How random is a highly denatured protein?

Toward an accurate theoretical framework for describing ensembles for proteins under strongly denaturing conditions

Our focus is on an appropriate theoretical framework for describing highly denatured proteins. In high concentrations of denaturants, proteins behave like polymers in a good solvent and ensembles for denatured proteins can be modeled by ignoring all interactions except excluded volume (EV) effects. To assay conformational preferences of highly denatured proteins, we quantify a variety of properties for EV-limit ensembles of 23 two-state proteins. We find that modeled denatured proteins can be best described as follows. Average shapes are consistent with prolate ellipsoids. Ensembles are characterized by large correlated fluctuations. Sequence-specific conformational preferences are restricted to local length scales that span five to nine residues. Beyond local length scales, chain properties follow well-defined power laws that are expected for generic polymers in the EV limit. The average available volume is filled inefficiently, and cavities of all sizes are found within the interiors of denatured proteins. All properties characterized from simulated ensembles match predictions from rigorous field theories. We use our results to resolve between conflicting proposals for structure in ensembles for highly denatured states.

A structural model for unfolded proteins from residual dipolar couplings and small-angle x-ray scattering

Natively unfolded proteins play key roles in normal and pathological biochemical processes. Despite their importance for function, this category of proteins remains beyond the reach of classical structural biology because of their inherent conformational heterogeneity. We present a description of the intrinsic conformational sampling of unfolded proteins based on residue-specific /Psi propensities from loop regions of a folded protein database and simple volume exclusion. This approach is used to propose a structural model of the 57-aa, natively disordered region of the nucleocapsid-binding domain of Sendai virus phosphoprotein. Structural ensembles obeying these simple rules of conformational sampling are used to simulate averaged residual dipolar couplings (RDCs) and small-angle x-ray scattering data. This protein is particularly informative because RDC data from the equally sized folded and unfolded domains both report on the unstructured region, allowing a quantitative analysis of the degree of order present in this part of the protein. Close agreement between experimental and simulated RDC and small-angle x-ray scattering data validates this simple model of conformational sampling, providing a precise description of local structure and dynamics and average dimensions of the ensemble of sampled structures. RDC data from two urea-unfolded systems are also closely reproduced. The demonstration that conformational behavior of unfolded proteins can be accurately predicted from the primary sequence by using a simple set of rules has important consequences for our understanding of the structure and dynamics of the unstructured state.

Polyelectrolyte-protein complexes: structure and conformation of each specie revealed by SANS

We report here the structure of complexes made of proteins (lysozyme, positively charged) and polyelectrolytes (PSSNa, negatively charged). We stay in conditions where the volume fractions of the components are of the same order and where PSS concentrations correspond to a semidilute regime. The final complexes structure is determined by SANS. We obtain three main types of structures: (i) For a protein excess and for long polyelectrolyte chains, the network preformed by PSS chains still exists but chains are partially shrunk due to cross-linking by lysozyme. Macroscopically, samples are gelled. (ii) For a protein excess and for short polyelectrolyte chains, PSS chains are locally shrunk and do not form a network anymore. Lysozyme and PSS chains are embedded in dense 3-D aggregates that arrange in a fractal network at a larger scale. Macroscopically, samples are liquid. (iii) For a polyelectrolyte excess and whatever the chain length, the internal structure of the lysozyme changes. After an initial strong electrostatic binding, lysozyme is progressively unfolded thanks to a hydrophobic contact with PSS. The two chainlike objects are finally organized in a homogeneous costructure. Macroscopically, samples are liquids.

