PPM: a side-chain and backbone chemical shift predictor for the assessment of protein conformational ensembles

EFG-CS: Predicting chemical shifts from amino acid sequences with protein structure prediction using machine learning and deep learning models

Nuclear magnetic resonance (NMR) crystallography is one of the main methods in structural biology for analyzing protein stereochemistry and structure. The chemical shift of the resonance frequency reflects the effect of the protons in a molecule producing distinct NMR signals in different chemical environments. Apprehending chemical shifts from NMR signals can be challenging since having an NMR structure does not necessarily provide all the required chemical shift information, making predictive models essential for accurately deducing chemical shifts, either from protein structures or, more ideally, directly from amino acid sequences. Here, we present EFG-CS, a web server that specializes in chemical shift prediction. EFG-CS employs a machine learning-based transfer prediction model for backbone atom chemical shift prediction, using ESMFold-predicted protein structures. Additionally, ESG-CS incorporates a graph neural network-based model to provide comprehensive side-chain atom chemical shift predictions. Our method demonstrated reliable performance in backbone atom prediction, achieving comparable accuracy levels with root mean square errors (RMSE) of 0.30 ppm for H, 0.22 ppm for Hα, 0.89 ppm for C, 0.89 ppm for Cα, 0.84 ppm for Cβ, and 1.69 ppm for N. Moreover, our approach also showed predictive capabilities in side-chain atom chemical shift prediction achieving RMSE values of 0.71 ppm for Hβ, 0.74-1.15 ppm for Hδ, and 0.58-0.94 ppm for Hγ, solely utilizing amino acid sequences without homology or feature curation. This work shows for the first time that generative AI protein models can predict NMR shifts nearly comparable to experimental models. This web server is freely available at https://biosig.lab.uq.edu.au/efg_cs, and the chemical shift prediction results can be downloaded in tabular format and visualized in 3D format.

Ensemble-based design of tau to inhibit aggregation while preserving biological activity

The microtubule-associated protein tau is implicated in neurodegenerative diseases characterized by amyloid formation. Mutations associated with frontotemporal dementia increase tau aggregation propensity and disrupt its endogenous microtubule-binding activity. The structural relationship between aggregation propensity and biological activity remains unclear. We employed a multi-disciplinary approach, including computational modeling, NMR, cross-linking mass spectrometry, and cell models to design tau sequences that stabilize its structural ensemble. Our findings reveal that substitutions near the conserved 'PGGG' beta-turn motif can modulate local conformation, more stably engaging in interactions with the 306 VQIVYK 311 amyloid motif to decrease aggregation in vitro and in cells. Designed tau sequences maintain microtubule binding and explain why 3R isoforms of tau exhibit reduced pathogenesis over 4R isoforms. We propose a simple mechanism to reduce the formation of pathogenic species while preserving biological function, offering insights for therapeutic strategies aimed at reducing protein misfolding in neurodegenerative diseases.

MIM-ML: A Novel Quantum Chemical Fragment-Based Random Forest Model for Accurate Prediction of NMR Chemical Shifts of Nucleic Acids

We developed a random forest machine learning (ML) model for the prediction of 1H and 13C NMR chemical shifts of nucleic acids. Our ML model is trained entirely on reproducing computed chemical shifts obtained previously on 10 nucleic acids using a Molecules-in-Molecules (MIM) fragment-based density functional theory (DFT) protocol including microsolvation effects. Our ML model includes structural descriptors as well as electronic descriptors from an inexpensive low-level semiempirical calculation (GFN2-xTB) and trained on a relatively small number of DFT chemical shifts (2080 1H chemical shifts and 1780 13C chemical shifts on the 10 nucleic acids). The ML model is then used to make chemical shift predictions on 8 new nucleic acids ranging in size from 600 to 900 atoms and compared directly to experimental data. Though no experimental data was used in the training, the performance of our model is excellent (mean absolute deviation of 0.34 ppm for 1H chemical shifts and 2.52 ppm for 13C chemical shifts for the test set), despite having some nonstandard structures. A simple analysis suggests that both structural and electronic descriptors are critical for achieving reliable predictions. This is the first attempt to combine ML from fragment-based DFT calculations to predict experimental chemical shifts accurately, making the MIM-ML model a valuable tool for NMR predictions of nucleic acids.

Conformational ensembles explain NMR spectra of frozen intrinsically disordered proteins

Protein regions which are intrinsically disordered, exist as an ensemble of rapidly interconverting structures. Cooling proteins to cryogenic temperatures for dynamic nuclear polarization (DNP) magic angle spinning (MAS) NMR studies suspends most of the motions, resulting in peaks that are broad but not featureless. To demonstrate that detailed conformational restraints can be retrieved from the peak shapes of frozen proteins alone, we developed and used a simulation framework to assign peak features to conformers in the ensemble. We validated our simulations by comparing them to spectra of α-synuclein acquired under different experimental conditions. Our assignments of peaks to discrete dihedral angle populations suggest that structural constraints are attainable under cryogenic conditions. The ability to infer ensemble populations from peak shapes has important implications for DNP MAS NMR studies of proteins with regions of disorder in living cells because chemical shifts are the most accessible measured parameter.

