Denaturant Concentration Research Articles

Sequence-Encoded Heterogeneity of Interactions Decouples Different Measures of Protein Sizes and Reconciles the Discrepant Inferences from Saxs versus Fret Experiments

Quantifying the conformational properties of folded proteins as a function of denaturant concentration is important for understanding the mechanism of protein folding. Additionally, quantifying the conformational properties of intrinsically disordered proteins (IDPs) can yield insights regarding the functions of IDPs. Radius of gyration, RG, which quantifies the average size of a protein, and end-to-end distance, REE, are two commonly used conformational descriptors as these values can be determined using small-angle x-ray scattering (SAXS) and single molecule Förster resonance energy transfer (smFRET), respectively. However, for several proteins, the RG profile determined directly from SAXS as a function of denaturant concentration differs from the RG profile inferred using REE values determined from smFRET and a given homopolymer model. Here, we show that this discrepancy is not due to any inherent flaws of either measurement, but instead arises as a result of sequence-specific interactions that exist within proteins under low denaturant conditions. Sequence-specific interactions induce heterogeneity within the conformational ensemble of a protein, which in turn decouples globally averaged (e.g., RG) and length-scale-specific (e.g., REE) conformational descriptors. The extent of decoupling of conformational descriptors, and thus the appropriateness of using a homopolymer model to convert between RG and REE, is sequence specific and is often unknown a priori. Here, we investigate the relationship between sequence-complexity and deviations from homopolymer models. Additionally, we show that by combining results from experimental measurements that yield distinct conformational descriptors with molecular simulations we can provide complete conformational descriptions of heterogeneous ensembles.

Deciphering hierarchical features in the energy landscape of adenylate kinase folding/unfolding

Hierarchical features of the energy landscape of the folding/unfolding behavior of adenylate kinase, including its dependence on denaturant concentration, are elucidated in terms of single-molecule fluorescence resonance energy transfer (smFRET) measurements in which the proteins are encapsulated in a lipid vesicle. The core in constructing the energy landscape from single-molecule time-series across different denaturant concentrations is the application of rate-distortion theory (RDT), which naturally considers the effects of measurement noise and sampling error, in combination with change-point detection and the quantification of the FRET efficiency-dependent photobleaching behavior. Energy landscapes are constructed as a function of observation time scale, revealing multiple partially folded conformations at small time scales that are situated in a superbasin. As the time scale increases, these denatured states merge into a single basin, demonstrating the coarse-graining of the energy landscape as observation time increases. Because the photobleaching time scale is dependent on the conformational state of the protein, possible nonequilibrium features are discussed, and a statistical test for violation of the detailed balance condition is developed based on the state sequences arising from the RDT framework.

Cooperative protein unfolding. A statistical-mechanical model for the action of denaturants

Knowledge of protein stability is of utmost importance in various fields of biotechnology. Protein stability can be assessed in solution by increasing the concentration of denaturant and recording the structural changes with spectroscopic or thermodynamic methods. The standard interpretation of the experimental data is to assume a 2-state equilibrium between completely folded and completely unfolded protein molecules. Here we propose a cooperative model based on the statistical-mechanical Zimm-Bragg theory. In this model protein unfolding is driven by the weak binding of a rather small number of denaturant molecules, inducing the cooperative unfolding with multiple dynamic intermediates. The modified Zimm-Bragg theory is applied to published thermodynamic and spectroscopic data leading to the following conclusions. (i) The binding constant KD is correlated with the midpoint concentration, c0, of the unfolding reaction according to c0≅1/KD. The better the binding of denaturant the lower is the concentration to achieve unfolding. (ii) The binding constant KD agrees with direct thermodynamic measurements. A rather small number of bound denaturants suffices to induce the cooperative unfolding of the whole protein. (iii) Chemical unfolding occurs in the concentration range ΔcD=cend−cini. The theory predicts the unfolding energy per amino acid residue as gnu=RTKD(cend−cini). The Gibbs free energy of an osmotic gradient of the same size is ΔGDiff=−RTln(cend/cini). In all examples investigated ΔGDiff exactly balances the unfolding energy gnu. The total unfolding energy is thus close to zero. (iv) Protein cooperativity in chemical unfolding is rather low with cooperativity parameters σ≥3x10−3. As a consequence, the theory predicts a dynamic mixture of conformations during the unfolding reaction. The probabilities of individual conformations are easily accessible via the partition function Z(cD,σ).

