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

The Analytical Flory Random Coil Is a Simple-to-Use Reference Model for Unfolded and Disordered Proteins

Denatured, unfolded, and intrinsically disordered proteins (collectively referred to here as unfolded proteins) can be described using analytical polymer models. These models capture various polymeric properties and can be fit to simulation results or experimental data. However, the model parameters commonly require users' decisions, making them useful for data interpretation but less clearly applicable as stand-alone reference models. Here we use all-atom simulations of polypeptides in conjunction with polymer scaling theory to parameterize an analytical model of unfolded polypeptides that behave as ideal chains (ν = 0.50). The model, which we call the analytical Flory random coil (AFRC), requires only the amino acid sequence as input and provides direct access to probability distributions of global and local conformational order parameters. The model defines a specific reference state to which experimental and computational results can be compared and normalized. As a proof-of-concept, we use the AFRC to identify sequence-specific intramolecular interactions in simulations of disordered proteins. We also use the AFRC to contextualize a curated set of 145 different radii of gyration obtained from previously published small-angle X-ray scattering experiments of disordered proteins. The AFRC is implemented as a stand-alone software package and is also available via a Google Colab notebook. In summary, the AFRC provides a simple-to-use reference polymer model that can guide intuition and aid in interpreting experimental or simulation results.

Structural Preferences Shape the Entropic Force of Disordered Protein Ensembles

Intrinsically disordered protein regions (IDRs) make up over 30% of the human proteome and exist in a dynamic conformational ensemble instead of a native, well-folded structure. Tethering IDRs to a surface (for example, the surface of a well-folded region of the same protein) can reduce the number of accessible conformations in these ensembles. This reduces the ensemble's conformational entropy, generating an effective entropic force that pulls away from the point of tethering. Recent experimental work has shown that this entropic force causes measurable, physiologically relevant changes to protein function. But how the magnitude of this force depends on IDR sequence remains unexplored. Here, we use all-atom simulations to analyze how structural preferences in IDR ensembles contribute to the entropic force they exert upon tethering. We show that sequence-encoded structural preferences play an important role in determining the magnitude of this force: compact, spherical ensembles generate an entropic force that can be several times higher than more extended ensembles. We further show that changes in the surrounding solution's chemistry can modulate the IDR entropic force strength. We propose that the entropic force is a sequence-dependent, environmentally tunable property of terminal IDR sequences.

The analytical Flory random coil is a simple-to-use reference model for unfolded and disordered proteins

Denatured, unfolded, and intrinsically disordered proteins (collectively referred to here as unfolded proteins) can be described using analytical polymer models. These models capture various polymeric properties and can be fit to simulation results or experimental data. However, the model parameters commonly require users' decisions, making them useful for data interpretation but less clearly applicable as stand-alone reference models. Here we use all-atom simulations of polypeptides in conjunction with polymer scaling theory to parameterize an analytical model of unfolded polypeptides that behave as ideal chains (ν = 0.50). The model, which we call the analytical Flory Random Coil (AFRC), requires only the amino acid sequence as input and provides direct access to probability distributions of global and local conformational order parameters. The model defines a specific reference state to which experimental and computational results can be compared and normalized. As a proof-of-concept, we use the AFRC to identify sequence-specific intramolecular interactions in simulations of disordered proteins. We also use the AFRC to contextualize a curated set of 145 different radii of gyration obtained from previously published small-angle X-ray scattering experiments of disordered proteins. The AFRC is implemented as a stand-alone software package and is also available via a Google colab notebook. In summary, the AFRC provides a simple-to-use reference polymer model that can guide intuition and aid in interpreting experimental or simulation results.

Structural preferences shape the entropic force of disordered protein ensembles

Intrinsically disordered protein regions (IDRs) make up over 30% of the human proteome and instead of a native, well-folded structure exist in a dynamic conformational ensemble. Tethering IDRs to a surface (for example, the surface of a well-folded region of the same protein) can reduce the number of accessible conformations in IDR ensembles. This reduces the ensemble's conformational entropy, generating an effective entropic force that pulls away from the point of tethering. Recent experimental work has shown that this entropic force causes measurable, physiologically relevant changes to protein function, but how the magnitude of this force depends on the IDR sequence remains unexplored. Here we use all-atom simulations to analyze how structural preferences encoded in dozens of IDR ensembles contribute to the entropic force they exert upon tethering. We show that sequence-encoded structural preferences play an important role in determining the magnitude of this force and that compact, spherical ensembles generate an entropic force that can be several times higher than more extended ensembles. We further show that changes in the surrounding solution's chemistry can modulate IDR entropic force strength. We propose that the entropic force is a sequence-dependent, environmentally tunable property of terminal IDR sequences.

The biophysics of disordered proteins from the point of view of single-molecule fluorescence spectroscopy

Intrinsically disordered proteins (IDPs) and regions (IDRs) have emerged as key players across many biological functions and diseases. Differently from structured proteins, disordered proteins lack stable structure and are particularly sensitive to changes in the surrounding environment. Investigation of disordered ensembles requires new approaches and concepts for quantifying conformations, dynamics, and interactions. Here, we provide a short description of the fundamental biophysical properties of disordered proteins as understood through the lens of single-molecule fluorescence observations. Single-molecule Förster resonance energy transfer (FRET) and fluorescence correlation spectroscopy (FCS) provides an extensive and versatile toolbox for quantifying the characteristics of conformational distributions and the dynamics of disordered proteins across many different solution conditions, both in vitro and in living cells.

Cavity-based free energy analysis of osmolyte effects on protein denaturation

Experimental measurements of the thermal effects of the same osmolytes on two different globular proteins, C-reactive protein (CRP) and tumor necrosis factor alpha (TNFα), have shown that quantifying the change...

