Random-coil behavior and the dimensions of chemically unfolded proteins

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.

The Equilibrium Unfolding Intermediate Observed at pH 4 and its Relationship with the Kinetic Folding Intermediates in Green Fluorescent Protein

Folding mechanisms of a variant of green fluorescent protein (F99S/M153T/V163A) were investigated by a wide variety of spectroscopic techniques. Equilibrium measurements on acid-induced denaturation of the protein monitored by chromophore and tryptophan fluorescence and small-angle X-ray scattering revealed that this protein accumulates at least two equilibrium intermediates, a native-like intermediate and an unfolding intermediate, the latter of which exhibits the characteristics of the molten globule state under moderately denaturing conditions at pH 4. To elucidate the role of the equilibrium unfolding intermediate in folding, a series of kinetic refolding experiments with various combinations of initial and final pH values, including pH 7.5 (the native condition), pH 4.0 (the moderately denaturing condition where the unfolding intermediate is accumulated), and pH 2.0 (the acid-denaturing condition) were carried out by monitoring chromophore and tryptophan fluorescence. Kinetic on-pathway intermediates were accumulated during the folding on the refolding reaction from pH 2.0 to 7.5. However, the signal change corresponding to the conversion from the acid-denatured to the kinetic intermediate states was significantly reduced on the refolding reaction from pH 4.0 to pH 7.5, whereas only the signal change corresponding to the above conversion was observed on the refolding reaction from pH 2.0 to pH 4.0. These results indicate that the equilibrium unfolding intermediate is composed of an ensemble of the folding intermediate species accumulated during the folding reaction, and thus support a hierarchical model of protein folding.

Exploring the relationship between funneled energy landscapes and two-state protein folding

It should take an astronomical time span for unfolded protein chains to find their native state based on an unguided conformational random search. The experimental observation that folding is fast can be rationalized by assuming that protein energy landscapes are sloped towards the native state minimum, such that rapid folding can proceed from virtually any point in conformational space. Folding transitions often exhibit two-state behavior, involving extensively disordered and highly structured conformers as the only two observable kinetic species. This study employs a simple Brownian dynamics model of "protein particles" moving in a spherically symmetrical potential. As expected, the presence of an overall slope towards the native state minimum is an effective means to speed up folding. However, the two-state nature of the transition is eradicated if a significant energetic bias extends too far into the non-native conformational space. The breakdown of two-state cooperativity under these conditions is caused by a continuous conformational drift of the unfolded proteins. Ideal two-state behavior can only be maintained on surfaces exhibiting large regions that are energetically flat, a result that is supported by other recent data in the literature (Kaya and Chan, Proteins: Struct Funct Genet 2003;52:510-523). Rapid two-state folding requires energy landscapes exhibiting the following features: (i) A large region in conformational space that is energetically flat, thus allowing for a significant degree of random sampling, such that unfolded proteins can retain a random coil structure; (ii) a trapping area that is strongly sloped towards the native state minimum.

End-to-end distance distributions and intrachain diffusion constants in unfolded polypeptide chains indicate intramolecular hydrogen bond formation

Characterization of the unfolded state is essential for the understanding of the protein folding reaction. We performed time-resolved FRET measurements to gain information on the dimensions and the internal dynamics of unfolded polypeptide chains. Using an approach based on global analysis of data obtained from two different donor-acceptor pairs allowed for the determination of distance distribution functions and diffusion constants between the chromophores. Results on a polypeptide chain consisting of 16 Gly-Ser repeats between the FRET chromophores reveal an increase in the average end-to-end distance from 18.9 to 39.2 Angstrom between 0 and 8 M GdmCl. The increase in chain dimensions is accompanied by an increase in the end-to-end diffusion constant from (3.6 +/- 1.0) x 10(-7) cm(2) s(-1) in water to (14.8 +/- 2.5) x 10(-7) cm(2) s(-1) in 8 M GdmCl. This finding suggests that intrachain interactions in water exist even in very flexible chains lacking hydrophobic groups, which indicates intramolecular hydrogen bond formation. The interactions are broken upon denaturant binding, which leads to increased chain flexibility and longer average end-to-end distances. This finding implies that rapid collapse of polypeptide chains during refolding of denaturant-unfolded proteins is an intrinsic property of polypeptide chains and can, at least in part, be ascribed to nonspecific intramolecular hydrogen bonding. Despite decreased intrachain diffusion constants, the conformational search is accelerated in the collapsed state because of shorter diffusion distances. The measured distance distribution functions and diffusion constants in combination with Szabo-Schulten-Schulten theory were able to reproduce experimentally determined rate constants for end-to-end loop formation.

