collapsed lysozyme. These results show that collapse leads to a distinct state in the folding process, which is separated from the ensemble of unfolded molecules by a significant energy barrier. NMR, fluorescence and small angle X-ray scattering data further show that some local interactions in unfolded lysozyme exist at denaturant concentrations above the coil-collapse transition. These interactions might play a crucial role in the kinetic partitioning between fast and slow folding pathways.     

The unfolded state of NTL9 is compact in the absence of denaturant

Interest in the unfolded state of proteins has grown with the realization that this state can have considerable structure in the absence of denaturants. Natively unfolded proteins, mutations that unfold proteins under native conditions, and changes in pH that induce unfolding are attractive models for the unfolded state in the absence of denaturant. The unfolded state of the N-terminal domain of ribosomal protein L9 (NTL9) was previously shown to contain significant non-native electrostatic interactions [Cho, J. H., Sato, S., and Raleigh, D. P. (2004) J. Mol. Biol. 338, 827-837]. NTL9 has a mixed alpha-beta structure and folds via a two-state mechanism. We have generated a model of the unfolded state of NTL9 in the absence of denaturant by substitution of an alanine for phenylalanine 5 located in the core of this protein. The CD spectrum of the variant, denoted as F5A, exhibits significantly less structure than the wild type; however, the mean residue ellipticity of F5A at 222 nm (-8200 deg cm(2) dmol(-)(1)) is considerably larger than expected for a fully unfolded protein, indicating that residual secondary structure is populated. F5A also has more residual structure than the urea-unfolded wild type. The stability of F5A is estimated to be at least 1 kcal/mol unfavorable, showing that the unfolded state is populated to 84% or more. NMR pulsed-field gradient measurements yield a hydrodynamic radius of 16.1 A for wild-type NTL9 and 20.8 A for the F5A variant in native buffer. The physiologically relevant unfolded state of wild-type NTL9 is likely to be even more compact than F5A since the mutation should reduce the level of hydrophobic clustering in the unfolded state in the absence of denaturant. The hydrodynamic radius of F5A increases to 25.9 A in 8 M urea, and a value of 23.5 A is obtained for the wild type under similar conditions. The results show that the unfolded state of F5A in the absence of denaturant is more compact and contains more structure than the urea-unfolded form.     

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.     

Salt-Dependent Folding Energy Landscape of RNA Three-Way Junction

RNAs are highly negatively charged chain molecules. Metal ions play a crucial role in RNA folding stability and conformational changes. In this work, we employ the recently developed tightly bound ion (TBI) model, which accounts for the correlation between ions and the fluctuation of ion distributions, to investigate the ion-dependent free energy landscape for the three-way RNA junction in a 16S rRNA domain. The predicted electrostatic free energy landscape suggests that 1), ion-mediated electrostatic interactions cause an ensemble of unfolded conformations narrowly populated around the maximally extended structure; and 2), Mg²⁺ ion-induced correlation effects help bring the helices to the folded state. Nonelectrostatic interactions, such as noncanonical interactions within the junctions and between junctions and helix stems, might further limit the conformational diversity of the unfolded state, resulting in a more ordered unfolded state than the one predicted from the electrostatic effect. Moreover, the folded state is predominantly stabilized by the coaxial stacking force. The TBI-predicted folding stability agrees well with the experimental measurements for the different Na⁺ and Mg²⁺ ion concentrations. For Mg²⁺ solutions, the TBI model, which accounts for the Mg²⁺ ion correlation effect, gives more improved predictions than the Poisson-Boltzmann theory, which tends to underestimate the role of Mg²⁺ in stabilizing the folded structure. Detailed control tests indicate that the dominant ion correlation effect comes from the charge-charge Coulombic correlation rather than the size (excluded volume) correlation between the ions. Furthermore, the model gives quantitative predictions for the ion size effect in the folding energy landscape and folding cooperativity.