Bayesian inference of protein ensembles from SAXS data

Insight into structural biophysics from solution X-ray scattering

The current challenges of structural biophysics include determining the structure of large self-assembled complexes, resolving the structure of ensembles of complex structures and their mass fraction, and unraveling the dynamic pathways and mechanisms leading to the formation of complex structures from their subunits. Modern synchrotron solution X-ray scattering data enable simultaneous high-spatial and high-temporal structural data required to address the current challenges of structural biophysics. These data are complementary to crystallography, NMR, and cryo-TEM data. However, the analysis of solution scattering data is challenging; hence many different analysis tools, listed in the SAS Portal (http://smallangle.org/), were developed. In this review, we start by briefly summarizing classical X-ray scattering analyses providing insight into fundamental structural and interaction parameters. We then describe recent developments, integrating simulations, theory, and advanced X-ray scattering modeling, providing unique insights into the structure, energetics, and dynamics of self-assembled complexes. The structural information is essential for understanding the underlying physical chemistry principles leading to self-assembled supramolecular architectures and computational structural refinement.

Bayesian methods in integrative structure modeling

There is a growing interest in characterizing the structure and dynamics of large biomolecular assemblies and their interactions within the cellular environment. A diverse array of experimental techniques allows us to study biomolecular systems on a variety of length and time scales. These techniques range from imaging with light, X-rays or electrons, to spectroscopic methods, cross-linking mass spectrometry and functional genomics approaches, and are complemented by AI-assisted protein structure prediction methods. A challenge is to integrate all of these data into a model of the system and its functional dynamics. This review focuses on Bayesian approaches to integrative structure modeling. We sketch the principles of Bayesian inference, highlight recent applications to integrative modeling and conclude with a discussion of current challenges and future perspectives.

Generation of unfolded outer membrane protein ensembles defined by hydrodynamic properties

Outer membrane proteins (OMPs) must exist as an unfolded ensemble while interacting with a chaperone network in the periplasm of Gram-negative bacteria. Here, we developed a method to model unfolded OMP (uOMP) conformational ensembles using the experimental properties of two well-studied OMPs. The overall sizes and shapes of the unfolded ensembles in the absence of a denaturant were experimentally defined by measuring the sedimentation coefficient as a function of urea concentration. We used these data to model a full range of unfolded conformations by parameterizing a targeted coarse-grained simulation protocol. The ensemble members were further refined by short molecular dynamics simulations to reflect proper torsion angles. The final conformational ensembles have polymer properties different from unfolded soluble and intrinsically disordered proteins and reveal inherent differences in the unfolded states that necessitate further investigation. Building these uOMP ensembles advances the understanding of OMP biogenesis and provides essential information for interpreting structures of uOMP-chaperone complexes.

Modeling of flexible membrane-bound biomolecular complexes for solution small-angle scattering

Recent advances in protein expression protocols, sample handling, and experimental set up of small-angle scattering experiments have allowed users of the technique to structurally investigate biomolecules of growing complexity and structural disorder. Notable examples include intrinsically disordered proteins, multi-domain proteins and membrane proteins in suitable carrier systems. Here, we outline a modeling scheme for calculating the scattering profiles from such complex samples. This kind of modeling is necessary for structural information to be refined from the corresponding data. The scheme bases itself on a hybrid of classical form factor based modeling and the well-known spherical harmonics-based formulation of small-angle scattering amplitudes. Our framework can account for flexible domains alongside other structurally elaborate components of the molecular system in question. We demonstrate the utility of this modeling scheme through a recent example of a structural model of the growth hormone receptor membrane protein in a phospholipid bilayer nanodisc which is refined against experimental SAXS data. Additionally we investigate how the scattering profiles from the complex would appear under different scattering contrasts. For each contrast situation we discuss what structural information is contained and the related consequences for modeling of the data.

Biophysical and Integrative Characterization of Protein Intrinsic Disorder as a Prime Target for Drug Discovery

Protein intrinsic disorder is increasingly recognized for its biological and disease-driven functions. However, it represents significant challenges for biophysical studies due to its high conformational flexibility. In addressing these challenges, we highlight the complementary and distinct capabilities of a range of experimental and computational methods and further describe integrative strategies available for combining these techniques. Integrative biophysics methods provide valuable insights into the sequence–structure–function relationship of disordered proteins, setting the stage for protein intrinsic disorder to become a promising target for drug discovery. Finally, we briefly summarize recent advances in the development of new small molecule inhibitors targeting the disordered N-terminal domains of three vital transcription factors.