Many faces of the unfolded state: conformational heterogeneity in denatured yeast cytochrome C

We have measured fluorescence energy-transfer (FET) kinetics from a dansyl fluorophore (Dns) introduced by derivatization of a Cys side-chain to the Fe(III) heme covalently attached to unfolded yeast iso-1 cytochrome c (cyt). To gain a global picture of the unfolded state, we examined variants with the fluorophore attached on three different helices (K4C, E66C, K99C) and in three different loops (H39C, D50C, L85C). Analysis of the FET kinetics data gave distributions of distances between the fluorescent donor and acceptor; these distributions demonstrate that the guanidine hydrochloride (GuHCl)-denatured polypeptide ensemble is not a simple random coil. Although misligation imposes some constraints, it is not the only source of structural complexity in the unfolded protein. Our FET kinetics data reveal a high degree of heterogeneity in the unfolded ensemble of cytochrome c. We detect relatively large populations of compact structures in unfolded Dns(C50)cyt, Dns(C39)cyt, and Dns(C66)cyt. These structures likely play a role in forming a hydrophobic core during the folding process.

Random-coil behavior and the dimensions of chemically unfolded proteins

Spectroscopic studies have identified a number of proteins that appear to retain significant residual structure under even strongly denaturing conditions. Intrinsic viscosity, hydrodynamic radii, and small-angle x-ray scattering studies, in contrast, indicate that the dimensions of most chemically denatured proteins scale with polypeptide length by means of the power-law relationship expected for random-coil behavior. Here we further explore this discrepancy by expanding the length range of characterized denatured-state radii of gyration (R(G)) and by reexamining proteins that reportedly do not fit the expected dimensional scaling. We find that only 2 of 28 crosslink-free, prosthetic-group-free, chemically denatured polypeptides deviate significantly from a power-law relationship with polymer length. The R(G) of the remaining 26 polypeptides, which range from 16 to 549 residues, are well fitted (r(2) = 0.988) by a power-law relationship with a best-fit exponent, 0.598 +/- 0.028, coinciding closely with the 0.588 predicted for an excluded volume random coil. Therefore, it appears that the mean dimensions of the large majority of chemically denatured proteins are effectively indistinguishable from the mean dimensions of a random-coil ensemble.

Synchrotron SAXS studies on the structural stability of Carcinus aestuarii hemocyanin in solution

The effect of GuHCl and of NaCl on the structural properties of the hemocyanin (Hc) from Carcinus aestuarii has been studied by small angle x-ray scattering (SAXS) using synchrotron radiation. SAXS data collected as a function of perturbant concentration have been used to analyze conformational states of hexameric holo and apoHc as well as the holo and apoforms of the monomeric subunit CaeSS2. In the case of the holoprotein in GuHCl, two concentration domains were identified: at lower concentration, the perturbant induces aggregation of Hc molecules, whereas at higher concentration the aggregates dissociate with concomitant denaturation of the protein. In contrast, with apoHc the denaturation occurs at rather low GuHCl, pointing to an important effect of the active site bound copper for the stabilization of Hc tertiary structure. The effects of NaCl are similar to those of GuHCl as far as CaeSS2 is concerned, namely oligomerization precedes denaturation, whereas in the case of the hexameric form no aggregation occurs. To improve data analysis, on the basis of the current models for Hc monomers and oligomers, the fraction of each aggregation state and/or unfolded protein has been determined by fitting experimental SAXS curves with form factors calculated from Monte Carlo methods. In addition, a global analysis has been carried out on the basis of a thermodynamic model involving an equilibrium between a monomer in a nativelike and denatured form as well as a class of equilibria among the monomer and other aggregates.

Collapse and search dynamics of apomyoglobin folding revealed by submillisecond observations of alpha-helical content and compactness

The characterization of protein folding dynamics in terms of secondary and tertiary structures is important in elucidating the features of intraprotein interactions that lead to specific folded structures. Apomyoglobin (apoMb), possessing seven helices termed A-E, G, and H in the native state, has a folding intermediate composed of the A, G, and H helices, whose formation in the submillisecond time domain has not been clearly characterized. In this study, we used a rapid-mixing device combined with circular dichroism and small-angle x-ray scattering to observe the submillisecond folding dynamics of apoMb in terms of helical content (f(H)) and radius of gyration (R(g)), respectively. The folding of apoMb from the acid-unfolded state at pH 2.2 was initiated by a pH jump to 6.0. A significant collapse, corresponding to approximately 50% of the overall change in R(g) from the unfolded to native conformation, was observed within 300 micros after the pH jump. The collapsed intermediate has a f(H) of 33% and a globular shape that involves >80% of all its atoms. Subsequently, a stepwise helix formation was detected, which was interpreted to be associated with a conformational search for the correct tertiary contacts. The characterized folding dynamics of apoMb indicates the importance of the initial collapse event, which is suggested to facilitate the subsequent conformational search and the helix formation leading to the native structure.

