Extended Experimental Inferential Structure Determination Method in Determining the Structural Ensembles of Disordered Protein States

Accounting for fast vs slow exchange in single molecule FRET experiments reveals hidden conformational states

Proteins are dynamic systems whose structural preferences determine their function. Unfortunately, building atomically detailed models of protein structural ensembles remains challenging, limiting our understanding of the relationships between sequence, structure, and function. Combining single molecule Förster resonance energy transfer (smFRET) experiments with molecular dynamics simulations could provide experimentally grounded, all-atom models of a protein's structural ensemble. However, agreement between the two techniques is often insufficient to achieve this goal. Here, we explore whether accounting for important experimental details like averaging across structures sampled during a given smFRET measurement is responsible for this apparent discrepancy. We present an approach to account for this time-averaging by leveraging the kinetic information available from Markov state models of a protein's dynamics. This allows us to accurately assess which timescales are averaged during an experiment. We find this approach significantly improves agreement between simulations and experiments in proteins with varying degrees of dynamics, including the well-ordered protein T4 lysozyme, the partially disordered protein apolipoprotein E (ApoE), and a disordered amyloid protein (Aβ40). We find evidence for hidden states that are not apparent in smFRET experiments because of time averaging with other structures, akin to states in fast exchange in NMR, and evaluate different force fields. Finally, we show how remaining discrepancies between computations and experiments can be used to guide additional simulations and build structural models for states that were previously unaccounted for. We expect our approach will enable combining simulations and experiments to understand the link between sequence, structure, and function in many settings.

Understanding the Energy Landscape of Intrinsically Disordered Protein Ensembles

A substantial portion of various organisms' proteomes comprises intrinsically disordered proteins (IDPs) that lack a defined three-dimensional structure. These IDPs exhibit a diverse array of conformations, displaying remarkable spatiotemporal heterogeneity and exceptional conformational flexibility. Characterizing the structure or structural ensemble of IDPs presents significant conceptual and methodological challenges owing to the absence of a well-defined native structure. While databases such as the Protein Ensemble Database (PED) provide IDP ensembles obtained through a combination of experimental data and molecular modeling, the absence of reaction coordinates poses challenges in comprehensively understanding pertinent aspects of the system. In this study, we leverage the energy landscape visualization method (JCTC, 6482, 2019) to scrutinize four IDP ensembles sourced from PED. ELViM, a methodology that circumvents the need for a priori reaction coordinates, aids in analyzing the ensembles. The specific IDP ensembles investigated are as follows: two fragments of nucleoporin (NUL: 884-993 and NUS: 1313-1390), yeast sic 1 N-terminal (1-90), and the N-terminal SH3 domain of Drk (1-59). Utilizing ELViM enables the comprehensive validation of ensembles, facilitating the detection of potential inconsistencies in the sampling process. Additionally, it allows for identifying and characterizing the most prevalent conformations within an ensemble. Moreover, ELViM facilitates the comparative analysis of ensembles obtained under diverse conditions, thereby providing a powerful tool for investigating the functional mechanisms of IDPs.

Using NMR diffusion data to validate MD models of disordered proteins: Test case of N-terminal tail of histone H4

MD simulations can provide uniquely detailed models of intrinsically disordered proteins (IDPs). However, these models need careful experimental validation. The coefficient of translational diffusion Dtr, measurable by pulsed field gradient NMR, offers a potentially useful piece of experimental information related to the compactness of the IDP's conformational ensemble. Here, we investigate, both experimentally and via the MD modeling, the translational diffusion of a 25-residue N-terminal fragment from histone H4 (N-H4). We found that the predicted values of Dtr, as obtained from mean-square displacement of the peptide in the MD simulations, are largely determined by the viscosity of the MD water (which has been reinvestigated as a part of our study). Beyond that, our analysis of the diffusion data indicates that MD simulations of N-H4 in the TIP4P-Ew water give rise to an overly compact conformational ensemble for this peptide. In contrast, TIP4P-D and OPC simulations produce the ensembles that are consistent with the experimental Dtr result. These observations are supported by the analyses of the 15N spin relaxation rates. We also tested a number of empirical methods to predict Dtr based on IDP's coordinates extracted from the MD snapshots. In particular, we show that the popular approach involving the program HYDROPRO can produce misleading results. This happens because HYDROPRO is not intended to predict the diffusion properties of highly flexible biopolymers such as IDPs. Likewise, recent empirical schemes that exploit the relationship between the small-angle x-ray scattering-informed conformational ensembles of IDPs and the respective experimental Dtr values also prove to be problematic. In this sense, the first-principle calculations of Dtr from the MD simulations, such as demonstrated in this work, should provide a useful benchmark for future efforts in this area.