Reweighting methods for elucidation of conformation ensembles of proteins

Proteins are inherently dynamic macromolecules that exist in equilibrium among multiple conformational states, and motions of protein backbone and side chains are fundamental to biological function. The ability to characterize the conformational landscape is particularly important for intrinsically disordered proteins, multidomain proteins, and weakly bound complexes, where single-structure representations are inadequate. As the focus of structural biology shifts from relatively rigid macromolecules toward larger and more complex systems and molecular assemblies, there is a need for structural approaches that can paint a more realistic picture of such conformationally heterogeneous systems. Here, we review reweighting methods for elucidation of structural ensembles based on experimental data, with the focus on applications to multidomain proteins.

From dilute to concentrated solutions of intrinsically disordered proteins: Interpretation and analysis of collected data

Intrinsically disordered proteins (IDPs) have a broad energy landscape and consequently sample many different conformations in solution. The innate flexibility of IDPs is exploited in their biological function, and in many instances allows a single IDP to regulate a range of processes in vivo. Due to their highly flexible nature, characterizing the structural properties of IDPs is not straightforward. Often solution-based methods such as Nuclear Magnetic Resonance (NMR), Förster Resonance Energy Transfer (FRET), and Small-Angle X-ray Scattering (SAXS) are used. SAXS is indeed a powerful technique to study the structural and conformational properties of IDPs in solution, and from the obtained SAXS spectra, information about the average size, shape, and extent of oligomerization can be determined. In this chapter, we will introduce model-free methods that can be used to interpret SAXS data and introduce methods that can be used to interpret SAXS data beyond analytical models, for example, by using atomistic and different levels of coarse-grained models in combination with molecular dynamics (MD) and Monte Carlo simulations.

Evolving Experimental Techniques for Structure-Based Drug Design

Structure-based drug design (SBDD) is a prominent method in rational drug development and has traditionally benefitted from the atomic models of protein targets obtained using X-ray crystallography at cryogenic temperatures. In this perspective, we highlight recent advances in the development of structural techniques that are capable of probing dynamic information about protein targets. First, we discuss advances in the field of X-ray crystallography including serial room-temperature crystallography as a method for obtaining high-resolution conformational dynamics of protein-inhibitor complexes. Next, we look at cryogenic electron microscopy (cryoEM), another high-resolution technique that has recently been used to study proteins and protein complexes that are too difficult to crystallize. Finally, we present small-angle X-ray scattering (SAXS) as a potential high-throughput screening tool to identify inhibitors that target protein complexes and protein oligomerization.

Extracting time series matching a small-angle X-ray scattering profile from trajectories of molecular dynamics simulations

Solving structural ensembles of flexible biomolecules is a challenging research area. Here, we propose a method to obtain possible structural ensembles of a biomolecule based on small-angle X-ray scattering (SAXS) and molecular dynamics simulations. Our idea is to clip a time series that matches a SAXS profile from a simulation trajectory. To examine its practicability, we applied our idea to a multi-domain protein ER-60 and successfully extracted time series longer than 1 micro second from trajectories of coarse-grained molecular dynamics simulations. In the extracted time series, the domain conformation was distributed continuously and smoothly in a conformational space. Preferred domain conformations were also observed. Diversity among scattering curves calculated from each ER-60 structure was interpreted to reflect an open-close motion of the protein. Although our approach did not provide a unique solution for the structural ensemble of the biomolecule, each extracted time series can be an element of the real behavior of ER-60. Considering its low computational cost, our approach will play a key role to identify biomolecular dynamics by integrating SAXS, simulations, and other experiments.

Recent Developments in Data-Assisted Modeling of Flexible Proteins

Many proteins can fold into well-defined conformations. However, intrinsically-disordered proteins (IDPs) do not possess a defined structure. Moreover, folded multi-domain proteins often digress into alternative conformations. Collectively, the conformational dynamics enables these proteins to fulfill specific functions. Thus, most experimental observables are averaged over the conformations that constitute an ensemble. In this article, we review the recent developments in the concept and methods for the determination of the dynamic structures of flexible peptides and proteins. In particular, we describe ways to extract information from nuclear magnetic resonance small-angle X-ray scattering (SAXS), and chemical cross-linking coupled with mass spectroscopy (XL-MS) measurements. All these techniques can be used to obtain ensemble-averaged restraints or to re-weight the simulated conformational ensembles.

