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

Critical Assessment of Self-Consistency Checks in the All-Atom Molecular Dynamics Simulation of Intrinsically Disordered Proteins

All atom simulations can be used to quantify conformational properties of Intrinsically Disordered Proteins (IDP). However, simulations must satisfy convergence checks to ensure observables computed from simulation are reliable and reproducible. While absolute convergence is purely a theoretical concept requiring infinitely long simulation, a more practical, yet rigorous, approach is to impose Self Consistency Checks (SCCs) to gain confidence in the simulated data. Currently there is no study of SCCs in IDPs, unlike their folded counterparts. In this paper, we introduce different criteria for self-consistency checks for IDPs. Next, we impose these SCCs to critically assess the performance of different simulation protocols using the N terminal domain of HIV Integrase and the linker region of SARS-CoV-2 Nucleoprotein as two model IDPs. All simulation protocols begin with all-atom implicit solvent Monte Carlo (MC) simulation and subsequent clustering of MC generated conformations to create the representative structures of the IDPs. These representative structures serve as the initial structure for subsequent molecular dynamics (MD) runs with explicit solvent. We conclude that generating multiple short (∼3 μs) MD simulation trajectories─all starting from the most representative MC generated conformation─and merging them is the protocol of choice due to (i) its ability to satisfy multiple SCCs, (ii) consistently reproducing experimental data, and (iii) the efficiency of running independent trajectories in parallel by harnessing multiple cores available in modern GPU clusters. Running one long trajectory (greater than 20 μs) can also satisfy the first two criteria but is less desirable due to prohibitive computation time. These findings help resolve the challenge of identifying a usable starting configuration, provide an objective measure of SCC, and establish rigorous criteria to determine the minimum length (for one long simulation) or number of trajectories needed in all-atom simulation of IDPs.

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

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

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.

Synergies of Single Molecule Fluorescence and NMR for the Study of Intrinsically Disordered Proteins

Single molecule fluorescence and nuclear magnetic resonance spectroscopy (NMR) are two very powerful techniques for the analysis of intrinsically disordered proteins (IDPs). Both techniques have individually made major contributions to deciphering the complex properties of IDPs and their interactions, and it has become evident that they can provide very complementary views on the distance-dynamics relationships of IDP systems. We now review the first approaches using both NMR and single molecule fluorescence to decipher the molecular properties of IDPs and their interactions. We shed light on how these two techniques were employed synergistically for multidomain proteins harboring intrinsically disordered linkers, for veritable IDPs, but also for liquid–liquid phase separated systems. Additionally, we provide insights into the first approaches to use single molecule Förster resonance energy transfer (FRET) and NMR for the description of multiconformational models of IDPs.

Denatured State Conformational Biases in Three-Helix Bundles Containing Divergent Sequences Localize near Turns and Helix Capping Residues

Rhodopseudomonas palustris cytochrome c', a four-helix bundle, and the second ubiquitin-associated domain, UBA(2), a three-helix bundle from the human homologue of yeast Rad23, HHR23A, deviate from random coil behavior under denaturing conditions in a fold-specific manner. The random coil deviations in each of these folds occur near interhelical turns and loops in their tertiary structures. Here, we examine an additional three-helix bundle with an identical fold to UBA(2), but a highly divergent sequence, the first ubiquitin-associated domain, UBA(1), of HHR23A. We use histidine-heme loop formation methods, employing eight single histidine variants, to probe for denatured state conformational bias of a UBA(1) domain fused to the N-terminus of iso-1-cytochrome c (iso-1-Cytc). Guanidine hydrochloride (GuHCl) denaturation shows that the iso-1-Cytc domain unfolds first, followed by the UBA(1) domain. Denatured state (4 and 6 M GuHCl) histidine-heme loop formation studies show that as the size of the histidine-heme loop increases, loop stability decreases, as expected for the Jacobson-Stockmayer relationship. However, loops formed with His35, His31, and His15, of UBA(1), are 0.6-1.1 kcal/mol more stable than expected from the Jacobson-Stockmayer relationship, confirming the importance of deviations of the denatured state from random coil behavior near interhelical turns of helical domains for facilitating folding to the correct topology. For UBA(1) and UBA(2), hydrophobic clusters on either side of the turns partially explain deviations from random coil behavior; however, helix capping also appears to be important.

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.

