How, when and why proteins collapse: the relation to folding

Collapse and Protein Folding: Should We Be Surprised That Biothermodynamics Works So Well?

A complete understanding of protein function and dynamics requires the characterization of the multiple thermodynamic states, including the denatured state ensemble (DSE). Whereas residual structure in the DSE (as well as in partially folded states) is pertinent in many biological contexts, here we are interested in how such structure affects protein thermodynamics. We examine issues related to chain collapse in light of new developments, focusing on potential complications arising from differences in the DSE's properties under various conditions. Despite some variability in the degree of collapse and structure in the DSE, stability measurements are remarkably consistent between two standard methods, calorimetry and chemical denaturation, as well as with hydrogen-deuterium exchange. This robustness is due in part to the DSEs obtained with different perturbations being thermodynamically equivalent and hence able to serve as a common reference state. An examination of the properties of the DSE points to it as being a highly expanded ensemble with minimal amounts of stable hydrogen bonded structure. These two features are likely to be critical in the broad and successful application of thermodynamics to protein folding. Our review concludes with a discussion of the impact of these findings on folding mechanisms and pathways.

Nonequilibrium dynamics of the helix-coil transition in polyalanine

In this work, the nonequilibrium pathways of the collapse of the helix-forming biopolymer polyalanine are investigated. To this end, the full time evolution of the helix-coil transition is simulated using molecular dynamics simulations. At the start of the transition, short 310-helices form, seemingly leading to the molecule becoming more aspherical midway through the collapse. After the completed collapse, the formation of α-helices becomes the prevalent ordering mechanism leading to helical bundles, a typical structural motif representative of the equilibrium behavior of longer chains. The dynamics of this transition is quantified in terms of the power-law scaling of two associated relaxation times as a function of chain length.

The standard coil or globule phases cannot describe the denatured state of structured proteins and intrinsically disordered proteins

The concepts of globule and random coil were developed to describe the phases of homopolymers and then used to characterize the denatured state of structured cytosolic proteins and intrinsically disordered proteins. Using multi-scale molecular dynamics simulations, we were able to explore the conformational space of the disordered conformations of both types of protein under biological conditions in an affordable amount of computational time. By studying the size of the protein and the density correlations in space, we conclude that the standard phases of homopolymers and the tools to detect them cannot be applied straightforwardly to proteins.

Accuracy of distance distributions and dynamics from single-molecule FRET

Single-molecule spectroscopy combined with Förster resonance energy transfer is widely used to quantify distance dynamics and distributions in biomolecules. Most commonly, measurements are interpreted using simple analytical relations between experimental observables and the underlying distance distributions. However, these relations make simplifying assumptions, such as a separation of timescales between interdye distance dynamics, fluorescence lifetimes, and dye reorientation, the validity of which is notoriously difficult to assess from experimental data alone. Here, we use experimentally validated long-timescale, all-atom explicit-solvent molecular dynamics simulations of a disordered peptide with explicit fluorophores for testing these assumptions, in particular the separation of the relevant timescales and the description of chain dynamics in terms of diffusion in a potential of mean force. Our results allow us to quantitatively assess the resulting errors; they indicate that, even outside the simple limiting regimes, the errors from common approximations in data analysis are generally smaller than the systematic uncertainty limiting the accuracy of Förster resonance energy transfer efficiencies. We also illustrate how the direct comparison between measured and simulated experimental data can be employed to optimize force field parameters and develop increasingly realistic simulation models.

From propensities to patterns to principles in protein folding

As proposed here, β-turns play an essential role in protein self-assembly. This compact, four-residue motif affects protein conformation dramatically by reversing the overall chain direction. Turns are the "hinges" in globular proteins. This new proposal broadens a previous hypothesis that globular proteins solve the folding problem in part by filtering conformers with unsatisfied backbone hydrogen bonds, thereby preorganizing the folding population. Recapitulating that hypothesis: unsatisfied conformers would be dramatically destabilizing, shifting the U(nfolded) ⇌ N(ative) equilibrium far to the left. If even a single backbone polar group is satisfied by solvent when unfolded but buried and unsatisfied when folded, that energy penalty alone, approximately +5 kcal/mol, would rival almost the entire free energy of protein stabilization at room temperature. Consequently, globular proteins are built on scaffolds of hydrogen-bonded α-helices and/or strands of β-sheet, motifs that can be extended indefinitely, with intra-segment hydrogen bond partners for their backbone polar groups and without steric clash. Scaffolds foster a protein-wide hydrogen-bonded network, and, of thermodynamic necessity, they self-assemble cooperatively. Unlike elements of repetitive secondary structure, α-helices and β-sheet, a four-residue β-turn has only a single hydrogen bond (from i + 3 → i), not a cooperatively formed assembly of hydrogen bonds. As such, turns can form autonomously and are poised to initiate assembly of scaffold elements by bringing them together in an orientation and registration that promotes cooperative "zipping". The overall effect of this self-assembly mechanism is to induce substantial preorganization in the thermodynamically accessible folding population and, concomitantly, to reduce the folding entropy.

Identifying Sequence Effects on Chain Dimensions of Disordered Proteins by Integrating Experiments and Simulations

It has become increasingly evident that the conformational distributions of intrinsically disordered proteins or regions are strongly dependent on their amino acid compositions and sequence. To facilitate a systematic investigation of these sequence-ensemble relationships, we selected a set of 16 naturally occurring intrinsically disordered regions of identical length but with large differences in amino acid composition, hydrophobicity, and charge patterning. We probed their conformational ensembles with single-molecule Förster resonance energy transfer (FRET), complemented by circular dichroism (CD) and nuclear magnetic resonance (NMR) spectroscopy as well as small-angle X-ray scattering (SAXS). The set of disordered proteins shows a strong dependence of the chain dimensions on sequence composition, with chain volumes differing by up to a factor of 6. The residue-specific intrachain interaction networks that underlie these pronounced differences were identified using atomistic simulations combined with ensemble reweighting, revealing the important role of charged, aromatic, and polar residues. To advance a transferable description of disordered protein regions, we further employed the experimental data to parametrize a coarse-grained model for disordered proteins that includes an explicit representation of the FRET fluorophores and successfully describes experiments with different dye pairs. Our findings demonstrate the value of integrating experiments and simulations for advancing our quantitative understanding of the sequence features that determine the conformational ensembles of intrinsically disordered proteins.