Molecular insights on CALX-CBD12 interdomain dynamics from MD simulations, RDCs, and SAXS

Na⁺/Ca²⁺ exchangers (NCXs) are secondary active transporters that couple the translocation of Na⁺ with the transport of Ca²⁺ in the opposite direction. The exchanger is an essential Ca²⁺ extrusion mechanism in excitable cells. It consists of a transmembrane domain and a large intracellular loop that contains two Ca²⁺-binding domains, CBD1 and CBD2. The two CBDs are adjacent to each other and form a two-domain Ca²⁺ sensor called CBD12. Binding of intracellular Ca²⁺ to CBD12 activates the NCX but inhibits the NCX of Drosophila, CALX. NMR spectroscopy and SAXS studies showed that CALX and NCX CBD12 constructs display significant interdomain flexibility in the apo state but assume rigid interdomain arrangements in the Ca²⁺-bound state. However, detailed structure information on CBD12 in the apo state is missing. Structural characterization of proteins formed by two or more domains connected by flexible linkers is notoriously challenging and requires the combination of orthogonal information from multiple sources. As an attempt to characterize the conformational ensemble of CALX-CBD12 in the apo state, we applied molecular dynamics (MD) simulations, NMR (¹H-¹⁵N residual dipolar couplings), and small-angle x-ray scattering (SAXS) data in a combined strategy to select an ensemble of conformations in agreement with the experimental data. This joint approach demonstrated that CALX-CBD12 preferentially samples closed conformations, whereas the wide-open interdomain arrangement characteristic of the Ca²⁺-bound state is less frequently sampled. These results are consistent with the view that Ca²⁺ binding shifts the CBD12 conformational ensemble toward extended conformers, which could be a key step in the NCXs' allosteric regulation mechanism. This strategy, combining MD with NMR and SAXS, provides a powerful approach to select ensembles of conformations that could be applied to other flexible multidomain systems.

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.

Recent Advances in the Label-Free Characterization of Exosomes for Cancer Liquid Biopsy: From Scattering and Spectroscopy to Nanoindentation and Nanodevices

Exosomes (EXOs) are nano-sized vesicles secreted by most cell types. They are abundant in bio-fluids and harbor specific molecular constituents from their parental cells. Due to these characteristics, EXOs have a great potential in cancer diagnostics for liquid biopsy and personalized medicine. Despite this unique potential, EXOs are not yet widely applied in clinical settings, with two main factors hindering their translational process in diagnostics. Firstly, conventional extraction methods are time-consuming, require large sample volumes and expensive equipment, and often do not provide high-purity samples. Secondly, characterization methods have some limitations, because they are often qualitative, need extensive labeling or complex sampling procedures that can induce artifacts. In this context, novel label-free approaches are rapidly emerging, and are holding potential to revolutionize EXO diagnostics. These methods include the use of nanodevices for EXO purification, and vibrational spectroscopies, scattering, and nanoindentation for characterization. In this progress report, we summarize recent key advances in label-free techniques for EXO purification and characterization. We point out that these methods contribute to reducing costs and processing times, provide complementary information compared to the conventional characterization techniques, and enhance flexibility, thus favoring the discovery of novel and unexplored EXO-based biomarkers. In this process, the impact of nanotechnology is systematically highlighted, showing how the effectiveness of these techniques can be enhanced using nanomaterials, such as plasmonic nanoparticles and nanostructured surfaces, which enable the exploitation of advanced physical phenomena occurring at the nanoscale level.

Molecular model of a sensor of two-component signaling system

Two-component systems (TCS) are widespread signaling systems present in all domains of life. TCS typically consist of a signal receptor/transducer and a response regulator. The receptors (histidine kinases, chemoreceptors and photoreceptors) are often embedded in the membrane and have a similar modular structure. Chemoreceptors were shown to function in highly ordered arrays, with trimers of dimers being the smallest functional unit. However, much less is known about photoreceptors. Here, we use small-angle scattering (SAS) to show that detergent-solubilized sensory rhodopsin II in complex with its cognate transducer forms dimers at low salt concentration, which associate into trimers of dimers at higher buffer molarities. We then fit an atomistic model of the whole complex into the SAS data. The obtained results suggest that the trimer of dimers is "tripod"-shaped and that the contacts between the dimers occur only through their cytoplasmic regions, whereas the transmembrane regions remain unconnected.

Reconciling Simulations and Experiments With BICePs: A Review

Bayesian Inference of Conformational Populations (BICePs) is an algorithm developed to reconcile simulated ensembles with sparse experimental measurements. The Bayesian framework of BICePs enables population reweighting as a post-simulation processing step, with several advantages over existing methods, including the proper use of reference potentials, and the estimation of a Bayes factor-like quantity called the BICePs score for model selection. Here, we summarize the theory underlying this method in context with related algorithms, review the history of BICePs applications to date, and discuss current shortcomings along with future plans for improvement.