Local Disordered Region Sampling (LDRS) for ensemble modeling of proteins with experimentally undetermined or low confidence prediction segments

SUMMARY

The Local Disordered Region Sampling (LDRS, pronounced loaders) tool is a new module developed for IDPConformerGenerator, a previously validated approach to model intrinsically disordered proteins (IDPs). The IDPConformerGenerator LDRS module provides a method for generating all-atom conformations of intrinsically disordered protein regions at N- and C-termini of and in loops or linkers between folded regions of an existing protein structure. These disordered elements often lead to missing coordinates in experimental structures or low confidence in predicted structures. Requiring only a pre-existing PDB or mmCIF formatted structural template of the protein with missing coordinates or with predicted confidence scores and its full-length primary sequence, LDRS will automatically generate physically meaningful conformational ensembles of the missing flexible regions to complete the full-length protein. The capabilities of the LDRS tool of IDPConformerGenerator include modeling phosphorylation sites using enhanced Monte Carlo-Side Chain Entropy, transmembrane proteins within an all-atom bilayer, and multi-chain complexes. The modeling capacity of LDRS capitalizes on the modularity, the ability to be used as a library and via command-line, and the computational speed of the IDPConformerGenerator platform.

AVAILABILITY AND IMPLEMENTATION

The LDRS module is part of the IDPConformerGenerator modeling suite, which can be downloaded from GitHub at https://github.com/julie-forman-kay-lab/IDPConformerGenerator. IDPConformerGenerator is written in Python3 and works on Linux, Microsoft Windows, and Mac OS versions that support DSSP. Users can utilize LDRS's Python API for scripting the same way they can use any part of IDPConformerGenerator's API, by importing functions from the "idpconfgen.ldrs_helper" library. Otherwise, LDRS can be used as a command line interface application within IDPConformerGenerator. Full documentation is available within the command-line interface as well as on IDPConformerGenerator's official documentation pages (https://idpconformergenerator.readthedocs.io/en/latest/).

Systematic identification of conditionally folded intrinsically disordered regions by AlphaFold2

The AlphaFold Protein Structure Database contains predicted structures for millions of proteins. For the majority of human proteins that contain intrinsically disordered regions (IDRs), which do not adopt a stable structure, it is generally assumed that these regions have low AlphaFold2 confidence scores that reflect low-confidence structural predictions. Here, we show that AlphaFold2 assigns confident structures to nearly 15% of human IDRs. By comparison to experimental NMR data for a subset of IDRs that are known to conditionally fold (i.e., upon binding or under other specific conditions), we find that AlphaFold2 often predicts the structure of the conditionally folded state. Based on databases of IDRs that are known to conditionally fold, we estimate that AlphaFold2 can identify conditionally folding IDRs at a precision as high as 88% at a 10% false positive rate, which is remarkable considering that conditionally folded IDR structures were minimally represented in its training data. We find that human disease mutations are nearly fivefold enriched in conditionally folded IDRs over IDRs in general and that up to 80% of IDRs in prokaryotes are predicted to conditionally fold, compared to less than 20% of eukaryotic IDRs. These results indicate that a large majority of IDRs in the proteomes of human and other eukaryotes function in the absence of conditional folding, but the regions that do acquire folds are more sensitive to mutations. We emphasize that the AlphaFold2 predictions do not reveal functionally relevant structural plasticity within IDRs and cannot offer realistic ensemble representations of conditionally folded IDRs.

Delineating Structural Propensities of the 4E-BP2 Protein via Integrative Modeling and Clustering

The intrinsically disordered 4E-BP2 protein regulates mRNA cap-dependent translation through interaction with the predominantly folded eukaryotic initiation factor 4E (eIF4E). Phosphorylation of 4E-BP2 dramatically reduces the level of eIF4E binding, in part by stabilizing a binding-incompatible folded domain. Here, we used a Rosetta-based sampling algorithm optimized for IDRs to generate initial ensembles for two phospho forms of 4E-BP2, non- and 5-fold phosphorylated (NP and 5P, respectively), with the 5P folded domain flanked by N- and C-terminal IDRs (N-IDR and C-IDR, respectively). We then applied an integrative Bayesian approach to obtain NP and 5P conformational ensembles that agree with experimental data from nuclear magnetic resonance, small-angle X-ray scattering, and single-molecule Förster resonance energy transfer (smFRET). For the NP state, inter-residue distance scaling and 2D maps revealed the role of charge segregation and pi interactions in driving contacts between distal regions of the chain (∼70 residues apart). The 5P ensemble shows prominent contacts of the N-IDR region with the two phosphosites in the folded domain, pT37 and pT46, and, to a lesser extent, delocalized interactions with the C-IDR region. Agglomerative hierarchical clustering led to partitioning of each of the two ensembles into four clusters with different global dimensions and contact maps. This helped delineate an NP cluster that, based on our smFRET data, is compatible with the eIF4E-bound state. 5P clusters were differentiated by interactions of C-IDR with the folded domain and of the N-IDR with the two phosphosites in the folded domain. Our study provides both a better visualization of fundamental structural poses of 4E-BP2 and a set of falsifiable insights on intrachain interactions that bias folding and binding of this protein.

