Refining conformational ensembles of flexible proteins against small-angle x-ray scattering data

Intrinsically disordered proteins and flexible regions in multidomain proteins display substantial conformational heterogeneity. Characterizing the conformational ensembles of these proteins in solution typically requires combining one or more biophysical techniques with computational modeling or simulations. Experimental data can either be used to assess the accuracy of a computational model or to refine the computational model to get a better agreement with the experimental data. In both cases, one generally needs a so-called forward model (i.e., an algorithm to calculate experimental observables from individual conformations or ensembles). In many cases, this involves one or more parameters that need to be set, and it is not always trivial to determine the optimal values or to understand the impact on the choice of parameters. For example, in the case of small-angle x-ray scattering (SAXS) experiments, many forward models include parameters that describe the contribution of the hydration layer and displaced solvent to the background-subtracted experimental data. Often, one also needs to fit a scale factor and a constant background for the SAXS data but across the entire ensemble. Here, we present a protocol to dissect the effect of the free parameters on the calculated SAXS intensities and to identify a reliable set of values. We have implemented this procedure in our Bayesian/maximum entropy framework for ensemble refinement and demonstrate the results on four intrinsically disordered proteins and a protein with three domains connected by flexible linkers. Our results show that the resulting ensembles can depend on the parameters used for solvent effects and suggest that these should be chosen carefully. We also find a set of parameters that work robustly across all proteins.     

Structural Characterization of N-WASP Domain V Using MD Simulations with NMR and SAXS Data

Because of their large conformational heterogeneity, structural characterization of intrinsically disordered proteins (IDPs) is very challenging using classical experimental methods alone. In this study, we use NMR and small-angle x-ray scattering (SAXS) data with multiple molecular dynamics (MD) simulations to describe the conformational ensemble of the fully disordered verprolin homology domain of the neural Aldrich syndrome protein involved in the regulation of actin polymerization. First, we studied several back-calculation software of SAXS scattering intensity and optimized the adjustable parameters to accurately calculate the SAXS intensity from an atomic structure. We also identified the most appropriate force fields for MD simulations of this IDP. Then, we analyzed four conformational ensembles of neural Aldrich syndrome protein verprolin homology domain, two generated with the program flexible-meccano with or without NMR-derived information as input and two others generated by MD simulations with two different force fields. These four conformational ensembles were compared to available NMR and SAXS data for validation. We found that MD simulations with the AMBER-03w force field and the TIP4P/2005s water model are able to correctly describe the conformational ensemble of this 67-residue IDP at both local and global level.     

An integrative NMR-SAXS approach for structural determination of large RNAs defines the substrate-free state of a trans-cleaving Neurospora Varkud Satellite ribozyme

The divide-and-conquer strategy is commonly used for protein structure determination, but its applications to high-resolution structure determination of RNAs have been limited. Here, we introduce an integrative approach based on the divide-and-conquer strategy that was undertaken to determine the solution structure of an RNA model system, the Neurospora VS ribozyme. NMR and SAXS studies were conducted on a minimal trans VS ribozyme as well as several isolated subdomains. A multi-step procedure was used for structure determination that first involved pairing refined NMR structures with SAXS data to obtain structural subensembles of the various subdomains. These subdomain structures were then assembled to build a large set of structural models of the ribozyme, which was subsequently filtered using SAXS data. The resulting NMR-SAXS structural ensemble shares several similarities with the reported crystal structures of the VS ribozyme. However, a local structural difference is observed that affects the global fold by shifting the relative orientation of the two three-way junctions. Thus, this finding highlights a global conformational change associated with substrate binding in the VS ribozyme that is likely critical for its enzymatic activity. Structural studies of other large RNAs should benefit from similar integrative approaches that allow conformational sampling of assembled fragments.     