Mis-translation of a computationally designed protein yields an exceptionally stable homodimer: implications for protein engineering and evolution

We recently used computational protein design to create an extremely stable, globular protein, Top7, with a sequence and fold not observed previously in nature. Since Top7 was created in the absence of genetic selection, it provides a rare opportunity to investigate aspects of the cellular protein production and surveillance machinery that are subject to natural selection. Here we show that a portion of the Top7 protein corresponding to the final 49 C-terminal residues is efficiently mis-translated and accumulates at high levels in Escherichia coli. We used circular dichroism, size-exclusion chromatography, small-angle X-ray scattering, analytical ultra-centrifugation, and NMR spectroscopy to show that the resulting C-terminal fragment (CFr) protein adopts a compact, extremely stable, homo-dimeric structure. Based on the solution structure, we engineered an even more stable variant of CFr by disulfide-induced covalent circularisation that should be an excellent platform for design of novel functions. The accumulation of high levels of CFr exposes the high error rate of the protein translation machinery. The rarity of correspondingly stable fragments in natural proteins coupled with the observation that high quality ribosome binding sites are found to occur within E. coli protein-coding regions significantly less often than expected by random chance implies a stringent evolutionary pressure against protein sub-fragments that can independently fold into stable structures. The symmetric self-association between two identical mis-translated CFr sub-domains to generate an extremely stable structure parallels a mechanism for natural protein-fold evolution by modular recombination of protein sub-structures.

Characterization of the residual structure in the unfolded state of the Δ131Δ fragment of staphylococcal nuclease

The determination of the conformational preferences in unfolded states of proteins constitutes an important challenge in structural biology. We use inter-residue distances estimated from site-directed spin-labeling NMR experimental measurements as ensemble-averaged restraints in all-atom molecular dynamics simulations to characterise the residual structure of the Delta131Delta fragment of staphylococcal nuclease under physiological conditions. Our findings indicate that Delta131Delta under these conditions shows a tendency to form transiently hydrophobic clusters similar to those present in the native state of wild-type staphylococcal nuclease. Only rarely, however, all these interactions are simultaneously realized to generate conformations with an overall native topology.

Effects of denaturants on the dynamics of loop formation in polypeptides

Quenching of the triplet state of tryptophan by close contact with cysteine has been used to measure the reaction-limited and diffusion-limited rates of loop formation in disordered polypeptides having the sequence cys-(ala-gly-gln)j-trp (j=1-9). The decrease in the length-dependence of the reaction-limited rate for short chains in aqueous buffer, previously attributed to chain stiffness, is not observed at high concentrations of chemical denaturant (6 M GdmCl and 8 M urea), showing that denaturants increase chain flexibility. For long chains, both reaction-limited and diffusion-limited rates are significantly smaller in denaturant and exhibit a steeper length dependence. The results can be explained using end-to-end distributions from a wormlike chain model in which excluded volume interactions are incorporated by associating a 0.4-0.5 nm diameter hard sphere with the end of each virtual peptide bond. Fitting the data with this model shows that the denaturants reduce the persistence length from approximately 0.6 nm to approximately 0.4 nm, only slightly greater than the length of a peptide bond. The same model also describes the reported length dependence for the radii of gyration of chemically denatured proteins containing 50-400 residues. The end-to-end diffusion coefficients obtained from the diffusion-limited rates are smaller than the sum of the monomer diffusion coefficients and exhibit significant temperature dependence, suggesting that diffusion is slowed by internal friction arising from barriers to backbone conformational changes.

Native state energetics of the Src SH2 domain: evidence for a partially structured state in the denatured ensemble

We have defined the free-energy profile of the Src SH2 domain using a variety of biophysical techniques. Equilibrium and kinetic experiments monitored by tryptophan fluorescence show that Src SH2 is quite stable and folds rapidly by a two-state mechanism, without populating any intermediates. Native state hydrogen-deuterium exchange confirms this two-state behavior; we detect no cooperative partially unfolded forms in equilibrium with the native conformation under any conditions. Interestingly, the apparent stability of the protein from hydrogen exchange is 2 kcal/mol greater than the stability determined by both equilibrium and kinetic studies followed by fluorescence. Native-state proteolysis demonstrates that this "super protection" does not result from a deviation from the linear extrapolation model used to fit the fluorescence data. Instead, it likely arises from a notable compaction in the unfolded state under native conditions, resulting in an ensemble of conformations with substantial solvent exposure of side chains and flexible regions sensitive to proteolysis, but backbone amides that exchange with solvent approximately 30-fold slower than would be expected for a random coil. The apparently simple behavior of Src SH2 in traditional unfolding studies masks the significant complexity present in the denatured-state ensemble.

Tandem Mass Spectrometry Reveals the Quaternary Organization of Macromolecular Assemblies

The application of mass spectrometry (MS) to the study of progressively larger and more complex macromolecular assemblies is proving increasingly useful for structural biologists. The scope of this approach has recently been widened through the application of a tandem MS procedure. This two-step technique involves the selection of specific assemblies in the gas phase and inducing their dissociation through collisions with argon atoms. Here, we investigate the mechanism of this process and show that dissociation of subunits from a macromolecular assembly follows a sequential pathway, with the partitioning of charge between the dissociation products governed primarily by their relative surface areas. Using this basis of understanding, we highlight differences in the dissociation pathways of three related macromolecular assemblies and show how these are a direct consequence of changes in both local and global oligomeric organization.