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.

Learning to evolve structural ensembles of unfolded and disordered proteins using experimental solution data

The structural characterization of proteins with a disorder requires a computational approach backed by experiments to model their diverse and dynamic structural ensembles. The selection of conformational ensembles consistent with solution experiments of disordered proteins highly depends on the initial pool of conformers, with currently available tools limited by conformational sampling. We have developed a Generative Recurrent Neural Network (GRNN) that uses supervised learning to bias the probability distributions of torsions to take advantage of experimental data types such as nuclear magnetic resonance J-couplings, nuclear Overhauser effects, and paramagnetic resonance enhancements. We show that updating the generative model parameters according to the reward feedback on the basis of the agreement between experimental data and probabilistic selection of torsions from learned distributions provides an alternative to existing approaches that simply reweight conformers of a static structural pool for disordered proteins. Instead, the biased GRNN, DynamICE, learns to physically change the conformations of the underlying pool of the disordered protein to those that better agree with experiments.

The influence of random-coil chemical shifts on the assessment of structural propensities in folded proteins and IDPs

In studying secondary structural propensities of proteins by nuclear magnetic resonance (NMR) spectroscopy, secondary chemical shifts (SCSs) serve as the primary atomic scale observables. For SCS calculation, the selection of an appropriate random coil chemical shift (RCCS) dataset is a crucial step, especially when investigating intrinsically disordered proteins (IDPs). The scientific literature is abundant in such datasets, however, the effect of choosing one over all the others in a concrete application has not yet been studied thoroughly and systematically. Hereby, we review the available RCCS prediction methods and to compare them, we conduct statistical inference by means of the nonparametric sum of ranking differences and comparison of ranks to random numbers (SRD-CRRN) method. We try to find the RCCS predictors best representing the general consensus regarding secondary structural propensities. The existence and the magnitude of resulting differences on secondary structure determination under varying sample conditions (temperature, pH) are demonstrated and discussed for globular proteins and especially IDPs.

Assessment of models for calculating the hydrodynamic radius of intrinsically disordered proteins

Diffusion measurements by pulsed-field gradient NMR and fluorescence correlation spectroscopy can be used to probe the hydrodynamic radius of proteins, which contains information about the overall dimension of a protein in solution. The comparison of this value with structural models of intrinsically disordered proteins is nonetheless impaired by the uncertainty of the accuracy of the methods for computing the hydrodynamic radius from atomic coordinates. To tackle this issue, we here build conformational ensembles of 11 intrinsically disordered proteins that we ensure are in agreement with measurements of compaction by small-angle x-ray scattering. We then use these ensembles to identify the forward model that more closely fits the radii derived from pulsed-field gradient NMR diffusion experiments. Of the models we examined, we find that the Kirkwood-Riseman equation provides the best description of the hydrodynamic radius probed by pulsed-field gradient NMR experiments. While some minor discrepancies remain, our results enable better use of measurements of the hydrodynamic radius in integrative modeling and for force field benchmarking and parameterization.

Recent advances in structural characterization of biomacromolecules in foods via small-angle X-ray scattering

Small-angle X-ray scattering (SAXS) is a method for examining the solution structure, oligomeric state, conformational changes, and flexibility of biomacromolecules at a scale ranging from a few Angstroms to hundreds of nanometers. Wide time scales ranging from real time (milliseconds) to minutes can be also covered by SAXS. With many advantages, SAXS has been extensively used, it is widely used in the structural characterization of biomacromolecules in food science and technology. However, the application of SAXS in charactering the structure of food biomacromolecules has not been reviewed so far. In the current review, the principle, theoretical calculations and modeling programs are summarized, technical advances in the experimental setups and corresponding applications of in situ capabilities: combination of chromatography, time-resolved, temperature, pressure, flow-through are elaborated. Recent applications of SAXS for monitoring structural properties of biomacromolecules in food including protein, carbohydrate and lipid are also highlighted, and limitations and prospects for developing SAXS based on facility upgraded and artificial intelligence to study the structural properties of biomacromolecules are finally discussed. Future research should focus on extending machine time, simplifying SAXS data treatment, optimizing modeling methods in order to achieve an integrated structural biology based on SAXS as a practical tool for investigating the structure-function relationship of biomacromolecules in food industry.