A Correspondence Between Solution-State Dynamics of an Individual Protein and the Sequence and Conformational Diversity of its Family

Conformational ensembles are increasingly recognized as a useful representation to describe fundamental relationships between protein structure, dynamics and function. Here we present an ensemble of ubiquitin in solution that is created by sampling conformational space without experimental information using “Backrub” motions inspired by alternative conformations observed in sub-Angstrom resolution crystal structures. Backrub-generated structures are then selected to produce an ensemble that optimizes agreement with nuclear magnetic resonance (NMR) Residual Dipolar Couplings (RDCs). Using this ensemble, we probe two proposed relationships between properties of protein ensembles: (i) a link between native-state dynamics and the conformational heterogeneity observed in crystal structures, and (ii) a relation between dynamics of an individual protein and the conformational variability explored by its natural family. We show that the Backrub motional mechanism can simultaneously explore protein native-state dynamics measured by RDCs, encompass the conformational variability present in ubiquitin complex structures and facilitate sampling of conformational and sequence variability matching those occurring in the ubiquitin protein family. Our results thus support an overall relation between protein dynamics and conformational changes enabling sequence changes in evolution. More practically, the presented method can be applied to improve protein design predictions by accounting for intrinsic native-state dynamics.     

Refinement of Peptide Conformational Ensembles by 2D IR Spectroscopy: Application to Ala‒Ala‒Ala

Characterizing ensembles of intrinsically disordered proteins is experimentally challenging because of the ill-conditioned nature of ensemble determination with limited data and the intrinsic fast dynamics of the conformational ensemble. Amide I two-dimensional infrared (2D IR) spectroscopy has picosecond time resolution to freeze structural ensembles as needed for probing disordered-protein ensembles and conformational dynamics. Also, developments in amide I computational spectroscopy now allow a quantitative and direct prediction of amide I spectra based on conformational distributions drawn from molecular dynamics simulations, providing a route to ensemble refinement against experimental spectra. We performed a Bayesian ensemble refinement method on Ala–Ala–Ala against isotope-edited Fourier-transform infrared spectroscopy and 2D IR spectroscopy and tested potential factors affecting the quality of ensemble refinements. We found that isotope-edited 2D IR spectroscopy provides a stringent constraint on Ala–Ala–Ala conformations and returns consistent conformational ensembles with the dominant ppII conformer across varying prior distributions from many molecular dynamics force fields and water models. The dominant factor influencing ensemble refinements is the systematic frequency uncertainty from spectroscopic maps. However, the uncertainty of conformer populations can be significantly reduced by incorporating 2D IR spectra in addition to traditional Fourier-transform infrared spectra. Bayesian ensemble refinement against isotope-edited 2D IR spectroscopy thus provides a route to probe equilibrium-complex protein ensembles and potentially nonequilibrium conformational dynamics.     

COCO: a simple tool to enrich the representation of conformational variability in NMR structures

NMR structures are typically deposited in databases such as the PDB in the form of an ensemble of structures. Generally, each of the models in such an ensemble satisfies the experimental data and is equally valid. No unique solution can be calculated because the experimental NMR data is insufficient, in part because it reflects the conformational variability and dynamical behavior of the molecule in solution. Even for relatively rigid molecules, the limited number of structures that are typically deposited cannot completely encompass the structural diversity allowed by the observed NMR data, but they can be chosen to try and maximize its representation. We describe here the adaptation and application of techniques more commonly used to examine large ensembles from molecular dynamics simulations, to the analysis of NMR ensembles. The approach, which is based on principal component analysis, we call COCO ("Complementary Coordinates"). The COCO approach analyses the distribution of an NMR ensemble in conformational space, and generates a new ensemble that fills "gaps" in the distribution. The method is very rapid, and analysis of a 25-member ensemble and generation of a new 25 member ensemble typically takes 1-2 min on a conventional workstation. Applied to the 545 structures in the RECOORD database, we find that COCO generates new ensembles that are as structurally diverse-both from each other and from the original ensemble-as are the structures within the original ensemble. The COCO approach does not explicitly take into account the NMR restraint data, yet in tests on selected structures from the RECOORD database, the COCO ensembles are frequently good matches to this data, and certainly are structures that can be rapidly refined against the restraints to yield high-quality, novel solutions. COCO should therefore be a useful aid in NMR structure refinement and in other situations where a richer representation of conformational variability is desired-for example in docking studies. COCO is freely accessible via the website www.ccpb.ac.uk/COCO.     