Amino Acid Residue-Specific Ramachandran Distributions Derived from a Simple Mean Field Potential

Protein dynamics in the unfolded state, in the context of early stage protein folding or intrinsically disordered proteins (IDPs), is not well understood. The discovery of IDPs, and their sequence-dependent dynamics, has led to many computational and experimental investigations regarding the conformational preferences of short oligopeptides and individual amino acid residues in the unfolded state. As proteins consist of sequences of amino acid residues, characterizing the intrinsic conformational preferences of the individual residues in the unfolded state is crucial for understanding the emergent conformations of peptides and proteins. While advances have been made in understanding conformational preferences, the atomistic mechanisms driving these preferences remain unresolved. In this work, we show that the distributions of atomic overlaps between backbone and side chain atoms in Ramachandran space are unique for amino acid residue mimetic structures alanine, valine, leucine, and isoleucine in Ramachandran space indicating unique intrapeptide energy landscapes for each residue. We then construct a mean field potential consisting of only an empirical peptide backbone-water and average intrapeptide Lennard-Jones contributions to explore their influence on the conformational preferences. With this fairly simple model, we were able to produce Ramachandran distributions that qualitatively agree with previously reported experimental and computational predictions about the conformational preferences of these amino acid residues in the unfolded state in water. Our results indicate these conformational preferences are the result of the balance between pPII-stabilizing backbone-water interactions and repulsive side chain-backbone interactions where the latter will depend uniquely on the atomic makeup and geometry of the side chain.

Probe capsid structure stability and dynamics of adeno-associated virus as an important viral vector for gene therapy by hydrogen-deuterium exchange-mass spectrometry

Adeno-associated virus (AAV), a widely used gene therapy vector, is a small, nonenveloped virus that contains a single-stranded DNA genome with a maximum length of 4.7 kb. Despite extensive biophysical and structural characterization, many aspects of AAV functions remain elusive. This knowledge gap is primarily due to a lack of structurally resolved dynamic information and the absence of structural coverage of functionally critical segments on the AAV capsid. Here, we developed a protocol to study AAV structural dynamics by hydrogen-deuterium exchange mass spectrometry (HDX-MS), a powerful method for monitoring protein structure stability and dynamics in solution. We performed HDX-MS measurements on AAVs without or with different DNA payloads of different sizes, and obtained detailed dynamic information on the entire AAV sequence including the two functionally important segments not previously structurally characterized. The unique N terminus of the capsid protein VP1 (VP1u) was found to adopt a highly dynamic and unstable conformation with low HDX protection across the entire region, whereas the presence of a DNA payload increased its protection. The VP1 and VP2 shared region (VP1/2) showed no measurable protection, with or without DNA. Differential HDX between empty and full capsid samples allowed us to identify potential new DNA-capsid interaction sites located primarily around the five-fold channel, which differ from the three-fold pocket binding site previously identified. Our HDX-MS method for characterizing AAV structural dynamics opens a new way for future efforts to understand AAV structure-function relationships and engineer next-generation AAV vectors with improved gene delivery properties.

Methotrexate for Drug Repurposing as an Anti-Aggregatory Agent to Mercuric Treated α-Chymotrypsinogen-A

Protein aggregation is related to numerous pathological conditions like Alzheimer's and Parkinson's disease. In our study, we have shown that an already existing FDA-approved drug; methotrexate (MTX) can be reprofiled on preformed α-chymotrypsinogen A (α-Cgn A) aggregates. The zymogen showed formation of aggregates upon interaction with mercuric ions, with increasing concentration of Hg2Cl2 (0-150 µM). The hike in ThT and ANS fluorescence concomitant with blue shift, bathochromic shift and the hyperchromic effect in the CR absorbance, RLS and turbidity measurements, substantiate the zymogen β-rich aggregate formation. The secondary structural alterations of α- Cgn A as analyzed by CD measurements, FTIR and Raman spectra showed the transformation of native β-barrel conformation to β-inter-molecular rich aggregates. The native α- Cgn A have about 30% α-helical content which was found to be about 3% in presence of mercuric ions suggesting the formation of aggregates. The amorphous aggregates were visualized by SEM. On incubation of Hg2Cl2 treated α- Cgn A with increasing concentration of the MTX resulted in reversing aggregates to the native-like structure. These results were supported by remarkable decrease in ThT and ANS fluorescence intensities and CR absorbance and also consistent with CD, FTIR, and Raman spectroscopy data. MTX was found to increase the α-helical content of the zymogen from 3 to 15% proposing that drug is efficient in disrupting the β-inter-molecular rich aggregates and reverting it to native like structure. The SEM images are in accordance with CD data showing the disintegration of aggregates. The most effective concentration of the drug was found to be 120 µM. Molecular docking analysis showed that MTX molecule was surrounded by the hydrophobic residues including Phe39, His40, Arg145, Tyr146, Thr151, Gly193, Ser195, and Gly216 and conventional hydrogen bonds, including Gln73 (bond length: 2.67Å), Gly142 (2.59Å), Thr144 (2.81Å), Asn150 (2.73Å), Asp153 (2.71Å), and Cys191 (2.53Å). This investigation will help to find the use of already existing drugs to cure protein misfolding-related abnormalities.

Structure of Single-Chain Nanoparticles under Crowding Conditions: A Random Phase Approximation Approach

The conformation of poly(methyl methacrylate) (PMMA)-based single-chain nanoparticles (SCNPs) and their corresponding linear precursors in the presence of deuterated linear PMMA in deuterated dimethylformamide (DMF) solutions has been studied by small-angle neutron scattering (SANS). The SANS profiles were analyzed in terms of a three-component random phase approximation (RPA) model. The RPA approach described well the scattering profiles in dilute and crowded solutions. Considering all the contributions of the RPA leads to an accurate estimation of the single chain form factor parameters and the Flory-Huggins interaction parameter between PMMA and DMF. The value of the latter in the dilute regime indicates that the precursors and the SCNPs are in good solvent conditions, while in crowding conditions, the polymer becomes less soluble.

