Integrating Molecular Simulation and Experimental Data: A Bayesian/Maximum Entropy Reweighting Approach

Conformational dynamics and multi-modal interaction of Paxillin with the Focal Adhesion Targeting Domain

Paxillin (PXN) and focal adhesion kinase (FAK) are two major components of the focal adhesion complex, a multiprotein structure linking the intracellular cytoskeleton to the cell exterior. PXN interacts directly with the C-terminal targeting domain of FAK (FAT) via its intrinsically disordered N-terminal domain. This interaction is necessary and sufficient for localizing FAK to focal adhesions. Furthermore, PXN serves as a platform for recruiting other proteins that together control the dynamic changes needed for cell migration and survival. Here, we show that the PXN disordered region undergoes large-scale conformational restriction upon binding to FAT, forming a 48-kDa multi-modal complex consisting of four major interconverting states. Although the complex is flexible, each state has unique sets of contacts involving disordered regions that are both highly represented in ensembles and conserved. Moreover, conserved intramolecular contacts from glutamine-rich regions in PXN contribute to high entropy and thus stability of the FAT bound complex. As PXN is a hub protein, the results provide a structural basis for understanding how perturbations that lead to cellular network rewiring, such as ligand binding and phosphorylation, may lead to shifts in the multi-state equilibrium and phenotypic switching.

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 time scales 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 nuclear magnetic resonance, 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 protein dynamics is crucial for understanding protein function, yet few methodologies report on protein motion at an atomic level. Combining single molecule Förster resonance energy transfer (smFRET) experiments with computer simulations could provide atomistic models of protein ensembles which are grounded in experiments, however, there has been limited agreement between the two methods to date. Here, we present an algorithm to recapitulate smFRET experiments from molecular dynamics simulations. This approach significantly improves agreement between simulations and experiments for proteins across the ordered spectrum. Moreover, with this approach we can confidently create atomic models for states observed during smFRET experiments which were otherwise difficult to model due to high amounts of flexibility, disorder, or large deviations from crystal-like states.

Determining accurate conformational ensembles of intrinsically disordered proteins at atomic resolution

Determining accurate atomic resolution conformational ensembles of intrinsically disordered proteins (IDPs) is extremely challenging. Molecular dynamics (MD) simulations provide atomistic conformational ensembles of IDPs, but their accuracy is highly dependent on the quality of physical models, or force fields, used. Here, we demonstrate how to determine accurate atomic resolution conformational ensembles of IDPs by integrating all-atom MD simulations with experimental data from nuclear magnetic resonance (NMR) spectroscopy and small-angle x-ray scattering (SAXS) with a simple, robust and fully automated maximum entropy reweighting procedure. We demonstrate that when this approach is applied with sufficient experimental data, IDP ensembles derived from different MD force fields converge to highly similar conformational distributions. The maximum entropy reweighting procedure presented here facilitates the integration of MD simulations with extensive experimental datasets and enables the calculation of accurate, force-field independent atomic resolution conformational ensembles of IDPs.

Integration of Hydrogen-Deuterium Exchange Mass Spectrometry with Molecular Dynamics Simulations and Ensemble Reweighting Enables High Resolution Protein-Ligand Modeling

Hydrogen-Deuterium exchange mass spectrometry's (HDX-MS) utility in identifying and characterizing protein-small molecule interaction sites has been established. The regions that are seen to be protected from exchange upon ligand binding indicate regions that may be interacting with the ligand, giving a qualitative understanding of the ligand binding pocket. However, quantitatively deriving an accurate high-resolution structure of the protein-ligand complex from the HDX-MS data remains a challenge, often limiting its use in applications such as small molecule drug design. Recent efforts have focused on the development of methods to quantitatively model Hydrogen-Deuterium exchange (HDX) data from computationally modeled structures to garner atomic level insights from peptide-level resolution HDX-MS. One such method, HDX ensemble reweighting (HDXer), employs maximum entropy reweighting of simulated HDX data to experimental HDX-MS to model structural ensembles. In this study, we implement and validate a workflow which quantitatively leverages HDX-MS data to accurately model protein-small molecule ligand interactions. To that end, we employ a strategy combining computational protein-ligand docking, molecular dynamics simulations, HDXer, and dimensional reduction and clustering approaches to extract high-resolution drug binding poses that most accurately conform with HDX-MS data. We apply this workflow to model the interaction of ERK2 and FosA with small molecule compounds and inhibitors they are known to bind. In five out of six of the protein-ligand pairs tested, the HDX derived protein-ligand complexes result in a ligand root-mean-square deviation (RMSD) within 2.5 Å of the known crystal structure ligand.

