Properties Of Intrinsically Disordered Proteins Research Articles

Mapping Full Conformational Transition Dynamics of Intrinsically Disordered Proteins Using a Single-Molecule Nanocircuit.

Intrinsically disordered proteins (IDPs) are emerging therapeutic targets for human diseases. However, probing their transient conformations remains challenging because of conformational heterogeneity. To address this problem, we developed a biosensor using a point-functionalized silicon nanowire (SiNW) that allows for real-time sampling of single-molecule dynamics. A single IDP, N-terminal transactivation domain of tumor suppressor protein p53 (p53TAD1), was covalently conjugated to the SiNW through chemical engineering, and its conformational transition dynamics was characterized as current fluctuations. Furthermore, when a globular protein ligand in solution bound to the targeted p53TAD1, protein-protein interactions could be unambiguously distinguished from large-amplitude current signals. These proof-of-concept experiments enable semiquantitative, realistic characterization of the structural properties of IDPs and constitute the basis for developing a valuable tool for protein profiling and drug discovery in the future.

Balancing thermodynamic stability, dynamics, and kinetics in phase separation of intrinsically disordered proteins.

Intrinsically disordered proteins (IDPs) are prevalent participants in liquid-liquid phase separation due to their inherent potential for promoting multivalent binding. Understanding the underlying mechanisms of phase separation is challenging, as phase separation is a complex process, involving numerous molecules and various types of interactions. Here, we used a simplified coarse-grained model of IDPs to investigate the thermodynamic stability of the dense phase, conformational properties of IDPs, chain dynamics, and kinetic rates of forming condensates. We focused on the IDP system, in which the oppositely charged IDPs are maximally segregated, inherently possessing a high propensity for phase separation. By varying interaction strengths, salt concentrations, and temperatures, we observed that IDPs in the dense phase exhibited highly conserved conformational characteristics, which are more extended than those in the dilute phase. Although the chain motions and global conformational dynamics of IDPs in the condensates are slow due to the high viscosity, local chain flexibility at the short timescales is largely preserved with respect to that at the free state. Strikingly, we observed a non-monotonic relationship between interaction strengths and kinetic rates for forming condensates. As strong interactions of IDPs result in high stable condensates, our results suggest that the thermodynamics and kinetics of phase separation are decoupled and optimized by the speed-stability balance through underlying molecular interactions. Our findings contribute to the molecular-level understanding of phase separation and offer valuable insights into the developments of engineering strategies for precise regulation of biomolecular condensates.

Interpreting Transient Interactions of Intrinsically Disordered Proteins.

The flexible nature of intrinsically disordered proteins (IDPs) gives rise to a conformational ensemble with a diverse set of conformations. The simplest way to describe this ensemble is through a homopolymer model without any specific interactions. However, there has been growing evidence that the conformational properties of IDPs and their relevant functions can be affected by transient interactions between specific and even nonlocal pairs of amino acids. Interpreting these interactions from experimental methods, each of which is most sensitive to a different distance regime referred to as probing length, remains a challenging and unsolved problem. Here, we first show that transient interactions can be realized between short fragments of charged amino acids by generating conformational ensembles using model disordered peptides and coarse-grained simulations. Using these ensembles, we investigate how sensitive different types of experimental measurements are to the presence of transient interactions. We find methods with shorter probing lengths to be more appropriate for detecting these transient interactions, but one experimental method is not sufficient due to the existence of other weak interactions typically seen in IDPs. Finally, we develop an adjusted polymer model with an additional short-distance peak which can robustly reproduce the distance distribution function from two experimental measurements with complementary short and long probing lengths. This new model can suggest whether a homopolymer model is insufficient for describing a specific IDP and meets the challenge of quantitatively identifying specific, transient interactions from a background of nonspecific, weak interactions.

Effects of phosphorylation to the conformational space of C-terminal domain of RNA polymerase II.

Intrinsically disordered proteins (IDPs) are known as proteins without a defined secondary structure and linked with many neurological diseases. Exploring the conformational space of IDPs is one of the major challenges faced by the experimental and computational studies due to its disordered nature. Obtaining an accurate conformational space is very important to identify the structural properties of IDPs linked with these biological phenomena. RNA polymerase II (Pol II) C-terminal domain (CTD) is an intrinsically disordered low complexity domain that has a heptapeptide repeating sequence with number of repeats varies according to the organism. CTD was documented to undergo liquid-liquid phase separation, which is affected by its length and phosphorylation level. In this study, we investigated the conformational space of CTD and the effects of phosphorylation to its conformation using enhanced sampling molecular dynamics (MD) simulations. We used CTD models with two repeating units with non-phosphorylated and phosphorylated states. In addition, we study a longer synthetic CTD sequence, which has available experimental observables as a reference point to compare with the simulations. Our results suggested that phosphorylation has complex effects on the conformations of the CTD that depend on the length of the CTD, spacing between the multiple phosphorylation sites, ion coordination and interactions with the nearby residues. With this study we provide a detailed explanation of conformational changes of CTD models upon their phosphorylation.