Comment on the Optimal Parameters to Derive Intrinsically Disordered Protein Conformational Ensembles from Small-Angle X-ray Scattering Data Using the Ensemble Optimization Method

The Ensemble Optimization Method (EOM) is a popular approach to describe small-angle X-ray scattering (SAXS) data from highly disordered proteins. The EOM algorithm selects subensembles of coexisting states from large pools of randomized conformations to fit the SAXS data. Based on the unphysical bimodal radius of gyration (R_g) distribution of conformations resulting from the EOM analysis, a recent article (Fagerberg et al. J. Chem. Theory Comput. 2019, 15 (12), 6968-6983) concluded that this approach inadequately described the SAXS data measured for human Histatin 5 (Hst5), a peptide with antifungal properties. Using extensive experimental and synthetic data, we explored the origin of this observation. We found that the one-bead-per-residue coarse-grained representation with averaged scattering form factors (provided in the EOM as an add-on to represent disordered missing loops or domains) may not be appropriate for EOM analyses of scattering data from short (below 50 residues) proteins/peptides. The method of choice for these proteins is to employ atomistic models (e.g., from molecular dynamics simulations) to sample the protein conformational landscape. As a convenient alternative, we have also improved the coarse-grained approach by introducing amino acid specific form factors in the calculations. We also found that, for small proteins, the search for relatively large subensembles of 20-50 conformers (as implemented in the original EOM version) more adequately describes the conformational space sampled in solution than the procedures optimizing the ensemble size. Our observations have been added as recommendations into the information for EOM users to promote the proper utilization of the program for ensemble-based modeling of SAXS data for all types of disordered systems.

Comprehensive Structural and Thermodynamic Analysis of Prefibrillar WT α-Synuclein and Its G51D, E46K, and A53T Mutants by a Combination of Small-Angle X-ray Scattering and Variational Bayesian Weighting

The in solution synchrotron small-angle X-ray scattering SAXS technique has been used to investigate an intrinsically disordered protein (IDP) related to Parkinson's disease, the α-synuclein (α-syn), in prefibrillar diluted conditions. SAXS experiments have been performed as a function of temperature and concentration on the wild type (WT) and on the three pathogenic mutants G51D, E46K, and A53T. To identify the conformers that populate WT α-syn and the pathogenic mutants in prefibrillar conditions, scattering data have been analyzed by a new variational bayesian weighting method (VBWSAS) based on an ensemble of conformers, which includes unfolded monomers, trimers, and tetramers, both in helical-rich and strand-rich forms. The developed VBWSAS method uses a thermodynamic scheme to account for temperature and concentration effects and considers long-range protein-protein interactions in the framework of the random phase approximation. The global analysis of the whole set of data indicates that WT α-syn is mostly present as unfolded monomers and trimers (helical-rich trimers at low T and strand-rich trimers at high T), but not tetramers, as previously derived by several studies. On the contrary, different conformer combinations characterize mutants. In the α-syn G51D mutant, the most abundant aggregates at all the temperatures are strand-rich tetramers. Strand-rich tetramers are also the predominant forms in the A53T mutant, but their weight decreases with temperature. Only monomeric conformers, with a preference for the ones with the smallest sizes, are present in the E46K mutant. The derived conformational behavior then suggests a different availability of species prone to aggregate, depending on mutation, temperature, and concentration and accounting for the different neurotoxicity of α-syn variants. Indeed, this approach may be of pivotal importance to describe conformational and aggregational properties of other IDPs.

Small-angle X-ray scattering experiments of monodisperse intrinsically disordered protein samples close to the solubility limit

The condensation of biomolecules into biomolecular condensates via liquid-liquid phase separation (LLPS) is a ubiquitous mechanism that drives cellular organization. To enable these functions, biomolecules have evolved to drive LLPS and facilitate partitioning into biomolecular condensates. Determining the molecular features of proteins that encode LLPS will provide critical insights into a plethora of biological processes. Problematically, probing biomolecular dense phases directly is often technologically difficult or impossible. By capitalizing on the symmetry between the conformational behavior of biomolecules in dilute solution and dense phases, it is possible to infer details critical to phase separation by precise measurements of the dilute phase thus circumventing complicated characterization of dense phases. The symmetry between dilute and dense phases is found in the size and shape of the conformational ensemble of a biomolecule-parameters that small-angle X-ray scattering (SAXS) is ideally suited to probe. Recent technological advances have made it possible to accurately characterize samples of intrinsically disordered protein regions at low enough concentration to avoid interference from intermolecular attraction, oligomerization or aggregation, all of which were previously roadblocks to characterizing self-assembling proteins. Herein, we describe the pitfalls inherent to measuring such samples, the experimental details required for circumventing these issues and analysis methods that place the results of SAXS measurements into the theoretical framework of LLPS.