Replacement of the native cis prolines by alanine leads to simplification of the complex folding mechanism of a small globular protein

The folding mechanism of MNEI, a single-chain variant of naturally occurring double-chain monellin, is complex, with multiple parallel refolding channels. To determine whether its folding energy landscape could be simplified, the two native cis-prolines, Pro41 and Pro93, were mutated, singly and together, to Ala. The stability of P93A was the same as that of the wild-type protein, pWT; however, P41A and P41AP93A were destabilized by ∼0.9 kcal mol-1. The effects of the mutations on the very fast, fast, slow, and very slow phases of folding were studied. They showed that heterogeneity in the unfolded state arises due to cis to trans isomerization of the Gly92-Pro93 peptide bond. The Pro41 to Ala mutation abolished the very slow phase of folding, whereas surprisingly, the Pro93 to Ala mutation abolished the very fast phase of folding. Double-jump, interrupted folding experiments indicated that two sequential trans to cis proline isomerization steps, of the Gly92-Pro93 peptide bond followed by the Arg40-Pro41 peptide bond, lead to the formation of the native state. They also revealed the accumulation of a late native-like intermediate, N∗, which differs from the native state in the isomeric status of the Arg40-Pro41 bond, as well as in a few tertiary contacts as monitored by near-UV CD measurements. The Pro to Ala mutations not only eliminated the cis to trans Pro isomerization reaction in the unfolded state, but also the two trans to cis Pro isomerization reactions during folding. By doing so, and by differentially affecting the relative stabilities of folding intermediates, the mutations resulted in a simplification of the folding mechanism. The two Pro to Ala mutations together accelerate folding to such an extent that the native state forms more than 1000-fold faster than in the case of pWT.

Modeling Coil-Globule-Helix Transition in Polymers by Self-Interacting Random Walks

Random walks (RWs) have been important in statistical physics and can describe the statistical properties of various processes in physical, chemical, and biological systems. In this study, we have proposed a self-interacting random walk model in a continuous three-dimensional space, where the walker and its previous visits interact according to a realistic Lennard-Jones (LJ) potential uLJr=εr0/r12-2r0/r6. It is revealed that the model shows a novel globule-to-helix transition in addition to the well-known coil-to-globule collapse in its trajectory when the temperature decreases. The dependence of the structural transitions on the equilibrium distance r0 of the LJ potential and the temperature T were extensively investigated. The system showed many different structural properties, including globule-coil, helix-globule-coil, and line-coil transitions depending on the equilibrium distance r0 when the temperature T increases from low to high. We also obtained a correlation form of kBTc = λε for the relationship between the transition temperature Tc and the well depth ε, which is consistent with our numerical simulations. The implications of the random walk model on protein folding are also discussed. The present model provides a new way towards understanding the mechanism of helix formation in polymers like proteins.

The Protein Unfolded State: One, No One and One Hundred Thousand

Many in vitro studies, in which proteins have been unfolded by the action of a variety of physical or chemical agents, have led to the definition of a folded versus an unfolded state and to the question of what is the nature of the unfolded state. The unstructured nature of this state could suggest that "the" unfolded state is a unique entity which holds true for all kinds of unfolding processes. This assumption has to be questioned because the unfolding processes under different stress conditions are dictated by entirely different mechanisms. As a consequence, it can be easily understood that the final state, generically referred to as "the unfolded state", can be completely different for each of the unfolding processes. The present review examines recent data on the characteristics of the unfolded states emerging from experiments under different conditions, focusing specific attention to the level of compaction of the unfolded species.

Linking Gas-Phase and Solution-Phase Protein Unfolding via Mobile Proton Simulations

Native mass spectrometry coupled to ion mobility (IM-MS) combined with collisional activation (CA) of ions in the gas phase (in vacuo) is an important method for the study of protein unfolding. It has advantages over classical biophysical and structural techniques as it can be used to analyze small volumes of low-concentration heterogeneous mixtures while maintaining solution-like behavior and does not require labeling with fluorescent or other probes. It is unclear, however, whether the unfolding observed during collision activation experiments mirrors solution-phase unfolding. To bridge the gap between in vacuo and in-solution behavior, we use unbiased molecular dynamics (MD) to create in silico models of in vacuo unfolding of a well-studied protein, the N-terminal domain of ribosomal L9 (NTL9) protein. We utilize a mobile proton algorithm (MPA) to create 100 thermally unfolded and coulombically unfolded in silico models for observed charge states of NTL9. The unfolding behavior in silico replicates the behavior in-solution and is in line with the in vacuo observations; however, the theoretical collision cross section (CCS) of the in silico models was lower compared to that of the in vacuo data, which may reflect reduced sampling.

Connecting conformational stiffness of the protein with energy landscape by a single experiment

The structure-function dynamics of a protein as a flexible polymer is essential to describe its biological functions. Here, using single-molecule magnetic tweezers, we have studied the effect of ionic strength on the folding mechanics of protein L, and probed its folding-associated physical properties by re-measuring the same protein in a range of ammonium sulfate concentrations from 150 mM to 650 mM. We observed an electrolyte-dependent conformational dynamics and folding landscape of the protein in a single experiment. Salt increases the refolding kinetics, while decreasing the unfolding kinetics under force, which in turn modifies the barrier heights towards the folded state. Additionally, salt enhances the molecular compaction by decreasing the Kuhn length of the protein polymer from 1.18 nm to 0.58 nm, which we have explained by modifying the freely jointed chain model. Finally, we correlated polymer chain physics to the folding dynamics, and thus provided an analytical framework for understanding compaction-induced folding mechanics across a range of ionic strengths from a single experiment.

ATP-Independent Chaperones

The folding of proteins into their native structure is crucial for the functioning of all biological processes. Molecular chaperones are guardians of the proteome that assist in protein folding and prevent the accumulation of aberrant protein conformations that can lead to proteotoxicity. ATP-independent chaperones do not require ATP to regulate their functional cycle. Although these chaperones have been traditionally regarded as passive holdases that merely prevent aggregation, recent work has shown that they can directly affect the folding energy landscape by tuning their affinity to various folding states of the client. This review focuses on emerging paradigms in the mechanism of action of ATP-independent chaperones and on the various modes of regulating client binding and release.

Protein chain collapse modulation and folding stimulation by GroEL-ES

The collapse of polypeptides is thought important to protein folding, aggregation, intrinsic disorder, and phase separation. However, whether polypeptide collapse is modulated in cells to control protein states is unclear. Here, using integrated protein manipulation and imaging, we show that the chaperonin GroEL-ES can accelerate the folding of proteins by strengthening their collapse. GroEL induces contractile forces in substrate chains, which draws them into the cavity and triggers a general compaction and discrete folding transitions, even for slow-folding proteins. This collapse enhancement is strongest in the nucleotide-bound states of GroEL and is aided by GroES binding to the cavity rim and by the amphiphilic C-terminal tails at the cavity bottom. Collapse modulation is distinct from other proposed GroEL-ES folding acceleration mechanisms, including steric confinement and misfold unfolding. Given the prevalence of collapse throughout the proteome, we conjecture that collapse modulation is more generally relevant within the protein quality control machinery.

