How accurate are polymer models in the analysis of Förster resonance energy transfer experiments on proteins?

Nanosecond chain dynamics of single-stranded nucleic acids

The conformational dynamics of single-stranded nucleic acids are fundamental for nucleic acid folding and function. However, their elementary chain dynamics have been difficult to resolve experimentally. Here we employ a combination of single-molecule Förster resonance energy transfer, nanosecond fluorescence correlation spectroscopy, and nanophotonic enhancement to determine the conformational ensembles and rapid chain dynamics of short single-stranded nucleic acids in solution. To interpret the experimental results in terms of end-to-end distance dynamics, we utilize the hierarchical chain growth approach, simple polymer models, and refinement with Bayesian inference to generate structural ensembles that closely align with the experimental data. The resulting chain reconfiguration times are exceedingly rapid, in the 10-ns range. Solvent viscosity-dependent measurements indicate that these dynamics of single-stranded nucleic acids exhibit negligible internal friction and are thus dominated by solvent friction. Our results provide a detailed view of the conformational distributions and rapid dynamics of single-stranded nucleic acids.

Electrostatics and hydrophobicity in the dynamics of intrinsically disordered proteins

Internal friction is a major contribution to the dynamics of intrinsically disordered proteins (IDPs). Yet, the molecular origin of internal friction has so far been elusive. Here, we investigate whether attractive electrostatic interactions in IDPs modulate internal friction differently than the hydrophobic effect. To this end, we used nanosecond fluorescence correlation spectroscopy (nsFCS) and single-molecule Förster resonance energy transfer (FRET) to quantify the conformation and dynamics of the disordered DNA-binding domains Myc, Max and Mad at different salt concentrations. We find that internal friction effects are stronger when the chain is compacted by electrostatic attractions compared to the hydrophobic effect. Although the effect is moderate, the results show that the heteropolymeric nature of IDPs is reflected in their dynamics.

Exploring Intra- and Inter-Regional Interactions in the IDP α-Synuclein Using smFRET and MD Simulations

Theoretical concepts from polymer physics are often used to describe intrinsically disordered proteins (IDPs). However, amino acid interactions within and between regions of the protein can lead to deviations from typical polymer scaling behavior and even to short-lived secondary structures. To investigate the key interactions in the dynamic IDP α-synuclein (αS) at the amino acid level, we conducted single-molecule fluorescence resonance energy transfer (smFRET) experiments and coarse-grained molecular dynamics (CG-MD) simulations. We find excellent agreement between experiments and simulations. Our results show that a physiological salt solution is a good solvent for αS and that the protein is highly dynamic throughout its entire chain, with local intra- and inter-regional interactions leading to deviations from global scaling. Specifically, we observe expansion in the C-terminal region, compaction in the NAC region, and a slightly smaller distance between the C- and N-termini than expected. Our simulations indicate that the compaction in the NAC region results from hydrophobic aliphatic contacts, mostly between valine and alanine residues, and cation-π interactions between lysine and tyrosine. In addition, hydrogen bonds also seem to contribute to the compaction of the NAC region. The expansion of the C-terminal region is due to intraregional electrostatic repulsion and increased chain stiffness from several prolines. Overall, our study demonstrates the effectiveness of combining smFRET experiments with CG-MD simulations to investigate the key interactions in highly dynamic IDPs at the amino acid level.

Semi-Synthetic CoA-α-Synuclein Constructs Trap N-Terminal Acetyltransferase NatB for Binding Mechanism Studies

N-terminal acetylation is a chemical modification carried out by N-terminal acetyltransferases. A major member of this enzyme family, NatB, acts on much of the human proteome, including α-synuclein (αS), a synaptic protein that mediates vesicle trafficking. NatB acetylation of αS modulates its lipid vesicle binding properties and amyloid fibril formation, which underlies its role in the pathogenesis of Parkinson's disease. Although the molecular details of the interaction between human NatB (hNatB) and the N-terminus of αS have been resolved, whether the remainder of the protein plays a role in interacting with the enzyme is unknown. Here, we execute the first synthesis, by native chemical ligation, of a bisubstrate inhibitor of NatB consisting of coenzyme A and full-length human αS, additionally incorporating two fluorescent probes for studies of conformational dynamics. We use cryo-electron microscopy (cryo-EM) to characterize the structural features of the hNatB/inhibitor complex and show that, beyond the first few residues, αS remains disordered when in complex with hNatB. We further probe changes in the αS conformation by single molecule Förster resonance energy transfer (smFRET) to reveal that the C-terminus expands when bound to hNatB. Computational models based on the cryo-EM and smFRET data help to explain the conformational changes as well as their implications for hNatB substrate recognition and specific inhibition of the interaction with αS. Beyond the study of αS and NatB, these experiments illustrate valuable strategies for the study of challenging structural biology targets through a combination of protein semi-synthesis, cryo-EM, smFRET, and computational modeling.

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.

The Action of Chemical Denaturants: From Globular to Intrinsically Disordered Proteins

Proteins perform their many functions by adopting either a minimal number of strictly similar conformations, the native state, or a vast ensemble of highly flexible conformations. In both cases, their structural features are highly influenced by the chemical environment. Even though a plethora of experimental studies have demonstrated the impact of chemical denaturants on protein structure, the molecular mechanism underlying their action is still debated. In the present review, after a brief recapitulation of the main experimental data on protein denaturants, we survey both classical and more recent interpretations of the molecular basis of their action. In particular, we highlight the differences and similarities of the impact that denaturants have on different structural classes of proteins, i.e., globular, intrinsically disordered (IDP), and amyloid-like assemblies. Particular attention has been given to the IDPs, as recent studies are unraveling their fundamental importance in many physiological processes. The role that computation techniques are expected to play in the near future is illustrated.