Combining molecular dynamics simulations with small-angle X-ray and neutron scattering data to study multi-domain proteins in solution

Many proteins contain multiple folded domains separated by flexible linkers, and the ability to describe the structure and conformational heterogeneity of such flexible systems pushes the limits of structural biology. Using the three-domain protein TIA-1 as an example, we here combine coarse-grained molecular dynamics simulations with previously measured small-angle scattering data to study the conformation of TIA-1 in solution. We show that while the coarse-grained potential (Martini) in itself leads to too compact conformations, increasing the strength of protein-water interactions results in ensembles that are in very good agreement with experiments. We show how these ensembles can be refined further using a Bayesian/Maximum Entropy approach, and examine the robustness to errors in the energy function. In particular we find that as long as the initial simulation is relatively good, reweighting against experiments is very robust. We also study the relative information in X-ray and neutron scattering experiments and find that refining against the SAXS experiments leads to improvement in the SANS data. Our results suggest a general strategy for studying the conformation of multi-domain proteins in solution that combines coarse-grained simulations with small-angle X-ray scattering data that are generally most easy to obtain. These results may in turn be used to design further small-angle neutron scattering experiments that exploit contrast variation through 1H/2H isotope substitutions.

Determination of Protein Structural Ensembles by Hybrid-Resolution SAXS Restrained Molecular Dynamics

Small-angle X-ray scattering (SAXS) experiments provide low-resolution but valuable information about the dynamics of biomolecular systems, which could be ideally integrated into molecular dynamics (MD) simulations to accurately determine conformational ensembles of flexible proteins. The applicability of this strategy is hampered by the high computational cost required to calculate scattering intensities from three-dimensional structures. We previously presented a hybrid resolution method that makes atomistic SAXS-restrained MD simulation feasible by adopting a coarse-grained approach to efficiently back-calculate scattering intensities; here, we extend this technique, applying it in the framework of metainference with the aim to investigate the dynamical behavior of flexible biomolecules. The efficacy of the method is assessed on the K63-diubiquitin, showing that the inclusion of SAXS restraints is effective in generating a reliable conformational ensemble, improving the agreement with independent experimental data.

How to learn from inconsistencies: Integrating molecular simulations with experimental data

Molecular simulations and biophysical experiments can be used to provide independent and complementary insights into the molecular origin of biological processes. A particularly useful strategy is to use molecular simulations as a modeling tool to interpret experimental measurements, and to use experimental data to refine our biophysical models. Thus, explicit integration and synergy between molecular simulations and experiments is fundamental for furthering our understanding of biological processes. This is especially true in the case where discrepancies between measured and simulated observables emerge. In this chapter, we provide an overview of some of the core ideas behind methods that were developed to improve the consistency between experimental information and numerical predictions. We distinguish between situations where experiments are used to refine our understanding and models of specific systems, and situations where experiments are used more generally to refine transferable models. We discuss different philosophies and attempt to unify them in a single framework. Until now, such integration between experiments and simulations have mostly been applied to equilibrium data, and we discuss more recent developments aimed to analyze time-dependent or time-resolved data.

Integrative Approaches in Structural Biology: A More Complete Picture from the Combination of Individual Techniques

With the recent technological and computational advancements, structural biology has begun to tackle more and more difficult questions, including complex biochemical pathways and transient interactions among macromolecules. This has demonstrated that, to approach the complexity of biology, one single technique is largely insufficient and unable to yield thorough answers, whereas integrated approaches have been more and more adopted with successful results. Traditional structural techniques (X-ray crystallography and Nuclear Magnetic Resonance (NMR)) and the emerging ones (cryo-electron microscopy (cryo-EM), Small Angle X-ray Scattering (SAXS)), together with molecular modeling, have pros and cons which very nicely complement one another. In this review, three examples of synergistic approaches chosen from our previous research will be revisited. The first shows how the joint use of both solution and solid-state NMR (SSNMR), X-ray crystallography, and cryo-EM is crucial to elucidate the structure of polyethylene glycol (PEG)ylated asparaginase, which would not be obtainable through any of the techniques taken alone. The second deals with the integrated use of NMR, X-ray crystallography, and SAXS in order to elucidate the catalytic mechanism of an enzyme that is based on the flexibility of the enzyme itself. The third one shows how it is possible to put together experimental data from X-ray crystallography and NMR restraints in order to refine a protein model in order to obtain a structure which simultaneously satisfies both experimental datasets and is therefore closer to the ‘real structure’.