Single-Molecule Fluorescence Spectroscopy Approaches for Probing Fast Biomolecular Dynamics and Interactions

Single-molecule fluorescence spectroscopy, and particularly its Förster resonance energy transfer implementation (SM-FRET), provides the opportunity to resolve the stochastic conformational fluctuations undergone by individual protein molecules while they fold-unfold, bind to their partners, or carry out catalysis. Such information is key to resolve the microscopic pathways and mechanisms underlying such processes, and cannot be obtained from bulk experiments. To fully resolve protein conformational dynamics, SM-FRET experiments need to reach microsecond, and even sub-microsecond, time resolutions. The key to reach such resolution lies in increasing the efficiency at which photons emitted by a single molecule are collected and detected by the instrument (photon count rates). In this chapter, we describe basic procedures that an end user can follow to optimize the confocal microscope optics in order to maximize the photon count rates. We also discuss the use of photoprotection cocktails specifically designed to reduce fluorophore triplet buildup at high irradiance (the major cause of limiting photon emission rates) while improving the mid-term photostability of the fluorophores. Complementary strategies based on the data analysis are discussed in depth by other authors in Chap. 14 .

Folding Intermediates, Heterogeneous Native Ensembles and Protein Function

Single domain proteins fold via diverse mechanisms emphasizing the intricate relationship between energetics and structure, which is a direct consequence of functional constraints and demands imposed at the level of sequence. On the other hand, elucidating the interplay between folding mechanisms and function is challenging in large proteins, given the inherent shortcomings in identifying metastable states experimentally and the sampling limitations associated with computational methods. Here, we show that free energy profiles and surfaces of large systems (>150 residues), as predicted by a statistical mechanical model, display a wide array of folding mechanisms with ubiquitous folding intermediates and heterogeneous native ensembles. Importantly, residues around the ligand binding or enzyme active site display a larger tendency to partially unfold and this manifests as intermediates or excited states along the folding coordinate in ligand binding domains, transcription repressors, and representative enzymes from all the six classes, including the SARS-CoV-2 receptor binding domain (RBD) of the spike protein and the protease M^pro. It thus appears that it is relatively easier to distill the imprints of function on the folding landscape of larger proteins as opposed to smaller systems. We discuss how an understanding of energetic-entropic features in ordered proteins can pinpoint specific avenues through which folding mechanisms, populations of partially structured states and function can be engineered.

Saturation Mutagenesis of the Transmembrane Region of HokC in Escherichia coli Reveals Its High Tolerance to Mutations

Cells adapt to different stress conditions, such as the antibiotics presence. This adaptation sometimes is achieved by changing relevant protein positions, of which the mutability is limited by structural constrains. Understanding the basis of these constrains represent an important challenge for both basic science and potential biotechnological applications. To study these constraints, we performed a systematic saturation mutagenesis of the transmembrane region of HokC, a toxin used by Escherichia coli to control its own population, and observed that 92% of single-point mutations are tolerated and that all the non-tolerated mutations have compensatory mutations that reverse their effect. We provide experimental evidence that HokC accumulates multiple compensatory mutations that are found as correlated mutations in the HokC family multiple sequence alignment. In agreement with these observations, transmembrane proteins show higher probability to present correlated mutations and are less densely packed locally than globular proteins; previous mutagenesis results on transmembrane proteins further support our observations on the high tolerability to mutations of transmembrane regions of proteins. Thus, our experimental results reveal the HokC transmembrane region high tolerance to loss-of-function mutations that is associated with low sequence conservation and high rate of correlated mutations in the HokC family sequences alignment, which are features shared with other transmembrane proteins.

Slow Escape from a Helical Misfolded State of the Pore-Forming Toxin Cytolysin A

The pore-forming toxin cytolysin A (ClyA) is expressed as a large α-helical monomer that, upon interaction with membranes, undergoes a major conformational rearrangement into the protomer conformation, which then assembles into a cytolytic pore. Here, we investigate the folding kinetics of the ClyA monomer with single-molecule Förster resonance energy transfer spectroscopy in combination with microfluidic mixing, stopped-flow circular dichroism experiments, and molecular simulations. The complex folding process occurs over a broad range of time scales, from hundreds of nanoseconds to minutes. The very slow formation of the native state occurs from a rapidly formed and highly collapsed intermediate with large helical content and nonnative topology. Molecular dynamics simulations suggest pronounced non-native interactions as the origin of the slow escape from this deep trap in the free-energy surface, and a variational enhanced path-sampling approach enables a glimpse of the folding process that is supported by the experimental data.

Small-Angle X-ray Scattering Signatures of Conformational Heterogeneity and Homogeneity of Disordered Protein Ensembles

An accurate account of disordered protein conformations is of central importance to deciphering the physicochemical basis of biological functions of intrinsically disordered proteins and the folding-unfolding energetics of globular proteins. Physically, disordered ensembles of nonhomopolymeric polypeptides are expected to be heterogeneous, i.e., they should differ from those homogeneous ensembles of homopolymers that harbor an essentially unique relationship between average values of end-to-end distance R_EE and radius of gyration R_g. It was posited recently, however, that small-angle X-ray scattering (SAXS) data on conformational dimensions of disordered proteins can be rationalized almost exclusively by homopolymer ensembles. Assessing this perspective, chain-model simulations are used to evaluate the discriminatory power of SAXS-determined molecular form factors (MFFs) with regard to homogeneous versus heterogeneous ensembles. The general approach adopted here is not bound by any assumption about ensemble encodability, in that the postulated heterogeneous ensembles we evaluated are not restricted to those entailed by simple interaction schemes. Our analysis of MFFs for certain heterogeneous ensembles with more narrowly distributed R_EE and R_g indicates that while they deviate from MFFs of homogeneous ensembles, the differences can be rather small. Remarkably, some heterogeneous ensembles with asphericity and R_EE drastically different from those of homogeneous ensembles can nonetheless exhibit practically identical MFFs, demonstrating that SAXS MFFs do not afford unique characterizations of basic properties of conformational ensembles in general. In other words, the ensemble to MFF mapping is practically many-to-one and likely nonsmooth. Heteropolymeric variations of the R_EE-R_g relationship were further showcased using an analytical perturbation theory developed here for flexible heteropolymers. Ramifications of our findings for interpretation of experimental data are discussed.