Combining NMR, SAXS and SANS to characterize the structure and dynamics of protein complexes

Understanding the structure and dynamics of biological macromolecules is essential to decipher the molecular mechanisms that underlie cellular functions. The description of structure and conformational dynamics often requires the integration of complementary techniques. In this review, we highlight the utility of combining nuclear magnetic resonance (NMR) spectroscopy with small angle scattering (SAS) to characterize these challenging biomolecular systems. NMR can assess the structure and conformational dynamics of multidomain proteins, RNAs and biomolecular complexes. It can efficiently provide information on interaction surfaces, long-distance restraints and relative domain orientations at residue-level resolution. Such information can be readily combined with high-resolution structural data available on subcomponents of biomolecular assemblies. Moreover, NMR is a powerful tool to characterize the dynamics of biomolecules on a wide range of timescales, from nanoseconds to seconds. On the other hand, SAS approaches provide global information on the size and shape of biomolecules and on the ensemble of all conformations present in solution. Therefore, NMR and SAS provide complementary data that are uniquely suited to investigate dynamic biomolecular assemblies. Here, we briefly review the type of data that can be obtained by both techniques and describe different approaches that can be used to combine them to characterize biomolecular assemblies. We then provide guidelines on which experiments are best suited depending on the type of system studied, ranging from fully rigid complexes, dynamic structures that interconvert between defined conformations and systems with very high structural heterogeneity.

IDPConformerGenerator: A Flexible Software Suite for Sampling the Conformational Space of Disordered Protein States

The power of structural information for informing biological mechanisms is clear for stable folded macromolecules, but similar structure–function insight is more difficult to obtain for highly dynamic systems such as intrinsically disordered proteins (IDPs) which must be described as structural ensembles. Here, we present IDPConformerGenerator, a flexible, modular open-source software platform for generating large and diverse ensembles of disordered protein states that builds conformers that obey geometric, steric, and other physical restraints on the input sequence. IDPConformerGenerator samples backbone phi (φ), psi (ψ), and omega (ω) torsion angles of relevant sequence fragments from loops and secondary structure elements extracted from folded protein structures in the RCSB Protein Data Bank and builds side chains from robust Monte Carlo algorithms using expanded rotamer libraries. IDPConformerGenerator has many user-defined options enabling variable fractional sampling of secondary structures, supports Bayesian models for assessing the agreement of IDP ensembles for consistency with experimental data, and introduces a machine learning approach to transform between internal and Cartesian coordinates with reduced error. IDPConformerGenerator will facilitate the characterization of disordered proteins to ultimately provide structural insights into these states that have key biological functions.

Integrative Conformational Ensembles of Sic1 Using Different Initial Pools and Optimization Methods

Intrinsically disordered proteins play key roles in regulatory protein interactions, but their detailed structural characterization remains challenging. Here we calculate and compare conformational ensembles for the disordered protein Sic1 from yeast, starting from initial ensembles that were generated either by statistical sampling of the conformational landscape, or by molecular dynamics simulations. Two popular, yet contrasting optimization methods were used, ENSEMBLE and Bayesian Maximum Entropy, to achieve agreement with experimental data from nuclear magnetic resonance, small-angle X-ray scattering and single-molecule Förster resonance energy transfer. The comparative analysis of the optimized ensembles, including secondary structure propensity, inter-residue contact maps, and the distributions of hydrogen bond and pi interactions, revealed the importance of the physics-based generation of initial ensembles. The analysis also provides insights into designing new experiments that report on the least restrained features among the optimized ensembles. Overall, differences between ensembles optimized from different priors were greater than when using the same prior with different optimization methods. Generating increasingly accurate, reliable and experimentally validated ensembles for disordered proteins is an important step towards a mechanistic understanding of their biological function and involvement in various diseases.

Rules of Physical Mathematics Govern Intrinsically Disordered Proteins

In stark contrast to foldable proteins with a unique folded state, intrinsically disordered proteins and regions (IDPs) persist in perpetually disordered ensembles. Yet an IDP ensemble has conformational features-even when averaged-that are specific to its sequence. In fact, subtle changes in an IDP sequence can modulate its conformational features and its function. Recent advances in theoretical physics reveal a set of elegant mathematical expressions that describe the intricate relationships among IDP sequences, their ensemble conformations, and the regulation of their biological functions. These equations also describe the molecular properties of IDP sequences that predict similarities and dissimilarities in their functions and facilitate classification of sequences by function, an unmet challenge to traditional bioinformatics. These physical sequence-patterning metrics offer a promising new avenue for advancing synthetic biology at a time when multiple novel functional modes mediated by IDPs are emerging.