Fluorescence Depolarization Kinetics Captures Short-Range Backbone Dihedral Rotations and Long-Range Correlated Dynamics of an Intrinsically Disordered Protein

Intrinsically disordered proteins (IDPs) do not autonomously fold into well-defined three-dimensional structures and are best described as a heterogeneous ensemble of rapidly interconverting conformers. It is challenging to elucidate their complex dynamic signatures using a single technique. In this study, we employed sensitive fluorescence depolarization kinetics by following picosecond time-resolved fluorescence anisotropy decays to directly capture the essential dynamical features of intrinsically disordered α-synuclein (α-syn) site-specifically labeled with thiol-active fluorophores. By utilizing a long-lifetime (≥10 ns) anisotropic label, we were able to discern three distinct rotational components of α-syn. The subnanosecond component represents the local wobbling-in-cone motion of the fluorophore, whereas the slower (∼1.4 ns) component corresponds to the short-range backbone dynamics governed by collective torsional fluctuations in the Ramachandran Φ-Ψ dihedral space. This backbone dihedral rotational time scale is sensitive to the local chain stiffness and slows down in the presence of an adjacent proline residue. We also observed a small-amplitude (≤10%) slower rotational correlation time (6-10 ns) that represents the long-range correlated dynamics involving a much longer segment of the polypeptide chain. These intrinsic dynamic signatures of IDPs will provide critical mechanistic underpinnings in a mosaic of biophysical phenomena involving internal friction, allosteric interactions, and phase separation.

General Counteraction Exerted by Sugars against Denaturants

The conformational stability of globular proteins is strongly influenced by the addition to water of different co-solutes. Some of the latter destabilize the native state, while others stabilize it. It is emerging that stabilizing agents are able to counteract the action of destabilizing agents. We have already provided experimental evidence that this counteraction is a general phenomenon and offered a rationalization. In the present work, we show that four different sugars, namely fructose, glucose, sucrose, and trehalose, counteract the effect of urea, tetramethylurea, sodium perchlorate, guanidinium chloride, and guanidinium thiocyanate despite the chemical and structural differences of those destabilizing agents. The rationalization we provide is as follows: (a) the solvent-excluded volume effect, a purely entropic effect, stabilizes the native state, whose solvent-accessible surface area is smaller than the one of denatured conformations; (b) the magnitude of the solvent-excluded volume effect increases markedly in ternary solutions because the experimental density of such solutions is larger than that of pure water.

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.

The evolutionary background and functional consequences of the rs2071307 polymorphism in human tropoelastin

Elastin is a major polymeric protein of the extracellular matrix, providing critical properties of extensibility and elastic recoil. The rs2071307 genomic polymorphism, resulting in the substitution of a serine for a glycine residue in a VPG motif in tropoelastin, has an unusually high minor allele frequency in humans. A consequence of such allelic heterozygosity would be the presence of a heterogeneous elastin polymer in up to 50% of the population, a situation which appears to be unique to Homo sapiens. VPG motifs are extremely common in hydrophobic domains of tropoelastins and are the sites of transient β-turns that are essential for maintaining the conformational flexibility required for its function as an entropic elastomer. Earlier data demonstrated that single amino acid substitutions in tropoelastin can have functional consequences for polymeric elastin, particularly when present in mixed polymers. Here, using NMR and molecular dynamics approaches, we show the rs2071307 polymorphism reduces local propensity for β-turn formation, with a consequent increase in polypeptide hydration and an expansion of the conformational ensemble manifested as an increased hydrodynamic radius, radius of gyration and asphericity. Furthermore, this substitution affects functional properties of polymeric elastin, particularly in heterogeneous polymers mimicking allelic heterozygosity. We discuss whether such effects, together with the unusually high minor allele frequency of the polymorphism, could imply some some evolutionary advantage for the heterozygous state.

Origin of subdiffusions in proteins: Insight from peptide systems

Subdiffusive kinetics are popular in proteins and peptides as observed in experiments and simulations. For protein systems with diverse interactions, are there multiple mechanisms to produce the common subdiffusion behavior? To approach this problem, long trajectories of two model peptides are simulated to study the mechanism of subdiffusion and the relations with their interactions. The free-energy profiles and the subdiffusive kinetics are observed for these two peptides. A hierarchical plateau analysis is employed to extract the features of the landscape from the mean square of displacement. The mechanism of subdiffusions can be postulated by comparing the exponents by simulations with those based on various models. The results indicate that the mechanisms of these two peptides are different and are related to the characteristics of their energy landscapes. The subdiffusion of the flexible peptide is mainly caused by depth distribution of traps on the energy landscape, while the subdiffusion of the helical peptide is attributed to the fractal topology of local minima on the landscape. The emergence of these different mechanisms reflects different kinetic scenarios in peptide systems though the peptides behave in a similar way of diffusion. To confirm these ideas, the transition networks between various conformations of these peptides are generated. Based on the network description, the controlled kinetics based only on the topology of the networks are calculated and compared with the results based on simulations. For the flexible peptide, the feature of controlled diffusion is distinct from that of simulation, and for the helical peptide, two kinds of kinetics have a similar exponent of subdiffusion. These results further exemplify the importance of the landscape topology in the kinetics of structural proteins and the effect of depth distribution of traps for the subdiffusion of disordered peptides.