A new look at an old view of denaturant induced protein unfolding

We re-examine a site-binding approach independently proposed by Schellman (Schellman, J.A. (1958) Compt. rend. Lab. Carlsberg Ser. Chim. 30, 439–449) and Aune and Tanford (Aune, K.C. and Tanford, D. (1969) Biochemistry, 8, 4586–4590) for explicitly including the denaturant concentration within the protein unfolding equilibrium. We extend and formalize the approach through development of a multi-dimensional analytical model in which the folding reaction coordinate is defined by the number of denaturant molecules bound to sites located on either the initially folded, or unfolded, states of the protein. We use the developed method to re-examine the mechanistic determinants underlying the sigmoidal shape of the unfolding transition. A natural feature of our method is that it presents a landscape picture of the denaturant induced protein unfolding reaction.

Denaturant-specific effects on the structural energetics of a protein-denatured ensemble.

Protein thermodynamic stability is intricately linked to cellular function, and altered stability can lead to dysfunction and disease. The linear extrapolation model (LEM) is commonly used to obtain protein unfolding free energies ([Formula: see text]) by extrapolation of solvent denaturation data to zero denaturant concentration. However, for some proteins, different denaturants result in non-coincident LEM-derived [Formula: see text] values, raising questions about the inherent assumption that the obtained [Formula: see text] values are intrinsic to the protein. Here, we used single-molecule FRET measurements to better understand such discrepancies by directly probing changes in the dimensions of the protein G B1 domain (GB1), a well-studied protein folding model, upon urea and guanidine hydrochloride denaturation. A comparison of the results for the two denaturants suggests denaturant-specific structural energetics in the GB1 denatured ensemble, revealing a role of the denatured state in the variable thermodynamic behavior of proteins.

Thermodynamics and Kinetics of Single-Chain Monellin Folding with Structural Insights into Specific Collapse in the Denatured State Ensemble

Proteins, which behave as random coils in high denaturant concentrations undergo collapse transition similar to polymers on denaturant dilution. We study collapse in the denatured ensemble of single-chain monellin (MNEI) using a coarse-grained protein model and molecular dynamics simulations. The model is validated by quantitatively comparing the computed guanidinium chloride and pH-dependent thermodynamic properties of MNEI folding with the experiments. The computed properties such as the fraction of the protein in the folded state and radius of gyration (Rg) as function of [GuHCl] are in good agreement with the experiments. The folded state of MNEI is destabilized with an increase in pH due to the deprotonation of the residues Glu24 and Cys42. On decreasing [GuHCl], the protein in the unfolded ensemble showed specific compaction. The Rg of the protein decreased steadily with [GuHCl] dilution due to increase in the number of native contacts in all the secondary structural elements present in the protein. MNEI folding kinetics is complex with multiple folding pathways and transiently stable intermediates are populated in these pathways. In strong stabilizing conditions, the protein in the unfolded ensemble showed transition to a more compact unfolded state where Rg decreased by ≈17% due to the formation of specific native contacts in the protein. The intermediate populated in the dominant MNEI folding pathway satisfies the structural features of the dry molten globule inferred from experiments.

SAXS versus FRET: A Matter of Heterogeneity?

Determining how conformational properties of unfolded proteins vary as a function of denaturant concentration has important implications for understanding the early stages of protein folding, and for our understanding of protein-solvent interactions. Upon dilution from a high concentration of denaturant into native conditions, does an unfolded protein undergo collapse first followed by folding, or does the chain remain expanded before folding and collapse occur concomitantly? The global dimensions of a protein are captured by its radius of gyration (Rg), meaning that, in principle, this question should be simple to answer by measuring Rg as a function of denaturant concentration.