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.

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.

Integrating single-molecule spectroscopy and simulations for the study of intrinsically disordered proteins

Over the last two decades, intrinsically disordered proteins and protein regions (IDRs) have emerged from a niche corner of biophysics to be recognized as essential drivers of cellular function. Various techniques have provided fundamental insight into the function and dysfunction of IDRs. Among these techniques, single-molecule fluorescence spectroscopy and molecular simulations have played a major role in shaping our modern understanding of the sequence-encoded conformational behavior of disordered proteins. While both techniques are frequently used in isolation, when combined they offer synergistic and complementary information that can help uncover complex molecular details. Here we offer an overview of single-molecule fluorescence spectroscopy and molecular simulations in the context of studying disordered proteins. We discuss the various means in which simulations and single-molecule spectroscopy can be integrated, and consider a number of studies in which this integration has uncovered biological and biophysical mechanisms.

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.

Probing Interdomain Linkers and Protein Supertertiary Structure In Vitro and in Live Cells with Fluorescent Protein Resonance Energy Transfer

Many proteins are composed of independently-folded domains connected by flexible linkers. The primary sequence and length of such linkers can set the effective concentration for the tethered domains, which impacts rates of association and enzyme activity. The length of such linkers can be sensitive to environmental conditions, which raises questions as to how studies in dilute buffer relate to the highly-crowded cellular environment. To examine the role of linkers in domain separation, we measured Fluorescent Protein-Fluorescence Resonance Energy Transfer (FP-FRET) for a series of tandem FPs that varied in the length of their interdomain linkers. We used discrete molecular dynamics to map the underlying conformational distribution, which revealed intramolecular contact states that we confirmed with single molecule FRET. Simulations found that attached FPs increased linker length and slowed conformational dynamics relative to the bare linkers. This makes the CLYs poor sensors of inherent linker properties. However, we also showed that FP-FRET in CLYs was sensitive to solvent quality and macromolecular crowding making them potent environmental sensors. Finally, we targeted the same proteins to the plasma membrane of living mammalian cells to measure FP-FRET in cellulo. The measured FP-FRET when tethered to the plasma membrane was the same as that in dilute buffer. While caveats remain regarding photophysics, this suggests that the supertertiary conformational ensemble of these CLY proteins may not be affected by this specific cellular environment.

Conformational Ensembles of an Intrinsically Disordered Protein Consistent with NMR, SAXS, and Single-Molecule FRET

Intrinsically disordered proteins (IDPs) have fluctuating heterogeneous conformations, which makes their structural characterization challenging. Although challenging, characterization of the conformational ensembles of IDPs is of great interest, since their conformational ensembles are the link between their sequences and functions. An accurate description of IDP conformational ensembles depends crucially on the amount and quality of the experimental data, how it is integrated, and if it supports a consistent structural picture. We used integrative modeling and validation to apply conformational restraints and assess agreement with the most common structural techniques for IDPs: Nuclear Magnetic Resonance (NMR) spectroscopy, Small-angle X-ray Scattering (SAXS), and single-molecule Förster Resonance Energy Transfer (smFRET). Agreement with such a diverse set of experimental data suggests that details of the generated ensembles can now be examined with a high degree of confidence. Using the disordered N-terminal region of the Sic1 protein as a test case, we examined relationships between average global polymeric descriptions and higher-moments of their distributions. To resolve apparent discrepancies between smFRET and SAXS inferences, we integrated SAXS data with NMR data and reserved the smFRET data for independent validation. Consistency with smFRET, which was not guaranteed a priori, indicates that, globally, the perturbative effects of NMR or smFRET labels on the Sic1 ensemble are minimal. Analysis of the ensembles revealed distinguishing features of Sic1, such as overall compactness and large end-to-end distance fluctuations, which are consistent with biophysical models of Sic1's ultrasensitive binding to its partner Cdc4. Our results underscore the importance of integrative modeling and validation in generating and drawing conclusions from IDP conformational ensembles.

Investigating the Conformational Ensembles of Intrinsically Disordered Proteins with a Simple Physics-Based Model

Intrinsically disordered proteins (IDPs) play an important role in an array of biological processes but present a number of fundamental challenges for computational modeling. Recently, simple polymer models have regained popularity for interpreting the experimental characterization of IDPs. Homopolymer theory provides a strong foundation for understanding generic features of phenomena ranging from single-chain conformational dynamics to the properties of entangled polymer melts, but is difficult to extend to the copolymer context. This challenge is magnified for proteins due to the variety of competing interactions and large deviations in side-chain properties. In this work, we apply a simple physics-based coarse-grained model for describing largely disordered conformational ensembles of peptides, based on the premise that sampling sterically forbidden conformations can compromise the faithful description of both static and dynamical properties. The Hamiltonian of the employed model can be easily adjusted to investigate the impact of distinct interactions and sequence specificity on the randomness of the resulting conformational ensemble. In particular, starting with a bead–spring-like model and then adding more detailed interactions one by one, we construct a hierarchical set of models and perform a detailed comparison of their properties. Our analysis clarifies the role of generic attractions, electrostatics, and side-chain sterics, while providing a foundation for developing efficient models for IDPs that retain an accurate description of the hierarchy of conformational dynamics, which is nontrivially influenced by interactions with surrounding proteins and solvent molecules.