An integrative characterization of proline cis and trans conformers in a disordered peptide

Intrinsically disordered proteins (IDPs) often contain proline residues that undergo cis/trans isomerization. While molecular dynamics (MD) simulations have the potential to fully characterize the proline cis and trans subensembles, they are limited by the slow timescales of isomerization and force field inaccuracies. NMR spectroscopy can report on ensemble-averaged observables for both the cis-proline and trans-proline states, but a full atomistic characterization of these conformers is challenging. Given the importance of proline cis/trans isomerization for influencing the conformational sampling of disordered proteins, we employed a combination of all-atom MD simulations with enhanced sampling (metadynamics), NMR, and small-angle x-ray scattering (SAXS) to characterize the two subensembles of the ORF6 C-terminal region (ORF6CTR) from SARS-CoV-2 corresponding to the proline-57 (P57) cis and trans states. We performed MD simulations in three distinct force fields: AMBER03ws, AMBER99SB-disp, and CHARMM36m, which are all optimized for disordered proteins. Each simulation was run for an accumulated time of 180-220 μs until convergence was reached, as assessed by blocking analysis. A good agreement between the cis-P57 populations predicted from metadynamic simulations in AMBER03ws was observed with populations obtained from experimental NMR data. Moreover, we observed good agreement between the radius of gyration predicted from the metadynamic simulations in AMBER03ws and that measured using SAXS. Our findings suggest that both the cis-P57 and trans-P57 conformations of ORF6CTR are extremely dynamic and that interdisciplinary approaches combining both multiscale computations and experiments offer avenues to explore highly dynamic states that cannot be reliably characterized by either approach in isolation.

MELD-Adapt: On-the-Fly Belief Updating in Integrative Molecular Dynamics

Integrative structural biology synergizes experimental data with computational methods to elucidate the structures and interactions within biomolecules, a task that becomes critical in the absence of high-resolution structural data. A challenging step for integrating the data is knowing the expected accuracy or belief in the dataset. We previously showed that the Modeling Employing Limited Data (MELD) approach succeeds at predicting structures and finding the best interpretation of the data when the initial belief is equal to or slightly lower than the real value. However, the initial belief might be unknown to the user, as it depends on both the technique and the system of study. Here we introduce MELD-Adapt, designed to dynamically evaluate and infer the reliability of input data while at the same time finding the best interpretation of the data and the structures compatible with it. We demonstrate the utility of this method across different systems, particularly emphasizing its capability to correct initial assumptions and identify the correct fraction of data to produce reliable structural models. The approach is tested with two benchmark sets: the folding of 12 proteins with coarse physical insights and the binding of peptides with varying affinities to the extraterminal domain using chemical shift perturbation data. We find that subtle differences in data structure (e.g., locally clustered or globally distributed), starting belief, and force field preferences can have an impact on the predictions, limiting the possibility of a transferable protocol across all systems and data types. Nonetheless, we find a wide range of initial setup conditions that will lead to successful sampling and identification of native states, leading to a robust pipeline. Furthermore, disagreements about how much data is enforced and satisfied rapidly serve to identify incorrect setup conditions.

Evolution of the conformational dynamics of the molecular chaperone Hsp90

Hsp90 is a molecular chaperone of central importance for protein homeostasis in the cytosol of eukaryotic cells, with key functional and structural traits conserved from yeast to man. During evolution, Hsp90 has gained additional functional importance, leading to an increased number of interacting co-chaperones and client proteins. Here, we show that the overall conformational transitions coupled to the ATPase cycle of Hsp90 are conserved from yeast to humans, but cycle timing as well as the dynamics are significantly altered. In contrast to yeast Hsp90, the human Hsp90 is characterized by broad ensembles of conformational states, irrespective of the absence or presence of ATP. The differences in the ATPase rate and conformational transitions between yeast and human Hsp90 are based on two residues in otherwise conserved structural elements that are involved in triggering structural changes in response to ATP binding. The exchange of these two mutations allows swapping of the ATPase rate and of the conformational transitions between human and yeast Hsp90. Our combined results show that Hsp90 evolved to a protein with increased conformational dynamics that populates ensembles of different states with strong preferences for the N-terminally open, client-accepting states.

The ribosome lowers the entropic penalty of protein folding

Most proteins fold during biosynthesis on the ribosome1, and co-translational folding energetics, pathways and outcomes of many proteins have been found to differ considerably from those in refolding studies2-10. The origin of this folding modulation by the ribosome has remained unknown. Here we have determined atomistic structures of the unfolded state of a model protein on and off the ribosome, which reveal that the ribosome structurally expands the unfolded nascent chain and increases its solvation, resulting in its entropic destabilization relative to the peptide chain in isolation. Quantitative 19F NMR experiments confirm that this destabilization reduces the entropic penalty of folding by up to 30 kcal mol-1 and promotes formation of partially folded intermediates on the ribosome, an observation that extends to other protein domains and is obligate for some proteins to acquire their active conformation. The thermodynamic effects also contribute to the ribosome protecting the nascent chain from mutation-induced unfolding, which suggests a crucial role of the ribosome in supporting protein evolution. By correlating nascent chain structure and dynamics to their folding energetics and post-translational outcomes, our findings establish the physical basis of the distinct thermodynamics of co-translational protein folding.

Are Protein Conformational Ensembles in Agreement with Experimental Data? A Geometrical Interpretation of the Problem

The conformational variability of biological macromolecules can play an important role in their biological function. Therefore, understanding conformational variability is expected to be key for predicting the behavior of a particular molecule in the context of organism-wide studies. Several experimental methods have been developed and deployed for accessing this information, and computational methods are continuously updated for the profitable integration of different experimental sources. The outcome of this endeavor is conformational ensembles, which may vary significantly in properties and composition when different ensemble reconstruction methods are used, and this raises the issue of comparing the predicted ensembles against experimental data. In this article, we discuss a geometrical formulation to provide a framework for understanding the agreement of an ensemble prediction to the experimental observations.