Interpreting transient interactions in intrinsically disordered proteins.

The flexible nature of intrinsically disordered proteins (IDPs) leads to a conformational ensemble with a diverse set of conformations. The simplest way to describe this ensemble is through a homopolymer model without any specific interactions. However, there has been growing evidence that the structural properties of IDPs and their relevant functions can be affected by transient interactions between specific and even non-local pairs of amino acids. Interpreting these interactions from experimental methods, each of which is sensitive to a different distance regime referred to as probing length, remains a challenging and unsolved problem. Here, we first show that transient interactions can be realized between short fragments of charged amino acids by generating conformational ensembles using model disordered peptides and coarse-grained simulations. Using these ensembles, we investigate how sensitive different types of experimental measurements are to the presence of transient interactions. We find methods with shorter probing lengths to be more sensitive, but further show that least two experimental methods with different probing lengths must be utilized to resolve both transient interactions between specific amino acids and weak interactions along the sequence. Finally, we develop an adjusted polymer model with an additional short-distance peak which can robustly reproduce the distance distribution function from two experimental measurements with complementary short and long-range probing lengths. This new model can suggest whether a homopolymer model is insufficient for a specific IDP, and quantitatively identify specific transient interactions from a background of nonspecific weak interactions.

Effects of Sequence Composition, Patterning and Hydrodynamics on the Conformation and Dynamics of Intrinsically Disordered Proteins.

Intrinsically disordered proteins (IDPs) and intrinsically disordered regions (IDRs) perform diverse functions in cellular organization, transport and signaling. Unlike the well-defined structures of the classical natively folded proteins, IDPs and IDRs dynamically span large conformational and structural ensembles. This dynamic disorder impedes the study of the relationship between the amino acid sequences of the IDPs and their spatial structures and dynamics, with different experimental techniques often offering seemingly contradictory results. Although experimental and theoretical evidence indicates that some IDP properties can be understood based on their average biophysical properties and amino acid composition, other aspects of IDP function are dictated by the specifics of the amino acid sequence. We investigate the effects of several key variables on the dimensions and the dynamics of IDPs using coarse-grained polymer models. We focus on the sequence "patchiness" informed by the sequence and biophysical properties of different classes of IDPs-and in particular FG nucleoporins of the nuclear pore complex (NPC). We show that the sequence composition and patterning are well reflected in the global conformational variables such as the radius of gyration and hydrodynamic radius, while the end-to-end distance and dynamics are highly sequence-specific. We find that in good solvent conditions highly heterogeneous sequences of IDPs can be well mapped onto averaged minimal polymer models for the purpose of prediction of the IDPs dimensions and dynamic relaxation times. The coarse-grained simulations are in a good agreement with the results of atomistic MD. We discuss the implications of these results for the interpretation of the recent experimental measurements, and for the further applications of mesoscopic models of FG nucleoporins and IDPs more broadly.

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.

Cross-Linking Mass Spectrometry Analysis of Metastable Compact Structures in Intrinsically Disordered Proteins.