Bayesian inference of protein conformational ensembles from limited structural data

Many proteins consist of folded domains connected by regions with higher flexibility. The details of the resulting conformational ensemble play a central role in controlling interactions between domains and with binding partners. Small-Angle Scattering (SAS) is well-suited to study the conformational states adopted by proteins in solution. However, analysis is complicated by the limited information content in SAS data and care must be taken to avoid constructing overly complex ensemble models and fitting to noise in the experimental data. To address these challenges, we developed a method based on Bayesian statistics that infers conformational ensembles from a structural library generated by all-atom Monte Carlo simulations. The first stage of the method involves a fast model selection based on variational Bayesian inference that maximizes the model evidence of the selected ensemble. This is followed by a complete Bayesian inference of population weights in the selected ensemble. Experiments with simulated ensembles demonstrate that model evidence is capable of identifying the correct ensemble and that correct number of ensemble members can be recovered up to high level of noise. Using experimental data, we demonstrate how the method can be extended to include data from Nuclear Magnetic Resonance (NMR) and structural energies of conformers extracted from the all-atom energy functions. We show that the data from SAXS, NMR chemical shifts and energies calculated from conformers can work synergistically to improve the definition of the conformational ensemble.

Direct examination of the relevance for folding, binding and electron transfer of a conserved protein folding intermediate

Near the minimum free energy basin of proteins where the native ensemble resides, partly unfolded conformations of slightly higher energy can be significantly populated under native conditions. It has been speculated that they play roles in molecular recognition and catalysis, but they might represent contemporary features of the evolutionary process without functional relevance. Obtaining conclusive evidence on these alternatives is difficult because it requires comparing the performance of a given protein when populating and when not populating one such intermediate, in otherwise identical conditions. Wild type apoflavodoxin populates under native conditions a partly unfolded conformation (10% of molecules) whose unstructured region includes the binding sites for the FMN cofactor and for redox partner proteins. We recently engineered a thermostable variant where the intermediate is no longer detectable. Using the wild type and variant, we assess the relevance of the intermediate comparing folding kinetics, cofactor binding kinetics, cofactor affinity, X-ray structure, intrinsic dynamics, redox potential of the apoflavodoxin-cofactor complex (Fld), its affinity for partner protein FNR, and electron transfer rate within the Fld/FNR physiological complex. Our data strongly suggest the intermediate state, conserved in long-chain apoflavodoxins, is not required for the correct assembly of flavodoxin nor does it contribute to shape its electron transfer properties. This analysis can be applied to evaluate other native basin intermediates.

Small Angle Scattering and Structural Biology: Data Quality and Model Validation

This chapter provides a brief review of the current state-of-the-art in small-angle scattering (SAS) from biomolecules in solution in regard to: (1) sample preparation and instrumentation, (2) data reduction and analysis, and (3) three-dimensional structural modelling and validation. In this context, areas of ongoing research in regard to the interpretation of SAS data will be discussed with a particular focus on structural modelling using computational methods and data from different experimental techniques, including SAS (hybrid methods). Finally, progress made in establishing community accepted publication guidelines and a standard reporting framework that includes SAS data deposition in a public data bank will be described. Importantly, SAS data with associated meta-data can now be held in a format that supports exchange between data archives and seamless interoperability with the world-wide Protein Data Bank (wwPDB). Biomolecular SAS is thus well positioned to contribute to an envisioned federation of data archives in support of hybrid structural biology.

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.

Solution scattering approaches to dynamical ordering in biomolecular systems

Clarification of solution structure and its modulation in proteins and protein complexes is crucially important to understand dynamical ordering in macromolecular systems. Small-angle x-ray scattering (SAXS) and small-angle neutron scattering (SANS) are among the most powerful techniques to derive structural information. Recent progress in sample preparation, instruments and software analysis is opening up a new era for small-angle scattering. In this review, recent progress and trends of SAXS and SANS are introduced from the point of view of instrumentation and analysis, touching on general features and standard methods of small-angle scattering. This article is part of a Special Issue entitled "Biophysical Exploration of Dynamical Ordering of Biomolecular Systems" edited by Dr. Koichi Kato.