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.

Labile assembly of a tardigrade protein induces biostasis

Tardigrades are microscopic animals that survive desiccation by inducing biostasis. To survive drying tardigrades rely on intrinsically disordered CAHS proteins, which also function to prevent perturbations induced by drying in vitro and in heterologous systems. CAHS proteins have been shown to form gels both in vitro and in vivo, which has been speculated to be linked to their protective capacity. However, the sequence features and mechanisms underlying gel formation and the necessity of gelation for protection have not been demonstrated. Here we report a mechanism of fibrillization and gelation for CAHS D similar to that of intermediate filament assembly. We show that in vitro, gelation restricts molecular motion, immobilizing and protecting labile material from the harmful effects of drying. In vivo, we observe that CAHS D forms fibrillar networks during osmotic stress. Fibrillar networking of CAHS D improves survival of osmotically shocked cells. We observe two emergent properties associated with fibrillization; (i) prevention of cell volume change and (ii) reduction of metabolic activity during osmotic shock. We find that there is no significant correlation between maintenance of cell volume and survival, while there is a significant correlation between reduced metabolism and survival. Importantly, CAHS D's fibrillar network formation is reversible and metabolic rates return to control levels after CAHS fibers are resolved. This work provides insights into how tardigrades induce reversible biostasis through the self-assembly of labile CAHS gels.

Hierarchical Assembly of Single-Stranded RNA

Single-stranded RNA (ssRNA) plays a major role in the flow of genetic information-most notably, in the form of messenger RNA (mRNA)-and in the regulation of biological processes. The highly dynamic nature of chains of unpaired nucleobases challenges structural characterizations of ssRNA by experiments or molecular dynamics (MD) simulations alike. Here, we use hierarchical chain growth (HCG) to construct ensembles of ssRNA chains. HCG assembles the structures of protein and nucleic acid chains from fragment libraries created by MD simulations. Applied to homo- and heteropolymeric ssRNAs of different lengths, we find that HCG produces structural ensembles that overall are in good agreement with diverse experiments, including nuclear magnetic resonance (NMR), small-angle X-ray scattering (SAXS), and single-molecule Förster resonance energy transfer (FRET). The agreement can be further improved by ensemble refinement using Bayesian inference of ensembles (BioEn). HCG can also be used to assemble RNA structures that combine base-paired and base-unpaired regions, as illustrated for the 5' untranslated region (UTR) of SARS-CoV-2 RNA.

The molecular basis for cellular function of intrinsically disordered protein regions

Intrinsically disordered protein regions exist in a collection of dynamic interconverting conformations that lack a stable 3D structure. These regions are structurally heterogeneous, ubiquitous and found across all kingdoms of life. Despite the absence of a defined 3D structure, disordered regions are essential for cellular processes ranging from transcriptional control and cell signalling to subcellular organization. Through their conformational malleability and adaptability, disordered regions extend the repertoire of macromolecular interactions and are readily tunable by their structural and chemical context, making them ideal responders to regulatory cues. Recent work has led to major advances in understanding the link between protein sequence and conformational behaviour in disordered regions, yet the link between sequence and molecular function is less well defined. Here we consider the biochemical and biophysical foundations that underlie how and why disordered regions can engage in productive cellular functions, provide examples of emerging concepts and discuss how protein disorder contributes to intracellular information processing and regulation of cellular function.

Recovery from desensitization in GluA2 AMPA receptors is affected by a single mutation in the N-terminal domain interface

AMPA-type ionotropic glutamate receptors (AMPARs) are central to various neurological processes, including memory and learning. They assemble as homo- or heterotetramers of GluA1, GluA2, GluA3, and GluA4 subunits, each consisting of an N-terminal domain (NTD), a ligand-binding domain, a transmembrane domain, and a C-terminal domain. While AMPAR gating is primarily controlled by reconfiguration in the ligand-binding domain layer, our study focuses on the NTDs, which also influence gating, yet the underlying mechanism remains enigmatic. In this investigation, we employ molecular dynamics simulations to evaluate the NTD interface strength in GluA1, GluA2, and NTD mutants GluA2-H229N and GluA1-N222H. Our findings reveal that GluA1 has a significantly weaker NTD interface than GluA2. The NTD interface of GluA2 can be weakened by a single point mutation in the NTD dimer-of-dimer interface, namely H229N, which renders GluA2 more GluA1-like. Electrophysiology recordings demonstrate that this mutation also leads to slower recovery from desensitization. Moreover, we observe that lowering the pH induces more splayed NTD states and enhances desensitization in GluA2. We hypothesized that H229 was responsible for this pH sensitivity; however, GluA2-H229N was also affected by pH, meaning that H229 is not solely responsible and that protons exert their effect across multiple domains of the AMPAR. In summary, our work unveils an allosteric connection between the NTD interface strength and AMPAR desensitization.