Single-Molecule FRET of Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) are now widely recognized as playing critical roles in a broad range of cellular functions as well as being implicated in diverse diseases. Their lack of stable secondary structure and tertiary interactions, coupled with their sensitivity to measurement conditions, stymies many traditional structural biology approaches. Single-molecule Förster resonance energy transfer (smFRET) is now widely used to characterize the physicochemical properties of these proteins in isolation and is being increasingly applied to more complex assemblies and experimental environments. This review provides an overview of confocal diffusion-based smFRET as an experimental tool, including descriptions of instrumentation, data analysis, and protein labeling. Recent papers are discussed that illustrate the unique capability of smFRET to provide insight into aggregation-prone IDPs, protein–protein interactions involving IDPs, and IDPs in complex experimental milieus.

How a local active force modifies the structural properties of polymers

We study the dynamics of a polymer, described as a variant of a Rouse chain, driven by an active terminal monomer (head). The local active force induces a transition from a globule-like to an elongated state, as revealed by the study of the end-to-end distance, the variance of which is analytically predicted under suitable approximations. The change in the relaxation times of the Rouse-modes produced by the local self-propulsion is consistent with the transition from globule to elongated conformations. Moreover, also the bond-bond spatial correlation for the chain head are affected by the self-propulsion and a gradient of over-stretched bonds along the chain is observed. We compare our numerical results both with the phenomenological stiff-polymer theory and several analytical predictions in the Rouse-chain approximation.

Emerging consensus on the collapse of unfolded and intrinsically disordered proteins in water

Establishing the degree of collapse of unfolded or disordered proteins is a fundamental problem in biophysics, because of its relation to protein folding and to the function of intrinsically disordered proteins. However, until recently, different experiments gave qualitatively different results on collapse and there were large discrepancies between experiments and all-atom simulations. New methodology introduced in the past three years has helped to resolve the differences between experiments, and improvements in simulations have closed the gap between experiment and simulation. These advances have led to an emerging consensus on the collapse of disordered proteins in water.

Untangling the Conformational Polymorphism of Disordered Proteins Associated With Neurodegeneration at the Single-Molecule Level

A large fraction of the human genome encodes intrinsically disordered proteins/regions (IDPs/IDRs) that are involved in diverse cellular functions/regulation and dysfunctions. Moreover, several neurodegenerative disorders are associated with the pathological self-assembly of neuronal IDPs, including tau [Alzheimer's disease (AD)], α-synuclein [Parkinson's disease (PD)], and huntingtin exon 1 [Huntington's disease (HD)]. Therefore, there is an urgent and emerging clinical interest in understanding the physical and structural features of their functional and disease states. However, their biophysical characterization is inherently challenging by traditional ensemble techniques. First, unlike globular proteins, IDPs lack stable secondary/tertiary structures under physiological conditions and may interact with multiple and distinct biological partners, subsequently folding differentially, thus contributing to the conformational polymorphism. Second, amyloidogenic IDPs display a high aggregation propensity, undergoing complex heterogeneous self-assembly mechanisms. In this review article, we discuss the advantages of employing cutting-edge single-molecule fluorescence (SMF) techniques to characterize the conformational ensemble of three selected neuronal IDPs (huntingtin exon 1, tau, and α-synuclein). Specifically, we survey the versatility of these powerful approaches to describe their monomeric conformational ensemble under functional and aggregation-prone conditions, and binding to biological partners. Together, the information gained from these studies provides unique insights into the role of gain or loss of function of these disordered proteins in neurodegeneration, which may assist the development of new therapeutic molecules to prevent and treat these devastating human disorders.

Measuring Interactions Between Tau and Aggregation Inducers with Single-Molecule Förster Resonance Energy Transfer

Tau is an intrinsically disordered protein implicated in the pathogenesis of Alzheimer's disease and other neurodegenerative disorders. Here we describe the application of single-molecule Förster resonance energy transfer (smFRET) for the characterization of the interactions between tau and polyphosphate, an intracellular polymer that accelerates tau aggregation. We describe the design of tau constructs, purification and fluorescent labeling of tau, and details of acquisition and analysis of smFRET data. The protocols provided here outline an approach that may be applied to the study of other intrinsically disordered proteins and their binding partners.

Independent tubulin binding and polymerization by the proline-rich region of Tau is regulated by Tau's N-terminal domain

Tau is an intrinsically disordered, microtubule-associated protein that has a role in regulating microtubule dynamics. Despite intensive research, the molecular mechanisms of Tau-mediated microtubule polymerization are poorly understood. Here we used single-molecule fluorescence to investigate the role of Tau's N-terminal domain (NTD) and proline-rich region (PRR) in regulating interactions of Tau with soluble tubulin. We assayed both full-length Tau isoforms and truncated variants for their ability to bind soluble tubulin and stimulate microtubule polymerization. We found that Tau's PRR is an independent tubulin-binding domain that has tubulin polymerization capacity. In contrast to the relatively weak interactions with tubulin mediated by sites distributed throughout Tau's microtubule-binding region (MTBR), resulting in heterogeneous Tau: tubulin complexes, the PRR bound tubulin tightly and stoichiometrically. Moreover, we demonstrate that interactions between the PRR and MTBR are reduced by the NTD through a conserved conformational ensemble. On the basis of these results, we propose that Tau's PRR can serve as a core tubulin-binding domain, whereas the MTBR enhances polymerization capacity by increasing the local tubulin concentration. Moreover, the NTD appears to negatively regulate tubulin-binding interactions of both of these domains. The findings of our study draw attention to a central role of the PRR in Tau function and provide mechanistic insight into Tau-mediated polymerization of tubulin.