Integrative ensemble modeling of proteins and their complexes with distance distribution restraints

Many proteins and protein complexes exhibit regions that are intrinsically disordered. Whereas an arsenal of techniques exists to characterize structured proteins or protein regions, characterization of the vast conformational space occupied by intrinsically disordered regions remains a challenging task due the ensemble-averaging nature of many techniques that provide mean value restraints. More representative information can be gained in the form of distribution restraints, such as EPR-derived distance distributions. Previously we developed the ensemble modeling tool MMM, where we partition the macromolecule into structured and unstructured domains and utilize an integrative structural approach with a focus on EPR-derived distance restraints. Here we present the successor program of MMM: MMMx. All the modeling functionality was ported to MMMx and is now accessed by a uniform script format, allowing to combine the different modules at will to modeling pipelines. During the conception of MMMx many of the tools were improved or updated. We discuss the general functionality of MMMx and its modules, and illustrate some of the modeling tools by application examples.

NMR Provides Unique Insight into the Functional Dynamics and Interactions of Intrinsically Disordered Proteins

Intrinsically disordered proteins are ubiquitous throughout all known proteomes, playing essential roles in all aspects of cellular and extracellular biochemistry. To understand their function, it is necessary to determine their structural and dynamic behavior and to describe the physical chemistry of their interaction trajectories. Nuclear magnetic resonance is perfectly adapted to this task, providing ensemble averaged structural and dynamic parameters that report on each assigned resonance in the molecule, unveiling otherwise inaccessible insight into the reaction kinetics and thermodynamics that are essential for function. In this review, we describe recent applications of NMR-based approaches to understanding the conformational energy landscape, the nature and time scales of local and long-range dynamics and how they depend on the environment, even in the cell. Finally, we illustrate the ability of NMR to uncover the mechanistic basis of functional disordered molecular assemblies that are important for human health.

Bayesian Inference Applied to NMR-Based Configurational Assignments by Floating Chirality Distance Geometry Calculations

Using NMR data, the assignment of the correct 3D configuration and conformation to unknown natural products is of pivotal importance in pharmaceutical and medicinal chemistry. In this report, we quantify the quality and probability of structural elucidations using Bayesian inference in combination with floating chirality distance geometry simulations. Here, we will discuss the configurational analysis of three complex natural products including isopinocampheol (1), plakilactone H (2), and iodocallophycoic acid A (3) using NMR restraints of various types and in different combinations (residual dipolar couplings (RDCs) and NOE-derived distances). Our results quantitatively demonstrate how reliably molecular geometries can be inferred from experimental NMR data, unequivocally unveiling remaining assignment ambiguities. The methodology presented here can dramatically reduce the risk of incorrect structural assignments based on the overinterpretation of incomplete data in chemistry.

Generating Ensembles of Dynamic Misfolding Proteins

The early stages of protein misfolding and aggregation involve disordered and partially folded protein conformers that contain a high degree of dynamic disorder. These dynamic species may undergo large-scale intra-molecular motions of intrinsically disordered protein (IDP) precursors, or flexible, low affinity inter-molecular binding in oligomeric assemblies. In both cases, generating atomic level visualization of the interconverting species that captures the conformations explored and their physico-chemical properties remains hugely challenging. How specific sub-ensembles of conformers that are on-pathway to aggregation into amyloid can be identified from their aggregation-resilient counterparts within these large heterogenous pools of rapidly moving molecules represents an additional level of complexity. Here, we describe current experimental and computational approaches designed to capture the dynamic nature of the early stages of protein misfolding and aggregation, and discuss potential challenges in describing these species because of the ensemble averaging of experimental restraints that arise from motions on the millisecond timescale. We give a perspective of how machine learning methods can be used to extract aggregation-relevant sub-ensembles and provide two examples of such an approach in which specific interactions of defined species within the dynamic ensembles of α-synuclein (αSyn) and β2-microgloblulin (β2m) can be captured and investigated.

Global Structure of the Intrinsically Disordered Protein Tau Emerges from Its Local Structure

The paradigmatic disordered protein tau plays an important role in neuronal function and neurodegenerative diseases. To disentangle the factors controlling the balance between functional and disease-associated conformational states, we build a structural ensemble of the tau K18 fragment containing the four pseudorepeat domains involved in both microtubule binding and amyloid fibril formation. We assemble 129-residue-long tau K18 chains with atomic detail from an extensive fragment library constructed with molecular dynamics simulations. We introduce a reweighted hierarchical chain growth (RHCG) algorithm that integrates experimental data reporting on the local structure into the assembly process in a systematic manner. By combining Bayesian ensemble refinement with importance sampling, we obtain well-defined ensembles and overcome the problem of exponentially varying weights in the integrative modeling of long-chain polymeric molecules. The resulting tau K18 ensembles capture nuclear magnetic resonance (NMR) chemical shift and J-coupling measurements. Without further fitting, we achieve very good agreement with measurements of NMR residual dipolar couplings. The good agreement with experimental measures of global structure such as single-molecule Förster resonance energy transfer (FRET) efficiencies is improved further by ensemble refinement. By comparing wild-type and mutant ensembles, we show that pathogenic single-point P301L, P301S, and P301T mutations shift the population from the turn-like conformations of the functional microtubule-bound state to the extended conformations of disease-associated tau fibrils. RHCG thus provides us with an atomically detailed view of the population equilibrium between functional and aggregation-prone states of tau K18, and demonstrates that global structural characteristics of this intrinsically disordered protein emerge from its local structure.