Boosting Ensemble Refinement with Transferable Force-Field Corrections: Synergistic Optimization for Molecular Simulations

A novel method combining the force-field fitting approach and ensemble refinement by the maximum entropy principle is presented. Its formulation allows us to continuously interpolate between these two methods, which can thus be interpreted as two limiting cases. A cross-validation procedure enables us to correctly assess the relative weight of both of them, distinguishing scenarios in which the combined approach is meaningful from those in which either ensemble refinement or force-field fitting separately prevails. The efficacy of their combination is examined for a realistic case study of RNA oligomers. Within the new scheme, molecular dynamics simulations are integrated with experimental data provided by nuclear magnetic resonance measures. We show that force-field corrections are in general superior when applied to the appropriate force-field terms but are automatically discarded by the method when applied to inappropriate force-field terms.

Bonds and bytes: The odyssey of structural biology

Characterizing structural and dynamic properties of proteins and large macromolecular assemblies is crucial to understand the molecular mechanisms underlying biological functions. In the field of structural biology, no single method comprehensively reveals the behavior of biological systems across various spatiotemporal scales. Instead, we have a versatile toolkit of techniques, each contributing a piece to the overall puzzle. Integrative structural biology combines different techniques to create accurate and precise multi-scale models that expand our understanding of complex biological systems. This review outlines recent advancements in computational and experimental methods in structural biology, with special focus on recent Artificial Intelligence techniques, emphasizes integrative approaches that combine different types of data for precise spatiotemporal modeling, and provides an outlook into future directions of this field.

Exploring the impact of alignment media on RDC analysis of phosphorus-containing compounds: a molecular docking approach

Residual dipolar couplings (RDCs) are employed in NMR analysis when conventional methods, such as J-couplings and nuclear Overhauser effects (NOEs) fail. Low-energy (optimized) conformers are often used as input structures in RDC analysis programs. However, these low-energy structures do not necessarily resemble conformations found in anisotropic environments due to interactions with the alignment medium, especially if the analyte molecules are flexible. Considering interactions with alignment media in RDC analysis, we developed and evaluated a molecular docking-based approach to generate more accurate conformer ensembles for compounds in the presence of the poly-γ-benzyl-L-glutamate alignment medium. We designed chiral phosphorus-containing compounds that enabled us to utilize 31P NMR parameters for the stereochemical analysis. Using P3D/PALES software to evaluate diastereomer discrimination, we found that our conformer ensembles outperform moderately the standard, low-energy conformers in RDC analysis. To further improve our results, we (i) averaged the experimental values of the molecular docking-based conformers by applying the Boltzmann distribution and (ii) optimized the structures through normal mode relaxation, thereby enhancing the Pearson correlation factor R and even diastereomer discrimination in some cases. Nevertheless, we presume that significant differences between J-couplings in isotropic and in anisotropic environments may preclude RDC measurements for flexible molecules. Therefore, generating conformer ensembles based on molecular docking enhances RDC analysis for mildly flexible systems while flexible molecules may require applying more advanced approaches, in particular approaches including dynamical effects.

Atomistic molecular simulations of Aβ-Zn conformational ensembles

The amyloid-forming Aβ peptide is able to interact with metal cations to form very stable complexes that influence fibril formation and contribute to the onset of Alzheimer's disease. Multiple structures of peptides derived from Aβ in complex with different metals have been resolved experimentally to provide an atomic-level description of the metal-protein interactions. However, Aβ is intrinsically disordered, and hence more amenable to an ensemble description. Molecular dynamics simulations can now reach the timescales needed to generate ensembles for these type of complexes. However, this requires accurate force fields both for the protein and the protein-metal interactions. Here we use state-of-the-art methods to generate force field parameters for the Zn(II) cations in a set of complexes formed by different Aβ variants and combine them with the Amber99SB*-ILDN optimized force field. Upon comparison of NMR experiments with the simulation results, further optimized with a Bayesian/Maximum entropy approach, we provide an accurate description of the molecular ensembles for most Aβ-metal complexes. We find that the resulting conformational ensembles are more heterogeneous than the NMR models deposited in the Protein Data Bank.

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/).

Driving forces behind phase separation of the carboxy-terminal domain of RNA polymerase II

Eukaryotic gene regulation and pre-mRNA transcription depend on the carboxy-terminal domain (CTD) of RNA polymerase (Pol) II. Due to its highly repetitive, intrinsically disordered sequence, the CTD enables clustering and phase separation of Pol II. The molecular interactions that drive CTD phase separation and Pol II clustering are unclear. Here, we show that multivalent interactions involving tyrosine impart temperature- and concentration-dependent self-coacervation of the CTD. NMR spectroscopy, molecular ensemble calculations and all-atom molecular dynamics simulations demonstrate the presence of diverse tyrosine-engaging interactions, including tyrosine-proline contacts, in condensed states of human CTD and other low-complexity proteins. We further show that the network of multivalent interactions involving tyrosine is responsible for the co-recruitment of the human Mediator complex and CTD during phase separation. Our work advances the understanding of the driving forces of CTD phase separation and thus provides the basis to better understand CTD-mediated Pol II clustering in eukaryotic gene transcription.