General Purpose Water Model Can Improve Atomistic Simulations of Intrinsically Disordered Proteins

Unconstrained atomistic simulations of intrinsically disordered proteins and peptides (IDP) remain a challenge: widely used, "general purpose" water models tend to favor overly compact structures relative to experiment. Here we have performed a total of 93 μs of unrestrained MD simulations to explore, in the context of IDPs, a recently developed "general-purpose" 4-point rigid water model OPC, which describes liquid state of water close to experiment. We demonstrate that OPC, together with a popular AMBER force field ff99SB, offers a noticeable improvement over TIP3P in producing more realistic structural ensembles of three common IDPs benchmarks: 55-residue apo N-terminal zinc-binding domain of HIV-1 integrase ("protein IN"), amyloid β-peptide (Aβ₄₂) (residues 1-42), and 26-reside H4 histone tail. As a negative control, computed folding profile of a regular globular miniprotein (CLN025) in OPC water is in appreciably better agreement with experiment than that obtained in TIP3P, which tends to overstabilize the compact native state relative to the extended conformations. We employed Aβ₄₂ peptide to investigate the possible influence of the solvent box size on simulation outcomes. We advocate a cautious approach for simulations of IDPs: we suggest that the solvent box size should be at least four times the radius of gyration of the random coil corresponding to the IDP. The computed free energy landscape of protein IN in OPC resembles a shallow "tub" - conformations with substantially different degrees of compactness that are within 2 k_B T of each other. Conformations with very different secondary structure content coexist within 1 k_B T of the global free energy minimum. States with higher free energy tend to have less secondary structure. Computed low helical content of the protein has virtually no correlation with its degree of compactness, which calls into question the possibility of using the helicity as a metric for assessing performance of water models for IDPs, when the helicity is low. Predicted radius of gyration ( R _g) of H4 histone tail in OPC water falls in-between that of a typical globular protein and a fully denatured protein of the same size; the predicted R _g is consistent with two independent predictions. In contrast, H4 tail in TIP3P water is as compact as the corresponding globular protein. The computed free energy landscape of H4 tail in OPC is relatively flat over a significant range of compactness, which, we argue, is consistent with its biological function as facilitator of internucleosome interactions.

A protein interaction free energy model based on amino acid residue contributions: Assessment of point mutation stability of T4 lysozyme

Here we present a model to estimate the interaction free energy contribution of each amino acid residue of a given protein. Protein interaction energy is described in terms of per-residue interaction factors, μ. Multibody interactions are implicitly captured in μ through the combination of amino acid terms (γ) guided by local conformation indices (σ). The model enables construction of an interaction factor heat map for a protein in a given fold, allows prima facie assessment of the degree of residue-residue interaction, and facilitates a qualitative and quantitative evaluation of protein association properties. The model was used to compute thermal stability of T4 bacteriophage lysozyme mutants across seven sites. Qualitative assessment of mutational effects provides a straightforward rationale regarding whether a particular site primarily perturbs native or non-native states, or both. The presented model was found to be in good agreement with experimental mutational data (R 2 = 0.73) and suggests an approach by which to convert structure space into energy space.

Counteraction of denaturant-induced protein unfolding is a general property of stabilizing agents

DSC measurements on RNase A at neutral pH show that five stabilizing agents, namely trimethylamine N-oxide, glucose, sucrose, betaine and sodium sulfate, can counteract the destabilizing action of urea, sodium perchlorate, guanidinium chloride and guanidinium thiocyanate. This is an important finding inferring that counteraction has a common physical origin, regardless of the chemical differences among the stabilizing agents and among the destabilizing ones. A rationalization is provided grounded on the following line of reasoning: (a) the decrease in solvent-excluded volume effect is the main stabilizing contribution of the native state; (b) its magnitude increases on increasing the density of the aqueous solution; (c) the density increases significantly in the ternary solutions containing water, a stabilizing agent and a destabilizing one, as indicated by the present experimental data.

Inferring properties of disordered chains from FRET transfer efficiencies

Förster resonance energy transfer (FRET) is a powerful tool for elucidating both structural and dynamic properties of unfolded or disordered biomolecules, especially in single-molecule experiments. However, the key observables, namely, the mean transfer efficiency and fluorescence lifetimes of the donor and acceptor chromophores, are averaged over a broad distribution of donor-acceptor distances. The inferred average properties of the ensemble therefore depend on the form of the model distribution chosen to describe the distance, as has been widely recognized. In addition, while the distribution for one type of polymer model may be appropriate for a chain under a given set of physico-chemical conditions, it may not be suitable for the same chain in a different environment so that even an apparently consistent application of the same model over all conditions may distort the apparent changes in chain dimensions with variation of temperature or solution composition. Here, we present an alternative and straightforward approach to determining ensemble properties from FRET data, in which the polymer scaling exponent is allowed to vary with solution conditions. In its simplest form, it requires either the mean FRET efficiency or fluorescence lifetime information. In order to test the accuracy of the method, we have utilized both synthetic FRET data from implicit and explicit solvent simulations for 30 different protein sequences, and experimental single-molecule FRET data for an intrinsically disordered and a denatured protein. In all cases, we find that the inferred radii of gyration are within 10% of the true values, thus providing higher accuracy than simpler polymer models. In addition, the scaling exponents obtained by our procedure are in good agreement with those determined directly from the molecular ensemble. Our approach can in principle be generalized to treating other ensemble-averaged functions of intramolecular distances from experimental data.