Insight into the functional and structural transition of garlic phytocystatin induced by urea and guanidine hydrochloride: A comparative biophysical study

Cysteine proteinase inhibitors play an essential role in maintaining the proper functioning of all living cells by virtue of its thiol protease regulatory properties. Chemical denaturation of a new variant of cystatin super family has been studied by various biophysical techniques in order to characterize the unfolded and denatured state. Denaturation of garlic phytocystatin (GPC) has been investigated using urea and guanidine hydrochloride (GdnHCl). Different biophysical techniques such as intrinsic fluorescence, circular dichroism and FTIR exhibited an altered structure of garlic phytocystatin with increasing concentration of denaturant. The inhibitory activity of GPC decreases with increasing concentration of denaturant. Increased fluorescence intensity along with red shift reflects the unfolding of GPC at higher concentration of denaturant. GdnHCl induced unfolding showed presence of indiscernible intermediate as followed by ANS binding studies. However, denaturation by urea did not show any intermediates. Mid-point transition was observed at 4.7±0.1M urea and 2.32±0.1M GdnHCl. Circular dichroism and FTIR results indicate the 50% loss of secondary structure at 5M urea and 2.5M GdnHCl. This study provides intriguing insight into the possible alteration of structure, stability and function of GPC induced by urea and GdnHCl.

Small monomeric and highly stable near-infrared fluorescent markers derived from the thermophilic phycobiliprotein, ApcF2

Biliproteins have extended the spectral range of fluorescent proteins into the region of maximal transmission of most tissues and are favorable for multiplexing, but their application presents considerable challenges. Their fluorescence derives from open-chain tetrapyrrole chromophores which often require the introduction of dedicated reductases and lyases. In addition, their fluorescence yield generally decreases with increasing wavelengths and depends strongly on the state of the binding protein. We report fluorescent biliproteins, termed BDFPs, that are derived from the phycobilisome core subunit, ApcF2: this subunit is induced in the thermophilic cyanobacterium, Chroococcidiopsis thermalis, by far-red light and binds phycocyanobilin non-covalently. The BDFPs obtained by molecular evolution of ApcF2 bind the more readily accessible biliverdin covalently while retaining the red-shifted fluorescence in the near-infrared spectral region (~710nm). They are small monomers (~15kDa) and not only show excellent photostability, but are also thermostable up to 80°C, tolerate acid down to pH2 and high concentrations of denaturants. The result indicates far-red adapting cyanobacteria as a useful source for designing extremely red-shifted fluorescent markers. In vivo performance of BDFPs as biomarkers in conventional and super-resolution microscopy, alone or fused to target proteins, is exemplified in several mammalian cells, including, human cell lines, in the nematode, Caenorhabditis elegans and, at low pH, in Lactobacillus lactis.

A Dry Transition State More Compact Than the Native State Is Stabilized by Non-Native Interactions during the Unfolding of a Small Protein.

Defining the role of non-native interactions in directing the course of protein folding or unfolding reactions has been a difficult challenge. In particular, the extent to which such interactions play a productive role by stabilizing the structures of transition states (TSs) found on the folding and unfolding pathways of proteins is not known. On the contrary, it is thought that the TSs are expanded forms of the N state stabilized by native interactions, and it is not known whether non-native interactions can modulate TS structure. In this study of the unfolding of the SH3 domain of PI3 kinase using a microsecond mixing methodology, partial non-native structure formation is shown to occur initially during unfolding. The TS of this partial "folding during unfolding" reaction is more compact than the N state: the apparent rate constant of Trp53 burial during this reaction decreases with an increase in denaturant concentration. Kinetic studies of the unfolding of mutant variants suggest that the unusually compact TS is stabilized by interactions not present in N and that these non-native interactions are hydrophobic in nature. It was determined that mutation could be used to tune the degree of compaction in the TS.

Unveiling the folding mechanism of the Bromodomains

Bromodomains (BRDs) are small protein domains often present in large multidomain proteins involved in transcriptional regulation in eukaryotic cells. They currently represent valuable targets for the development of inhibitors of aberrant transcriptional processes in a variety of human diseases. Here we report urea-induced equilibrium unfolding experiments monitored by circular dichroism (CD) and fluorescence on two structurally similar BRDs: BRD2(2) and BRD4(1), showing that BRD4(1) is more stable than BRD2(2). Moreover, we report a description of their kinetic folding mechanism, as obtained by careful analysis of stopped-flow and temperature-jump data. The presence of a high energy intermediate for both proteins, suggested by the non-linear dependence of the folding rate on denaturant concentration in the millisec time regime, has been experimentally observed by temperature-jump experiments. Quantitative global analysis of all the rate constants obtained over a wide range of urea concentrations, allowed us to propose a common, three-state, folding mechanism for these two BRDs. Interestingly, the intermediate of BRD4(1) appears to be more stable and structurally native-like than that populated by BRD2(2). Our results underscore the role played by structural topology and sequence in determining and tuning the folding mechanism.