Pathway regulation mechanism revealed by cotranslational folding of villin headpiece subdomain HP35

Cotranslational folding is one of the most important features of protein folding in vivo. Although many studies have shown that the folding pathways of cotranslational folding are different from free folding in vitro, the detailed mechanism of folding dynamics is lacking. Here we combine all-atom molecular simulations with an ideal ribosome tunnel model to investigate the cotranslational folding of villin headpiece subdomain HP35. By comparing the folding dynamics between cotranslational folding and free folding, we found that cotranslational folding tends to fold along the pathway that is easier to fold into native state in the latter. In addition, the roles of the ribosome tunnel and sequential folding are analyzed separately. Our results show that the ribosome can prevent the untimely folding of the C segment of HP35 to reduce the non-native interactions, while the translation speed can regulate the amounts of native and non-native interactions and the balance between them. Overall, these results give insights into the general mechanisms of cotranslational protein folding.

Thermal inactivation scaling applied for SARS-CoV-2

Based on a model of protein denaturation rate limited by an entropy-related barrier, we derive a simple formula for virus inactivation time as a function of temperature. Loss of protein structure is described by two reaction coordinates: conformational disorder of the polymer and wetting by the solvent. These establish a competition between conformational entropy and hydrophobic interaction favoring random coil or globular states, respectively. Based on the Landau theory of phase transition, the resulting free energy barrier is found to decrease linearly with the temperature difference T - Tm, and the inactivation rate should scale as U to the power of T - Tm. This form recalls an accepted model of thermal damage to cells in hyperthermia. For SARS-CoV-2 the value of U in Celsius units is found to be 1.32. Although the fitting of the model to measured data is practically indistinguishable from Arrhenius law with an activation energy, the entropy barrier mechanism is more suitable and could explain the pronounced sensitivity of SARS-CoV-2 to thermal damage. Accordingly, we predict the efficacy of mild fever over a period of ∼24 h in inactivating the virus.

Fluorescence correlation spectroscopy to unravel the interactions between macromolecules in wine

In this work, the interaction of wine macromolecules with a bovine serum albumin (BSA) was investigated using fluorescence correlation spectroscopy (FCS). FCS offers the opportunity to study molecular and macromolecular aggregation without disturbing the wine by introducing only very small amounts of fluorescently labelled molecules to the system. It was observed that the diffusion coefficient of fluorescently labelled BSA varies with the addition of wine macromolecules, indicating changes in the protein conformation and the formation of complexes and aggregates. The addition of a wine polysaccharide rhamnogalacturonan II-enriched fraction led to aggregation, while addition of a mannoprotein-enriched fraction exhibited a protective effect on protein aggregation. Proteins strongly interacted with tannins, leading to the precipitation of protein-tannin complexes, while the presence of polysaccharides prevented this precipitation. Finally, the application of FCS was demonstrated in real wines, to investigate the problem of protein haze formation through live monitoring of heat-induced aggregation in wine.

Understanding and applications of Ser/Gly linkers in protein engineering

Peptide linkers consisting of repeats of glycine and serine residues are commonly chosen by protein engineers to introduce flexible and hydrophilic spacers between protein domains. Given the popularity of these linkers, gaining a quantitative insight in their conformational behavior is important to understand the effect on functional properties of fusion proteins, including energy transfer efficiency in luminescent sensor proteins, intramolecular domain interactions and (multivalent) binding. In this chapter, we discuss how the conformational behavior of Ser/Gly linkers can be described using random coil models, and how measuring FRET as a function of linker length can be used to obtain empirical values for the stiffness of linkers containing different Ser-to-Gly ratios. Subsequently, we show how these models and the experimentally determined linker stiffness can be used to explain and predict the functional properties of multidomain proteins, providing useful rules-of-thumb and design tools for optimal linker engineering.

Thermosensitive Hydration of Four Acrylamide-Based Polymers in Coil and Globule Conformations

To characterize the thermosensitive coil–globule transition in atomistic detail, the conformational dynamics of linear polymer chains of acrylamide-based polymers have been investigated at multiple temperatures. Therefore, molecular dynamic simulations of 30mers of polyacrylamide (AAm), poly-N-methylacrylamide (NMAAm), poly-N-ethylacrylamide (NEAAm), and poly-N-isopropylacrylamide (NIPAAm) have been performed at temperatures ranging from 250 to 360 K for 2 μs. While two of the polymers are known to exhibit thermosensitivity (NEAAm, NIPAAm), no thermosensitivity is observed for AAm and NMAAm in aqueous solution. Our computer simulations consistently reproduce these properties. To understand the thermosensitivity of the respective polymers, the conformational ensembles at different temperatures have been separated according to the coil–globule transition. The coil and globule conformational ensembles were exhaustively analyzed in terms of hydrogen bonding with the solvent, the change of the solvent accessible surface, and enthalpic contributions. Surprisingly, independent of different thermosensitive properties of the four polymers, the surface affinity to water of coil conformations is higher than for globule conformations. Therefore, polymer–solvent interactions stabilize coil conformations at all temperatures. Nevertheless, the enthalpic contributions alone cannot explain the differences in thermosensitivity. This clearly implies that entropy is the distinctive factor for thermosensitivity. With increasing side chain length, the lifetime of the hydrogen bonds between the polymer surface and water is extended. Thus, we surmise that a longer side chain induces a larger entropic penalty due to immobilization of water molecules.

The Last Secret of Protein Folding: The Real Relationship Between Long-Range Interactions and Local Structures

The protein folding problem has been extensively studied for decades, and hundreds of thousands of protein structures have been solved. Yet, how proteins fold from a linear peptide chain to their unique 3D structures is not fully understood. With key clues having emerged unexpectedly from the field of nanoscience, a "Confined Lowest Energy Fragment" (CLEF) hypothesis was proposed. The CLEF hypothesis states that a protein chain can be divided into CLEFs, the semi-independent folding units, by a small number of key residues that form key long-range interactions. The native structure of a CLEF is the lowest energy state under the constraints of the key long-range interactions, but the native structure of the whole protein is not necessary the lowest energy state as Anfinsen's thermodynamic hypothesis suggested. The CLEF hypothesis proposes a unified CLEF mechanism for protein folding, basically a two-step process. In the first step, the favorable enthalpy of CLEFs for native structures quickly brings those residues for the key long-range interactions together, forming intermediates corresponding to the so-called hydrophobic collapse. In the second step, those collapsed key residues shuffle for the right combination to form the native key long-range interactions. The CLEF hypothesis provides a simple solution to all protein folding paradoxes, and proposes a "CLEF Age" or "Stone Age" for the prebiotic evolution of proteins.