Protein assembly into beta-sheet-rich amyloids is a common phenomenon in neurodegenerative diseases including Alzheimer's (AD) and Parkinson's (PD). The proteins implicated in amyloid deposition are often intrinsically disordered proteins (IDPs) and are characterized by not folding into a defined globular conformation. The amyloidogenic properties of IDPs are determined by the presence of short sequence elements, referred to as amyloid motifs, that drive ordered aggregation (Thompson MJ, Sievers SA, Karanicolas J et al. Proc Natl Acad Sci USA 103(11):4074-8, 2006; Goldschmidt L, Teng PK, Riek R et al. Proc Natl Acad Sci USA 107(8):3487-92, 2010]. The microtubule-associated protein tau adopts amyloid assemblies in over 20 different diseases commonly referred to as tauopathies. However, native tau is aggregation-resistant despite encoding at least three amyloid motifs (Chen D, Drombosky KW, Hou Z et al. Nat Commun 10(1):2493, 2019). Recent cryogenic electron microscopy (cryo-EM) structures of tau amyloid fibrils isolated from patient brains showed the involvement of amyloid motifs in the fibril core (Fitzpatrick AWP, Falcon B, He S et al. Nature 547(7662):185-90, 2017; Falcon B, Zhang W, Murzin AG et al. Nature 561(7721):137-40, 2018; Zhang W, Tarutani A, Newell KL et al. Nature 580(7802):283-7, 2020). How does tau change from an aggregation-resistant state to an aggregation-prone state? Consistent with the fibril structures, we hypothesize that tau must change conformation to expose the amyloid motifs that allow self-association into beta-sheet-rich aggregates. This would suggest that the amyloid motifs are likely buried in natively folded tau to prevent self-assembly. We developed an approach that couples cross-linking mass spectrometry (XL-MS) with temperature denaturation to probe the loss of contacts as a proxy to measure protein unfolding with sequence resolution. Using thismethod, we demonstrated that disease-associated mutations in tau located near an amyloid motif disrupt the protective local structure, promote amyloid motif exposure, and thus lead to aggregation (Chen D, Drombosky KW, Hou Z et al. Nat Commun 10(1):2493, 2019). In this chapter, we describe the detailed protocol for this approach. We anticipate that our protocol can be generalized to other IDPs and will help discover critical structural elements to better understand important biological questions including protein aggregation.

Toward Accurate Coarse-Grained Simulations of Disordered Proteins and Their Dynamic Interactions.

Intrinsically disordered proteins (IDPs) play crucial roles in cellular regulatory networks and are now recognized to often remain highly dynamic even in specific interactions and assemblies. Accurate description of these dynamic interactions is extremely challenging using atomistic simulations because of the prohibitive computational cost. Efficient coarse-grained approaches could offer an effective solution to overcome this bottleneck if they could provide an accurate description of key local and global properties of IDPs in both unbound and bound states. The recently developed hybrid-resolution (HyRes) protein model has been shown to be capable of providing a semiquantitative description of the secondary structure propensities of IDPs. Here, we show that greatly improved description of global structures and transient interactions can be achieved by introducing a solvent-accessible surface area-based implicit solvent term followed by reoptimization of effective interaction strengths. The new model, termed HyRes II, can semiquantitatively reproduce a wide range of local and global structural properties of a set of IDPs of various lengths and complexities. It can also distinguish the level of compaction between folded proteins and IDPs. In particular, applied to the disordered N-terminal transactivation domain (TAD) of tumor suppressor p53, HyRes II is able to recapitulate various nontrivial structural properties compared to experimental results, some of them to a level of accuracy that is almost comparable to results from atomistic explicit solvent simulations. Furthermore, we demonstrate that HyRes II can be used to simulate the dynamic interactions of TAD with the DNA-binding domain of p53, generating structural ensembles that are highly consistent with existing NMR data. We anticipate that HyRes II will provide an efficient and relatively reliable tool toward accurate coarse-grained simulations of dynamic protein interactions.

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.

Intrinsic Conformational Preferences of the Charged Amino Acids in Disordered Proteins

Conformational equilibria in the unfolded states of proteins have many important biological roles, from regulating how some proteins fold and maintain structural stability, to describing the macromolecular details of intrinsically disordered proteins (IDPs), a protein class that does not adopt physiologically stable structures and instead utilizes unfolded states to facilitate their functions. Recently, to better understand the structural properties of IDPs, we analyzed both the sequence dependence to the mean hydrodynamic size of IDPs in water, as well as the impact of heat on the coil dimensions, showing that the sequence dependence and thermodynamic energies associated with intrinsic biases for the polyproline II (PPII) backbone conformation could be obtained. This result is important because PPII is used biologically for protein–protein and protein–nucleic acid interactions and thus has a role in molecular recognition. Experiments that evaluate how the hydrodynamic size changes with compositional changes in the IDP revealed amino acid-specific preferences for PPII that were in excellent quantitative agreement with calorimetry-measured values from small unfolded peptides and also those inferred by a survey of the protein coil library. Here, a set of charge-substitution experiments were used to measure the intrinsic preferences of the charged amino acids (i.e., lysine, arginine, glutamic acid, and aspartic acid) for the PPII backbone conformation, the results of which provide insight into how long-range charge-charge interactions and short-range effects, such as hydration and sterics, can modulate the structural and dynamical properties of IDPs, an increasingly important protein class in cell function.

Molecular Transfer Model for pH Effects on Intrinsically Disordered Proteins: Theory and Applications.