The liquid structure of elastin

The protein elastin imparts extensibility, elastic recoil, and resilience to tissues including arterial walls, skin, lung alveoli, and the uterus. Elastin and elastin-like peptides are hydrophobic, disordered, and undergo liquid-liquid phase separation upon self-assembly. Despite extensive study, the structure of elastin remains controversial. We use molecular dynamics simulations on a massive scale to elucidate the structural ensemble of aggregated elastin-like peptides. Consistent with the entropic nature of elastic recoil, the aggregated state is stabilized by the hydrophobic effect. However, self-assembly does not entail formation of a hydrophobic core. The polypeptide backbone forms transient, sparse hydrogen-bonded turns and remains significantly hydrated even as self-assembly triples the extent of non-polar side chain contacts. Individual chains in the assembly approach a maximally-disordered, melt-like state which may be called the liquid state of proteins. These findings resolve long-standing controversies regarding elastin structure and function and afford insight into the phase separation of disordered proteins.

Effect of heavy water on the conformational stability of globular proteins

It is well established from the experimental point of view that the native state of globular proteins is more stable in heavy water than in water. No robust explanation, however, has been provided up to now. The application of the theoretical approach, originally devised to rationalize the general occurrence of cold denaturation, indicates that the magnitude of the solvent-excluded volume effect is slightly smaller in heavy water than in water and cannot explain the observed protein stabilization. The latter has to be due to the strength of protein-water van der Waals attractions which are weaker in heavy water due to the smaller molecular polarizability of D₂ O compared with that of H₂ O molecules. Since protein-water van der Waals attractions occur more in the denatured than in the native state, this contribution leads to a stabilization of the latter through a destabilization of the former.

Decoupling of size and shape fluctuations in heteropolymeric sequences reconciles discrepancies in SAXS vs. FRET measurements

Unfolded states of proteins and native states of intrinsically disordered proteins (IDPs) populate heterogeneous conformational ensembles in solution. The average sizes of these heterogeneous systems, quantified by the radius of gyration (R_G ), can be measured by small-angle X-ray scattering (SAXS). Another parameter, the mean dye-to-dye distance (R_E ) for proteins with fluorescently labeled termini, can be estimated using single-molecule Förster resonance energy transfer (smFRET). A number of studies have reported inconsistencies in inferences drawn from the two sets of measurements for the dimensions of unfolded proteins and IDPs in the absence of chemical denaturants. These differences are typically attributed to the influence of fluorescent labels used in smFRET and to the impact of high concentrations and averaging features of SAXS. By measuring the dimensions of a collection of labeled and unlabeled polypeptides using smFRET and SAXS, we directly assessed the contributions of dyes to the experimental values R_G and R_E For chemically denatured proteins we obtain mutual consistency in our inferences based on R_G and R_E , whereas for IDPs under native conditions, we find substantial deviations. Using computations, we show that discrepant inferences are neither due to methodological shortcomings of specific measurements nor due to artifacts of dyes. Instead, our analysis suggests that chemical heterogeneity in heteropolymeric systems leads to a decoupling between R_E and R_G that is amplified in the absence of denaturants. Therefore, joint assessments of R_G and R_E combined with measurements of polymer shapes should provide a consistent and complete picture of the underlying ensembles.

Direct Observation of the Intrinsic Backbone Torsional Mobility of Disordered Proteins

The fundamental backbone dynamics of unfolded proteins arising due to intrinsic ϕ-ψ dihedral angle fluctuations dictate the course of protein folding, binding, assembly, and function. These internal fluctuations are also critical for protein misfolding associated with a range of human diseases. However, direct observation and unambiguous assignment of this inherent dynamics in chemically denatured proteins is extremely challenging due to various experimental limitations. To directly map the backbone torsional mobility in the ϕ-ψ dihedral angle space, we used a model intrinsically disordered protein, namely, α-synuclein, that adopts an expanded state under native conditions. We took advantage of nonoccurrence of tryptophan in α-synuclein and created a number of single-tryptophan variants encompassing the entire polypeptide chain. We then utilized highly sensitive picosecond time-resolved fluorescence depolarization measurements that allowed us to discern the site-specific torsional relaxation at a low protein concentration under physiological conditions. For all the locations, the depolarization kinetics exhibited two well-separated rotational-correlation-time components. The shorter, subnanosecond component arises due to the local mobility of the indole side chain, whereas the longer rotational-correlation-time component (1.37 ± 0.15 ns), independent of global tumbling, represents a characteristic timescale for short-range conformational exchange in the ϕ-ψ dihedral space. This correlation time represents an intrinsic timescale for torsional relaxation and is independent of position, which is expected for an extended polypeptide chain having little or no propensity to form persistent structures. We were also able to capture this intrinsic timescale at the N-terminal unstructured domain of the prion protein. Our estimated timescale of the segmental mobility is similar to that of unfolded proteins studied by nuclear magnetic resonance in conjunction with molecular dynamics simulations. Our results have broader implications for a diverse range of functionally and pathologically important intrinsically disordered proteins and disordered regions.

Protein Composition Determines the Effect of Crowding on the Properties of Disordered Proteins

Unlike dilute experimental conditions under which biological molecules are typically characterized, the cell interior is crowded by macromolecules, which affects both the thermodynamics and kinetics of in vivo processes. Although the excluded-volume effects of macromolecular crowding are expected to cause compaction of unfolded and disordered proteins, the extent of this effect is uncertain. We use a coarse-grained model to represent proteins with varying sequence content and directly observe changes in chain dimensions in the presence of purely repulsive spherical crowders. We find that the extent of crowding-induced compaction is dependent not only on crowder size and concentration, but also on the properties of the protein itself. In fact, we observe a nonmonotonic trend between the dimensions of the polypeptide chain in bulk and the degree of compaction: the most extended chains experience up to 24% compaction, the most compact chains show virtually no change, and intermediate chains compress by up to 40% in size at a 40% crowder volume fraction. Free-volume theory combined with an impenetrable ellipsoidal representation of the chains predicts the crowding effects only for collapsed protein chains. An additional scaling factor, which can be easily computed from protein-crowder potential of mean force, corrects for the penetrability of extended chains and is sufficient to capture the observed nonmonotonic trend in compaction.