Exploring the mechanism of formation of native-like and precursor amyloid oligomers for the native acylphosphatase from Sulfolobus solfataricus

Over 40 human diseases are associated with the formation of well-defined proteinaceous fibrillar aggregates. Since the oligomers precursors to the fibrils are increasingly recognized to be the causative agents of such diseases, it is important to elucidate the mechanism of formation of these early species. The acylphosphatase from Sulfolobus solfataricus is an ideal system as it was found to form, under conditions in which it is initially native, two types of prefibrillar aggregates: (1) initial enzymatically active aggregates and (2) oligomers with characteristics reminiscent of amyloid protofibrils, with the latter originating from the structural reorganization of the initial assemblies. By studying a number of protein variants with a variety of biophysical techniques, we have identified the regions of the sequence and the driving forces that promote the first aggregation phase and show that the second phase consists in a cooperative conversion involving the entire globular fold.

Dynamics of proteins encapsulated in silica sol-gel glasses studied with IR vibrational echo spectroscopy

Spectrally resolved infrared stimulated vibrational echo spectroscopy is used to measure the fast dynamics of heme-bound CO in carbonmonoxy-myoglobin (MbCO) and -hemoglobin (HbCO) embedded in silica sol-gel glasses. On the time scale of approximately 100 fs to several picoseconds, the vibrational dephasing of the heme-bound CO is measurably slower for both MbCO and HbCO relative to that of aqueous protein solutions. The fast structural dynamics of MbCO, as sensed by the heme-bound CO, are influenced more by the sol-gel environment than those of HbCO. Longer time scale structural dynamics (tens of picoseconds), as measured by the extent of spectral diffusion, are the same for both proteins encapsulated in sol-gel glasses compared to that in aqueous solutions. A comparison of the sol-gel experimental results to viscosity-dependent vibrational echo data taken on various mixtures of water and fructose shows that the sol-gel-encapsulated MbCO exhibits dynamics that are the equivalent of the protein in a solution that is nearly 20 times more viscous than bulk water. In contrast, the HbCO dephasing in the sol-gel reflects only a 2-fold increase in viscosity. Attempts to alter the encapsulating pore size by varying the molar ratio of silane precursor to water (R value) used to prepare the sol-gel glasses were found to have no effect on the fast or steady-state spectroscopic results. The vibrational echo data are discussed in the context of solvent confinement and protein-pore wall interactions to provide insights into the influence of a confined environment on the fast structural dynamics experienced by a biomolecule.

pH-induced intracellular protein transport

A new mechanism of selective transport and localization of proteins inside any living cell is presented. The mechanism is based on pH-induced protein trapping. It is shown that spontaneous and unique spatial redistribution of different proteins is possible in any aqueous solution with stable non-uniform distribution of H(+) ions. This phenomenon was observed in artificial systems with fixed non-uniform pH distribution and in living cells.

Characterization of Intra-molecular Distances and Site-specific Dynamics in Chemically Unfolded Barstar: Evidence for Denaturant-dependent Non-random Structure

The structure and dynamics of the unfolded form of a protein are expected to play critical roles in determining folding pathways. In this study, the urea and guanidine hydrochloride (GdnHCl)-unfolded forms of the small protein barstar were explored by time-resolved fluorescence techniques. Barstar was labeled specifically with thionitrobenzoate (TNB), by coupling it to the thiol side-chain of a cysteine residue at one of the following positions on the sequence: 14, 25, 40, 42, 62, 82 and 89, in single cysteine-containing mutant proteins. Seven intra-molecular distances (R(DA)) under unfolding conditions were estimated from measurements of time-resolved fluorescence resonance energy transfer between the donor Trp53 and the non-fluorescent acceptor TNB coupled to one of the seven cysteine side-chains. The unfolded protein chain expands with an increase in the concentration of the denaturants. The extent of expansion was found to be non-uniform, with different intra-molecular distances expanding to different extents. In general, shorter distances were found to expand less when compared to longer spans. The extent of expansion was higher in the case of GdnHCl when compared to urea. A comparison of the measured values of R(DA) with those derived from a model based on excluded volume, revealed that while shorter spans showed good agreement, the experimental values of R(DA) of longer spans were smaller when compared to the theoretical values. Sequence-specific flexibility of the polypeptide was determined by time-resolved fluorescence anisotropy decay measurements on acrylodan or 1,5-IAEDANS labeled single cysteine-containing proteins under unfolding conditions. Rotational dynamics derived from these measurements indicated that the level of flexibility increased with increase in the concentration of denaturants and showed a graded increase towards the C-terminal end. Taken together, these results appear to indicate the presence of specific non-random coil structures and show that the deviation from random coil structure is different for the two denaturants.