Dramatic Shape Changes Occur as Cytochrome c Folds

Extensive experimental studies on the folding of cytochrome c (Cyt c) make this small protein an ideal target for atomic detailed simulations for the purposes of quantitatively characterizing the structural transitions and the associated time scales for folding to the native state from an ensemble of unfolded states. We use previously generated atomically detailed folding trajectories by the stochastic difference equation in length to calculate the time-dependent changes in the small-angle X-ray scattering (SAXS) profiles. Excellent agreement is obtained between experiments and simulations for the time-dependent SAXS spectra, allowing us to identify the structures of the folding intermediates, which shows that Cyt c reaches the native state by a sequential folding mechanism. Using the ensembles of structures along the folding pathways, we show that compaction and the sphericity of Cyt c change dramatically from the prolate ellipsoid shape in the unfolded state to the spherical native state. Our data, which are in unprecedented quantitative agreement with all aspects of time-resolved SAXS experiments, show that hydrophobic collapse and amide group protection coincide on the 100 microseconds time scale, which is in accordance with ultrafast hydrogen/deuterium exchange studies. Based on these results, we propose that compaction of polypeptide chains, accompanied by dramatic shape changes, is a universal characteristic of globular proteins, regardless of the underlying folding mechanism.

Mechanisms of Disulfide Bond Formation in Nascent Polypeptides Entering the Secretory Pathway

Disulfide bonds are an abundant feature of proteins across all domains of life that are important for structure, stability, and function. In eukaryotic cells, a major site of disulfide bond formation is the endoplasmic reticulum (ER). How cysteines correctly pair during polypeptide folding to form the native disulfide bond pattern is a complex problem that is not fully understood. In this paper, the evidence for different folding mechanisms involved in ER-localised disulfide bond formation is reviewed with emphasis on events that occur during ER entry. Disulfide formation in nascent polypeptides is discussed with focus on (i) its mechanistic relationship with conformational folding, (ii) evidence for its occurrence at the co-translational stage during ER entry, and (iii) the role of protein disulfide isomerase (PDI) family members. This review highlights the complex array of cellular processes that influence disulfide bond formation and identifies key questions that need to be addressed to further understand this fundamental process.

Friction-Limited Folding of Disulfide-Reduced Monomeric SOD1

The folding reaction of a stable monomeric variant of Cu/Zn superoxide dismutase (mSOD1), an enzyme responsible for the conversion of superoxide free radicals into hydrogen peroxide and oxygen, is known to be among the slowest folding processes that adhere to two-state behavior. The long lifetime, ∼10 s, of the unfolded state presents ample opportunities for the polypeptide chain to transiently sample nonnative structures before the formation of the productive folding transition state. We recently observed the formation of a nonnative structure in a peptide model of the C-terminus of SOD1, a sequence that might serve as a potential source of internal chain friction-limited folding. To test for friction-limited folding, we performed a comprehensive thermodynamic and kinetic analysis of the folding mechanism of mSOD1 in the presence of the viscogens glycerol and glucose. Using a, to our knowledge, novel analysis of the folding reactions, we found the disulfide-reduced form of the protein that exposes the C-terminal sequence, but not its disulfide-oxidized counterpart that protects it, experiences internal chain friction during folding. The sensitivity of the internal friction to the disulfide bond status suggests that one or both of the cross-linked regions play a critical role in driving the friction-limited folding. We speculate that the molecular mechanisms giving rise to the internal friction of disulfide-reduced mSOD1 might play a role in the amyotrophic lateral sclerosis-linked aggregation of SOD1.

Water as a Good Solvent for Unfolded Proteins: Folding and Collapse are Fundamentally Different

The argument that the hydrophobic effect is the primary effect driving the folding of globular proteins is nearly universally accepted (including by the authors). But does this view also imply that water is a "poor" solvent for the unfolded states of these same proteins? Here we argue that the answer is "no," that is, folding to a well-packed, extensively hydrogen-bonded native structure differs fundamentally from the nonspecific chain collapse that defines a poor solvent. Thus, the observation that a protein folds in water does not necessitate that water is a poor solvent for its unfolded state. Indeed, chain-solvent interactions that are marginally more favorable than nonspecific intrachain interactions are beneficial to protein function because they destabilize deleterious misfolded conformations and inter-chain interactions.

Protein secondary structure determines the temporal relationship between folding and disulfide formation

How and when disulfide bonds form in proteins relative to the stage of their folding is a fundamental question in cell biology. Two models describe this relationship: the folded precursor model, in which a nascent structure forms before disulfides do, and the quasi-stochastic model, where disulfides form prior to folding. Here we investigated oxidative folding of three structurally diverse substrates, β2-microglobulin, prolactin, and the disintegrin domain of ADAM metallopeptidase domain 10 (ADAM10), to understand how these mechanisms apply in a cellular context. We used a eukaryotic cell-free translation system in which we could identify disulfide isomers in stalled translation intermediates to characterize the timing of disulfide formation relative to translocation into the endoplasmic reticulum and the presence of non-native disulfides. Our results indicate that in a domain lacking secondary structure, disulfides form before conformational folding through a process prone to nonnative disulfide formation, whereas in proteins with defined secondary structure, native disulfide formation occurs after partial folding. These findings reveal that the nascent protein structure promotes correct disulfide formation during cotranslational folding.

Conformational behavior of a semiflexible dipolar chain with a variable relative size of charged groups via molecular dynamics simulations

The conformational behavior of an isolated semiflexible dipolar chain has been studied by molecular dynamics simulations. The dipolar chain was modeled as a backbone chain of charged beads, each containing an oppositely charged unit connected to it by a rigid spring. The main focus was on the effect of the backbone chain rigidity and the size of the charged groups on the morphology of the collapsed states of the chain formed in low-polar media where the electrostatic interactions are essential. It has been found that the stable globular conformations of the long chain of N = 256 backbone beads are a toroid and an elliptical globule. The macroscopic parameters (such as the radius of gyration and shape factors) as well as the local characteristics of these conformations (radial density distributions of ions, orientational correlations of chain segments, dipoles etc.) are studied depending on the chain stiffness. The regions of stability of a torus and an elliptical globule are found for the dipolar chains with variable dipole length and stiffness, which depend on the strength of electrostatic interactions. It has been shown that a size asymmetry of oppositely charged beads destabilizes globular states favoring elongated chain conformations. A coexistence of various metastable states was demonstrated for shorter chains of N = 128, 64, and 32.