Shedding light on the extra thermal stability of thermophilic proteins

An entropic stabilization mechanism has recently gained attention and credibility as the physical ground for the extra thermal stability of globular proteins from thermophilic microorganisms. An empirical result, obtained from the analysis of thermodynamic data for a large set of proteins, strengthens the general reliability of the theoretical approach originally devised to rationalize the occurrence of cold denaturation [Graziano, PCCP 2014, 16, 21755-21767]. It is shown that this theoretical approach can readily account for the entropic stabilization mechanism. On decreasing the conformational entropy gain associated with denaturation, the thermal stability of a model globular protein increases markedly.

A driving force for polypeptide and protein collapse

Polypeptide collapse is driven by the solvent-excluded volume decrease, the presence of nonpolar side chains is not so important.

Comprehensive structural and dynamical view of an unfolded protein from the combination of single-molecule FRET, NMR, and SAXS

The properties of unfolded proteins are essential both for the mechanisms of protein folding and for the function of the large group of intrinsically disordered proteins. However, the detailed structural and dynamical characterization of these highly dynamic and conformationally heterogeneous ensembles has remained challenging. Here we combine and compare three of the leading techniques for the investigation of unfolded proteins, NMR spectroscopy (NMR), small-angle X-ray scattering (SAXS), and single-molecule Förster resonance energy transfer (FRET), with the goal of quantitatively testing their consistency and complementarity and for obtaining a comprehensive view of the unfolded-state ensemble. Using unfolded ubiquitin as a test case, we find that its average dimensions derived from FRET and from structural ensembles calculated using the program X-PLOR-NIH based on NMR and SAXS restraints agree remarkably well; even the shapes of the underlying intramolecular distance distributions are in good agreement, attesting to the reliability of the approaches. The NMR-based results provide a highly sensitive way of quantifying residual structure in the unfolded state. FRET-based nanosecond fluorescence correlation spectroscopy allows long-range distances and chain dynamics to be probed in a time range inaccessible by NMR. The combined techniques thus provide a way of optimally using the complementarity of the available methods for a quantitative structural and dynamical description of unfolded proteins both at the global and the local level.

Adjusting Local Molecular Environment for Giant Ambient Thermal Contraction

A low-energy triggered switch that can generate mechanoresponse has great technological potential. A submolecular moiety, S-dibenzocyclooctadiene (DBCOD) that is composed of a flexible eight-membered ring connecting to a phenyl ring at each end, undergoes a conformational change from twist-boat to chair under a low-energy stimulus such as near infrared irradiation, resulting in thermal contraction of DBCOD-based polymer. Experimental evidence corroborated by theoretical calculations indicates that introducing molecular asymmetry can reduce crystallinity significantly and consequently facilitate the kinetics of the conformational change. It has been demonstrated that the negative thermal expansion (NTE) coefficient of a DBCOD-based polymer system can be adjusted in a range from -1140 to -2350 ppm K^-1 . -2350 ppm K^-1 is ≈10 times better than the value reported by the second best NTE system.

On the Effect of Sodium Chloride and Sodium Sulfate on Cold Denaturation

Both sodium chloride and sodium sulfate are able to stabilize yeast frataxin, causing an overall increase of its thermodynamic stability curve, with a decrease in the cold denaturation temperature and an increase in the hot denaturation one. The influence of low concentrations of these two salts on yeast frataxin stability can be assessed by the application of a theoretical model based on scaled particle theory. First developed to figure out the mechanism underlying cold denaturation in water, this model is able to predict the stabilization of globular proteins provided by these two salts. The densities of the salt solutions and their temperature dependence play a fundamental role.

Quantitative assessments of the distinct contributions of polypeptide backbone amides versus side chain groups to chain expansion via chemical denaturation

In aqueous solutions with high concentrations of chemical denaturants such as urea and guanidinium chloride (GdmCl) proteins expand to populate heterogeneous conformational ensembles. These denaturing environments are thought to be good solvents for generic protein sequences because properties of conformational distributions align with those of canonical random coils. Previous studies showed that water is a poor solvent for polypeptide backbones, and therefore, backbones form collapsed globular structures in aqueous solvents. Here, we ask if polypeptide backbones can intrinsically undergo the requisite chain expansion in aqueous solutions with high concentrations of urea and GdmCl. We answer this question using a combination of molecular dynamics simulations and fluorescence correlation spectroscopy. We find that the degree of backbone expansion is minimal in aqueous solutions with high concentrations of denaturants. Instead, polypeptide backbones sample conformations that are denaturant-specific mixtures of coils and globules, with a persistent preference for globules. Therefore, typical denaturing environments cannot be classified as good solvents for polypeptide backbones. How then do generic protein sequences expand in denaturing environments? To answer this question, we investigated the effects of side chains using simulations of two archetypal sequences with amino acid compositions that are mixtures of charged, hydrophobic, and polar groups. We find that side chains lower the effective concentration of backbone amides in water leading to an intrinsic expansion of polypeptide backbones in the absence of denaturants. Additional dilution of the effective concentration of backbone amides is achieved through preferential interactions with denaturants. These effects lead to conformational statistics in denaturing environments that are congruent with those of canonical random coils. Our results highlight the role of side chain-mediated interactions as determinants of the conformational properties of unfolded states in water and in influencing chain expansion upon denaturation.