A Data-Driven Hydrophobicity Scale for Predicting Liquid-Liquid Phase Separation of Proteins

An accurate model for macroscale disordered assemblies of biological macromolecules such as those formed in so-called membraneless organelles would greatly assist in studying their structure, function, and dynamics. Recent evidence has suggested that liquid-liquid phase separation (LLPS) underlies the formation of membraneless organelles. While the general mechanism of exchange of macromolecule/water for macromolecule/macromolecule interactions is known to be the driving force for LLPS, the specific interactions involved are not well understood. One way that protein-water and protein-protein interactions have been understood historically is via hydrophobicity scales. However, these scales are typically optimized for describing these relative interactions in certain cases, such as protein folding or insertion of proteins into membranes. To better describe the relative interactions of proteins that undergo LLPS, we have developed a new, data-driven hydrophobicity scale. To determine the new scale, we used coarse-grained molecular dynamics simulations using the hydrophobicity scale coarse-grained model, which relates the interactions between amino acids to their hydrophobicity. Hydrophobicity values were determined via the force-balance method on a library of proteins that includes unfolded, intrinsically disordered, and phase-separating proteins (PSP). The resulting hydrophobicity scale can better predict whether a given protein will undergo LLPS at physiological conditions by using coarse-grained molecular dynamics simulations than existing hydrophobicity scales. This new scale confirms the importance of π-π interactions between amino acids as important drivers of LLPS. This new hydrophobicity scale provides a convenient and compact description of protein-protein interactions for proteins that undergo LLPS and could be used to develop new models to describe interactions between PSP and other components, such as nucleic acids.

Modern Kinetics and Mechanism of Protein Folding: A Retrospective

Modern experimental kinetics of protein folding began in the early 1990s with the introduction of nanosecond laser pulses to trigger the folding reaction, providing an almost 10⁶-fold improvement in time resolution over the stopped-flow method being employed at the time. These experiments marked the beginning of the "fast-folding" subfield that enabled investigation of the kinetics of formation of secondary structural elements and disordered loops for the first time, as well as the fastest folding proteins. When I started to work on this subject, a fast folding protein was one that folded in milliseconds. There were, moreover, no analytical theoretical models and no atomistic or coarse-grained molecular dynamics simulations to describe the mechanism. Two of the most important discoveries from my lab since then are a protein that folds in hundreds of nanoseconds, as determined from nanosecond laser temperature experiments, and the discovery that the theoretically predicted barrier crossing time is about the same for proteins that differ in folding rates by 10⁴-fold, as determined from single molecule fluorescence measurements. We also developed what has been called the "Hückel model" of protein folding, which quantitatively explains a wide range of equilibrium and kinetic measurements. This retrospective traces the history of contributions to the "fast folding" subfield from my lab until about 3 years ago, when I left protein folding to spend the rest of my research career trying to discover an inexpensive drug for treating sickle cell disease.

FRET-based dynamic structural biology: Challenges, perspectives and an appeal for open-science practices

Single-molecule FRET (smFRET) has become a mainstream technique for studying biomolecular structural dynamics. The rapid and wide adoption of smFRET experiments by an ever-increasing number of groups has generated significant progress in sample preparation, measurement procedures, data analysis, algorithms and documentation. Several labs that employ smFRET approaches have joined forces to inform the smFRET community about streamlining how to perform experiments and analyze results for obtaining quantitative information on biomolecular structure and dynamics. The recent efforts include blind tests to assess the accuracy and the precision of smFRET experiments among different labs using various procedures. These multi-lab studies have led to the development of smFRET procedures and documentation, which are important when submitting entries into the archiving system for integrative structure models, PDB-Dev. This position paper describes the current 'state of the art' from different perspectives, points to unresolved methodological issues for quantitative structural studies, provides a set of 'soft recommendations' about which an emerging consensus exists, and lists openly available resources for newcomers and seasoned practitioners. To make further progress, we strongly encourage 'open science' practices.

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.

Protein structural changes characterized by high-pressure, pulsed field gradient diffusion NMR spectroscopy

Pulsed-field gradient NMR spectroscopy is widely used to measure the translational diffusion and hydrodynamic radius (R_h) of biomolecules in solution. For unfolded proteins, the R_h provides a sensitive reporter on the ensemble-averaged conformation and the extent of polypeptide chain expansion as a function of added denaturant. Hydrostatic pressure is a convenient and reversible alternative to chemical denaturants for the study of protein folding, and enables NMR measurements to be performed on a single sample. While the impact of pressure on the viscosity of water is well known, and our water diffusivity measurements agree closely with theoretical expectations, we find that elevated pressures increase the R_h of dioxane and other small molecules by amounts that correlate with their hydrophobicity, with parallel increases in rotational friction indicated by ¹³C longitudinal relaxation times. These data point to a tighter coupling with water for hydrophobic surfaces at elevated pressures. Translational diffusion measurement of the unfolded state of a pressure-sensitized ubiquitin mutant (VA2-ubiquitin) as a function of hydrostatic pressure or urea concentration shows that R_h values of both the folded and the unfolded states remain nearly invariant. At ca 23 Å, the R_h of the fully pressure-denatured state is essentially indistinguishable from the urea-denatured state, and close to the value expected for an idealized random coil of 76 residues. The intrinsically disordered protein (IDP) α-synuclein shows slight compaction at pressures above 2 kbar. Diffusion of unfolded ubiquitin and α-synuclein is significantly impacted by sample concentration, indicating that quantitative measurements need to be carried out under dilute conditions.