Validating Solution Ensembles from Molecular Dynamics Simulation by Wide-Angle X-ray Scattering Data

Wide-angle x-ray scattering (WAXS) experiments of biomolecules in solution have become increasingly popular because of technical advances in light sources and detectors. However, the structural interpretation of WAXS profiles is problematic, partly because accurate calculations of WAXS profiles from structural models have remained challenging. In this work, we present the calculation of WAXS profiles from explicit-solvent molecular dynamics (MD) simulations of five different proteins. Using only a single fitting parameter that accounts for experimental uncertainties because of the buffer subtraction and dark currents, we find excellent agreement to experimental profiles both at small and wide angles. Because explicit solvation eliminates free parameters associated with the solvation layer or the excluded solvent, which would require fitting to experimental data, we minimize the risk of overfitting. We further find that the influence from water models and protein force fields on calculated profiles are insignificant up to q ≈ 15 nm^?1. Using a series of simulations that allow increasing flexibility of the proteins, we show that incorporating thermal fluctuations into the calculations significantly improves agreement with experimental data, demonstrating the importance of protein dynamics in the interpretation of WAXS profiles. In addition, free MD simulations up to one microsecond suggest that the calculated profiles are highly sensitive with respect to minor conformational rearrangements of proteins, such as an increased flexibility of a loop or an increase of the radius of gyration by  <  1%. The present study suggests that quantitative comparison between MD simulations and experimental WAXS profiles emerges as an accurate tool to validate solution ensembles of biomolecules.     

Validation of macromolecular flexibility in solution by small-angle X-ray scattering (SAXS)

The dynamics of macromolecular conformations are critical to the action of cellular networks. Solution X-ray scattering studies, in combination with macromolecular X-ray crystallography (MX) and nuclear magnetic resonance (NMR), strive to determine complete and accurate states of macromolecules, providing novel insights describing allosteric mechanisms, supramolecular complexes, and dynamic molecular machines. This review addresses theoretical and practical concepts, concerns, and considerations for using these techniques in conjunction with computational methods to productively combine solution-scattering data with high-resolution structures. I discuss the principal means of direct identification of macromolecular flexibility from SAXS data followed by critical concerns about the methods used to calculate theoretical SAXS profiles from high-resolution structures. The SAXS profile is a direct interrogation of the thermodynamic ensemble and techniques such as, for example, minimal ensemble search (MES), enhance interpretation of SAXS experiments by describing the SAXS profiles as population-weighted thermodynamic ensembles. I discuss recent developments in computational techniques used for conformational sampling, and how these techniques provide a basis for assessing the level of the flexibility within a sample. Although these approaches sacrifice atomic detail, the knowledge gained from ensemble analysis is often appropriate for developing hypotheses and guiding biochemical experiments. Examples of the use of SAXS and combined approaches with X-ray crystallography, NMR, and computational methods to characterize dynamic assemblies are presented.     

β-Branched Amino Acids Stabilize Specific Conformations of Cyclic Hexapeptides

Cyclic peptides (CPs) are a promising class of molecules for drug development, particularly as inhibitors of protein-protein interactions. Predicting low-energy structures and global structural ensembles of individual CPs is critical for the design of bioactive molecules, but these are challenging to predict and difficult to verify experimentally. In our previous work, we used explicit-solvent molecular dynamics simulations with enhanced sampling methods to predict the global structural ensembles of cyclic hexapeptides containing different permutations of glycine, alanine, and valine. One peptide, cyclo-(VVGGVG) or P7, was predicted to be unusually well structured. In this work, we synthesized P7, along with a less well-structured control peptide, cyclo-(VVGVGG) or P6, and characterized their global structural ensembles in water using NMR spectroscopy. The NMR data revealed a structural ensemble similar to the prediction for P7 and showed that P6 was indeed much less well-structured than P7. We then simulated and experimentally characterized the global structural ensembles of several P7 analogs and discovered that β-branching at one critical position within P7 is important for overall structural stability. The simulations allowed deconvolution of thermodynamic factors that underlie this structural stabilization. Overall, the excellent correlation between simulation and experimental data indicates that our simulation platform will be a promising approach for designing well-structured CPs and also for understanding the complex interactions that control the conformations of constrained peptides and other macrocycles.     