Generation of the configurational ensemble of an intrinsically disordered protein from unbiased molecular dynamics simulation

Intrinsically disordered proteins (IDPs) are abundant in eukaryotic proteomes, play a major role in cell signaling, and are associated with human diseases. To understand IDP function it is critical to determine their configurational ensemble, i.e., the collection of 3-dimensional structures they adopt, and this remains an immense challenge in structural biology. Attempts to determine this ensemble computationally have been hitherto hampered by the necessity of reweighting molecular dynamics (MD) results or biasing simulation in order to match ensemble-averaged experimental observables, operations that reduce the precision of the generated model because different structural ensembles may yield the same experimental observable. Here, by employing enhanced sampling MD we reproduce the experimental small-angle neutron and X-ray scattering profiles and the NMR chemical shifts of the disordered N terminal (SH4UD) of c-Src kinase without reweighting or constraining the simulations. The unbiased simulation results reveal a weakly funneled and rugged free energy landscape of SH4UD, which gives rise to a heterogeneous ensemble of structures that cannot be described by simple polymer theory. SH4UD adopts transient helices, which are found away from known phosphorylation sites and could play a key role in the stabilization of structural regions necessary for phosphorylation. Our findings indicate that adequately sampled molecular simulations can be performed to provide accurate physical models of flexible biosystems, thus rationalizing their biological function.

Conformational heterogeneity in human interphase chromosome organization reconciles the FISH and Hi-C paradox

Hi-C experiments are used to infer the contact probabilities between loci separated by varying genome lengths. Contact probability should decrease as the spatial distance between two loci increases. However, studies comparing Hi-C and FISH data show that in some cases the distance between one pair of loci, with larger Hi-C readout, is paradoxically larger compared to another pair with a smaller value of the contact probability. Here, we show that the FISH-Hi-C paradox can be resolved using a theory based on a Generalized Rouse Model for Chromosomes (GRMC). The FISH-Hi-C paradox arises because the cell population is highly heterogeneous, which means that a given contact is present in only a fraction of cells. Insights from the GRMC is used to construct a theory, without any adjustable parameters, to extract the distribution of subpopulations from the FISH data, which quantitatively reproduces the Hi-C data. Our results show that heterogeneity is pervasive in genome organization at all length scales, reflecting large cell-to-cell variations.

Studies comparing Hi-C and FISH data show that in some cases the distance between one pair of loci is paradoxically larger compared to another pair with a smaller value of the contact probability. Here the authors use a theory based on a Generalized Rouse Model for Chromosomes to resolve this paradox.

Residual Structures and Transient Long-Range Interactions of p53 Transactivation Domain: Assessment of Explicit Solvent Protein Force Fields

Molecular dynamics simulations using physics-based atomistic force fields have been increasingly used to characterize the heterogeneous structural ensembles of intrinsically disordered proteins (IDPs). To evaluate the accuracy of the latest atomistic explicit-solvent force fields in modeling larger IDPs with nontrivial structural features, we focus on the 61-residue N-terminal transactivation domain (TAD) of tumor suppressor p53, an important protein in cancer biology that has been extensively studied, and abundant experimental data is available for evaluation of simulated ensembles. We performed extensive replica exchange with solute tempering simulations, in excess of 1.0 μs/replica, to generate disordered structural ensembles of p53-TAD using six latest explicit solvent protein force fields. Multiple local and long-range structural properties, including chain dimension, residual secondary structures, and transient long-range contacts, were analyzed and compared against available experimental data. The results show that IDPs such as p53-TAD remain highly challenging for atomistic simulations due to conformational complexity and difficulty in achieving adequate convergence. Structural ensembles of p53-TAD generated using various force fields differ significantly from each other. The a99SB-disp force field demonstrates the best agreement with experimental data at all levels and proves to be suitable for simulating unbound p53-TAD and how its conformational properties may be modulated by phosphorylation and other cellular signals or cancer-associated mutations. Feasibility of such detailed structural characterization is a key step toward establishing the sequence-disordered ensemble-function-disease relationship of p53 and other biologically important IDPs.

Force-displacement relations at compression of dsDNA macromolecules

The elasticity of dsDNA molecules is investigated by Monte Carlo simulations based on a coarse-grained model of DNA. The force-displacement (f-r) curves are computed under the constraints of the constant force (Gibbs) or the constant length (Helmholtz) ensemble. Particular attention was paid to the compressional (negative) and weak tensile forces. It was confirmed that simulations using the vector Gibbs ensemble fail to represent the compression behavior of polymers. Simulations using the scalar Gibbs protocol resulted in a qualitatively correct compressional response of DNA provided that the quadratic averages of displacements were employed. Furthermore, a well-known shortcoming of the popular Marko-Siggia relation for DNA elasticity at weak tensile forces is elucidated. Conversely, the function f-r from the simulation at the constant length constraint, as well as the new closed-form expressions, provides a realistic depiction of the DNA elasticity over the wide range of negative and positive forces. Merely a qualitative resemblance of the compression functions f-r predicted by the employed approaches supports the notion that the elastic response of DNA molecules may be greatly affected by the specifics of the experimental setups and the kind of averaging of the measured variable.