Protein Dynamics to Define and Refine Disordered Protein Ensembles

Intrinsically disordered proteins and unfolded proteins have fluctuating conformational ensembles that are fundamental to their biological function and impact protein folding, stability, and misfolding. Despite the importance of protein dynamics and conformational sampling, time-dependent data types are not fully exploited when defining and refining disordered protein ensembles. Here we introduce a computational framework using an elastic network model and normal-mode displacements to generate a dynamic disordered ensemble consistent with NMR-derived dynamics parameters, including transverse R₂ relaxation rates and Lipari-Szabo order parameters (S² values). We illustrate our approach using the unfolded state of the drkN SH3 domain to show that the dynamical ensembles give better agreement than a static ensemble for a wide range of experimental validation data including NMR chemical shifts, J-couplings, nuclear Overhauser effects, paramagnetic relaxation enhancements, residual dipolar couplings, hydrodynamic radii, single-molecule fluorescence Förster resonance energy transfer, and small-angle X-ray scattering.

NMR-Based Configurational Assignments of Natural Products: Gibbs Sampling and Bayesian Inference Using Floating Chirality Distance Geometry Calculations

Floating chirality restrained distance geometry (fc-rDG) calculations are used to directly evolve structures from NMR data such as NOE-derived intramolecular distances or anisotropic residual dipolar couplings (RDCs). In contrast to evaluating pre-calculated structures against NMR restraints, multiple configurations (diastereomers) and conformations are generated automatically within the experimental limits. In this report, we show that the "unphysical" rDG pseudo energies defined from NMR violations bear statistical significance, which allows assigning probabilities to configurational assignments made that are fully compatible with the method of Bayesian inference. These "diastereomeric differentiabilities" then even become almost independent of the actual values of the force constants used to model the restraints originating from NOE or RDC data.

Resolving Dynamics in the Ensemble: Finding Paths through Intermediate States and Disordered Protein Structures

Proteins have been found to inhabit a diverse set of three-dimensional structures. The dynamics that govern protein interconversion between structures happen over a wide range of time scales─picoseconds to seconds. Our understanding of protein functions and dynamics is largely reliant upon our ability to elucidate physically populated structures. From an experimental structural characterization perspective, we are often limited to measuring the ensemble-averaged structure both in the steady-state and time-resolved regimes. Generating kinetic models and understanding protein structure-function relationships require atomistic knowledge of the populated states in the ensemble. In this Perspective, we present ensemble refinement methodologies that integrate time-resolved experimental signals with molecular dynamics models. We first discuss integration of experimental structural restraints to molecular models in disordered protein systems that adhere to the principle of maximum entropy for creating a complete set of ensemble structures. We then propose strategies to find kinetic pathways between the refined structures, using time-resolved inputs to guide molecular dynamics trajectories and the use of inference to generate tailored stimuli to prepare a desired ensemble of protein states.

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.

Aggregation-Prone Structural Ensembles of Transthyretin Collected With Regression Analysis for NMR Chemical Shift

Monomer dissociation and subsequent misfolding of the transthyretin (TTR) is one of the most critical causative factors of TTR amyloidosis. TTR amyloidosis causes several human diseases, such as senile systemic amyloidosis and familial amyloid cardiomyopathy/polyneuropathy; therefore, it is important to understand the molecular details of the structural deformation and aggregation mechanisms of TTR. However, such molecular characteristics are still elusive because of the complicated structural heterogeneity of TTR and its highly sensitive nature to various environmental factors. Several nuclear magnetic resonance (NMR) spectroscopy and molecular dynamics (MD) studies of TTR variants have recently reported evidence of transient aggregation-prone structural states of TTR. According to these studies, the stability of the DAGH β-sheet, one of the two main β-sheets in TTR, is a crucial determinant of the TTR amyloidosis mechanism. In addition, its conformational perturbation and possible involvement of nearby structural motifs facilitates TTR aggregation. This study proposes aggregation-prone structural ensembles of TTR obtained by MD simulation with enhanced sampling and a multiple linear regression approach. This method provides plausible structural models that are composed of ensemble structures consistent with NMR chemical shift data. This study validated the ensemble models with experimental data obtained from circular dichroism (CD) spectroscopy and NMR order parameter analysis. In addition, our results suggest that the structural deformation of the DAGH β-sheet and the AB loop regions may correlate with the manifestation of the aggregation-prone conformational states of TTR. In summary, our method employing MD techniques to extend the structural ensembles from NMR experimental data analysis may provide new opportunities to investigate various transient yet important structural states of amyloidogenic proteins.