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.

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.

Using Small-Angle Scattering Data and Parametric Machine Learning to Optimize Force Field Parameters for Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) and proteins with intrinsically disordered regions (IDRs) play important roles in many aspects of normal cell physiology, such as signal transduction and transcription, as well as pathological states, including Alzheimer's, Parkinson's, and Huntington's disease. Unlike their globular counterparts that are defined by a few structures and free energy minima, IDP/IDR comprise a large ensemble of rapidly interconverting structures and a corresponding free energy landscape characterized by multiple minima. This aspect has precluded the use of structural biological techniques, such as X-ray crystallography and nuclear magnetic resonance (NMR) for resolving their structures. Instead, low-resolution techniques, such as small-angle X-ray or neutron scattering (SAXS/SANS), have become a mainstay in characterizing coarse features of the ensemble of structures. These are typically complemented with NMR data if possible or computational techniques, such as atomistic molecular dynamics, to further resolve the underlying ensemble of structures. However, over the past 10–15 years, it has become evident that the classical, pairwise-additive force fields that have enjoyed a high degree of success for globular proteins have been somewhat limited in modeling IDP/IDR structures that agree with experiment. There has thus been a significant effort to rehabilitate these models to obtain better agreement with experiment, typically done by optimizing parameters in a piecewise fashion. In this work, we take a different approach by optimizing a set of force field parameters simultaneously, using machine learning to adapt force field parameters to experimental SAXS scattering profiles. We demonstrate our approach in modeling three biologically IDP ensembles based on experimental SAXS profiles and show that our optimization approach significantly improve force field parameters that generate ensembles in better agreement with experiment.

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.

Evolution of All-Atom Protein Force Fields to Improve Local and Global Properties

Experimental studies on intrinsically disordered and unfolded proteins have shown that in isolation they typically have low populations of secondary structure and exhibit distance scalings suggesting that they are at near-theta-solvent conditions. Until recently, however, all-atom force fields failed to reproduce these fundamental properties of intrinsically disordered proteins (IDPs). Recent improvements by refining against ensemble-averaged experimental observables for polypeptides in aqueous solution have addressed deficiencies including secondary structure bias, global conformational properties, and thermodynamic parameters of biophysical reactions such as folding and collapse. To date, studies utilizing these improved all-atom force fields have mostly been limited to a small set of unfolded or disordered proteins. Here, we present data generated for a diverse library of unfolded or disordered proteins using three progressively improved generations of Amber03 force fields, and we explore how global and local properties are affected by each successive change in the force field. We find that the most recent force field refinements significantly improve the agreement of the global properties such as radii of gyration and end-to-end distances with experimental estimates. However, these global properties are largely independent of the local secondary structure propensity. This result stresses the need to validate force fields with reference to a combination of experimental data providing information about both local and global structure formation.

Sequence Effects on Size, Shape, and Structural Heterogeneity in Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) lack well-defined three-dimensional structures, thus challenging the archetypal notion of structure-function relationships. Determining the ensemble of conformations that IDPs explore under physiological conditions is the first step toward understanding their diverse cellular functions. Here, we quantitatively characterize the structural features of IDPs as a function of sequence and length using coarse-grained simulations. For diverse IDP sequences, with the number of residues ( NT) ranging from 20 to 441, our simulations not only reproduce the radii of gyration ( Rg) obtained from experiments, but also predict the full scattering intensity profiles in excellent agreement with small-angle X-ray scattering experiments. The Rg values are well-described by the standard Flory scaling law, Rg = Rg0 NTν, with ν ≈ 0.588, making it tempting to assert that IDPs behave as polymers in a good solvent. However, clustering analysis reveals that the menagerie of structures explored by IDPs is diverse, with the extent of heterogeneity being highly sequence-dependent, even though ensemble-averaged properties, such as the dependence of Rg on chain length, may suggest synthetic polymer-like behavior in a good solvent. For example, we show that for the highly charged Prothymosin-α, a substantial fraction of conformations is highly compact. Even if the sequence compositions are similar, as is the case for α-Synuclein and a truncated construct from the Tau protein, there are substantial differences in the conformational heterogeneity. Taken together, these observations imply that metrics based on net charge or related quantities alone cannot be used to anticipate the phases of IDPs, either in isolation or in complex with partner IDPs or RNA. Our work sets the stage for probing the interactions of IDPs with each other, with folded protein domains, or with partner RNAs, which are critical for describing the structures of stress granules and biomolecular condensates with important cellular functions.