Tetramerization of the LexA repressor in solution: implications for gene regulation of the E.coli SOS system at acidic pH

Structural changes on LexA repressor promoted by acidic pH have been investigated. Intense protein aggregation occurred around pH 4.0 but was not detected at pH values lower than pH 3.5. The center of spectral mass of the Trp increased 400 cm(-1) at pH 2.5 relatively to pH 7.2, an indication that LexA has undergone structural reorganization but not denaturation. The Trp fluorescence polarization of LexA at pH 2.5 indicated that its hydrodynamic volume was larger than its dimer at pH 7.2. 4,4'-Dianilino-1,1'-binaphthyl-5,5'- disulfonic acid (bis-ANS) experiments suggested that the residues in the hydrophobic clefts already present at the LexA structure at neutral pH had higher affinity to it at pH 2.5. A 100 kDa band corresponding to a tetramer was obtained when LexA was subject to pore-limiting native polyacrylamide gel electrophoresis at this pH. The existence of this tetrameric state was also confirmed by small angle X-ray scattering (SAXS) analysis at pH 2.5. 1D 1H NMR experiments suggested that it was composed of a mixture of folded and unfolded regions. Although 14,000-fold less stable than the dimeric LexA, it showed a tetramer-monomer dissociation at pH 2.5 from the hydrostatic pressure and urea curves. Albeit with half of the affinity obtained at pH 7.2 (Kaff of 170 nM), tetrameric LexA remained capable of binding recA operator sequence at pH 2.5. Moreover, different from the absence of binding to the negative control polyGC at neutral pH, LexA bound to this sequence with a Kaff value of 1415 nM at pH 2.5. A binding stoichiometry experiment at both pH 7.2 and pH 2.5 showed a [monomeric LexA]/[recA operator] ratio of 2:1. These results are discussed in relation to the activation of the Escherichia coli SOS regulon in response to environmental conditions resulting in acidic intracellular pH. Furthermore, oligomerization of LexA is proposed to be a possible regulation mechanism of this regulon.

Time-resolved Small-angle X-ray Scattering Investigation of the Folding Dynamics of Heme Oxygenase: Implication of the Scaling Relationship for the Submillisecond Intermediates of Protein Folding

Polypeptide collapse is generally observed as the initial folding dynamics of proteins with more than 100 residues, and is suggested to be caused by the coil-globule transition explained by Flory's theory of polymers. To support the suggestion by establishing a scaling behavior between radius of gyration (Rg) and chain length for the initial folding intermediates, the folding dynamics of heme oxygenase (HO) was characterized by time-resolved, small-angle X-ray scattering. HO is a highly helical protein without disulfide bridges, and is the largest protein (263 residues) characterized by the method. The folding process of HO was found to contain a transient oligomerization; however, the conformation within 10 ms was demonstrated to be monomeric and to possess Rg of 26.1(+/-1.1) A. Together with the corresponding data for proteins with different chain lengths, the seven Rg values demonstrated the scaling relationship to chain length with a scaling exponent of 0.35+/-0.11, which is close to the theoretical value of 1/3 predicted for globules in solutions where monomer-monomer interactions are favored over monomer-solvent interactions (poor solvent). The finding indicated that the initial folding dynamics of proteins bears the signature of the coil-globule transition, and offers a clue to explain the folding mechanisms of proteins with different chain lengths.

The Denatured State under Native Conditions: A Non-native-like Collapsed State of N-PGK

The guanidinium-denatured state of the N-domain of phosphoglycerate kinase (PGK) has been characterized using solution NMR. Rather than behaving as a homogenous ensemble of random coils, chemical shift changes for the majority of backbone amide resonances indicate that the denatured ensemble undergoes two definable equilibrium transitions upon titration with guanidinium, in addition to the major refolding event. (13)C and (15)N chemical shift changes indicate that both intermediary states have distinct helical character. At denaturant concentrations immediately above the mid-point of unfolding, size-exclusion chromatography shows N-PGK to have a compact, denatured form, suggesting that it forms a helical molten globule. Within this globule, the helices extend into some regions that become beta strands in the native state. This predisposition of the denatured state to extensive non-native-like conformation, illustrates that, rather than directing folding, conformational pre-organization in the denatured state can compete with the normal folding direction. The corresponding reduction in control of the direction of folding as proteins become larger, could thus constitute a restriction on the size of protein domains.