Architecture of the MKK6-p38α complex defines the basis of MAPK specificity and activation

The mitogen-activated protein kinase (MAPK) p38α is a central component of signaling in inflammation and the immune response and is, therefore, an important drug target. Little is known about the molecular mechanism of its activation by double phosphorylation from MAPK kinases (MAP2Ks), because of the challenge of trapping a transient and dynamic heterokinase complex. We applied a multidisciplinary approach to generate a structural model of p38α in complex with its MAP2K, MKK6, and to understand the activation mechanism. Integrating cryo-electron microscopy with molecular dynamics simulations, hydrogen-deuterium exchange mass spectrometry, and experiments in cells, we demonstrate a dynamic, multistep phosphorylation mechanism, identify catalytically relevant interactions, and show that MAP2K-disordered amino termini determine pathway specificity. Our work captures a fundamental step of cell signaling: a kinase phosphorylating its downstream target kinase.

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.

SANS Spectra with PLUMED: Implementation and Application to Metainference

Using small-angle scattering with either X-ray or neutron sources has become common in the investigation of soft-matter systems. These experiments provide information about the coarse shape of the scattered objects, but obtaining more-detailed information can usually only be achieved with the aid of molecular simulations. In this Application Note, we report the implementation of an extension in PLUMED to compute the small-angle neutron scattering (SANS), which can be used for data processing as well for enhanced sampling, in particular with the metainference method to bias simulations and sample structures with a resulting spectrum in agreement with an experimental reference. Our implementation includes a resolution function that can be used to smear the SANS intensities according to beamline error sources and is compatible with both all-atom and coarse-grained simulations. Scripts to aid in the calculation of the scattering lengths when the system is coarse-grained and to aid in preparing the inputs are provided. We illustrate the use of the implementation with metainference by performing coarse-grained simulations of beta-octylglucoside and dodecylphosphocholine micelles in water. With different software and different Hamiltonians, we show that the metainference SANS bias can drive micelles to be split and to change shapes to achieve a better agreement with the experimental reference.

Hybrid computational methods combining experimental information with molecular dynamics

A goal of structural biology is to understand how macromolecules carry out their biological roles by identifying their metastable states, mechanisms of action, pathways leading to conformational changes, and the thermodynamic and kinetic relationships between those states. Integrative modeling brings structural insights into systems where traditional structure determination approaches cannot help. We focus on the synergies and challenges of integrative modeling combining experimental data with molecular dynamics simulations.

Local Disordered Region Sampling (LDRS) for Ensemble Modeling of Proteins with Experimentally Undetermined or Low Confidence Prediction Segments

The Local Disordered Region Sampling (LDRS, pronounced loaders) tool, developed for the IDPConformerGenerator platform (Teixeira et al. 2022), provides a method for generating all-atom conformations of intrinsically disordered regions (IDRs) 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 structure 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 (MC-SCE) (Bhowmick and Head-Gordon 2015), transmembrane proteins within an all-atom bilayer, and multi-chain complexes. The modeling capacity of LDRS capitalizes on the modularity, ability to be used as a library and via command-line, and computational speed of the IDPConformerGenerator platform.

Clustering Heterogeneous Conformational Ensembles of Intrinsically Disordered Proteins with t-Distributed Stochastic Neighbor Embedding

Intrinsically disordered proteins (IDPs) populate a range of conformations that are best described by a heterogeneous ensemble. Grouping an IDP ensemble into "structurally similar" clusters for visualization, interpretation, and analysis purposes is a much-desired but formidable task, as the conformational space of IDPs is inherently high-dimensional and reduction techniques often result in ambiguous classifications. Here, we employ the t-distributed stochastic neighbor embedding (t-SNE) technique to generate homogeneous clusters of IDP conformations from the full heterogeneous ensemble. We illustrate the utility of t-SNE by clustering conformations of two disordered proteins, Aβ42, and α-synuclein, in their APO states and when bound to small molecule ligands. Our results shed light on ordered substates within disordered ensembles and provide structural and mechanistic insights into binding modes that confer specificity and affinity in IDP ligand binding. t-SNE projections preserve the local neighborhood information, provide interpretable visualizations of the conformational heterogeneity within each ensemble, and enable the quantification of cluster populations and their relative shifts upon ligand binding. Our approach provides a new framework for detailed investigations of the thermodynamics and kinetics of IDP ligand binding and will aid rational drug design for IDPs.

Integrated NMR/Molecular Dynamics Determination of the Ensemble Conformation of a Thermodynamically Stable CUUG RNA Tetraloop

Both experimental and theoretical structure determinations of RNAs have remained challenging due to the intrinsic dynamics of RNAs. We report here an integrated nuclear magnetic resonance/molecular dynamics (NMR/MD) structure determination approach to describe the dynamic structure of the CUUG tetraloop. We show that the tetraloop undergoes substantial dynamics, leading to averaging of the experimental data. These dynamics are particularly linked to the temperature-dependent presence of a hydrogen bond within the tetraloop. Interpreting the NMR data by a single structure represents the low-temperature structure well but fails to capture all conformational states occurring at a higher temperature. We integrate MD simulations, starting from structures of CUUG tetraloops within the Protein Data Bank, with an extensive set of NMR data, and provide a structural ensemble that describes the dynamic nature of the tetraloop and the experimental NMR data well. We thus show that one of the most stable and frequently found RNA tetraloops displays substantial dynamics, warranting such an integrated structural approach.