Conformational landscape of cytochrome c folding studied by microsecond-resolved small-angle x-ray scattering

To investigate protein folding dynamics in terms of compactness, we developed a continuous-flow mixing device to make small-angle x-ray scattering measurements with the time resolution of 160 micros and characterized the radius of gyration (R(g)) of two folding intermediates of cytochrome c (cyt c). The early intermediate possesses approximately 20 A of R(g), which is smaller by approximately 4 A than that of the acid-unfolded state. The R(g) of the later intermediate is approximately 18 A, which is close to that of the molten globule state. Considering the alpha-helix content (f(H)) of the intermediates, we clarified the folding pathway of cyt c on the conformational landscape defined by R(g) and f(H). Cyt c folding proceeds with a collapse around a specific region of the protein followed by a cooperative acquisition of secondary structures and compactness.

NMR and SAXS characterization of the denatured state of the chemotactic protein CheY: implications for protein folding initiation

The denatured state of a double mutant of the chemotactic protein CheY (F14N/V83T) has been analyzed in the presence of 5 M urea, using small angle X-ray scattering (SAXS) and heteronuclear magnetic resonance. SAXS studies show that the denatured protein follows a wormlike chain model. Its backbone can be described as a chain composed of rigid elements connected by flexible links. A comparison of the contour length obtained for the chain at 5 M urea with the one expected for a fully expanded chain suggests that approximately 25% of the residues are involved in residual structures. Conformational shifts of the alpha-protons, heteronuclear (15)N-[(1)H] NOEs and (15)N relaxation properties have been used to identify some regions in the protein that deviate from a random coil behavior. According to these NMR data, the protein can be divided into two subdomains, which largely coincide with the two folding subunits identified in a previous kinetic study of the folding of the protein. The first of these subdomains, spanning residues 1-70, is shown here to exhibit a restricted mobility as compared to the rest of the protein. Two regions, one in each subdomain, were identified as deviating from the random coil chemical shifts. Peptides corresponding to these sequences were characterized by NMR and their backbone (1)H chemical shifts were compared to those in the intact protein under identical denaturing conditions. For the region located in the first subdomain, this comparison shows that the observed deviation from random coil parameters is caused by interactions with the rest of the molecule. The restricted flexibility of the first subdomain and the transient collapse detected in that subunit are consistent with the conclusions obtained by applying the protein engineering method to the characterization of the folding reaction transition state.

Heat-induced unfolding of neocarzinostatin, a small all-β protein investigated by small-angle X-ray scattering 1 1Edited by M. F. Moody

Neocarzinostatin is an all-beta protein, 113 amino acid residues long, with an immunoglobulin-like fold. Its thermal unfolding has been studied by small-angle X-ray scattering. Preliminary differential scanning calorimetry and fluorescence measurements suggest that the transition is not a simple, two-state transition. The apparent radius of gyration is determined using three different approaches, the validity of which is critically assessed using our experimental data as well as a simple, two-state model. Similarly, each step of data analysis is evaluated and the underlying assumptions plainly stated. The existence of at least one intermediate state is formally demonstrated by a singular value decomposition of the set of scattering patterns. We assume that the pattern of the solution before the onset of the transition is that of the native protein, and that of the solution at the highest temperature is that of the completely unfolded protein. Given these, actually not very restrictive, boundary constraints, a least-squares procedure yields a scattering pattern of the intermediate state. However, this solution is not unique: a whole class of possible solutions is derived by adding to the previous linear combination of the native and completely unfolded states. Varying the initial conditions of the least-squares calculation leads to very similar solutions. Whatever member of the class is considered, the conformation of this intermediate state appears to be weakly structured, probably less than the transition state should be according to some proposals. Finally, we tried and used the classical model of three thermodynamically well-defined states to account for our data. The failure of the simple thermodynamic model suggests that there is more than the single intermediate structure required by singular value decomposition analysis. Formally, there could be several discrete intermediate species at equilibrium, or an ensemble of conformations differently populated according to the temperature. In the latter case, a third state would be a weighted average of all non native and not completely unfolded states of the protein but, since the weights change with temperature, no meaningful curve is likely to be derived by a global analysis using the simple model of three thermodynamically well-defined states.