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.

Disordered RNA chaperones can enhance nucleic acid folding via local charge screening

RNA chaperones are proteins that aid in the folding of nucleic acids, but remarkably, many of these proteins are intrinsically disordered. How can these proteins function without a well-defined three-dimensional structure? Here, we address this question by studying the hepatitis C virus core protein, a chaperone that promotes viral genome dimerization. Using single-molecule fluorescence spectroscopy, we find that this positively charged disordered protein facilitates the formation of compact nucleic acid conformations by acting as a flexible macromolecular counterion that locally screens repulsive electrostatic interactions with an efficiency equivalent to molar salt concentrations. The resulting compaction can bias unfolded nucleic acids towards folding, resulting in faster folding kinetics. This potentially widespread mechanism is supported by molecular simulations that rationalize the experimental findings by describing the chaperone as an unstructured polyelectrolyte.

RNA chaperones, such as the hepatitic C virus (HCV) core protein, are proteins that aid in the folding of nucleic acids. Here authors use single‐molecule spectroscopy and simulation to show that the HCV core protein acts as a flexible macromolecular counterion which facilitates nucleic acid folding.

Recent Advances in Computational Protocols Addressing Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDP) are abundant in the human genome and have recently emerged as major therapeutic targets for various diseases. Unlike traditional proteins that adopt a definitive structure, IDPs in free solution are disordered and exist as an ensemble of conformations. This enables the IDPs to signal through multiple signaling pathways and serve as scaffolds for multi-protein complexes. The challenge in studying IDPs experimentally stems from their disordered nature. Nuclear magnetic resonance (NMR), circular dichroism, small angle X-ray scattering, and single molecule Förster resonance energy transfer (FRET) can give the local structural information and overall dimension of IDPs, but seldom provide a unified picture of the whole protein. To understand the conformational dynamics of IDPs and how their structural ensembles recognize multiple binding partners and small molecule inhibitors, knowledge-based and physics-based sampling techniques are utilized in-silico, guided by experimental structural data. However, efficient sampling of the IDP conformational ensemble requires traversing the numerous degrees of freedom in the IDP energy landscape, as well as force-fields that accurately model the protein and solvent interactions. In this review, we have provided an overview of the current state of computational methods for studying IDP structure and dynamics and discussed the major challenges faced in this field.

Solvent effect on FRET spectroscopic ruler

A discrepancy has emerged in recent years between single-molecule Förster resonance energy transfer (smFRET) measurements and small angle X-ray scattering (SAXS) or small angle neutron scattering experiments in the study of unfolded or intrinsically disordered proteins in denaturing solutions. Despite significant advances that have been made in identifying various factors which may have contributed to the manifestation of the so-called smFRET-SAXS discrepancy, no consensus has been reached so far on its original source or eventual resolution. In this study, we investigate this problem from the perspective of the solvent effect on FRET spectroscopic ruler (SEFSR), a generic term we use to describe various solvent-dependent factors affecting the accuracy of the FRET experimental method that is known as a "spectroscopic ruler." Some factors belonging to SEFSR, such as direct dye-solvent interaction and labeling configuration, seem to have not received due attention regarding their significance in contributing to the discrepancy. We identify SEFSR by measuring a rigid segment of a double-stranded DNA in various solutions using the smFRET method and evaluate its relative importance in smFRET experiments by measuring segments of a single-stranded DNA and polyethylene glycol (PEG) in solutions. We find that SEFSR can produce non-negligible FRET-inferred interdye distance changes in various solutions, with an intensity following the Hofmeister series in ionic solutions and dependent on labeling configurations. SEFSR is found to be significant in GuHCl and urea solutions, which can fully cover the apparent expansion signal of dye-labeled PEG. Our findings suggest that SEFSR may have played an important role in contributing to the smFRET-SAXS discrepancy.

Accurate Transfer Efficiencies, Distance Distributions, and Ensembles of Unfolded and Intrinsically Disordered Proteins From Single-Molecule FRET

Intrinsically disordered proteins (IDPs) sample structurally diverse ensembles. Characterizing the underlying distributions of conformations is a key step toward understanding the structural and functional properties of IDPs. One increasingly popular method for obtaining quantitative information on intramolecular distances and distributions is single-molecule Förster resonance energy transfer (FRET). Here we describe two essential elements of the quantitative analysis of single-molecule FRET data of IDPs: the sample-specific calibration of the single-molecule instrument that is required for determining accurate transfer efficiencies, and the use of state-of-the-art methods for inferring accurate distance distributions from these transfer efficiencies. First, we illustrate how to quantify the correction factors for instrument calibration with alternating donor and acceptor excitation measurements of labeled samples spanning a wide range of transfer efficiencies. Second, we show how to infer distance distributions based on suitably parameterized simple polymer models, and how to obtain conformational ensembles from Bayesian reweighting of molecular simulations or from parameter optimization in simplified coarse-grained models.