We present a theoretical method to study how changes in pH shape the heterogeneous conformational ensemble explored by intrinsically disordered proteins (IDPs). The theory is developed in the context of coarse-grained models, which enable a fast, accurate, and extensive exploration of conformational space at a given protonation state. In order to account for pH effects, we generalize the molecular transfer model (MTM), in which conformations are re-weighted using the transfer free energy, which is the free energy necessary for bringing to equilibrium in a new environment a "frozen" conformation of the system. Using the semi-grand ensemble, we derive an exact expression of the transfer free energy, which amounts to the appropriate summation over all the protonation states. Because the exact result is computationally too demanding to be useful for large polyelectrolytes or IDPs, we introduce a mean-field (MF) approximation of the transfer free energy. Using a lattice model, we compare the exact and MF results for the transfer free energy and a variety of observables associated with the model IDP. We find that the precise location of the charged groups (the sequence), and not merely the net charge, determines the structural properties. We demonstrate that some of the limitations previously noted for MF theory in the context of globular proteins are mitigated when disordered polymers are studied. The excellent agreement between the exact and MF results poises us to use the method presented here as a computational tool to study the properties of IDPs and other biological systems as a function of pH.

Glassy Dynamics in an Intrinsically Disordered Protein

Intrinsically disordered proteins (IDPs) are characterized by their extreme conformational flexibility which gives them unique functional advantages, such as acting as entropic springs in the cytoskeleton. Here, we investigate the dynamic mechanical properties of a model IDP derived from neurofilament tail domains. We use a single-molecule manipulation technique, magnetic tweezers, to force the protein out of equilibrium and observe the relaxation of its end-to-end extension. We observe that the protein's extension decreases logarithmically for hours. We explain our results in terms of a phenomenological model, originally developed for bulk glassy systems, that assumes the total extension change is the sum of many independent structural transitions. Such a model makes sense for bulk measurements but is surprising to observe in a single molecule. Yet, the model accounts for our observation of a nonmonotonic (Kovacs) relaxation when subjecting the protein to a multi-step force protocol. This memory effect is an unambiguous signature that many independent and parallel structural transitions are contributing to the overall dynamic mechanical properties of the IDP. This is fundamentally different from previous examples of glassy behavior in folded proteins which rely on a heterogenous population of folded states. To our knowledge, this is the first reported example of this type of glassiness in proteins.

Predicting Conformational Properties of Intrinsically Disordered Proteins from Sequence.

Intrinsically disordered proteins (IDPs) can adopt a range of conformations from globules to swollen coils. This large range of conformational preferences for different IDPs raises the question of how conformational preferences are encoded by sequence. Global compositional features of a sequence such as the fraction of charged residues and the net charge per residue engender certain conformational biases. However, more specific sequence features such as the patterning of oppositely charged residues, expansion driving residues, or residues that can undergo posttranslational modifications can also influence the conformational ensembles of an IDP. Here, we outline how to calculate important global compositional features and patterning metrics that can be used to classify IDPs into different conformational classes and predict relative changes in conformation for sequences with the same amino acid composition. Although increased effort has been devoted to determining conformational properties of IDPs in recent years, quantitative predictions of conformation directly from sequence remain difficult and often inaccurate. Thus, if quantitative predictions of conformational properties are desired, then sequence-specific simulations must be performed.

Production of Intrinsically Disordered Proteins for Biophysical Studies: Tips and Tricks.

Intrinsically disordered proteins (IDPs) have no single, fixed tertiary structure, yet they take on many vital functions in biology. In recent years, considerable effort has been put into the structural characterization of their conformational ensembles, to understand the link between the transient, short- and long-range organizations of IDPs and their functions. Such biophysical studies require substantial amounts of pure protein, representing a major bottleneck in the studies of IDPs. However, the unique physicochemical properties resulting from their compositional bias may be exploited for simple yet effective purification strategies. In this chapter, we provide tips and tricks for IDP production and describe the most important analyses to carry out before bringing an IDP of interest to the laboratory. We outline four purification protocols utilizing the unique properties of IDPs as well as some commonly encountered challenges and pitfalls.

Evaluating Models of Varying Complexity of Crowded Intrinsically Disordered Protein Solutions Against SAXS.

Intrinsically disordered proteins (IDPs) adopt heterogeneous conformational ensembles in solution. The properties of the conformational ensemble are dependent upon the solution conditions, including the presence of ions, temperature, and crowding, and often directly impact biological function. Many in vitro investigations focus on the properties of IDPs under dilute conditions, rather than the crowded environment found in vivo. Due to their heterogeneous nature, the study of IDPs under crowded conditions is challenging both experimentally and computationally. Despite this, such studies are worth pursuing due to the insight gained into biologically relevant phenomena. Here, we study the highly charged IDP Histatin 5 under self-crowded conditions in low and high salt conditions. A combination of small-angle X-ray scattering and different simulation models, spanning a range of computational complexity and detail, is used. Most models are found to have limited application when compared to results from experiments. The best performing model is the highly coarse-grained, bead-necklace model. This model shows that Histatin 5 has a conserved radius of gyration and a decreasing flexibility with increasing protein concentration. Due to its computational efficiency, we propose that it is a suitable model to study crowded IDP solutions, despite its simplicity.