A quantitative measure for protein conformational heterogeneity

Conformational heterogeneity is a defining characteristic of proteins. Intrinsically disordered proteins (IDPs) and denatured state ensembles are extreme manifestations of this heterogeneity. Inferences regarding globule versus coil formation can be drawn from analysis of polymeric properties such as average size, shape, and density fluctuations. Here we introduce a new parameter to quantify the degree of conformational heterogeneity within an ensemble to complement polymeric descriptors. The design of this parameter is guided by the need to distinguish between systems that couple their unfolding-folding transitions with coil-to-globule transitions and those systems that undergo coil-to-globule transitions with no evidence of acquiring a homogeneous ensemble of conformations upon collapse. The approach is as follows: Each conformation in an ensemble is converted into a conformational vector where the elements are inter-residue distances. Similarity between pairs of conformations is quantified using the projection between the corresponding conformational vectors. An ensemble of conformations yields a distribution of pairwise projections, which is converted into a distribution of pairwise conformational dissimilarities. The first moment of this dissimilarity distribution is normalized against the first moment of the distribution obtained by comparing conformations from the ensemble of interest to conformations drawn from a Flory random coil model. The latter sets an upper bound on conformational heterogeneity thus ensuring that the proposed measure for intra-ensemble heterogeneity is properly calibrated and can be used to compare ensembles for different sequences and across different temperatures. The new measure of conformational heterogeneity will be useful in quantitative studies of coupled folding and binding of IDPs and in de novo sequence design efforts that are geared toward controlling the degree of heterogeneity in unbound forms of IDPs.

Single-molecule spectroscopy reveals polymer effects of disordered proteins in crowded environments

Intrinsically disordered proteins (IDPs) are involved in a wide range of regulatory processes in the cell. Owing to their flexibility, their conformations are expected to be particularly sensitive to the crowded cellular environment. Here we use single-molecule Förster resonance energy transfer to quantify the effect of crowding as mimicked by commonly used biocompatible polymers. We observe a compaction of IDPs not only with increasing concentration, but also with increasing size of the crowding agents, at variance with the predictions from scaled-particle theory, the prevalent paradigm in the field. However, the observed behavior can be explained quantitatively if the polymeric nature of both the IDPs and the crowding molecules is taken into account explicitly. Our results suggest that excluded volume interactions between overlapping biopolymers and the resulting criticality of the system can be essential contributions to the physics governing the crowded cellular milieu.

Protein crowder charge and protein stability

Macromolecular crowding effects arise from steric repulsions and weak, nonspecific, chemical interactions. Steric repulsions stabilize globular proteins, but the effect of chemical interactions depends on their nature. Repulsive interactions such as those between similarly charged species should reinforce the effect of steric repulsions, increasing the equilibrium thermodynamic stability of a test protein. Attractive chemical interactions, on the other hand, counteract the effect of hard-core repulsions, decreasing stability. We tested these ideas by using the anionic proteins from Escherichia coli as crowding agents and assessing the stability of the anionic test protein chymotrypsin inhibitor 2 at pH 7.0. The anionic protein crowders destabilize the test protein despite the similarity of their net charges. Thus, weak, nonspecific, attractive interactions between proteins can overcome the charge-charge repulsion and counterbalance the stabilizing effect of steric repulsion.

Denatured state ensembles with the same radii of gyration can form significantly different long-range contacts

Defining the structural, dynamic, and energetic properties of the unfolded state of proteins is critical for an in-depth understanding of protein folding, protein thermodynamics, and protein aggregation. Here we analyze long-range contacts and compactness in two apparently fully unfolded ensembles of the same protein: the acid unfolded state of the C-terminal domain of ribosomal protein L9 in the absence of high concentrations of urea as well as the urea unfolded state at low pH. Small angle X-ray scattering reveals that the two states are expanded with values of Rg differing by <7%. Paramagnetic relaxation enhancement (PRE) nuclear magnetic resonance studies, however, reveal that the acid unfolded state samples conformations that facilitate contacts between residues that are distant in sequence while the urea unfolded state ensemble does not. The experimental PRE profiles for the acid unfolded state differ significantly from these predicted using an excluded volume limit ensemble, but these long-range contacts are largely eliminated by the addition of 8 M urea. The work shows that expanded unfolded states can sample very different distributions of long-range contacts yet still have similar radii of gyration. The implications for protein folding and for the characterization of unfolded states are discussed.

Experiments and simulations show how long-range contacts can form in expanded unfolded proteins with negligible secondary structure

The sizes of unfolded proteins under highly denaturing conditions scale as N(0.59) with chain length. This suggests that denaturing conditions mimic good solvents, whereby the preference for favorable chain-solvent interactions causes intrachain interactions to be repulsive, on average. Beyond this generic inference, the broader implications of N(0.59) scaling for quantitative descriptions of denatured state ensembles (DSEs) remain unresolved. Of particular interest is the degree to which N(0.59) scaling can simultaneously accommodate intrachain attractions and detectable long-range contacts. Here we present data showing that the DSE of the N-terminal domain of the L9 (NTL9) ribosomal protein in 8.3 M urea lacks detectable secondary structure and forms expanded conformations in accord with the expected N(0.59) scaling behavior. Paramagnetic relaxation enhancements, however, indicate the presence of detectable long-range contacts in the denatured-state ensemble of NTL9. To explain these observations we used atomistic thermal unfolding simulations to identify ensembles whose properties are consistent with all of the experimental observations, thus serving as useful proxies for the DSE of NTL9 in 8.3 M urea. Analysis of these ensembles shows that residual attractions are present under mimics of good solvent conditions, and for NTL9 they result from low-likelihood, medium/long-range contacts between hydrophobic residues. Our analysis provides a quantitative framework for the simultaneous observation of N(0.59) scaling and low-likelihood long-range contacts for the DSE of NTL9. We propose that such low-likelihood intramolecular hydrophobic clusters might be a generic feature of DSEs that play a gatekeeping role to protect against aggregation during protein folding.