Polyproline II conformation is one of many local conformational states and is not an overall conformation of unfolded peptides and proteins

The alanine-based peptide Ac-XX(A)7OO-NH2, referred to as XAO (where X, A, and O denote diaminobutyric acid, alanine, and ornithine, respectively), has recently been proposed to possess a well defined polyproline II (P(II)) conformation at low temperatures. Based on the results of extensive NMR and CD investigations combined with theoretical calculations, reported here, we present evidence that, on the contrary, this peptide does not have any significant amount of organized P(II) structure but exists in an ensemble of conformations with a distorted bend in the N- and C-terminal regions. The conformational ensemble was obtained by molecular dynamics/simulated annealing calculations using the amber suite of programs with time-averaged distance and dihedral-angle restraints obtained from rotating-frame nuclear Overhauser effect (ROE) volumes and vicinal coupling constants 3J(HN Eta alpha), respectively. The computed ensemble-averaged radius of gyration Rg (7.4 +/- 1.0) A is in excellent agreement with that measured by small-angle x-ray scattering (SAXS) whereas, if the XAO peptide were in the P(II) conformation, Rg would be 11.6 A. Depending on the pH, peptide concentration, and temperature, the CD spectra of XAO do or do not possess the maximum with positive ellipticity in the 217-nm region, which is characteristic of the P(II) structure, reflecting a shifting conformational equilibrium rather than an all-or-none transition. The "P(II) conformation" should, therefore, be considered as one of the accessible conformational states of individual amino acid residues in peptides and proteins rather than as a structure of most of the chain in the early stage of folding.

Methionine oxidation of monomeric lambda repressor: the denatured state ensemble under nondenaturing conditions

Although poorly understood, the properties of the denatured state ensemble are critical to the thermodynamics and the kinetics of protein folding. The most relevant conformations to cellular protein folding are the ones populated under physiological conditions. To avoid the problem of low expression that is seen with unstable variants, we used methionine oxidation to destabilize monomeric lambda repressor and predominantly populate the denatured state under nondenaturing buffer conditions. The denatured ensemble populated under these conditions comprises conformations that are compact. Analytical ultracentrifugation sedimentation velocity experiments indicate a small increase in Stokes radius over that of the native state. A significant degree of alpha-helical structure in these conformations is detected by far-UV circular dichroism, and some tertiary interactions are suggested by near-UV circular dichroism. The characteristics of the denatured state populated by methionine oxidation in nondenaturing buffer are very different from those found in chemical denaturant.

A Nanofilter Array Chip for Fast Gel-Free Biomolecule Separation

We report here a microfabricated nanofilter array chip that can size-fractionate SDS-protein complexes and small DNA molecules based on the Ogston sieving mechanism. Nanofilter arrays with a gap size of 40-180nm were fabricated and characterized. Complete separation of SDS-protein complexes and small DNA molecules were achieved in several minutes with a separation length of 5mm. The fabrication strategy for the nanofilter array chip allows further increasing of the nanofilter density and decreasing of the nanofilter gap size, leading, in principle, to even faster separation.

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.

Characterizing the conformational ensemble of monomeric polyglutamine

Studies of synthetic polyglutamine peptides in vitro have established that polyglutamine peptides aggregate via a classic nucleation and growth mechanism. Chen and colleagues [Proc Natl Acad Sci U S A 2002;99:11884-11889] have found that monomeric polyglutamine, which is a disordered statistical coil in solution, is the critical nucleus for aggregation. Therefore, nucleation of beta-sheet-rich aggregates requires an initial disorder to order transition, which is a highly unfavorable thermodynamic reaction. The questions of interest to us are as follows: What are the statistical fluctuations that drive beta-sheet formation in monomeric polyglutamine? How do these fluctuations vary with chain length? And why is this process thermodynamically unfavorable, that is, why is monomeric polyglutamine disordered? To answer these questions we use multiple molecular dynamics simulations to provide quantitative characterization of conformational ensembles for two short polyglutamine peptides. We find that the ensemble for polyglutamine is indeed disordered. However, the disorder is inherently different from that of denatured proteins and the average compactness and magnitude of conformational fluctuations increase with chain length. Most importantly, the effective concentration of sidechain primary amides around backbone units is inherently high and peptide units are solvated either by hydrogen bonds to sidechains or surrounding water molecules. Due to the multiplicity of backbone solvation modes the probability associated with any specific backbone conformation is small, resulting in a conformational entropy bottleneck which makes beta-sheet formation in monomeric polyglutamine thermodynamically unfavorable.

Building native protein conformation from highly approximate backbone torsion angles

Reconstructing a protein in three dimensions from its backbone torsion angles is an ongoing challenge because minor inaccuracies in these angles produce major errors in the structure. As a familiar example, a small change in an elbow angle causes a large displacement at the end of your arm, the longer the arm, the larger the displacement. Even accurate knowledge of the backbone torsions and Psi is insufficient, owing to the small, but cumulative, deviations from ideality in backbone planarity, which, if ignored, also lead to major errors in the structure. Against this background, we conducted a computational experiment to assess whether protein conformation can be determined from highly approximate backbone torsion angles, the kind of information that is now obtained readily from NMR. Specifically, backbone torsion angles were taken from proteins of known structure and mapped into 60 degrees x 60 degrees grid squares, called mesostates. Side-chain atoms beyond the beta -carbon were discarded. A mesostate representation of the protein backbone was then used to extract likely candidates from a fragment library of mesostate pentamers, followed by Monte Carlo-based fragment-assembly simulations to identify stable conformations compatible with the given mesostate sequence. Only three simple energy terms were used to gauge stability: molecular compaction, soft-sphere repulsion, and hydrogen bonding. For the six representative proteins described here, stable conformers can be partitioned into a remarkably small number of topologically distinct clusters. Among these, the native topology is found with high frequency and can be identified as the cluster with the most favorable energy.