Interpretation of HDX Data by Maximum-Entropy Reweighting of Simulated Structural Ensembles

Hydrogen-deuterium exchange combined with mass spectrometry (HDX-MS) is a widely applied biophysical technique that probes the structure and dynamics of biomolecules without the need for site-directed modifications or bio-orthogonal labels. The mechanistic interpretation of HDX data, however, is often qualitative and subjective, owing to a lack of quantitative methods to rigorously translate observed deuteration levels into atomistic structural information. To help address this problem, we have developed a methodology to generate structural ensembles that faithfully reproduce HDX-MS measurements. In this approach, an ensemble of protein conformations is first generated, typically using molecular dynamics simulations. A maximum-entropy bias is then applied post hoc to the resulting ensemble such that averaged peptide-deuteration levels, as predicted by an empirical model, agree with target values within a given level of uncertainty. We evaluate this approach, referred to as HDX ensemble reweighting (HDXer), for artificial target data reflecting the two major conformational states of a binding protein. We demonstrate that the information provided by HDX-MS experiments and by the model of exchange are sufficient to recover correctly weighted structural ensembles from simulations, even when the relevant conformations are rarely observed. Degrading the information content of the target data—e.g., by reducing sequence coverage, by averaging exchange levels over longer peptide segments, or by incorporating different sources of uncertainty—reduces the structural accuracy of the reweighted ensemble but still allows for useful insights into the distinctive structural features reflected by the target data. Finally, we describe a quantitative metric to rank candidate structural ensembles according to their correspondence with target data and illustrate the use of HDXer to describe changes in the conformational ensemble of the membrane protein LeuT. In summary, HDXer is designed to facilitate objective structural interpretations of HDX-MS data and to inform experimental approaches and further developments of theoretical exchange models.     

Modeling conformational states of proteins with AlphaFold

Many proteins exert their function by switching among different structures. Knowing the conformational ensembles affiliated with these states is critical to elucidate key mechanistic aspects that govern protein function. While experimental determination efforts are still bottlenecked by cost, time, and technical challenges, the machine-learning technology AlphaFold showed near experimental accuracy in predicting the three-dimensional structure of monomeric proteins. However, an AlphaFold ensemble of models usually represents a single conformational state with minimal structural heterogeneity. Consequently, several pipelines have been proposed to either expand the structural breadth of an ensemble or bias the prediction toward a desired conformational state. Here, we analyze how those pipelines work, what they can and cannot predict, and future directions.     

Characterizing RNA ensembles from NMR data with kinematic models

Functional mechanisms of biomolecules often manifest themselves precisely in transient conformational substates. Researchers have long sought to structurally characterize dynamic processes in non-coding RNA, combining experimental data with computer algorithms. However, adequate exploration of conformational space for these highly dynamic molecules, starting from static crystal structures, remains challenging. Here, we report a new conformational sampling procedure, KGSrna, which can efficiently probe the native ensemble of RNA molecules in solution. We found that KGSrna ensembles accurately represent the conformational landscapes of 3D RNA encoded by NMR proton chemical shifts. KGSrna resolves motionally averaged NMR data into structural contributions; when coupled with residual dipolar coupling data, a KGSrna ensemble revealed a previously uncharacterized transient excited state of the HIV-1 trans-activation response element stem–loop. Ensemble-based interpretations of averaged data can aid in formulating and testing dynamic, motion-based hypotheses of functional mechanisms in RNAs with broad implications for RNA engineering and therapeutic intervention.     

Evidence of Functional Protein Dynamics from X-Ray Crystallographic Ensembles

It is widely recognized that representing a protein as a single static conformation is inadequate to describe the dynamics essential to the performance of its biological function. We contrast the amino acid displacements below and above the protein dynamical transition temperature, T_D∼215K, of hen egg white lysozyme using X-ray crystallography ensembles that are analyzed by molecular dynamics simulations as a function of temperature. We show that measuring structural variations across an ensemble of X-ray derived models captures the activation of conformational states that are of functional importance just above T_D, and they remain virtually identical to structural motions measured at 300K. Our results highlight the ability to observe functional structural variations across an ensemble of X-ray crystallographic data, and that residue fluctuations measured in MD simulations at room temperature are in quantitative agreement with the experimental observable.     

X-ray solution scattering studies of the structural diversity intrinsic to protein ensembles

It is becoming increasingly clear that characterization of the protein ensemble-the collection of all conformations of which the protein is capable-will be a critical step in developing a full understanding of the linkage between structure, dynamics, and function. X-ray solution scattering in the small angle (SAXS) and wide-angle (WAXS) regimes represents an important new window to exploring the behavior of ensembles. The characteristics of the ensemble express themselves in X-ray solution scattering data in predictable ways. Here we present an overview of the effect that structural diversity intrinsic to protein ensembles has on scattering data. We then demonstrate the observation of these effects in scattering from four molecular systems; myoglobin; ubiquitin; alcohol dehydrogenase; and HIV protease; and demonstrate the modulation of these ensembles by ligand binding, mutation, and environmental factors. The observations are analyzed quantitatively in terms of the average spatial extent of structural fluctuations occurring within these proteins under different experimental conditions. The insights which these analyses support are discussed in terms of the function of the various proteins.     