A new alternative method to quantify residual structure in 'unfolded' proteins

Pig (pCSD1) and human (hCSD1) calpastatin domain 1 proteins were studied to characterize common features of the denatured state of proteins. These proteins were chosen for the present investigation, because pCSD1 was suggested previously to be unstructured in water even at 25 degrees C (1) [T. Konno et al., Biochim. Biophys. Acta 1342 (1997) 73-82]. hCSD1 could be expected to exhibit similar features on the basis of preliminary spectroscopic studies. In the present study, the experimental grounds for the estimate of residual structure in the unfolded state were differential scanning calorimetry heat capacity and circular dichroism (CD) measurements over the temperature range 10-80 degrees C. At selected temperatures, we studied also the effect of guanidinium hydrochloride (GdnHCl) which is known to promote further unfolding of the polypeptide chain. All other measurements were performed at pH 6 in pure water. The present results support the conclusion that the comparison of the experimentally obtained heat capacity data with theoretical heat capacity values calculated on the basis of a newly established increment system gives insight into the degree of hydration of the unfolded polypeptide chain. The percentage by which the experimental heat capacity of the unfolded polypeptide chain differs from the calculated heat capacity permits a quantitative estimate of the residual structure. This estimate is in good agreement with that based on CD absorption. The heat capacity approach has the advantage of comparing fully hydrated and partially hydrated residues in the same aqueous environment, whereas for example spectroscopic measurements, such as CD, are generally referred to the fully unfolded chain in concentrated urea or GdnHCl solutions. As the unfolded chains of pCSD1 and hCSD1 exhibit a smaller heat capacity than that calculated on the new peptide-based increment system [M. Häckel et al., J. Mol. Biol. 291 (1999) 197-213], we conclude that the residues in the unfolded polypeptide chain are less hydrated than the same residues in oligopeptides. This suboptimal hydration is the result of residual structure in the chain as observed in both CD and heat capacity measurements.

Change in backbone torsion angle distribution on protein folding

Understanding protein folding requires the determination of the configurational space accessible to the protein at different stages in folding. Here, computer simulation analysis of small angle neutron scattering results is used to probe the change in the distribution of configurations on strong denaturation of a globular protein, phosphoglycerate kinase, in 4 M guanidine hydrochloride solution. To do this atomic-detail ensembles of the unfolded protein chain are modeled and their scattering profiles compared with the experiment. The local conformational statistics are found to strongly influence the experimental intensity at scattering vectors between 0.05 and 0.3 A(-1). Denaturation leads to a reduction in the protein atom-pair distance distribution function over the approximately 3-15 A region that is associated with a quantifiable shift in the backbone torsional angle (phi, psi) distribution toward the beta region of the Ramachandran plot.

Excluded volume in the configurational distribution of a strongly-denatured protein

The configurational distribution of phosphoglycerate kinase (PGK) strongly-denatured in 4 M guanidine hydrochloride solution is investigated using small-angle neutron scattering (SANS) and Monte Carlo computer simulation. It is shown that the experimental scattering profile can be represented by a random flexible chain of spheres of excess scattering density with excluded volume interactions, the best agreement being achieved when partial sphere intersection is allowed. The radius of gyration of the chain increases by a factor of 4 on denaturation, whereas the average length of segments approximately 5 residues long increases by only approximately 10%, consistent with a picture in which the large expansion on denaturation originates primarily from increased long-range flexibility of the polypeptide chain. The results provide a description of the chain statistics from which the construction of starting points for simulation studies of folding of the protein can be envisaged.