Probabilistic Modeling of RNA Ensembles Using NMR Chemical Shifts

NMR-derived chemical shifts are structural fingerprints that are sensitive to the underlying conformational distributions of molecules. Thus, chemical shift data are now routinely used to infer the dynamical or conformational ensembles of peptides and proteins. However, for RNAs, techniques for inferring their conformational ensembles from chemical shift data have received less attention. Here, we used chemical shift data and the Bayesian/maximum entropy (BME) approach to model the secondary structure ensembles of several single-stranded RNAs. Inspection of the resulting ensembles indicates that the secondary structure of the highest weighted (most probable) conformer in the ensemble typically resembled the known NMR structure. Furthermore, using apo chemical shifts measured for the HIV-1 TAR RNA, we found that our framework reproduces the expected structure yet predicts the existence of a previously unobserved base pair, which we speculate may be sampled transiently. We expect that the chemical shift-based BME (CS-BME) framework we describe here should find utility as a general strategy for modeling RNA ensembles using chemical shift data.

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

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

Exploring Curated Conformational Ensembles of Intrinsically Disordered Proteins in the Protein Ensemble Database

The Protein Ensemble Database (PED; https://proteinensemble.org/) is the major repository of conformational ensembles of intrinsically disordered proteins (IDPs). Conformational ensembles of IDPs are primarily provided by their authors or occasionally collected from literature, and are subsequently deposited in PED along with the corresponding structured, manually curated metadata. The modeling of conformational ensembles usually relies on experimental data from small-angle X-ray scattering (SAXS), fluorescence resonance energy transfer (FRET), NMR spectroscopy, and molecular dynamics (MD) simulations, or a combination of these techniques. The growing number of scientific studies based on these data, along with the astounding and swift progress in the field of protein intrinsic disorder, has required a significant update and upgrade of PED, first published in 2014. To this end, the database was entirely renewed in 2020 and now has a dedicated team of biocurators providing manually curated descriptions of the methods and conditions applied to generate the conformational ensembles and for checking consistency of the data. Here, we present a detailed description on how to explore PED with its protein pages and experimental pages, and how to interpret entries of conformational ensembles. We describe how to efficiently search conformational ensembles deposited in PED by means of its web interface and API. We demonstrate how to make sense of the PED protein page and its associated experimental entry pages with reference to the yeast Sic1 use case. © 2021 The Authors. Current Protocols published by Wiley Periodicals LLC. Basic Protocol 1: Performing a search in PED Support Protocol 1: Programmatic access with the PED API Basic Protocol 2: Interpreting the protein page and the experimental entry page-the Sic1 use case Support Protocol 2: Downloading options Support Protocol 3: Understanding the validation report-the Sic1 use case Basic Protocol 3: Submitting new conformational ensembles to PED Basic Protocol 4: Providing feedback in PED.

Physics-based computational and theoretical approaches to intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) are an important class of proteins that do not fold to a well-defined three-dimensional shape but rather adopt an ensemble of inter-converting conformations. This feature makes their experimental characterization challenging and invites a theoretical and computational approach to complement experimental studies. In this review, we highlight the recent progress in developing new computational and theoretical approaches to study the structure and dynamics of monomeric and order higher assemblies of IDPs, with a particular emphasis on their phase separation into protein-rich condensates.

Configurational Entropy of Folded Proteins and Its Importance for Intrinsically Disordered Proteins

Many pairwise additive force fields are in active use for intrinsically disordered proteins (IDPs) and regions (IDRs), some of which modify energetic terms to improve the description of IDPs/IDRs but are largely in disagreement with solution experiments for the disordered states. This work considers a new direction-the connection to configurational entropy-and how it might change the nature of our understanding of protein force field development to equally well encompass globular proteins, IDRs/IDPs, and disorder-to-order transitions. We have evaluated representative pairwise and many-body protein and water force fields against experimental data on representative IDPs and IDRs, a peptide that undergoes a disorder-to-order transition, for seven globular proteins ranging in size from 130 to 266 amino acids. We find that force fields with the largest statistical fluctuations consistent with the radius of gyration and universal Lindemann values for folded states simultaneously better describe IDPs and IDRs and disorder-to-order transitions. Hence, the crux of what a force field should exhibit to well describe IDRs/IDPs is not just the balance between protein and water energetics but the balance between energetic effects and configurational entropy of folded states of globular proteins.