Bayesian refinement of protein structures and ensembles against SAXS data using molecular dynamics

Small-angle X-ray scattering is an increasingly popular technique used to detect protein structures and ensembles in solution. However, the refinement of structures and ensembles against SAXS data is often ambiguous due to the low information content of SAXS data, unknown systematic errors, and unknown scattering contributions from the solvent. We offer a solution to such problems by combining Bayesian inference with all-atom molecular dynamics simulations and explicit-solvent SAXS calculations. The Bayesian formulation correctly weights the SAXS data versus prior physical knowledge, it quantifies the precision or ambiguity of fitted structures and ensembles, and it accounts for unknown systematic errors due to poor buffer matching. The method further provides a probabilistic criterion for identifying the number of states required to explain the SAXS data. The method is validated by refining ensembles of a periplasmic binding protein against calculated SAXS curves. Subsequently, we derive the solution ensembles of the eukaryotic chaperone heat shock protein 90 (Hsp90) against experimental SAXS data. We find that the SAXS data of the apo state of Hsp90 is compatible with a single wide-open conformation, whereas the SAXS data of Hsp90 bound to ATP or to an ATP-analogue strongly suggest heterogenous ensembles of a closed and a wide-open state.

SAS profile correlations reveal SAS hierarchical nature and information content

In structural biology, Small-Angle Scattering experiments (SAS) are unique, because although they provide low resolution data, they can be performed in closer-to-native conditions than those arising in X-Ray crystallography. A number of questions on SAS, however, remain unsolved, particularly in the light of modelling ensembles of conformers in solution. In this article, we study the ensemble average and covariance of SAS profiles analytically. Using this ensemble covariance, we demonstrate the hierarchical nature of SAS profiles. Furthermore, we show that the information content is not uniform and reaches its maximum in the intermediate q range. The arguments are generalized using microsecond-scale molecular dynamics trajectories of the lysozyme and on an ensemble of the intrinsically disordered protein p15PAF. We show that for highly flexible systems, the SAS profile is a representation of the ensemble of conformers in solution, and not that of one conformer in particular.

Principles of protein structural ensemble determination

The biological functions of protein molecules are intimately dependent on their conformational dynamics. This aspect is particularly evident for disordered proteins, which constitute perhaps one-third of the human proteome. Therefore, structural ensembles often offer more useful representations of proteins than individual conformations. Here, we describe how the well-established principles of protein structure determination should be extended to the case of protein structural ensembles determination. These principles concern primarily how to deal with conformationally heterogeneous states, and with experimental measurements that are averaged over such states and affected by a variety of errors. We first review the growing literature of recent methods that combine experimental and computational information to model structural ensembles, highlighting their similarities and differences. We then address some conceptual problems in the determination of structural ensembles and define future goals towards the establishment of objective criteria for the comparison, validation, visualization and dissemination of such ensembles.

Structural studies of RNA-protein complexes: A hybrid approach involving hydrodynamics, scattering, and computational methods

The diverse functional cellular roles played by ribonucleic acids (RNA) have emphasized the need to develop rapid and accurate methodologies to elucidate the relationship between the structure and function of RNA. Structural biology tools such as X-ray crystallography and Nuclear Magnetic Resonance are highly useful methods to obtain atomic-level resolution models of macromolecules. However, both methods have sample, time, and technical limitations that prevent their application to a number of macromolecules of interest. An emerging alternative to high-resolution structural techniques is to employ a hybrid approach that combines low-resolution shape information about macromolecules and their complexes from experimental hydrodynamic (e.g. analytical ultracentrifugation) and solution scattering measurements (e.g., solution X-ray or neutron scattering), with computational modeling to obtain atomic-level models. While promising, scattering methods rely on aggregation-free, monodispersed preparations and therefore the careful development of a quality control pipeline is fundamental to an unbiased and reliable structural determination. This review article describes hydrodynamic techniques that are highly valuable for homogeneity studies, scattering techniques useful to study the low-resolution shape, and strategies for computational modeling to obtain high-resolution 3D structural models of RNAs, proteins, and RNA-protein complexes.

Small-angle scattering studies of intrinsically disordered proteins and their complexes

Intrinsically Disordered Proteins (IDPs) perform a broad range of biological functions. Their relevance has motivated intense research activity seeking to characterize their sequence/structure/function relationships. However, the conformational plasticity of these molecules hampers the application of traditional structural approaches, and new tools and concepts are being developed to address the challenges they pose. Small-Angle Scattering (SAS) is a structural biology technique that probes the size and shape of disordered proteins and their complexes with other biomolecules. The low-resolution nature of SAS can be compensated with specially designed computational tools and its combined interpretation with complementary structural information. In this review, we describe recent advances in the application of SAS to disordered proteins and highly flexible complexes and discuss current challenges.