Mutational Analysis Demonstrates that Specific Electrostatic Interactions can Play a Key Role in the Denatured State Ensemble of Proteins

The nature of the denatured state ensemble has been controversial for decades owing, in large part, to the difficulty in characterizing the structure and energetics of denatured state interactions. There is increasing evidence for relatively non-specific hydrophobic clustering in the denatured states of some proteins but other types of interactions are much less well characterized. Here, we report the characterization of highly specific electrostatic interactions in the denatured state of a small alpha-beta protein, the N-terminal domain of the ribosomal protein L9 (NTL9). Mutation of Lys12 to Met has been shown to increase the stability of NTL9 significantly through the disruption of denatured state interactions. Here, we describe the analysis of the pH-dependent stability of 13 mutants designed to probe the nature of the Lys12 denatured state interaction. Lys12 is located in a lysine-rich region of the protein but analysis of a set of Lys to Met mutants shows that it plays a unique role in the denatured state. Analysis of mutants of all of the acidic residues in NTL9 shows that Lys12 forms a specific non-native electrostatic interaction with Asp8 in the denatured state ensemble. Thus the distribution of charge-charge interactions in the denatured state ensemble of NTL9 appears to be biased by few key interactions and is very different from that expected in a random coil. We propose that these interactions are not encoded by local sequence effects but rather reflect interactions among residues more distant in sequence. These results demonstrate that electrostatic as well as hydrophobic interactions can play an important role in the denatured state ensemble.

Kinetics of Loop Formation and Breakage in the Denatured State of Iso-1-cytochrome c

The earliest events in protein folding involve the formation of simple loops. Observing the rates of loop closure under denaturing conditions can provide direct insight into the relative probability and sequence determinants for formation of loops of different sizes. The persistence of these initial contacts is equally important for efficient folding, so measurement of rates of loop breakage under denaturing conditions is also essential. We have used stopped-flow and continuous-flow methods to measure the rates of histidine-heme loop formation and breakage in the denatured state of iso-1-cytochrome c (in the presence of 3 M guanidine HCl). The data indicate that the mechanism for forming loops is a two-step process, the first step being the deprotonation of the histidine, and the second step being the binding of the histidine to the heme. This mechanism makes it possible to extract both the rate constants of formation, k(f), and breakage, k(b), of loops from the pH dependence of the observed rate constant, k(obs). To determine the dependence of k(f) and k(b) on loop size, we have carried out kinetic measurements for seven single surface histidine variants of iso-1-cytochrome c. A scaling factor (the dependence of k(f) on log[loop size]) of approximately -1.8 is observed for loop formation, similar to that observed in other systems. The magnitude of k(b) varies from 30 s(-1) to 300 s(-1), indicating that the stability of different loops varies considerably. The implications of the kinetics of loop formation and breakage in the denatured state for the mechanism of protein folding are discussed.

A critical assessment of the topomer search model of protein folding using a continuum explicit-chain model with extensive conformational sampling

Recently, a series of closely related theoretical constructs termed the "topomer search model" (TSM) has been proposed for the folding mechanism of small, single-domain proteins. A basic assumption of the proposed scenarios is that the rate-limiting step in folding is an essentially unbiased, diffusive search for a conformational state called the native topomer defined by an overall native-like topological pattern. Successes in correlating TSM-predicted folding rates with that of real proteins have been interpreted as experimental support for the model. To better delineate the physics entailed, key TSM concepts are examined here using extensive Langevin dynamics simulations of continuum C(alpha) chain models. The theoretical native topomers of four experimentally well-studied two-state proteins are characterized. Consistent with the TSM perspective, we found that the sizes of the native topomers increase with experimental folding rate. However, a careful determination of the corresponding probabilities that the native topomers are populated during a random search fails to reproduce the previously predicted folding rates. Instead, our results indicate that an unbiased TSM search for the native topomer amounts to a Levinthal-like process that would take an impossibly long average time to complete. Furthermore, intraprotein contacts in all four native topomers considered exhibit no apparent correlation with the experimental phi-values determined from the folding kinetics of these proteins. Thus, the present findings suggest that certain basic, generic yet essential energetic features in protein folding are not accounted for by TSM scenarios to date.