Partition decoupling for multi-gene analysis of gene expression profiling data

Background

Molecular dynamics (MD) simulations are powerful tools to investigate the conformational dynamics of proteins that is often a critical element of their function. Identification of functionally relevant conformations is generally done clustering the large ensemble of structures that are generated. Recently, Self-Organising Maps (SOMs) were reported performing more accurately and providing more consistent results than traditional clustering algorithms in various data mining problems. We present a novel strategy to analyse and compare conformational ensembles of protein domains using a two-level approach that combines SOMs and hierarchical clustering.

Results

The conformational dynamics of the α-spectrin SH3 protein domain and six single mutants were analysed by MD simulations. The Cα's Cartesian coordinates of conformations sampled in the essential space were used as input data vectors for SOM training, then complete linkage clustering was performed on the SOM prototype vectors. A specific protocol to optimize a SOM for structural ensembles was proposed: the optimal SOM was selected by means of a Taguchi experimental design plan applied to different data sets, and the optimal sampling rate of the MD trajectory was selected. The proposed two-level approach was applied to single trajectories of the SH3 domain independently as well as to groups of them at the same time. The results demonstrated the potential of this approach in the analysis of large ensembles of molecular structures: the possibility of producing a topological mapping of the conformational space in a simple 2D visualisation, as well as of effectively highlighting differences in the conformational dynamics directly related to biological functions.

Conclusions

The use of a two-level approach combining SOMs and hierarchical clustering for conformational analysis of structural ensembles of proteins was proposed. It can easily be extended to other study cases and to conformational ensembles from other sources.     

Assessing the native state conformational distribution of ubiquitin by peptide acidity

At equilibrium, every energetically feasible conformation of a protein occurs with a non-zero probability. Quantitative analysis of protein flexibility is thus synonymous with determining the proper Boltzmann-weighting of this conformational distribution. The exchange reactivity of solvent-exposed amide hydrogens greatly varies with conformation, while the short-lived peptide anion intermediate implies an insensitivity to the dynamics of conformational motion. Amides that are well-exposed in model conformational ensembles of ubiquitin vary a million-fold in exchange rates which continuum dielectric methods can predict with an rmsd of 3. However, the exchange rates for many of the more rarely exposed amides are markedly overestimated in the PDB-deposited 2K39 and 2KN5 ubiquitin ensembles, while the 2NR2 ensemble predictions are largely consistent with those of the Boltzmann-weighted conformational distribution sampled at the level of 1%. The correlation between the fraction of solvent-accessible conformations for a given amide hydrogen and the exchange rate constant for that residue provides a useful monitor of the degree of completeness with which a given ensemble has sampled the energetically accessible conformational space. These exchange predictions correlate with the degree to which each ensemble deviates from a set of 46 ubiquitin X-ray structures. Kolmogorov-Smirnov analysis for the distribution of intra- and inter-ensemble pairwise structural rmsd values assisted the identification of a subensemble of 2K39 that eliminates the overestimations of hydrogen exchange rates observed for the full ensemble. The relative merits of incorporating experimental restraints into the conformational sampling process are compared to using these restraints as filters to select subpopulations consistent with the experimental data.     

Hierarchical Conformational Analysis of Native Lysozyme Based on Sub-Millisecond Molecular Dynamics Simulations

Hierarchical organization of free energy landscape (FEL) for native globular proteins has been widely accepted by the biophysics community. However, FEL of native proteins is usually projected onto one or a few dimensions. Here we generated collectively 0.2 milli-second molecular dynamics simulation trajectories in explicit solvent for hen egg white lysozyme (HEWL), and carried out detailed conformational analysis based on backbone torsional degrees of freedom (DOF). Our results demonstrated that at micro-second and coarser temporal resolutions, FEL of HEWL exhibits hub-like topology with crystal structures occupying the dominant structural ensemble that serves as the hub of conformational transitions. However, at 100ns and finer temporal resolutions, conformational substates of HEWL exhibit network-like topology, crystal structures are associated with kinetic traps that are important but not dominant ensembles. Backbone torsional state transitions on time scales ranging from nanoseconds to beyond microseconds were found to be associated with various types of molecular interactions. Even at nanoseconds temporal resolution, the number of conformational substates that are of statistical significance is quite limited. These observations suggest that detailed analysis of conformational substates at multiple temporal resolutions is both important and feasible. Transition state ensembles among various conformational substates at microsecond temporal resolution were observed to be considerably disordered. Life times of these transition state ensembles are found to be nearly independent of the time scales of the participating torsional DOFs.     