Combining Experiments and Simulations to Examine the Temperature-Dependent Behavior of a Disordered Protein

Intrinsically disordered proteins are a class of proteins that lack stable folded conformations and instead adopt a range of conformations that determine their biochemical functions. The temperature-dependent behavior of such disordered proteins is complex and can vary depending on the specific protein and environment. Here, we have used molecular dynamics simulations and previously published experimental data to investigate the temperature-dependent behavior of histatin 5, a 24-residue-long polypeptide. We examined the hypothesis that histatin 5 undergoes a loss of polyproline II (PPII) structure with increasing temperature, leading to more compact conformations. We found that the conformational ensembles generated by the simulations generally agree with small-angle X-ray scattering data for histatin 5, but show some discrepancies with the hydrodynamic radius as probed by pulsed-field gradient NMR spectroscopy, and with the secondary structure information derived from circular dichroism. We attempted to reconcile these differences by reweighting the conformational ensembles against the scattering and NMR data. By doing so, we were in part able to capture the temperature-dependent behavior of histatin 5 and to link the observed decrease in hydrodynamic radius with increasing temperature to a loss of PPII structure. We were, however, unable to achieve agreement with both the scattering and NMR data within experimental errors. We discuss different possible reasons for this including inaccuracies in the force field, differences in conditions of the NMR and scattering experiments, and issues related to the calculation of the hydrodynamic radius from conformational ensembles. Our study highlights the importance of integrating multiple types of experimental data when modeling conformational ensembles of disordered proteins and how environmental factors such as the temperature influence them.

Generation of unfolded outer membrane protein ensembles defined by hydrodynamic properties

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

BICePs v2.0: Software for Ensemble Reweighting Using Bayesian Inference of Conformational Populations

Bayesian Inference of Conformational Populations (BICePs) version 2.0 (v2.0) is a free, open-source Python package that reweights theoretical predictions of conformational state populations using sparse and/or noisy experimental measurements. In this article, we describe the implementation and usage of the latest version of BICePs (v2.0), a powerful, user-friendly and extensible package which makes several improvements upon the previous version. The algorithm now supports many experimental NMR observables (NOE distances, chemical shifts, J-coupling constants, and hydrogen-deuterium exchange protection factors), and enables convenient data preparation and processing. BICePs v2.0 can perform automatic analysis of the sampled posterior, including visualization, and evaluation of statistical significance and sampling convergence. We provide specific coding examples for these topics, and present a detailed example illustrating how to use BICePs v2.0 to reweight a theoretical ensemble using experimental measurements.

Effective Molecular Dynamics from Neural Network-Based Structure Prediction Models

Recent breakthroughs in neural network-based structure prediction methods, such as AlphaFold2 and RoseTTAFold, have dramatically improved the quality of computational protein structure prediction. These models also provide statistical confidence scores that can estimate uncertainties in the predicted structures, but it remains unclear to what extent these scores are related to the intrinsic conformational dynamics of proteins. Here, we compare AlphaFold2 prediction scores with explicit large-scale molecular dynamics simulations of 28 one- and two-domain proteins with varying degrees of flexibility. We demonstrate a strong correlation between the statistical prediction scores and the explicit motion derived from extensive atomistic molecular dynamics simulations and further derive an elastic network model based on the statistical scores of AlphFold2 (AF-ENM), which we benchmark in combination with coarse-grained molecular dynamics simulations. We show that our AF-ENM method reproduces the global protein dynamics with improved accuracy, providing a powerful way to derive effective molecular dynamics using neural network-based structure prediction models.

Conformational and oligomeric states of SPOP from small-angle X-ray scattering and molecular dynamics simulations

Speckle-type POZ protein (SPOP) is a substrate adaptor in the ubiquitin proteasome system, and plays important roles in cell-cycle control, development, and cancer pathogenesis. SPOP forms linear higher-order oligomers following an isodesmic self-association model. Oligomerization is essential for SPOP's multivalent interactions with substrates, which facilitate phase separation and localization to biomolecular condensates. Structural characterization of SPOP in its oligomeric state and in solution is, however, challenging due to the inherent conformational and compositional heterogeneity of the oligomeric species. Here, we develop an approach to simultaneously and self-consistently characterize the conformational ensemble and the distribution of oligomeric states of SPOP by combining small-angle X-ray scattering (SAXS) and molecular dynamics (MD) simulations. We build initial conformational ensembles of SPOP oligomers using coarse-grained molecular dynamics simulations, and use a Bayesian/maximum entropy approach to refine the ensembles, along with the distribution of oligomeric states, against a concentration series of SAXS experiments. Our results suggest that SPOP oligomers behave as rigid, helical structures in solution, and that a flexible linker region allows SPOP's substrate-binding domains to extend away from the core of the oligomers. Additionally, our results are in good agreement with previous characterization of the isodesmic self-association of SPOP. In the future, the approach presented here can be extended to other systems to simultaneously characterize structural heterogeneity and self-assembly.