Single Molecule FRET: A Powerful Tool to Study Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) are often modeled using ideas from polymer physics that suggest they smoothly explore all corners of configuration space. Experimental verification of this random, dynamic behavior is difficult as random fluctuations of IDPs cannot be synchronized across an ensemble. Single molecule fluorescence (or Förster) resonance energy transfer (smFRET) is one of the few approaches that are sensitive to transient populations of sub-states within molecular ensembles. In some implementations, smFRET has sufficient time resolution to resolve transitions in IDP behaviors. Here we present experimental issues to consider when applying smFRET to study IDP configuration. We illustrate the power of applying smFRET to IDPs by discussing two cases in the literature of protein systems for which smFRET has successfully reported phosphorylation-induced modification (but not elimination) of the disordered properties that have been connected to impacts on the related biological function. The examples we discuss, PAGE4 and a disordered segment of the GluN2B subunit of the NMDA receptor, illustrate the great potential of smFRET to inform how IDP function can be regulated by controlling the detailed ensemble of disordered states within biological networks.

Dispersion Correction Alleviates Dye Stacking of Single-Stranded DNA and RNA in Simulations of Single-Molecule Fluorescence Experiments

We combine single-molecule Förster resonance energy transfer (single-molecule FRET) experiments with extensive all-atom molecular dynamics (MD) simulations (>100 μs) to characterize the conformational ensembles of single-stranded (ss) DNA and RNA in solution. From MD simulations with explicit dyes attached to single-stranded nucleic acids via flexible linkers, we calculate FRET efficiencies and fluorescence anisotropy decays. We find that dispersion-corrected water models alleviate the problem of overly abundant interactions between fluorescent dyes and the aromatic ring systems of nucleobases. To model dye motions in a computationally efficient and conformationally exhaustive manner, we introduce a dye-conformer library, built from simulations of dinucleotides with covalently attached dye molecules. We use this library to calculate FRET efficiencies for dT₁₉, dA₁₉, and rA₁₉ simulated without explicit labels over a wide range of salt concentrations. For end-labeled homopolymeric pyrimidine ssDNA, MD simulations with the parmBSC1 force field capture the overall trend in salt-dependence of single-molecule FRET based distance measurements. For homopolymeric purine ssRNA and ssDNA, the DESRES and parmBSC1 force fields, respectively, provide useful starting points, even though our comparison also identifies clear deviations from experiment.

Comment on "Innovative scattering analysis shows that hydrophobic disordered proteins are expanded in water"

Riback et al (Reports, 13 October 2017, p. 238) used small-angle x-ray scattering (SAXS) experiments to infer a degree of compaction for unfolded proteins in water versus chemical denaturant that is highly consistent with the results from Förster resonance energy transfer (FRET) experiments. There is thus no "contradiction" between the two methods, nor evidence to support their claim that commonly used FRET fluorophores cause protein compaction.

Comment on "Innovative scattering analysis shows that hydrophobic disordered proteins are expanded in water"

Editors at Science requested our input on the above discussion (comment by Best et al and response by Riback et al) because both sets of authors use our data from Fuertes et al (2017) to support their arguments. The topic of discussion pertains to the discrepant inferences drawn from SAXS versus FRET measurements regarding the dimensions of intrinsically disordered proteins (IDPs) in aqueous solvents. Using SAXS measurements on labeled and unlabeled proteins, we ruled out the labels used for FRET measurements as the cause of discrepant inferences between the two methods. Instead, we propose that FRET and SAXS provide complementary readouts because of a decoupling of size and shape fluctuations that is intrinsic to finite-sized, heteropolymeric IDPs. Accounting for this decoupling resolves the discrepant inferences between the two methods, thus making a case for the utility of both methods.

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.

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.

An Extended Guinier Analysis for Intrinsically Disordered Proteins

Guinier analysis allows model-free determination of the radius of gyration (R_g) of a biomolecule from X-ray or neutron scattering data, in the limit of very small scattering angles. Its range of validity is well understood for globular proteins, but is known to be more restricted for unfolded or intrinsically disordered proteins (IDPs). We have used ensembles of disordered structures from molecular dynamics simulations to investigate which structural properties cause deviations from the Guinier approximation at small scattering angles. We find that the deviation from the Guinier approximation is correlated with the polymer scaling exponent ν describing the unfolded ensemble. We therefore introduce an empirical, ν-dependent, higher-order correction term, to augment the standard Guinier analysis. We test the new fitting scheme using all-atom simulation data for several IDPs and experimental data for both an IDP and a destabilized mutant of a folded protein. In all cases tested, we achieve an accuracy of the inferred R_g within ∼3% of the true R_g. The method is straightforward to implement and extends the range of validity to a maximum qR_g of ∼2 versus ∼1.1 for Guinier analysis. Compared with the Guinier or Debye approaches, our method allows data from wider angles with lower noise to be used to analyze scattering data accurately. In addition to R_g, our fitting scheme also yields estimates of the scaling exponent ν in excellent agreement with the reference ν determined from the underlying molecular ensemble.