Highly sampled tetranucleotide and tetraloop motifs enable evaluation of common RNA force fields

Recent modifications and improvements to standard nucleic acid force fields have attempted to fix problems and issues that have been observed as longer timescale simulations have become routine. Although previous work has shown the ability to fold the UUCG stem–loop structure, until now no group has attempted to quantify the performance of current force fields using highly converged structural populations of the tetraloop conformational ensemble. In this study, we report the use of multiple independent sets of multidimensional replica exchange molecular dynamics (M-REMD) simulations with different initial conditions to generate well-converged conformational ensembles for the tetranucleotides r(GACC) and r(CCCC), as well as the larger UUCG tetraloop motif. By generating what is to our knowledge the most complete RNA structure ensembles reported to date for these systems, we remove the coupling between force field errors and errors due to incomplete sampling, providing a comprehensive comparison between current top-performing MD force fields for RNA. Of the RNA force fields tested in this study, none demonstrate the ability to correctly identify the most thermodynamically stable structure for all three systems. We discuss the deficiencies present in each potential function and suggest areas where improvements can be made. The results imply that although “short” (nsec-μsec timescale) simulations may stay close to their respective experimental structures and may well reproduce experimental observables, inevitably the current force fields will populate alternative incorrect structures that are more stable than those observed via experiment.     

The role of protein conformational fluctuations in allostery, function, and evolution

It is now well-known that proteins exist at equilibrium as ensembles of conformational states rather than as unique static structures. Here we review from an ensemble perspective important biological effects of such spontaneous fluctuations on protein allostery, function, and evolution. However, rather than present a thorough literature review on each subject, we focus instead on connecting these phenomena through the ensemble-based experimental, theoretical, and computational investigations from our laboratory over the past decade. Special emphasis is given to insights that run counter to some of the prevailing ideas that have emerged over the past 40 years of structural biology research. For instance, when proteins are viewed as conformational ensembles rather than as single structures, the commonly held notion of an allosteric pathway as an obligate series of individual structural distortions loses its meaning. Instead, allostery can result from energetic linkage between distal sites as one Boltzmann distribution of states transitions to another. Additionally, the emerging principles from this ensemble view of proteins have proven surprisingly useful in describing the role of intrinsic disorder in inter-domain communication, functional adaptation mediated by mutational control of fluctuations, and evolutionary conservation of the energetics of protein stability.     

Structure and Disorder in an Unfolded State under Nondenaturing Conditions from Ensemble Models Consistent with a Large Number of Experimental Restraints

Obtaining detailed structural models of disordered states of proteins under nondenaturing conditions is important for a better understanding of both functional intrinsically disordered proteins and unfolded states of folded proteins. Extensive experimental characterization of the drk N-terminal SH3 domain unfolded state has shown that, although it appears to be highly disordered, it possesses significant nonrandom secondary and tertiary structure. In our previous attempts to generate structural models of the unfolded state using the program ENSEMBLE, we were limited by insufficient experimental restraints and conformational sampling. In this study, we have vastly expanded our experimental restraint set to include ¹H-¹⁵N residual dipolar couplings, small-angle X-ray scattering measurements, nitroxide paramagnetic relaxation enhancements, O₂-induced ¹³C paramagnetic shifts, hydrogen-exchange protection factors, and ¹⁵N R₂ data, in addition to the previously used nuclear Overhauser effects, amino terminal Cu²⁺-Ni²⁺ binding paramagnetic relaxation enhancements, J-couplings, chemical shifts, hydrodynamic radius, and solvent accessibility restraints. We have also implemented a new ensemble calculation methodology that uses iterative conformational sampling and seeks to calculate the simplest possible ensemble models. As a result, we can now generate ensembles that are consistent with much larger experimental data sets than was previously possible. Although highly heterogeneous and having broad molecular size distributions, the calculated drk N-terminal SH3 domain unfolded-state ensembles have very different properties than expected for random or statistical coils and possess significant nonnative α-helical structure and both native-like and nonnative tertiary structure.