Quantum conformational transition in biological macromolecule

BackgroundRecently we proposed a quantum theory on the conformational change of biomolecule, deduced several equations on protein folding rate from the first principles and discussed the experimental tests of the theory. The article is a review of these works.MethodsBased on the general equation of the conformation‐transitional rate several theoretical results are deduced and compared with experimental data through bioinformatics methods.ResultsThe temperature dependence and the denaturant concentration dependence of the protein folding rate are deduced and compared with experimental data. The quantitative relation between protein folding rate and torsional mode number (or chain length) is deduced and the obtained formula can be applied to RNA folding as well. The quantum transition theory of two‐state protein is successfully generalized to multi‐state protein folding. Then, how to make direct experimental tests on the quantum property of the conformational transition of biomolecule is discussed, which includes the study of protein photo‐folding and the observation of the fluctuation of the fluorescence intensity emitted from the protein folding/unfolding event. Finally, the potential applications of the present quantum folding theory to molecular biological problems are sketched in two examples: the glucose transport across membrane and the induced pluripotency in stem cell.ConclusionsThe above results show that the quantum mechanics provides a unifying and logically simple theoretical starting point in studying the conformational change of biological macromolecules. The far‐reaching results in practical application of the theory are expected.

Highly Heterogeneous Nature of the Native and Unfolded States of the B Domain of Protein A Revealed by Two-Dimensional Fluorescence Lifetime Correlation Spectroscopy

Elucidating the protein folding mechanism is crucial to understand how proteins acquire their unique structures to realize various biological functions. With this aim, the folding/unfolding of small globular proteins has been extensively studied. Interestingly, recent studies have revealed that even such small proteins represent considerably complex processes. In this study, we examined the folding/unfolding process of a small α-helical protein, the B domain of protein A (BdpA), at equilibrium using two-dimensional fluorescence lifetime correlation spectroscopy with 10 μs time resolution. The results showed that although the BdpA is a two-state folder, both the native and unfolded states are highly heterogeneous and the conformational conversion within each ensemble occurs within 10 μs. Furthermore, it was shown that the average structures of both ensembles gradually change and become more elongated as the denaturant concentration increases. The analysis on two mutants suggested that fraying of the N-terminal helix is the origin of the inhomogeneity of the native state. Because the direct observation of the ensemble nature of the native state at the single-molecule level has not been reported, the data obtained in this study give new insights into complex conformational properties of small proteins.

FRET studies of various conformational states adopted by transthyretin.

Transthyretin (TTR) is an extracellular protein able to deposit into well-defined protein aggregates called amyloid, in pathological conditions known as senile systemic amyloidosis, familial amyloid polyneuropathy, familial amyloid cardiomyopathy and leptomeningeal amyloidosis. At least three distinct partially folded states have been described for TTR, including the widely studied amyloidogenic state at mildly acidic pH. Here, we have used fluorescence resonance energy transfer (FRET) experiments in a monomeric variant of TTR (M-TTR) and in its W41F and W79F mutants, taking advantage of the presence of a unique, solvent-exposed, cysteine residue at position 10, that we have labelled with a coumarin derivative (DACM, acceptor), and of the two natural tryptophan residues at positions 41 and 79 (donors). Trp41 is located in an ideal position as it is one of the residues of β-strand C, whose degree of unfolding is debated. We found that the amyloidogenic state at low pH has the same FRET efficiency as the folded state at neutral pH in both M-TTR and W79F-M-TTR, indicating an unmodified Cys10-Trp41 distance. The partially folded state populated at low denaturant concentrations also has a similar FRET efficiency, but other spectroscopic probes indicate that it is distinct from the amyloidogenic state at acidic pH. By contrast, the off-pathway state accumulating transiently during refolding has a higher FRET efficiency, indicating non-native interactions that reduce the Cys10-Trp41 spatial distance, revealing a third distinct conformational state. Overall, our results clarify a negligible degree of unfolding of β-strand C in the formation of the amyloidogenic state and establish the concept that TTR is a highly plastic protein able to populate at least three distinct conformational states.