Sequence determinants of protein phase behavior from a coarse-grained model

Membraneless organelles important to intracellular compartmentalization have recently been shown to comprise assemblies of proteins which undergo liquid-liquid phase separation (LLPS). However, many proteins involved in this phase separation are at least partially disordered. The molecular mechanism and the sequence determinants of this process are challenging to determine experimentally owing to the disordered nature of the assemblies, motivating the use of theoretical and simulation methods. This work advances a computational framework for conducting simulations of LLPS with residue-level detail, and allows for the determination of phase diagrams and coexistence densities of proteins in the two phases. The model includes a short-range contact potential as well as a simplified treatment of electrostatic energy. Interaction parameters are optimized against experimentally determined radius of gyration data for multiple unfolded or intrinsically disordered proteins (IDPs). These models are applied to two systems which undergo LLPS: the low complexity domain of the RNA-binding protein FUS and the DEAD-box helicase protein LAF-1. We develop a novel simulation method to determine thermodynamic phase diagrams as a function of the total protein concentration and temperature. We show that the model is capable of capturing qualitative changes in the phase diagram due to phosphomimetic mutations of FUS and to the presence or absence of the large folded domain in LAF-1. We also explore the effects of chain-length, or multivalency, on the phase diagram, and obtain results consistent with Flory-Huggins theory for polymers. Most importantly, the methodology presented here is flexible so that it can be easily extended to other pair potentials, be used with other enhanced sampling methods, and may incorporate additional features for biological systems of interest.

Liquid liquid phase separation (LLPS) of low-complexity protein sequences has emerged as an important research topic due to its relevance to membraneless organelles and intracellular compartmentalization. However a molecular level understanding of LLPS cannot be easily obtained by experimental methods due to difficulty of determining structural properties of phase separated protein assemblies, and of choosing appropriate mutations. Here we advance a coarse-grained computational framework for accessing the long time scale phase separation process and for obtaining molecular details of LLPS, in conjunction with state of the art enhanced sampling methods. We are able to qualitatively capture the changes of the phase diagram due to specific mutations, inclusion of a folded domain, and variation of chain length. The model is flexible and can be used with different knowledge-based potential energy functions, as we demonstrate. We expect a wide application of the presented framework for advancing our understanding of the formation of liquid-like protein assemblies.

Conformational Heterogeneity and FRET Data Interpretation for Dimensions of Unfolded Proteins

A mathematico-physically valid formulation is required to infer properties of disordered protein conformations from single-molecule Förster resonance energy transfer (smFRET). Conformational dimensions inferred by conventional approaches that presume a homogeneous conformational ensemble can be unphysical. When all possible-heterogeneous as well as homogeneous-conformational distributions are taken into account without prejudgment, a single value of average transfer efficiency 〈E〉 between dyes at two chain ends is generally consistent with highly diverse, multiple values of the average radius of gyration 〈R_g〉. Here we utilize unbiased conformational statistics from a coarse-grained explicit-chain model to establish a general logical framework to quantify this fundamental ambiguity in smFRET inference. As an application, we address the long-standing controversy regarding the denaturant dependence of 〈R_g〉 of unfolded proteins, focusing on Protein L as an example. Conventional smFRET inference concluded that 〈R_g〉 of unfolded Protein L is highly sensitive to [GuHCl], but data from SAXS suggested a near-constant 〈R_g〉 irrespective of [GuHCl]. Strikingly, our analysis indicates that although the reported 〈E〉 values for Protein L at [GuHCl] = 1 and 7 M are very different at 0.75 and 0.45, respectively, the Bayesian R_g² distributions consistent with these two 〈E〉 values overlap by as much as 75%. Our findings suggest, in general, that the smFRET-SAXS discrepancy regarding unfolded protein dimensions likely arise from highly heterogeneous conformational ensembles at low or zero denaturant, and that additional experimental probes are needed to ascertain the nature of this heterogeneity.

Monomeric Huntingtin Exon 1 Has Similar Overall Structural Features for Wild-Type and Pathological Polyglutamine Lengths

Huntington's disease is caused by expansion of a polyglutamine (polyQ) domain within exon 1 of the huntingtin gene (Httex1). The prevailing hypothesis is that the monomeric Httex1 protein undergoes sharp conformational changes as the polyQ length exceeds a threshold of 36-37 residues. Here, we test this hypothesis by combining novel semi-synthesis strategies with state-of-the-art single-molecule Förster resonance energy transfer measurements on biologically relevant, monomeric Httex1 proteins of five different polyQ lengths. Our results, integrated with atomistic simulations, negate the hypothesis of a sharp, polyQ length-dependent change in the structure of monomeric Httex1. Instead, they support a continuous global compaction with increasing polyQ length that derives from increased prominence of the globular polyQ domain. Importantly, we show that monomeric Httex1 adopts tadpole-like architectures for polyQ lengths below and above the pathological threshold. Our results suggest that higher order homotypic and/or heterotypic interactions within distinct sub-populations of neurons, which are inevitable at finite cellular concentrations, are likely to be the main source of sharp polyQ length dependencies of HD.

Insights into tau function and dysfunction through single-molecule fluorescence

Fluorescence correlation spectroscopy and single-molecule Förster resonance energy transfer are powerful and versatile techniques to quantify and describe molecular interactions. They are particularly well suited to the study of dynamic proteins and assemblies, as they can overcome some of the challenges that stymie more conventional ensemble approaches. In this chapter, we describe the application of these methods to study the interaction of tau with the molecular aggregation inducer, heparin, and the functional binding partner, soluble tubulin. Specifically, we outline the practical aspects of both techniques to characterize the critical first steps of tau aggregation and tau-mediated microtubule polymerization. The information gained from these measurements provides unique insight into tau function and its role in disease.