NMR Studies of Aromatic Ring Flips to Probe Conformational Fluctuations in Proteins

Aromatic residues form a significant part of the protein core, where they make tight interactions with multiple surrounding side chains. Despite the dense packing of internal side chains, the aromatic rings of phenylalanine and tyrosine residues undergo 180° rotations, or flips, which are mediated by transient and large-scale "breathing" motions that generate sufficient void volume around the aromatic ring. Forty years after the seminal work by Wagner and Wüthrich, NMR studies of aromatic ring flips are now undergoing a renaissance as a powerful means of probing fundamental dynamic properties of proteins. Recent developments of improved NMR methods and isotope labeling schemes have enabled a number of advances in addressing the mechanisms and energetics of aromatic ring flips. The nature of the transition states associated with ring flips can be described by thermodynamic activation parameters, including the activation enthalpy, activation entropy, activation volume, and also the isothermal volume compressibility of activation. Consequently, it is of great interest to study how ring flip rate constants and activation parameters might vary with protein structure and external conditions like temperature and pressure. The field is beginning to gather such data for aromatic residues in a variety of environments, ranging from surface exposed to buried. In the future, the combination of solution and solid-state NMR spectroscopy together with molecular dynamics simulations and other computational approaches is likely to provide detailed information about the coupled dynamics of aromatic rings and neighboring residues. In this Perspective, we highlight recent developments and provide an outlook toward the future.

Improvements and new functionalities of UNRES server for coarse-grained modeling of protein structure, dynamics, and interactions

In this paper we report the improvements and extensions of the UNRES server (https://unres-server.chem.ug.edu.pl) for physics-based simulations with the coarse-grained UNRES model of polypeptide chains. The improvements include the replacement of the old code with the recently optimized one and adding the recent scale-consistent variant of the UNRES force field, which performs better in the modeling of proteins with the β and the α+β structures. The scope of applications of the package was extended to data-assisted simulations with restraints from nuclear magnetic resonance (NMR) and chemical crosslink mass-spectroscopy (XL-MS) measurements. NMR restraints can be input in the NMR Exchange Format (NEF), which has become a standard. Ambiguous NMR restraints are handled without expert intervention owing to a specially designed penalty function. The server can be used to run smaller jobs directly or to prepare input data to run larger production jobs by using standalone installations of UNRES.

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.

Conformer Weighting and Differently Sized Cluster Weighting for Nicotine and Its Phosphorus Derivatives

Weighting methods applied to systems with many conformers have been broadly employed to calculate thermodynamic properties, structural characteristics, and populations. To better understand and test the sensitivity of conventional weighting methods, the conformational distributions of nicotine and its phosphorus-substituted derivatives are investigated. The weighting schemes used for this are all based on Boltzmann statistics. Classical Boltzmann factors based on the electronic energy and the Gibbs free energy are calculated at different quantum chemical levels of theory and compared to cluster weights obtained by the quantum cluster equilibrium method. Furthermore, the influence of the modified rigid-rotor-harmonic-oscillator (mRRHO) approximation on the cluster weights is investigated. The substitution of the nitrogen atom in the methylpyrrolidine ring by a phosphorus atom results in more monomer conformers and clusters being populated. The conformational distribution of the monomers remained stable at different levels of theory and weighting methods. However, going to dimers and trimers, we observe a significant influence of the level of theory, weighting method, and mRRHO cutoff on the populations of these clusters. We show that mRRHO cutoff values of 50 and 100 cm^-1 yield similar results, which is why 50 cm^-1 is recommended as a robust choice. Furthermore, we observe that the global minimum for ΔE₀ and ΔG varies in a few cases and that the global minimum is not always the dominantly occupied structure.

Characterisation of HOIP RBR E3 ligase conformational dynamics using integrative modelling

Multidomain proteins composed of individual domains connected by flexible linkers pose a challenge for structural studies due to their intrinsic conformational dynamics. Integrated modelling approaches provide a means to characterise protein flexibility by combining experimental measurements with molecular simulations. In this study, we characterise the conformational dynamics of the catalytic RBR domain of the E3 ubiquitin ligase HOIP, which regulates immune and inflammatory signalling pathways. Specifically, we combine small angle X-ray scattering experiments and molecular dynamics simulations to generate weighted conformational ensembles of the HOIP RBR domain using two different approaches based on maximum parsimony and maximum entropy principles. Both methods provide optimised ensembles that are instrumental in rationalising observed differences between SAXS-based solution studies and available crystal structures and highlight the importance of interdomain linker flexibility.

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.

Conformational heterogeneity of UCAAUC RNA oligonucleotide from molecular dynamics simulations, SAXS, and NMR experiments

We describe the conformational ensemble of the single-stranded r(UCAAUC) oligonucleotide obtained using extensive molecular dynamics (MD) simulations and Rosetta's FARFAR2 algorithm. The conformations observed in MD consist of A-form-like structures and variations thereof. These structures are not present in the pool generated using FARFAR2. By comparing with available nuclear magnetic resonance (NMR) measurements, we show that the presence of both A-form-like and other extended conformations is necessary to quantitatively explain experimental data. To further validate our results, we measure solution X-ray scattering (SAXS) data on the RNA hexamer and find that simulations result in more compact structures than observed from these experiments. The integration of simulations with NMR via a maximum entropy approach shows that small modifications to the MD ensemble lead to an improved description of the conformational ensemble. Nevertheless, we identify persisting discrepancies in matching experimental SAXS data.