The native state of prion protein (PrP) directly inhibits formation of PrP-amyloid fibrils in vitro

The conversion of globular proteins into amyloid fibrils is associated with a wide variety of human diseases. One example is the prion protein (PrP), which adopts an α-helical structure in the native state but its amyloid form is implicated in the pathogenesis of prion diseases. Previous evidence has suggested that destabilization of the native state promotes amyloid formation, but the underlying mechanism remains unknown. In this study, we report that the native state of PrP serves as a potent inhibitor in the formation of PrP amyloid fibrils. By monitoring the time courses of thioflavin T fluorescence, the kinetics of amyloid formation was studied in vitro under various concentrations of pre-formed amyloid, monomer, and denaturant. Quantitative analysis of the kinetic data using various models of enzyme kinetics suggested that the native state of PrP is either an uncompetitive or noncompetitive inhibitor of amyloid formation. This study highlights the significant role of the native state in inhibiting amyloid formation, which provides new insights into the pathogenesis of misfolding diseases.

SAXS: A Versatile Tool to Study Biological Macromolecules in Solution

The Biophysics Collaborative Access Team (BioCAT), which operates the high‐brilliance undulator Beamline 18ID at the Advanced Photon Source, Argonne National Laboratory, is dedicated to studying disordered macromolecules in solution using Small‐Angle X‐ray Scattering (SAXS). In SAXS, the solution scattering profile contains three dimensional information of macromolecules at nanometer scale in solution. The combination of a highly brilliant X‐ray source and advanced micro‐focusing optics at BioCAT enables significant insights into the structure and dynamic of bio‐macromolecules from both static and time‐resolved SAXS experiment.The quality and interpretability of SAXS data is largely contingent on sample homogeneity. Size‐exclusion chromatography (SEC)‐SAXS, which was pioneered at BioCAT has therefore emerged as a powerful mode of data acquisition as it ensures optimal sample quality by purification immediately before exposure to x‐rays. In addition, we have also incorporated multi‐angle light scattering (MALS), dynamic light scattering (DLS), and differential refractive index (dRI) detectors in line with the SAXS camera thus enabling acquisition of a full complement of biophysical data typically required to structurally characterize biological macromolecules simultaneously with SAXS data.The new frontier in the field is to study real‐time structural changes in biological systems as a response to very specific environmental stimuli such as a change in denaturant concentration, ionic strength, pH or ligand binding. Forefront time resolved SAXS techniques using chaotic mixing continuous flow, continuous laminar flow and stopped flow mixing are now available to a wide variety of bio‐medical projects at BioCAT primarily on account of being optimized over the past few years both for sample consumption and mixing efficiency.Support or Funding Information9 P41 GM103622

Structure and Conformational Properties of d-Glucose/d-Galactose-Binding Protein in Crowded Milieu.

Conformational changes of d-glucose/d-galactose-binding protein (GGBP) were studied under molecular crowding conditions modeled by concentrated solutions of polyethylene glycols (PEG-12000, PEG-4000, and PEG-600), Ficoll-70, and Dextran-70, addition of which induced noticeable structural changes in the GGBP molecule. All PEGs promoted compaction of GGBP and lead to the increase in ordering of its structure. Concentrated solutions of PEG-12000 and PEG-4000 caused GGBP aggregation. Although Ficoll-70 and Dextran-70 also promoted increase in the GGBP ordering, the structural outputs were different for different crowders. For example, in comparison with the GGBP in buffer, the intrinsic fluorescence spectrum of this protein was shifted to short-wave region in the presence of PEGs but was red-shifted in the presence of Ficoll-70 and Dextran-70. It was hypothesized that this difference could be due to the specific interaction of GGBP with the sugar-based polymers (Ficoll-70 and Dextran-70), indicating that protein can adopt different conformations in solutions containing molecular crowders of different chemical nature. It was also shown that all tested crowding agents were able to stabilize GGBP structure shifting the GGBP guanidine hydrochloride (GdnHCl)-induced unfolding curves to higher denaturant concentrations, but their stabilization capabilities did not depend on the hydrodynamic dimensions of the polymers molecules. Refolding of GGBP was complicated by protein aggregation in all tested solutions of crowding agents. The lowest yield of refolded protein was achieved in the highly concentrated solutions of PEG-12000. These data support the previous notion that the influence of macromolecular crowders on proteins is rather complex phenomenon that extends beyond the excluded volume effects.