Dimension conversion and scaling of disordered protein chains

To extract protein dimension and energetics information from single-molecule fluorescence resonance energy transfer spectroscopy (smFRET) data, it is essential to establish the relationship between the distributions of the radius of gyration (Rg) and the end-to-end (donor-to-acceptor) distance (Ree). Here, we performed a coarse-grained molecular dynamics simulation to obtain a conformational ensemble of denatured proteins and intrinsically disordered proteins. For any disordered chain with fixed length, there is an excellent linear correlation between the average values of Rg and Ree under various solvent conditions, but the relationship deviates from the prediction of a Gaussian chain. A modified conversion formula was proposed to analyze smFRET data. The formula reduces the discrepancy between the results obtained from FRET and small-angle X-ray scattering (SAXS). The scaling law in a coil-globule transition process was examined where a significant finite-size effect was revealed, i.e., the scaling exponent may exceed the theoretical critical boundary [1/3, 3/5] and the prefactor changes notably during the transition. The Sanchez chain model was also tested and it was shown that the mean-field approximation works well for expanded chains.

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.

Slow Interconversion in a Heterogeneous Unfolded-State Ensemble of Outer-Membrane Phospholipase A

Structural and dynamic investigations of unfolded proteins are important for understanding protein-folding mechanisms as well as the interactions of unfolded polypeptide chains with other cell components. In the case of outer-membrane proteins (OMPs), unfolded-state properties are of particular physiological relevance, because these proteins remain unfolded for extended periods of time during their biogenesis and rely on interactions with binding partners to support proper folding. Using a combination of ensemble and single-molecule spectroscopy, we have scrutinized the unfolded state of outer-membrane phospholipase A (OmpLA) to provide a detailed view of its structural dynamics on timescales from nanoseconds to milliseconds. We find that even under strongly denaturing conditions and in the absence of residual secondary structure, OmpLA populates an ensemble of slowly (>100 ms) interconverting and conformationally heterogeneous unfolded states that lack the fast chain-reconfiguration motions expected for an unstructured, fully unfolded chain. The drastically slowed sampling of potentially folding-competent states, as compared with a random-coil polypeptide, may contribute to the slow in vitro folding kinetics observed for many OMPs. In vivo, however, slow intramolecular long-range dynamics might be advantageous for entropically favored binding of unfolded OMPs to chaperones and, by facilitating conformational selection after release from chaperones, for preserving binding-competent conformations before insertion into the outer membrane.

Computational and theoretical advances in studies of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) are increasingly realized to play diverse biological roles, ranging from molecular signaling to the formation of membraneless organelles. Their high degree of disorder makes them more challenging to study using the techniques of conventional structural biology, because any observable will be averaged over a heterogeneous ensemble of structures. Molecular simulations and theory are therefore a natural complement to experiment for studying the structure, dynamics and function of IDPs. The diverse time and length scales relevant to the roles played by IDPs require flexibility in the techniques applied. Here, I summarize some of the developments in simulation and theory in recent years, which have been driven by the desire to better capture IDP properties at different time- and length-scales. I also provide an outlook for how methods can be improved in the future and emerging problems which may be addressed by theory and simulation.

On the polymer physics origins of protein folding thermodynamics

A remarkable feature of the spontaneous folding of many small proteins is the striking similarity in the thermodynamics of the folding process. This process is characterized by simple two-state thermodynamics with large and compensating changes in entropy and enthalpy and a funnel-like free energy landscape with a free-energy barrier that varies linearly with temperature. One might attribute the commonality of this two-state folding behavior to features particular to these proteins (e.g., chain length, hydrophobic/hydrophilic balance, attributes of the native state) or one might suspect that this similarity in behavior has a more general polymer-physics origin. Here we show that this behavior is also typical for flexible homopolymer chains with sufficiently short range interactions. Two-state behavior arises from the presence of a low entropy ground (folded) state separated from a set of high entropy disordered (unfolded) states by a free energy barrier. This homopolymer model exhibits a funneled free energy landscape that reveals a complex underlying dynamics involving competition between folding and non-folding pathways. Despite the presence of multiple pathways, this simple physics model gives the robust result of two-state thermodynamics for both the cases of folding from a basin of expanded coil states and from a basin of compact globule states.

A functional role for intrinsic disorder in the tau-tubulin complex

Tau is an intrinsically disordered protein with an important role in maintaining the dynamic instability of neuronal microtubules. Despite intensive study, a detailed understanding of the functional mechanism of tau is lacking. Here, we address this deficiency by using intramolecular single-molecule Förster Resonance Energy Transfer (smFRET) to characterize the conformational ensemble of tau bound to soluble tubulin heterodimers. Tau adopts an open conformation on binding tubulin, in which the long-range contacts between both termini and the microtubule binding region that characterize its compact solution structure are diminished. Moreover, the individual repeats within the microtubule binding region that directly interface with tubulin expand to accommodate tubulin binding, despite a lack of extension in the overall dimensions of this region. These results suggest that the disordered nature of tau provides the significant flexibility required to allow for local changes in conformation while preserving global features. The tubulin-associated conformational ensemble is distinct from its aggregation-prone one, highlighting differences between functional and dysfunctional states of tau. Using constraints derived from our measurements, we construct a model of tubulin-bound tau, which draws attention to the importance of the role of tau's conformational plasticity in function.