Repulsive interparticle interactions in a denatured protein solution revealed by small angle neutron scattering

In order to investigate the effect of concentration in biological processes such as protein folding, small angle neutron scattering measurements were used to determine the second virial coefficient of solutions of both native and strongly denatured phosphoglycerate kinase and the radius of gyration of the protein at zero concentration. The value of the second virial coefficient is a good probe of the non-ideality of a solution. The present results show that the unfolding of the protein leads to a drastic change in the repulsive intermolecular interactions. We conclude that these interactions are due mainly to the behaviour of the denatured polypeptide chain as an excluded volume polymer.

Simulations of the structural and dynamical properties of denatured proteins: the "molten coil" state of bovine pancreatic trypsin inhibitor

The dynamic nature of denatured, unfolded proteins makes it difficult to characterize their structures experimentally. To complement experiment and to obtain more detailed information about the structure and dynamic behavior of the denatured state, we have performed eleven 2.5 ns molecular dynamics simulations of reduced bovine pancreatic trypsin inhibitor (BPTI) at high temperature in water and a control simulation at 298 K, for a total of 30 ns of simulation time. In a neutral pH environment (acidic residues ionized), the unfolded protein structures were compact with an average radius of gyration 9% greater than the native state. The compact conformations resulted from the transient formation of non-native hydrophobic clusters, turns and salt bridges. However, when the acidic residues were protonated, the protein periodically expanded to a radius of gyration of 18 to 20 A. The early steps in unfolding were similar in the different simulations until passing through the major transition state of unfolding. Afterwards, unfolding proceeded through one of two general pathways with respect to secondary structure: loss of the C-terminal helix followed by loss of beta-structure or the opposite. To determine whether the protein preferentially sampled particular conformational substates in the denatured state, pairwise Calpha root-mean-square deviations were measured between all structures, but similar structures were found between only two trajectories. Yet, similar composite properties (secondary structure content, side-chain and water contacts, solvent accessible surface area, etc.) were observed for the structures that unfolded through different pathways. Somewhat surprisingly, the unfolded structures are in agreement with both past experiments suggesting that reduced BPTI is a random coil and more recent experiments providing evidence for non-random structure, demonstrating how ensembles of fluctuating structures can give rise to experimental observables that are seemingly at odds.

Small-angle neutron scattering by a strongly denatured protein: analysis using random polymer theory

Small-angle neutron scattering profiles are presented from phosphoglycerate kinase, in the native form and strongly denatured in 4 M guanidinium chloride (GdnHCl) solution. The data are interpreted using a model in which the excess scattering density associated with the protein is represented as a finite freely jointed chain of spheres. The similarity of the model-derived scattering function to experiment increases asymptotically with the number of spheres. The improvement of the fit obtained with more than approximately 200 spheres (i.e., two residues per sphere) is insignificant. The effects of finite size of the scattering units and of scattering length variation along the polypeptide chain are examined. Improved agreement with experiment is obtained when these effects are taken into account. A method for rapid calculation of the scattering profile of a full, all-atom configuration is examined. It is found that a representation of the chain containing two scattering units per residue, placed at the backbone and side-chain scattering length centroids, reproduces the full, all-atom profile to within 2%.

X-ray solution scattering studies of protein folding

Protein folding is a reaction in which an extended polypeptide chain acquires maximal packing through formation of secondary and tertiary structures. Compactness and shape are, therefore, critical properties characterizing the process of protein folding. Because the stability of the native state is determined by the subtle free energy balance between the native and denatured states, the characterization of the denatured state is also essential to understand the conformational stability of the native state. We show that solution X-ray scattering is the best technique available today to address these problems. Although the structural resolution of the unfolded or compact denatured states elucidated from solution X-ray scattering is low, it provides a variety of information complementary to that obtained by NMR or X-ray crystallography.