Resolving the Controversy between SAXS and FRET Measurements on Unfolded Proteins

Chemical denaturants are the most commonly used agents for unfolding proteins. An expansion of unfolded chains with increasing denaturant concentration is expected due to improved solvation. However, experiments have yielded qualitatively different results. Studies using Forster resonance energy transfer (FRET) and other methods found an increase in radius of gyration (Rg) with denaturant concentration, but most small-angle X-ray scattering (SAXS) studies found no change. This discrepancy challenges our understanding of denaturation mechanism and the accuracy of these experiments on intrinsically disordered proteins. We use all-atom molecular simulations to investigate the effect of urea and guanidinium chloride on the intrinsically disordered protein ACTR, which can be studied by both FRET and SAXS over a wide range of denaturant concentration. Using a carefully calibrated denaturant model, we find that the chain expands with increasing denaturant concentration. This is due to the favorable association of urea or guanidinium chloride with the backbone of all residues and with the side-chains of most residues. The denaturant-water transfer free energies inferred from this association are in reasonable agreement with experiment. By computing FRET efficiencies and SAXS intensities, we showed that the simulations are in accord with both experiments on this protein, demonstrating that there is no fundamental inconsistency between the two experimental methods. In addition, our simulations suggest that some potential artefacts are unlikely, i.e. the commonly used FRET chromophores do not qualitatively alter the results and that SAXS data are not distorted by preferential solvent partitioning into the interior of the chain. A careful analysis of the experimental data suggests that the discrepancy is largely related to the challenging inverse problem of inferring Rg from ensemble-averaged data. We show how this can be overcome by fitting the data to explicit molecular ensembles.

Theory of Amyloid Fibril Nucleation from Folded Proteins

We present a theoretical model for the nucleation of amyloid fibrils. In our model we use helix-coil theory to describe the equilibrium between a soluble native state and an aggregation-prone unfolded state. We then extend the theory to include oligomers with β-sheet cores and calculate the free energy of these states using estimates for the energies of H-bonds, steric zipper interactions, and the conformational entropy cost of forming secondary structure. We find that states with fewer than ~10 β-strands are unstable relative to the dissociated state and three β-strands is the highest free energy state. We then use a modified version of Classical Nucleation Theory to compute the nucleation rate of fibrils from a supersaturated solution of monomers, dimers, and trimers. The nucleation rate has a non-monotonic dependence on denaturant concentration reflecting the competing effects of destabilizing the fibril and increasing the concentration of unfolded monomers. We estimate heterogeneous nucleation rates and discuss the application of our model to secondary nucleation.

Collapse Precedes Folding in Denaturant-Dependent Assembly of Ubiquitin.

The folding of small protein ubiquitin (Ub), which plays an indispensable role in targeting proteins for degradation and DNA damage response, is complex. A number of experiments on Ub folding have reached differing conclusions regarding the relation between collapse and folding, and whether intermediates are populated. In order to resolve these vexing issues, we elucidate the denaturant-dependent thermodynamics and kinetics of Ub folding at low and neutral pH as a function of guanidinium chloride and urea using coarse-grained molecular simulations. The changes in the fraction of the folded Ub, and the radius of gyration (Rg) as a function of the denaturant concentration, [C], are in quantitative agreement with experiments. Under conditions used in experiments, Rg of the unfolded state at neutral pH changes only by ≈17% as the [GdmCl] decreases from 6 to 0 M. We predict that the extent of compaction of the unfolded state increases as temperature decreases. A two-dimensional folding landscape as a function of Rg and a measure of similarity to the folded state reveals unambiguously that the native state assembly is preceded by collapse, as discovered in fast mixing experiments on several proteins. Analyses of the folding trajectories, under mildly denaturing conditions ([GdmCl] = 1.0 M or [Urea] = 1.0 M), shows that Ub folds by collision between preformed secondary structural elements involving kinetic intermediates that are primarily stabilized by long-range contacts. Our work explains the results of small angle X-ray scattering (SAXS) experiments on Ub quantitatively, and establishes that evolved globular proteins in the unfolded ensemble are poised to collapse as the solvent conditions for the biopolymer changes from good solvent to Θ-solvent like conditions on denaturant dilution. In the process, we explain the discrepancy between SAXS and single molecule fluorescent resonant energy transfer (smFRET) experiments, which have arrived at a contradicting conclusion concerning the collapse of polypeptide chains.