Describing sequence-ensemble relationships for intrinsically disordered proteins

Intrinsically disordered proteins participate in important protein-protein and protein-nucleic acid interactions and control cellular phenotypes through their prominence as dynamic organizers of transcriptional, post-transcriptional and signalling networks. These proteins challenge the tenets of the structure-function paradigm and their functional mechanisms remain a mystery given that they fail to fold autonomously into specific structures. Solving this mystery requires a first principles understanding of the quantitative relationships between information encoded in the sequences of disordered proteins and the ensemble of conformations they sample. Advances in quantifying sequence-ensemble relationships have been facilitated through a four-way synergy between bioinformatics, biophysical experiments, computer simulations and polymer physics theories. In the present review we evaluate these advances and the resultant insights that allow us to develop a concise quantitative framework for describing the sequence-ensemble relationships of intrinsically disordered proteins.

Investigation of the Polymeric Properties of α-Synuclein and Comparison with NMR Experiments: A Replica Exchange Molecular Dynamics Study

Intrinsically disordered proteins (IDPs) have been shown to be involved in a number of cellular functions, in addition to their predominance in diseased states. α-synuclein may be described as one such IDP implicated in the pathology of Parkinson's disease. Understanding the conformational characteristics of the monomeric state of α-synuclein is necessary for understanding the role of the monomer conformation in aggregation. Polymer theories have been applied to investigate the statistical properties of homopolymeric IDPs. Here we use Replica Exchange Molecular Dynamics (REMD) simulations using temperature as a proxy for solvent quality to examine how well these theories developed for homopolymeric chains describe heteropolymeric α-synuclein. Our results indicate that α-synuclein behaves like a homopolymer at the extremes of solvent quality, while in the intermediate solvent regime, the uneven distribution of charged residues along the sequence strongly influences the conformations adopted by the chain. We refine the ensemble extracted from the REMD simulations of α-synuclein, which shows the best qualitative agreement with experiment, by fitting to the experimental NMR Residual Dipolar Couplings (RDCs) and Paramagnetic Relaxation Enhancements (PREs). Our results demonstrate that the detailed shape of the RDC patterns are sensitive to the angular correlations that are local in sequence while longer range anti-correlations which arise from packing constraints affect the RDC magnitudes.

Polymer scaling laws of unfolded and intrinsically disordered proteins quantified with single-molecule spectroscopy

The dimensions of unfolded and intrinsically disordered proteins are highly dependent on their amino acid composition and solution conditions, especially salt and denaturant concentration. However, the quantitative implications of this behavior have remained unclear, largely because the effective theta-state, the central reference point for the underlying polymer collapse transition, has eluded experimental determination. Here, we used single-molecule fluorescence spectroscopy and two-focus correlation spectroscopy to determine the theta points for six different proteins. While the scaling exponents of all proteins converge to 0.62 ± 0.03 at high denaturant concentrations, as expected for a polymer in good solvent, the scaling regime in water strongly depends on sequence composition. The resulting average scaling exponent of 0.46 ± 0.05 for the four foldable protein sequences in our study suggests that the aqueous cellular milieu is close to effective theta conditions for unfolded proteins. In contrast, two intrinsically disordered proteins do not reach the Θ-point under any of our solvent conditions, which may reflect the optimization of their expanded state for the interactions with cellular partners. Sequence analyses based on our results imply that foldable sequences with more compact unfolded states are a more recent result of protein evolution.

Interaction of melittin peptides with perfluorocarbon nanoemulsion particles

Melittin, an antimicrobial peptide, forms pores in biological membranes and triggers cell death. Therefore, it has potential as an anticancer therapy. However, until recently, the therapeutic application of melittin has been impractical because a suitable platform for delivery was not available. Recently, we showed that phospholipid-stabilized perfluorooctyl bromide based nanoemulsion particles (PFOB-NEPs) were resistant to destruction by melittin and enabled specific delivery of melittin to tumor cells, killing them and reducing tumor growth. Earlier, prior work also showed that melittin adsorbed onto the stabilizing phospholipid monolayer of PFOB-NEP but did not disrupt the phospholipid monolayer or produce "cracking" of the PFOB-NEPs. The present work identifies the important structural motifs for melittin binding to PFOB-NEPs through a series of atomistic molecular dynamics simulations. The conformational ensemble of melittin bound to PFOB-NEP lipid monolayer was compared to structure from a control simulation of melittin bound to a lipid bilayer to identify several differences in melittin-lipid interactions between the two systems. First, melittin was deeply buried in the hydrophobic tail region of bilayer, while its depth was attenuated in the PFOB-NEP monolayer. Second, a helical conformation was the major secondary structure in the bilayer, but the fraction of helix was reduced in the PFOB-NEP. Finally, the overall pattern for the direct interaction of melittin with surrounding lipids was similar between liposome and PFOB-NEP, but the level of interaction was slightly decreased in the PFOB-NEP. These results suggest that melittin interacts with the monolayer of PFOB-NEP in a way that is similar way to its interaction with bilayers but that deeper penetration into the hydrophobic interior is inhibited.