Unfolding bovine α-lactalbumin with T-jump: Characterizing disordered intermediates via time-resolved x-ray solution scattering and molecular dynamics simulations

The protein folding process often proceeds through partially folded transient states. Therefore, a structural understanding of these disordered states is crucial for developing mechanistic models of the folding process. Characterization of unfolded states remains challenging due to their disordered nature, and incorporating multiple methods is necessary. Combining the time-resolved x-ray solution scattering (TRXSS) signal with molecular dynamics (MD), we are able to characterize transient partially folded states of bovine α-lactalbumin, a model system widely used for investigation of molten globule states, during its unfolding triggered by a temperature jump. We track the unfolding process between 20 µs and 70 ms and demonstrate that it passes through three distinct kinetic states. The scattering signals associated with these transient species are then analyzed with TRXSS constrained MD simulations to produce protein structures that are compatible with the input signals. Without utilizing any experimentally extracted kinetic information, the constrained MD simulation successfully drove the protein to an intermediate molten globule state; signals for two later disordered states are refined to terminal unfolded states. From our examination of the structural characteristics of these disordered states, we discuss the implications disordered states have on the folding process, especially on the folding pathway. Finally, we discuss the potential applications and limitations of this method.

Conformational Preferences of an Intrinsically Disordered Protein Domain: A Case Study for Modern Force Fields

Molecular simulations of intrinsically disordered proteins (IDPs) are challenging because they require sampling a very large number of relevant conformations, corresponding to a multitude of shallow minima in a flat free energy landscape. However, in the presence of a binding partner, the free energy landscape of an IDP can be dominated by few deep minima. This characteristic imposes high demands on the accuracy of the force field used to describe the molecular interactions. Here, as a model system for an IDP that is unstructured in solution but folds upon binding to a structured interaction partner, the transactivation domain of c-Myb was studied both in the unbound (free) form and when bound to the KIX domain. Six modern biomolecular force fields were systematically tested and compared in terms of their ability to describe the structural ensemble of the IDP. The protein force field/water model combinations included in this study are AMBER ff99SB-disp with its corresponding water model that was derived from TIP4P-D, CHARMM36m with TIP3P, ff15ipq with SPC/E_b, ff99SB*-ILDNP with TIP3P and TIP4P-D, and FB15 with TIP3P-FB water. Comparing the results from REST2-enhanced sampling simulations with experimental CD spectra and secondary chemical shifts reveals that the ff99SB-disp force field can realistically capture the broad and mildly helical structural ensemble of free c-Myb. The structural ensembles yielded by CHARMM36m, ff99SB*-ILDNP together with TIP4P-D water, and FB15 are also mildly helical; however, each of these force fields can be assigned a specific subset of c-Myb residues for which the simulations could not reproduce the experimental secondary chemical shifts. In addition, microsecond-timescale MD simulations of the KIX/c-Myb complex show that most force fields used preserve a stable helix fold of c-Myb in the complex. Still, all force fields predict a KIX/c-Myb complex interface that differs slightly from the structures provided by NMR because several NOE-derived distances between KIX and c-Myb were exceeded in the simulations. Taken together, the ff99SB-disp force field in the first place but also CHARMM36m, ff99SB*-ILDNP together with TIP4P-D water, and FB15 can be suitable choices for future simulation studies of the coupled folding and binding mechanism of the KIX/c-Myb complex and potentially also other IDPs.

Artificial intelligence techniques for integrative structural biology of intrinsically disordered proteins

We outline recent developments in artificial intelligence (AI) and machine learning (ML) techniques for integrative structural biology of intrinsically disordered proteins (IDP) ensembles. IDPs challenge the traditional protein structure-function paradigm by adapting their conformations in response to specific binding partners leading them to mediate diverse, and often complex cellular functions such as biological signaling, self-organization and compartmentalization. Obtaining mechanistic insights into their function can therefore be challenging for traditional structural determination techniques. Often, scientists have to rely on piecemeal evidence drawn from diverse experimental techniques to characterize their functional mechanisms. Multiscale simulations can help bridge critical knowledge gaps about IDP structure-function relationships-however, these techniques also face challenges in resolving emergent phenomena within IDP conformational ensembles. We posit that scalable statistical inference techniques can effectively integrate information gleaned from multiple experimental techniques as well as from simulations, thus providing access to atomistic details of these emergent phenomena.

Combining Experimental Data and Computational Methods for the Non-Computer Specialist

Experimental methods are indispensable for the study of the function of biological macromolecules, not just as static structures, but as dynamic systems that change conformation, bind partners, perform reactions, and respond to different stimulus. However, providing a detailed structural interpretation of the results is often a very challenging task. While experimental and computational methods are often considered as two different and separate approaches, the power and utility of combining both is undeniable. The integration of the experimental data with computational techniques can assist and enrich the interpretation, providing new detailed molecular understanding of the systems. Here, we briefly describe the basic principles of how experimental data can be combined with computational methods to obtain insights into the molecular mechanism and expand the interpretation through the generation of detailed models.

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

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