Sequence Versus Composition: What Prescribes IDP Biophysical Properties?

Intrinsically disordered proteins (IDPs) represent a distinct class of proteins and are distinguished from globular proteins by conformational plasticity, high evolvability and a broad functional repertoire. Some of their properties are reminiscent of early proteins, but their abundance in eukaryotes, functional properties and compositional bias suggest that IDPs appeared at later evolutionary stages. The spectrum of IDP properties and their determinants are still not well defined. This study compares rudimentary physicochemical properties of IDPs and globular proteins using bioinformatic analysis on the level of their native sequences and random sequence permutations, addressing the contributions of composition versus sequence as determinants of the properties. IDPs have, on average, lower predicted secondary structure contents and aggregation propensities and biased amino acid compositions. However, our study shows that IDPs exhibit a broad range of these properties. Induced fold IDPs exhibit very similar compositions and secondary structure/aggregation propensities to globular proteins, and can be distinguished from unfoldable IDPs based on analysis of these sequence properties. While amino acid composition seems to be a major determinant of aggregation and secondary structure propensities, sequence randomization does not result in dramatic changes to these properties, but for both IDPs and globular proteins seems to fine-tune the tradeoff between folding and aggregation.

Does Intrinsic Disorder in Proteins Favor Their Interaction with Lipids?

Intrinsically disordered proteins (IDPs) are implicated in a range of human diseases, some of which are associated with the ability to bind to lipids. Although the presence of solvent-exposed hydrophobic regions in IDPs should favor their interactions with low-molecular-weight hydrophobic/amphiphilic compounds, this hypothesis has not been systematically explored as of yet. In this study, the analysis of the DisProt database with regard to the presence of lipid-binding IDPs (LBIDPs) reveals that they comprise, at least, 15% of DisProt entries. LBIDPs are classified into four groups by ligand type, functional categories, domain structure, and conformational state. 57% of LBIDPs are classified as ordered according to the CH-CDF analysis, and 70% of LBIDPs possess lengths of disordered regions below 50%. To investigate the lipid-binding properties of IDPs for which lipid binding is not reported, three proteins from different conformational groups are rationally selected. They all are shown to bind linoleic (LA) and oleic (OA) acids with capacities ranging from 9 to 34 LA/OA molecules per protein molecule. The association with LA/OA causes the formation of high-molecular-weight lipid-protein complexes. These findings suggest that lipid binding is common among IDPs, which can favor their involvement in lipid metabolism.

Saxs Confirms that FRET Dyes Promote Collapse of an Otherwise Fully Disordered Protein

Significance: The dimensions of intrinsically disordered proteins (IDPs) remains controversial. Using SAXS, we previously found that even relatively hydrophobic IDPs remain expanded in the complete absence of denaturant, contrary to conclusions drawn from FRET studies that foldable sequences collapse in water. Here we use our methodology to demonstrate that labeling with Alexa488 causes the IDP to undergo significant dye-induced contraction. These results demonstrate that the addition of dyes influences the properties of IDPs and is likely the primary origin of the discrepancy between prior SAXS and FRET results. ABSTRACT: The origins of the discrepancy between SAXS and FRET measurements of IDP dimensions remain controversial. To address this, we recently developed a robust analysis for extracting Rg and ν (the Flory exponent; Rg∼Nν) from single SAXS experiments using a molecular form factor derived from simulations. Performing this analysis on a 334 AA IDP, we find that the addition of a dye pair promotes collapse, decreasing Rg from 51 to 45 Å and ν from 0.54 to 0.50. This observation is consistent with prior studies on PEG, which found the addition of dyes induces similar contraction1 despite the fact that, as we show here, the polymer behaves as a self-avoiding random walk. Recent studies have suggested that FRET and SAXS results can be reconciled if SAXS reports on Rg while remaining relatively insensitive to Rend-to-end, essentially decoupling the two. To the contrary, our analysis finds that the entire SAXS profile is sensitive to conformational ensembles enriched in shortened end-to-end distances, such as those produced by dye-dye interactions. More broadly, our simulations define a route to characterize the deviations from homopolymeric behavior inherent in disordered proteins. 1Watkins et al, PNAS 2015.

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.