Disordered binding of small molecules to Aβ(12-28)

In recent years, an increasing number of small molecules and short peptides have been identified that interfere with aggregation and/or oligomerization of the Alzheimer β-amyloid peptide (Aβ). Many of them possess aromatic moieties, suggesting a dominant role for those in interacting with Aβ along various stages of the aggregation process. In this study, we attempt to elucidate whether interactions of such aromatic inhibitors with monomeric Aβ(12-28) point to a common mechanism of action by performing atomistic molecular dynamics simulations at equilibrium. Our results suggest that, independently of the presence of inhibitors, monomeric Aβ(12-28) populates a partially collapsed ensemble that is largely devoid of canonical secondary structure at 300 K and neutral pH. The small molecules have different affinities for Aβ(12-28) that can be partially rationalized by the balance of aromatic and charged moieties constituting the molecules. There are no predominant binding modes, although aggregation inhibitors preferentially interact with the N-terminal portion of the fragment (residues 13-20). Analysis of the free energy landscape of Aβ(12-28) reveals differences highlighted by altered populations of a looplike conformer in the presence of inhibitors. We conclude that intrinsic disorder of Aβ persists at the level of binding small molecules and that inhibitors can significantly alter properties of monomeric Aβ via multiple routes of differing specificity.

A comparative study of the second-order hydrophobic moments for globular proteins: the consensus scale of hydrophobicity and the CHARMM partial atomic charges

In this paper, the second-order hydrophobic moment for fifteen globular proteins in 150 nonhomologous protein chains was performed in a comparative study involving two sets of hydrophobicity: one selected from the consensus scale and the other derived from the CHARMM partial atomic charges. These proteins were divided into three groups, based on their number of residues (N) and the asphericity (δ). Proteins in Group I were spherical and those in Groups II and III were prolate. The size of the proteins is represented by the mean radius of gyration (R_g ), which follows the Flory scaling law, R_g ∝ N^ν. The mean value of v was 0.35, which is similar to a polymer chain in a poor solvent. The spatial distributions of the second-order moment for each of the proteins, obtained from the two sets of hydrophobicity, were compared using the Pearson correlation coefficient; the results reveal that there is a strong correlation between the two data sets for each protein structure when the CHARMM partial atomic charges, |q_i| ≥ 0.3, assigned for polar atoms, are used. The locations at which these distributions vanish and approach a negative value are at approximately 50% of the percentage of solvent accessibility, indicating that there is a transition point from hydrophobic interior to hydrophilic exterior in the proteins. This may suggest that there is a position for the proteins to determine the residues at exposed sites beyond this range.

DNA and nucleosomes direct distinct folding of a linker histone H1 C-terminal domain

We previously documented condensation of the H1 CTD consistent with adoption of a defined structure upon nucleosome binding using a bulk FRET assay, supporting proposals that the CTD behaves as an intrinsically disordered domain. In the present study, by determining the distances between two different pairs of sites in the C-terminal domain of full length H1 by FRET, we confirm that nucleosome binding directs folding of the disordered H1 C-terminal domain and provide additional distance constraints for the condensed state. In contrast to nucleosomes, FRET observed upon H1 binding to naked DNA fragments includes both intra- and inter-molecular resonance energy transfer. By eliminating inter-molecular transfer, we find that CTD condensation induced upon H1-binding naked DNA is distinct from that induced by nucleosomes. Moreover, analysis of fluorescence quenching indicates that H1 residues at either end of the CTD experience distinct environments when bound to nucleosomes, and suggest that the penultimate residue in the CTD (K195) is juxtaposed between the two linker DNA helices, proposed to form a stem structure in the H1-bound nucleosome.

Energy landscape analyses of disordered histone tails reveal special organization of their conformational dynamics

Histone tails are highly flexible N- or C-terminal protrusions of histone proteins which facilitate the compaction of DNA into dense superstructures known as chromatin. On a molecular scale histone tails are polyelectrolytes with high degree of conformational disorder which allows them to function as biomolecular "switches", regulating various genetic processes. Unfortunately, their intrinsically disordered nature creates obstacles for comprehensive experimental investigation of both the structural and dynamical aspects of histone tails, because of which their conformational behaviors are still not well understood. In this work we have carried out ∼3 microsecond long all atom replica exchange molecular dynamics (REMD) simulations for each of four histone tails, H4, H3, H2B, and H2A, and probed their intrinsic conformational preferences. Our subsequent free energy landscape analysis demonstrated that most tails are not fully disordered, but show distinct conformational organization, containing specific flickering secondary structural elements. In particular, H4 forms β-hairpins, H3 and H2B adopt α-helical elements, while H2A is fully disordered. We rationalized observed patterns of conformational dynamics of various histone tails using ideas from physics of polyelectrolytes and disordered systems. We also discovered an intriguing re-entrant contraction-expansion of the tails upon heating, which is caused by subtle interplay between ionic screening and chain entropy.

Nucleosome linker DNA contacts and induces specific folding of the intrinsically disordered H1 carboxyl-terminal domain

Linker histones play essential roles in the chromatin structure of higher eukaryotes. While binding to the surface of nucleosomes is directed by an ∼ 80-amino-acid-residue globular domain, the structure and interactions of the lysine-rich ∼ 100-residue C-terminal domain (CTD), primarily responsible for the chromatin-condensing functions of linker histones, are poorly understood. By quantitatively analyzing binding of a set of H1 CTD deletion mutants to nucleosomes containing various lengths of linker DNA, we have identified interactions between distinct regions of the CTD and nucleosome linker DNA at least 21 bp from the edge of the nucleosome core. Importantly, partial CTD truncations caused increases in H1 binding affinity, suggesting that significant entropic costs are incurred upon binding due to CTD folding. van't Hoff entropy/enthalpy analysis and intramolecular fluorescent resonance energy transfer (FRET) studies indicate that the CTD undergoes substantial nucleosome-directed folding, in a manner that is distinct from that which occurs upon H1 binding to naked DNA. In addition to defining critical interactions between the H1 CTD and linker DNA, our data indicate that the H1 CTD is an intrinsically disordered domain and provide important insights into the biological function of this protein.