Commonly used FRET fluorophores promote collapse of an otherwise disordered protein

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

The combined force field-sampling problem in simulations of disordered amyloid-β peptides

Molecular dynamics simulations of intrinsically disordered proteins (IDPs) can provide high resolution structural ensembles if the force field is accurate enough and if the simulation sufficiently samples the conformational space of the IDP with the correct weighting of sub-populations. Here, we investigate the combined force field-sampling problem by testing a standard force field as well as newer fixed charge force fields, the latter specifically motivated for better description of unfolded states and IDPs, and comparing them with a standard temperature replica exchange (TREx) protocol and a non-equilibrium Temperature Cool Walking (TCW) sampling algorithm. The force field and sampling combinations are used to characterize the structural ensembles of the amyloid-beta peptides Aβ42 and Aβ43, which both should be random coils as shown recently by experimental nuclear magnetic resonance (NMR) and 2D Förster resonance energy transfer (FRET) experiments. The results illustrate the key importance of the sampling algorithm: while the standard force field using TREx is in poor agreement with the NMR J-coupling and nuclear Overhauser effect and 2D FRET data, when using the TCW method, the standard and optimized protein-water force field combinations are in very good agreement with the same experimental data since the TCW sampling method produces qualitatively different ensembles than TREx. We also discuss the relative merit of the 2D FRET data when validating structural ensembles using the different force fields and sampling protocols investigated in this work for small IDPs such as the Aβ42 and Aβ43 peptides.

Binding Affinity and Function of the Extremely Disordered Protein Complex Containing Human Linker Histone H1.0 and Its Chaperone ProTα

It was recently reported that human linker histone H1.0 and its chaperone prothymosin-α (ProTα) form an extremely disordered 1:1 complex with an ultrahigh affinity (equilibrium dissociation constant K_D of ∼2 × 10^-12 M) measured using a single-molecule Förster resonance energy transfer method. It was hypothesized that the ultrahigh affinity and extreme disorder may be required for the chaperone function of ProTα, in which it displaces the linker histone from condensed chromatin. Here, we measure the binding affinity for the ProTα-H1.0 complex using isothermal titration calorimetry and report a K_D value of (4.6 ± 0.5) × 10^-7 M. In addition, we show that ProTα facilitates the formation of the H1.0-nucleosome complex in vitro. The results of our study contrast with those of the previous report and provide new insights into the chaperone function of ProTα. Possible causes for the observed discrepancy in binding affinity are discussed.

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.

Origin of Internal Friction in Disordered Proteins Depends on Solvent Quality

Protein dynamics often exhibit internal friction; i.e., contributions to friction that cannot solely be attributed to the viscosity of the solvent. Remarkably, even unfolded and intrinsically disordered proteins (IDPs) exhibit this behavior, despite typically being solvent-exposed. Several competing molecular mechanisms have been suggested to underlie this phenomenon, in particular dihedral relaxation and intrachain interactions. It has also recently been shown that single-molecule data reflecting internal friction in the disordered protein ACTR cannot be explained using polymer models unless this friction is dependent on protein collapse. However, the connection between the collapse of the chain and the underlying mechanism of internal friction has been unclear. To address this issue, we combine molecular simulation and single-molecule experimental data to investigate how chain compaction affects protein dynamics in the context of ACTR. Chain reconfiguration times and internal friction estimated from all-atom simulations are in semiquantitative agreement with experimental data. We dissect the underlying molecular mechanism with all-atom and coarse-grained simulations and clearly identify both intrachain interactions and dihedral angle transitions as contributions to internal friction. However, their relative contribution is strongly dependent on the compactness of the IDP; while dihedral relaxation dominates internal friction in expanded configurations, intrachain interactions dominate for more compact chains. Our results thus imply a continuous transition between mechanisms and provide a link between internal friction in IDPs and that in more compact and folded states of proteins.

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.

Response to Comment on “Innovative scattering analysis shows that hydrophobic disordered proteins are expanded in water”

Best et al. claim that we provide no convincing basis to assert that a discrepancy remains between FRET and SAXS results on the dimensions of disordered proteins under physiological conditions. We maintain that a clear discrepancy is apparent in our and other recent publications, including results shown in the Best et al. comment. A plausible origin is fluorophore interactions in FRET experiments.