Extended conformational states dominate the Hsp90 chaperone dynamics

The heat shock protein 90 (Hsp90) is a molecular chaperone central to client protein folding and maturation in eukaryotic cells. During its chaperone cycle, Hsp90 undergoes ATPase-coupled large-scale conformational changes between open and closed states, where the N-terminal and middle domains of the protein form a compact dimerized conformation. However, the molecular principles of the switching motion between the open and closed states remain poorly understood. Here we show by integrating atomistic and coarse-grained molecular simulations with small-angle X-ray scattering experiments and NMR spectroscopy data that Hsp90 exhibits rich conformational dynamics modulated by the charged linker, which connects the N-terminal with the middle domain of the protein. We show that the dissociation of these domains is crucial for the conformational flexibility of the open state, with the separation distance controlled by a β-sheet motif next to the linker region. Taken together, our results suggest that the conformational ensemble of Hsp90 comprises highly extended states, which could be functionally crucial for client processing.

Using Unassigned NMR Chemical Shifts to Model RNA Secondary Structure

NMR-derived chemical shifts are sensitive probes of RNA structure. However, the need to assign NMR spectra hampers their utility as a direct source of structural information. In this report, we describe a simple method that uses unassigned 2D NMR spectra to model the secondary structure of RNAs. As in the case of assigned chemical shifts, we could use unassigned chemical shift data to reweight conformational libraries such that the highest weighted structure closely resembles their reference NMR structure. Furthermore, the application of our approach to the 3'- and 5'-UTR of the SARS-CoV-2 genome yields structures that are, for the most part, consistent with the secondary structure models derived from chemical probing data. Therefore, we expect the framework we describe here will be useful as a general strategy for rapidly generating preliminary structural RNA models directly from unassigned 2D NMR spectra. As we demonstrated for the 337-nt and 472-nt UTRs of SARS-CoV-2, our approach could be especially valuable for modeling the secondary structures of large RNA.

Simulation-based inference with approximately correct parameters via maximum entropy

Inferring the input parameters of simulators from observations is a crucial challenge with applications from epidemiology to molecular dynamics. Here we show a simple approach in the regime of sparse data and approximately correct models, which is common when trying to use an existing model to infer latent variables with observed data. This approach is based on the principle of maximum entropy (MaxEnt) and provably makes the smallest change in the latent joint distribution to fit new data. This method requires no likelihood or model derivatives and its fit is insensitive to prior strength, removing the need to balance observed data fit with prior belief. The method requires the ansatz that data is fit in expectation, which is true in some settings and may be reasonable in all settings with few data points. The method is based on sample reweighting, so its asymptotic run time is independent of prior distribution dimension. We demonstrate this MaxEnt approach and compare with other likelihood-free inference methods across three systems: a point particle moving in a gravitational field, a compartmental model of epidemic spread and molecular dynamics simulation of a protein.

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.

Mg2+-dependent conformational equilibria in CorA and an integrated view on transport regulation

The CorA family of proteins regulates the homeostasis of divalent metal ions in many bacteria, archaea, and eukaryotic mitochondria, making it an important target in the investigation of the mechanisms of transport and its functional regulation. Although numerous structures of open and closed channels are now available for the CorA family, the mechanism of the transport regulation remains elusive. Here, we investigated the conformational distribution and associated dynamic behaviour of the pentameric Mg²⁺ channel CorA at room temperature using small-angle neutron scattering (SANS) in combination with molecular dynamics (MD) simulations and solid-state nuclear magnetic resonance spectroscopy (NMR). We find that neither the Mg²⁺-bound closed structure nor the Mg²⁺-free open forms are sufficient to explain the average conformation of CorA. Our data support the presence of conformational equilibria between multiple states, and we further find a variation in the behaviour of the backbone dynamics with and without Mg²⁺. We propose that CorA must be in a dynamic equilibrium between different non-conducting states, both symmetric and asymmetric, regardless of bound Mg²⁺ but that conducting states become more populated in Mg²⁺-free conditions. These properties are regulated by backbone dynamics and are key to understanding the functional regulation of CorA.

Conformational ensembles of intrinsically disordered proteins and flexible multidomain proteins

Intrinsically disordered proteins (IDPs) and multidomain proteins with flexible linkers show a high level of structural heterogeneity and are best described by ensembles consisting of multiple conformations with associated thermodynamic weights. Determining conformational ensembles usually involves the integration of biophysical experiments and computational models. In this review, we discuss current approaches to determine conformational ensembles of IDPs and multidomain proteins, including the choice of biophysical experiments, computational models used to sample protein conformations, models to calculate experimental observables from protein structure, and methods to refine ensembles against experimental data. We also provide examples of recent applications of integrative conformational ensemble determination to study IDPs and multidomain proteins and suggest future directions for research in the field.

Characterizing conformational ensembles of multi-domain proteins using anisotropic paramagnetic NMR restraints

It has been over two decades since paramagnetic NMR started to form part of the essential techniques for structural analysis of proteins under physiological conditions. Paramagnetic NMR has significantly expanded our understanding of the inherent flexibility of proteins, in particular, those that are formed by combinations of two or more domains. Here, we present a brief overview of techniques to characterize conformational ensembles of such multi-domain proteins using paramagnetic NMR restraints produced through anisotropic metals, with a focus on the basics of anisotropic paramagnetic effects, the general procedures of conformational ensemble reconstruction, and some representative reweighting approaches.

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.