Site-specific Dimensions Across a Highly Denatured Protein; A Single Molecule Study

Do highly denatured proteins adopt random coil configurations? Here, we address this question by measuring residue-to-residue separations across the denatured FynSH3 domain. Using single-molecule Forster resonance energy transfer techniques, we have collected transfer efficiency probability distributions for dye-labeled, denatured protein. Applying maximum likelihood analysis to the interpretation of these distributions, we have determined the through-space distance between five residue pairs in the protein's guanidine hydrochloride-unfolded and trifluoroethanol-unfolded states. We find that, while the dimensions of the guanidine hydrochloride -unfolded molecule generally coincide with the dimensions predicted for a random coil ensemble, potentially statistically significant deviations from random coil behavior are also evident. These small, site-specific deviations may provide a means of reconciling earlier, scattering-based evidence for the random coil nature of the unfolded state with more site-specific spectroscopic evidence suggesting residual structure. We have also studied the unfolded ensemble populated in 50% trifluoroethanol, a denaturant that induces a highly helical unfolded state. We find that the size and shape of the unfolded ensemble under these conditions is effectively indistinguishable from that populated in guanidinium hydrochloride solutions, suggesting that the gross structure of the denatured state is, perhaps surprisingly, independent of the chemistry of the cosolvent.

Statistical coil model of the unfolded state: resolving the reconciliation problem

An unfolded state ensemble is generated by using a self-avoiding statistical coil model that is based on backbone conformational frequencies in a coil library, a subset of the Protein Data Bank. The model reproduces two apparently contradicting behaviors observed in the chemically denatured state for a variety of proteins, random coil scaling of the radius of gyration and the presence of significant amounts of local backbone structure (NMR residual dipolar couplings). The most stretched members of our unfolded ensemble dominate the residual dipolar coupling signal, whereas the uniformity of the sign of the couplings follows from the preponderance of polyproline II and beta conformers in the coil library. Agreement with the NMR data substantially improves when the backbone conformational preferences include correlations arising from the chemical and conformational identity of neighboring residues. Although the unfolded ensembles match the experimental observables, they do not display evidence of native-like topology. By providing an accurate representation of the unfolded state, our statistical coil model can be used to improve thermodynamic and kinetic modeling of protein folding.

Unusual compactness of a polyproline type II structure

Polyproline type II (PPII) helix has emerged recently as the dominant paradigm for describing the conformation of unfolded polypeptides. However, most experimental observables used to characterize unfolded proteins typically provide only short-range, sequence-local structural information that is both time- and ensemble-averaged, giving limited detail about the long-range structure of the chain. Here, we report a study of a long-range property: the radius of gyration of an alanine-based peptide, Ace-(diaminobutyric acid)2-(Ala)7-(ornithine)2-NH2. This molecule has previously been studied as a model for the unfolded state of proteins under folding conditions and is believed to adopt a PPII fold based on short-range techniques such as NMR and CD. By using synchrotron radiation and small-angle x-ray scattering, we have determined the radius of gyration of this peptide to be 7.4 +/- 0.5 angstroms, which is significantly less than the value expected from an ideal PPII helix in solution (13.1 angstroms). To further study this contradiction, we have used molecular dynamics simulations using six variants of the AMBER force field and the GROMOS 53A6 force field. However, in all cases, the simulated ensembles underestimate the PPII content while overestimating the experimental radius of gyration. The conformational model that we propose, based on our small angle x-ray scattering results and what is known about this molecule from before, is that of a very flexible, fluctuating structure that on the level of individual residues explores a wide basin around the ideal PPII geometry but is never, or only rarely, in the ideal extended PPII helical conformation.

Scaling Behavior and Structure of Denatured Proteins

An ensemble of random-coil conformations with no persistent structures has long been accepted as the classical model of denatured proteins due to its consistency with the experimentally determined scaling of protein sizes. However, recent NMR spectroscopy studies on proteins at high chemical denaturant concentrations suggest the presence of significant amounts of native-like structures, in contrast to the classical random-coil picture. To reconcile these seemingly controversial observations, we examine thermally denatured states of experimentally characterized proteins by using molecular dynamics simulations. For all studied proteins, we find that denatured states indeed have strong local conformational bias toward native states while a random-coil power law scaling of protein sizes is preserved. In addition, we explain why experimentally determined size of the protein creatine kinase does not follow general scaling. In simulations, we observe that this protein exhibits a stable intermediate state, the size of which is consistent with the reported experimental observation.

Direct characterization of the folded, unfolded and urea-denatured states of the C-terminal domain of the ribosomal protein L9

The stability of the isolated C-terminal domain of the ribosomal protein L9 (CTL9) is strongly dependent upon pH. Below pH 4.2, the folded and unfolded states are both populated significantly. Their interconversion is slow on the NMR chemical shift time-scale and separate, well-resolved resonances from each state are observed. This allows the hydrodynamic properties of both states to be studied under identical conditions by using pulse field gradient NMR experiments. Hydrodynamic radii of the folded, unfolded and urea denatured protein molecules at pD 3.8 have been derived. The acid-denatured protein has a significantly smaller hydrodynamic radius, 28.2A, compared to that of the urea-denatured protein, which is 33.6A at pD 3.8. Far-UV CD spectra show that there is more residual secondary structure retained in the acid-denatured ensemble than in the urea-denatured one. ANS binding experiments and analysis of the CD data show that this acid-denatured species is not a molten globule state. Diffusion measurements of CTL9 were conducted over the pD range from 2.1 to 7.0. The hydrodynamic radii of both the folded and the acid-unfolded protein start to increase below pD 4, with the radius of hydration of the acid-unfolded state increasing from 25.1A at pD 4.2 to 33.5A at pD 2.1. The hydrodynamic radius of the urea-denatured protein is much less sensitive to pH. The unfolded protein at pD 2.1, no urea, has almost the same hydrodynamic radius as the urea-denatured protein at pD 3.8. The CD spectra, however, show significant differences in residual secondary structure, and the acid-denatured state contains more structure.