Consistent View of Polypeptide Chain Expansion in Chemical Denaturants from Multiple Experimental Methods

There has been a long-standing controversy regarding the effect of chemical denaturants on the dimensions of unfolded and intrinsically disordered proteins: A wide range of experimental techniques suggest that polypeptide chains expand with increasing denaturant concentration, but several studies using small-angle X-ray scattering (SAXS) have reported no such increase of the radius of gyration (Rg). This inconsistency challenges our current understanding of the mechanism of chemical denaturants, which are widely employed to investigate protein folding and stability. Here, we use a combination of single-molecule Förster resonance energy transfer (FRET), SAXS, dynamic light scattering (DLS), and two-focus fluorescence correlation spectroscopy (2f-FCS) to characterize the denaturant dependence of the unfolded state of the spectrin domain R17 and the intrinsically disordered protein ACTR in two different denaturants. Standard analysis of the primary data clearly indicates an expansion of the unfolded state with increasing denaturant concentration irrespective of the protein, denaturant, or experimental method used. This is the first case in which SAXS and FRET have yielded even qualitatively consistent results regarding expansion in denaturant when applied to the same proteins. To more directly illustrate this self-consistency, we used both SAXS and FRET data in a Bayesian procedure to refine structural ensembles representative of the observed unfolded state. This analysis demonstrates that both of these experimental probes are compatible with a common ensemble of protein configurations for each denaturant concentration. Furthermore, the resulting ensembles reproduce the trend of increasing hydrodynamic radius with denaturant concentration obtained by 2f-FCS and DLS. We were thus able to reconcile the results from all four experimental techniques quantitatively, to obtain a comprehensive structural picture of denaturant-induced unfolded state expansion, and to identify the most likely sources of earlier discrepancies.

Finding Our Way in the Dark Proteome

The traditional structure-function paradigm has provided significant insights for well-folded proteins in which structures can be easily and rapidly revealed by X-ray crystallography beamlines. However, approximately one-third of the human proteome is comprised of intrinsically disordered proteins and regions (IDPs/IDRs) that do not adopt a dominant well-folded structure, and therefore remain "unseen" by traditional structural biology methods. This Perspective considers the challenges raised by the "Dark Proteome", in which determining the diverse conformational substates of IDPs in their free states, in encounter complexes of bound states, and in complexes retaining significant disorder requires an unprecedented level of integration of multiple and complementary solution-based experiments that are analyzed with state-of-the art molecular simulation, Bayesian probabilistic models, and high-throughput computation. We envision how these diverse experimental and computational tools can work together through formation of a "computational beamline" that will allow key functional features to be identified in IDP structural ensembles.

Experimental Inferential Structure Determination of Ensembles for Intrinsically Disordered Proteins

We develop a Bayesian approach to determine the most probable structural ensemble model from candidate structures for intrinsically disordered proteins (IDPs) that takes full advantage of NMR chemical shifts and J-coupling data, their known errors and variances, and the quality of the theoretical back-calculation from structure to experimental observables. Our approach differs from previous formulations in the optimization of experimental and back-calculation nuisance parameters that are treated as random variables with known distributions, as opposed to structural or ensemble weight optimization or use of a reference ensemble. The resulting experimental inferential structure determination (EISD) method is size extensive with O(N) scaling, with N = number of structures, that allows for the rapid ranking of large ensemble data comprising tens of thousands of conformations. We apply the EISD approach on singular folded proteins and a corresponding set of ∼25 000 misfolded states to illustrate the problems that can arise using Boltzmann weighted priors. We then apply the EISD method to rank IDP ensembles most consistent with the NMR data and show that the primary error for ranking or creating good IDP ensembles resides in the poor back-calculation from structure to simulated experimental observable. We show that a reduction by a factor of 3 in the uncertainty of the back-calculation error can improve the discrimination among qualitatively different IDP ensembles for the amyloid-beta peptide.

Phase separation in biology; functional organization of a higher order

Inside eukaryotic cells, macromolecules are partitioned into membrane-bounded compartments and, within these, some are further organized into non-membrane-bounded structures termed membrane-less organelles. The latter structures are comprised of heterogeneous mixtures of proteins and nucleic acids and assemble through a phase separation phenomenon similar to polymer condensation. Membrane-less organelles are dynamic structures maintained through multivalent interactions that mediate diverse biological processes, many involved in RNA metabolism. They rapidly exchange components with the cellular milieu and their properties are readily altered in response to environmental cues, often implicating membrane-less organelles in responses to stress signaling. In this review, we discuss: (1) the functional roles of membrane-less organelles, (2) unifying structural and mechanistic principles that underlie their assembly and disassembly, and (3) established and emerging methods used in structural investigations of membrane-less organelles.