New pathologic mechanisms in nucleotide repeat expansion disorders

Tandem microsatellite repeats are common throughout the human genome and intrinsically unstable, exhibiting expansions and contractions both somatically and across generations. Instability in a small subset of these repeats are currently linked to human disease, although recent findings suggest more disease-causing repeats await discovery. These nucleotide repeat expansion disorders (NREDs) primarily affect the nervous system and commonly lead to neurodegeneration through toxic protein gain-of-function, protein loss-of-function, and toxic RNA gain-of-function mechanisms. However, the lines between these categories have blurred with recent findings of unconventional Repeat Associated Non-AUG (RAN) translation from putatively non-coding regions of the genome. Here we review two emerging topics in NREDs: 1) The mechanisms by which RAN translation occurs and its role in disease pathogenesis and 2) How nucleotide repeats as RNA and translated proteins influence liquid-liquid phase separation, membraneless organelle dynamics, and nucleocytoplasmic transport. We examine these topics with a particular eye on two repeats: the CGG repeat expansion responsible for Fragile X syndrome and Fragile X-associated Tremor Ataxia Syndrome (FXTAS) and the intronic GGGGCC repeat expansion in C9orf72, the most common inherited cause of amyotrophic lateral sclerosis (ALS) and frontotemporal dementia (FTD). Our thesis is that these emerging disease mechanisms can inform a broader understanding of the native roles of microsatellites in cellular function and that aberrations in these native processes provide clues to novel therapeutic strategies for these currently untreatable disorders.

Unfolded states under folding conditions accommodate sequence-specific conformational preferences with random coil-like dimensions

Proteins are marginally stable molecules that fluctuate between folded and unfolded states. Here, we provide a high-resolution description of unfolded states under refolding conditions for the N-terminal domain of the L9 protein (NTL9). We use a combination of time-resolved Förster resonance energy transfer (FRET) based on multiple pairs of minimally perturbing labels, time-resolved small-angle X-ray scattering (SAXS), all-atom simulations, and polymer theory. Upon dilution from high denaturant, the unfolded state undergoes rapid contraction. Although this contraction occurs before the folding transition, the unfolded state remains considerably more expanded than the folded state and accommodates a range of local and nonlocal contacts, including secondary structures and native and nonnative interactions. Paradoxically, despite discernible sequence-specific conformational preferences, the ensemble-averaged properties of unfolded states are consistent with those of canonical random coils, namely polymers in indifferent (theta) solvents. These findings are concordant with theoretical predictions based on coarse-grained models and inferences drawn from single-molecule experiments regarding the sequence-specific scaling behavior of unfolded proteins under folding conditions.

Thermally versus Chemically Denatured Protein States

Protein unfolding thermodynamic parameters are conventionally extracted from equilibrium thermal and chemical denaturation experiments. Despite decades of work, the degree of structure and the compactness of denatured states populated in these experiments are still open questions. Here, building on previous works, we show that thermally and chemically denatured protein states are distinct from the viewpoint of far-ultraviolet circular dichroism experiments that report on the local conformational status of peptide bonds. The differences identified are independent of protein length, structural class, or experimental conditions, highlighting the presence of two sub-ensembles within the denatured states. The sub-ensembles, U_T and U_D for thermally induced and denaturant-induced unfolded states, respectively, can exclusively exchange populations as a function of temperature at high chemical denaturant concentrations. Empirical analysis suggests that chemically denatured states are ∼50% more expanded than the thermally denatured chains of the same protein. Our observations hint that the strength of protein backbone-backbone interactions and identity versus backbone-solvent/co-solvent interactions determine the conformational distributions. We discuss the implications for protein folding mechanisms, the heterogeneity in relaxation rates, and folding diffusion coefficients.

Commonly used FRET fluorophores promote collapse of an otherwise disordered protein

The dimensions that unfolded proteins, including intrinsically disordered proteins (IDPs), adopt in the absence of denaturant remain controversial. We developed an analysis procedure for small-angle X-ray scattering (SAXS) profiles and used it to demonstrate that even relatively hydrophobic IDPs remain nearly as expanded in water as they are in high denaturant concentrations. In contrast, as demonstrated here, most fluorescence resonance energy transfer (FRET) measurements have indicated that relatively hydrophobic IDPs contract significantly in the absence of denaturant. We use two independent approaches to further explore this controversy. First, using SAXS we show that fluorophores employed in FRET can contribute to the observed discrepancy. Specifically, we find that addition of Alexa-488 to a normally expanded IDP causes contraction by an additional 15%, a value in reasonable accord with the contraction reported in FRET-based studies. Second, using our simulations and analysis procedure to accurately extract both the radius of gyration (R_g) and end-to-end distance (R_ee) from SAXS profiles, we tested the recent suggestion that FRET and SAXS results can be reconciled if the R_g and R_ee are "uncoupled" (i.e., no longer simply proportional), in contrast to the case for random walk homopolymers. We find, however, that even for unfolded proteins, these two measures of unfolded state dimensions remain proportional. Together, these results suggest that improved analysis procedures and a correction for significant, fluorophore-driven interactions are sufficient to reconcile prior SAXS and FRET studies, thus providing a unified picture of the nature of unfolded polypeptide chains in the absence of denaturant.

Nonlocal statistical field theory of dipolar particles in electrolyte solutions

We present a nonlocal statistical field theory of a dilute electrolyte solution with a small additive of dipolar particles. We postulate that every dipolar particle is associated with an arbitrary probability distribution function (PDF) of distance between its charge centers. Using the standard Hubbard-Stratonovich transformation, we represent the configuration integral of the system in the functional integral form. We show that in the limit of a small permanent dipole moment, the functional in integrand exponent takes the well known form of the Poisson-Boltzmann-Langevin (PBL) functional. In the mean-field approximation we obtain a non-linear integro-differential equation with respect to the mean-field electrostatic potential, generalizing the PBL equation for the point-like dipoles obtained first by Abrashkin et al. We apply the obtained equation in its linearized form to derivation of the expressions for the mean-field electrostatic potential of the point-like test ion and its solvation free energy in salt-free solution, as well as in solution with salt ions. For the 'Yukawa'-type PDF we obtain analytic relations for both the electrostatic potential and the solvation free energy of the point-like test ion. We obtain a general expression for the bulk electrostatic free energy of the solution within the Random phase approximation (RPA). For the salt-free solution of the dipolar particles for the Yukawa-type PDF we obtain an analytic relation for the electrostatic free energy, resulting in two limiting regimes. Finally, we analyze the limiting laws, following from the general relation for the electrostatic free energy of solution in presence of both the ions and the dipolar particles for the case of Yukawa-type PDF.