Molecular crowding enhances native state stability and refolding rates of globular proteins

The presence of macromolecules in cells geometrically restricts the available space for poplypeptide chains. To study the effects of macromolecular crowding on folding thermodynamics and kinetics, we used an off-lattice model of the all-beta-sheet WW domain in the presence of large spherical particles whose interaction with the polypeptide chain is purely repulsive. At all volume fractions, phi(c), of the crowding agents the stability of the native state is enhanced. Remarkably, the refolding rates, which are larger than the value at phi(c) = 0, increase nonmonotonically as phi(c) increases, reaching a maximum at phi(c)=phi(c)(*). At high values of phi(c), the depletion-induced intramolecular attraction produces compact structures with considerable structure in the denatured state. Changes in native state stability and folding kinetics at phi(c) can be quantitatively mapped onto confinement in a volume-fraction-dependent spherical pore with radius R(s) approximately (4pi/3phi(c))(1/3) R(c) (R(c) is the radius of the crowding particles) as long as phi(c)< or =phi(c)(*). We show that the extent of native state stabilization at finite phi(c) is comparable with that in a spherical pore. In both situations, rate enhancement is due to destabilization of the denatured states with respect to phi(c) = 0.

Finite size effects on thermal denaturation of globular proteins

Finite size effects on the cooperative thermal denaturation of proteins are considered. A dimensionless measure of cooperativity, Omegac, scales as Nzeta, where N is the number of amino acids. Surprisingly, we find that zeta is universal with zeta=1+gamma, where the exponent gamma characterizes the divergence of the susceptibility for a self-avoiding walk. Our lattice model simulations and experimental data are consistent with the theory. Our finding rationalizes the marginal stability of proteins and substantiates the earlier predictions that the efficient folding of two-state proteins requires TF approximately Ttheta, where Ttheta and TF are the collapse and folding transition temperatures, respectively.

Measuring unfolding of proteins in the presence of denaturant using fluorescence correlation spectroscopy

IFABP is a small (15 kDa) protein consisting mostly of antiparallel beta-strands that surround a large cavity into which ligands bind. We have previously used FCS to show that the native protein, labeled with fluorescein, exhibits dynamic fluctuation with a relaxation time of 35 micros. Here we report the use of FCS to study the unfolding of the protein induced by guanidine hydrochloride. Although the application of this technique to measure diffusion coefficients and molecular dynamics is straightforward, the FCS results need to be corrected for both viscosity and refractive index changes as the guanidine hydrochloride concentration increases. We present here a detailed study of the effects of viscosity and refractive index of guanidine hydrochloride solutions to calibrate FCS data. After correction, the increase in the diffusion time of IFABP corresponds well with the unfolding transition monitored by far ultraviolet circular dichroism. We also show that the magnitude of the 35 micros phase, reflecting the conformational fluctuation in the native state, decreases sharply as the concentration of denaturant increases and the protein unfolds. Although FCS experiments indicate that the unfolded state at pH 2 is rather compact and native-like, the radius in the presence of guanidine hydrochloride falls well within the range expected for a random coil.

Reassessing random-coil statistics in unfolded proteins

The Gaussian-distributed random coil has been the dominant model for denatured proteins since the 1950s, and it has long been interpreted to mean that proteins are featureless, statistical coils in 6 M guanidinium chloride. Here, we demonstrate that random-coil statistics are not a unique signature of featureless polymers. The random-coil model does predict the experimentally determined coil dimensions of denatured proteins successfully. Yet, other equally convincing experiments have shown that denatured proteins are biased toward specific conformations, in apparent conflict with the random-coil model. We seek to resolve this paradox by introducing a contrived counterexample in which largely native protein ensembles nevertheless exhibit random-coil characteristics. Specifically, proteins of known structure were used to generate disordered conformers by varying backbone torsion angles at random for approximately 8% of the residues; the remaining approximately 92% of the residues remained fixed in their native conformation. Ensembles of these disordered structures were generated for 33 proteins by using a torsion-angle Monte Carlo algorithm with hard-sphere sterics; bulk statistics were then calculated for each ensemble. Despite this extreme degree of imposed internal structure, these ensembles have end-to-end distances and mean radii of gyration that agree well with random-coil expectations in all but two cases.