Perspective: Chain dynamics of unfolded and intrinsically disordered proteins from nanosecond fluorescence correlation spectroscopy combined with single-molecule FRET

The dynamics of unfolded proteins are important both for the process of protein folding and for the behavior of intrinsically disordered proteins. However, methods for investigating the global chain dynamics of these structurally diverse systems have been limited. A versatile experimental approach is single-molecule spectroscopy in combination with Förster resonance energy transfer and nanosecond fluorescence correlation spectroscopy. The concepts of polymer physics offer a powerful framework both for interpreting the results and for understanding and classifying the properties of unfolded and intrinsically disordered proteins. This information on long-range chain dynamics can be complemented with spectroscopic techniques that probe different length scales and time scales, and integration of these results greatly benefits from recent advances in molecular simulations. This increasing convergence between the experiment, theory, and simulation is thus starting to enable an increasingly detailed view of the dynamics of disordered proteins.

Co-Translational Folding Trajectory of the HemK Helical Domain

Protein folding begins co-translationally within the restricted space of the peptide exit tunnel of the ribosome. We have already shown that the N-terminal α-helical domain of the universally conserved N⁵-glutamine methyltransferase HemK is compacted within the exit tunnel and rearranges into the native fold upon emerging from the ribosome. However, the exact folding pathway of the domain remained unclear. Here we analyzed the rapid kinetics of translation and folding monitored by fluorescence resonance energy transfer and photoinduced electron transfer using global fitting to a model for synthesis of the 112-amino acid HemK fragment. Our results suggest that the co-translational folding trajectory of HemK starts within the tunnel and passes through four kinetically distinct folding intermediates that may represent sequential docking of helices to a growing compact core. The kinetics of the process is defined entirely by translation. The results show how analysis of ensemble kinetic data can be used to dissect complex trajectories of rapid conformational rearrangements in multicomponent systems.

An interplay of electrostatic and excluded volume interactions in the conformational behavior of a dipolar chain: theory and computer simulations

The effect of an interplay between electrostatic and excluded volume interactions on the conformational behavior of a dipolar chain has been studied theoretically and by means of molecular dynamics simulations. Every monomer unit of the dipolar chain comprises a dipole formed by a charged group of the chain and an oppositely charged counterion. The counterion is assumed to freely move around the chain but keeping the distance between oppositely charged ions (the dipole length) fixed. The novelty of the developed mean-field theory is that variations of the dipole parameters (the dipole length and the counterion size) have been accounted for in both electrostatic and excluded volume contributions to the total free energy of the dipolar chain. It has been shown that conformational transitions between swollen and collapsed states of the chain can be induced by fine-tuning the balance between electrostatic and excluded volume interactions. In particular, in low-polar media not only globule but also extended coil conformations can be realized even under strong electrostatic attraction. The results of MD simulations of a dipolar chain with variable dipolar length support theoretical conclusions.

"Cooperative collapse" of the denatured state revealed through Clausius-Clapeyron analysis of protein denaturation phase diagrams

Protein phase diagrams have a unique potential to identify the presence of additional thermodynamic states even when non-2-state character is not readily apparent from the experimental observables used to follow protein unfolding transitions. Two-state analysis of the von Willebrand factor A3 domain has previously revealed a discrepancy in the calorimetric enthalpy obtained from thermal unfolding transitions as compared with Gibbs-Helmholtz analysis of free energies obtained from the Linear Extrapolation Method (Tischer and Auton, Prot Sci 2013; 22(9):1147-60). We resolve this thermodynamic conundrum using a Clausius-Clapeyron analysis of the urea-temperature phase diagram that defines how Δ H and the urea m-value interconvert through the slope of c_m versus T, ( ∂ c m / ∂ T ) = Δ H / ( m T ) . This relationship permits the calculation of Δ H at low temperature from m-values obtained through iso-thermal urea denaturation and high temperature m-values from Δ H obtained through iso-urea thermal denaturation. Application of this equation uncovers sigmoid transitions in both cooperativity parameters as temperature is increased. Such residual thermal cooperativity of Δ H and the m-value confirms the presence of an additional state which is verified to result from a cooperative phase transition between urea-expanded and thermally-compact denatured states. Comparison of the equilibria between expanded and compact denatured ensembles of disulfide-intact and carboxyamidated A3 domains reveals that introducing a single disulfide crosslink does not affect the presence of the additional denatured state. It does, however, make a small thermodynamically favorable free energy (∼-13 ± 1 kJ/mol) contribution to the cooperative denatured state collapse transition as temperature is raised and urea concentration is lowered. The thermodynamics of this "cooperative collapse" of the denatured state retain significant compensations between the enthalpy and entropy contributions to the overall free energy.

Hypothesis: structural heterogeneity of the unfolded proteins originating from the coupling of the local clusters and the long-range distance distribution

We propose a hypothesis that explains two apparently contradicting observations for the heterogeneity of the unfolded proteins. First, the line confocal method of the single-molecule Förster resonance energy transfer (sm-FRET) spectroscopy revealed that the unfolded proteins possess broad peaks in the FRET efficiency plot, implying the significant heterogeneity that lasts longer than milliseconds. Second, the fluorescence correlation method demonstrated that the unfolded proteins fluctuate in the time scale shorter than 100 ns. To formulate the hypothesis, we first summarize the recent consensus for the structure and dynamics of the unfolded proteins. We next discuss the conventional method of the sm-FRET spectroscopy and its limitations for the analysis of the unfolded proteins, followed by the advantages of the line confocal method that revealed the heterogeneity. Finally, we propose that the structural heterogeneity formed by the local clustering of hydrophobic residues modulates the distribution of the long-range distance between the labeled chromophores, resulting in the broadening of the peak in the FRET efficiency plot. A clustering of hydrophobic residues around the chromophore might further contribute to the broadening. The proposed clusters are important for the understanding of protein folding mechanism.