Accurate and Cost-Effective NMR Chemical Shift Predictions for Nucleic Acids Using a Molecules-in-Molecules Fragmentation-Based Method

We have developed, implemented, and assessed an efficient protocol for the prediction of NMR chemical shifts of large nucleic acids using our molecules-in-molecules (MIM) fragment-based quantum chemical approach. To assess the performance of our approach, MIM-NMR calculations are calibrated on a test set of three nucleic acids, where the structure is derived from solution-phase NMR studies. For DNA systems with multiple conformers, the one-layer MIM method with trimer fragments (MIM1trimer) is benchmarked to get the lowest energy structure, with an average error of only 0.80 kcal/mol with respect to unfragmented full molecule calculations. The MIMI-NMRdimer calibration with respect to unfragmented full molecule calculations shows a mean absolute deviation (MAD) of 0.06 and 0.11 ppm, respectively, for 1H and 13C nuclei, but the performance with respect to experimental NMR chemical shifts is comparable to the more expensive MIM1-NMR and MIM2-NMR methods with trimer subsystems. To compare with the experimental chemical shifts, a standard protocol is derived using DNA systems with Protein Data Bank (PDB) IDs 1SY8, 1K2K, and 1KR8. The effect of structural minimizations is employed using a hybrid mechanics/semiempirical approach and used for computations in solution with implicit and explicit-implicit solvation models in our MIM1-NMRdimer methodology. To demonstrate the applicability of our protocol, we tested it on seven nucleic acids, including structures with nonstandard residues, heteroatom substitutions (F and B atoms), and side chain mutations with a size ranging from ∼300 to 1100 atoms. The major improvement for predicted MIM1-NMRdimer calculations is obtained from structural minimizations and implicit solvation effects. A significant improvement with the explicit-implicit solvation model is observed only for two smaller nucleic acid systems (1KR8 and 7NBK), where the expensive first solvation shell is replaced by the microsolvation model, in which a single water molecule is added for each solvent-exposed amino and imino protons, along with the implicit solvation. Overall, our target accuracy of ∼0.2-0.3 ppm for 1H and ∼2-3 ppm for 13C has been achieved for large nucleic acids. The proposed MIM-NMR approach is accurate and cost-effective (linear scaling with system size), and it can aid in the structural assignments of a wide range of complex biomolecules.

High-Resolution Conformational Analysis of RGDechi-Derived Peptides Based on a Combination of NMR Spectroscopy and MD Simulations

The crucial role of integrin in pathological processes such as tumor progression and metastasis formation has inspired intense efforts to design novel pharmaceutical agents modulating integrin functions in order to provide new tools for potential therapies. In the past decade, we have investigated the biological proprieties of the chimeric peptide RGDechi, containing a cyclic RGD motif linked to an echistatin C-terminal fragment, able to specifically recognize αvβ3 without cross reacting with αvβ5 and αIIbβ3 integrin. Additionally, we have demonstrated using two RGDechi-derived peptides, called RGDechi1-14 and ψRGDechi, that chemical modifications introduced in the C-terminal part of the peptide alter or abolish the binding to the αvβ3 integrin. Here, to shed light on the structural and dynamical determinants involved in the integrin recognition mechanism, we investigate the effects of the chemical modifications by exploring the conformational space sampled by RGDechi1-14 and ψRGDechi using an integrated natural-abundance NMR/MD approach. Our data demonstrate that the flexibility of the RGD-containing cycle is driven by the echistatin C-terminal region of the RGDechi peptide through a coupling mechanism between the N- and C-terminal regions.

Quantitative prediction of ensemble dynamics, shapes and contact propensities of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) are highly dynamic systems that play an important role in cell signaling processes and their misfunction often causes human disease. Proper understanding of IDP function not only requires the realistic characterization of their three-dimensional conformational ensembles at atomic-level resolution but also of the time scales of interconversion between their conformational substates. Large sets of experimental data are often used in combination with molecular modeling to restrain or bias models to improve agreement with experiment. It is shown here for the N-terminal transactivation domain of p53 (p53TAD) and Pup, which are two IDPs that fold upon binding to their targets, how the latest advancements in molecular dynamics (MD) simulations methodology produces native conformational ensembles by combining replica exchange with series of microsecond MD simulations. They closely reproduce experimental data at the global conformational ensemble level, in terms of the distribution properties of the radius of gyration tensor, and at the local level, in terms of NMR properties including 15N spin relaxation, without the need for reweighting. Further inspection revealed that 10-20% of the individual MD trajectories display the formation of secondary structures not observed in the experimental NMR data. The IDP ensembles were analyzed by graph theory to identify dominant inter-residue contact clusters and characteristic amino-acid contact propensities. These findings indicate that modern MD force fields with residue-specific backbone potentials can produce highly realistic IDP ensembles sampling a hierarchy of nano- and picosecond time scales providing new insights into their biological function.

Analysis of conformational exchange processes using methyl-TROSY-based Hahn echo measurements of quadruple-quantum relaxation

Transverse nuclear spin relaxation is a sensitive probe of chemical exchange on timescales on the order of microseconds to milliseconds. Here we present an experiment for the simultaneous measurement of the relaxation rates of two quadruple-quantum transitions in 13 CH3 -labelled methyl groups. These coherences are protected against relaxation by intra-methyl dipolar interactions and so have unexpectedly long lifetimes within perdeuterated biomacromolecules. However, these coherences also have an order of magnitude higher sensitivity to chemical exchange broadening than lower order coherences and therefore provide ideal probes of dynamic processes. We show that analysis of the static magnetic field dependence of zero-, double- and quadruple-quantum Hahn echo relaxation rates provides a robust indication of chemical exchange and can determine the signed relative magnitudes of proton and carbon chemical shift differences between ground and excited states. We also demonstrate that this analysis can be combined with established Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion measurements, providing improved precision in parameter estimates, particularly in the determination of 1 H chemical shift differences.

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.

On the potential of machine learning to examine the relationship between sequence, structure, dynamics and function of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) constitute a broad set of proteins with few uniting and many diverging properties. IDPs-and intrinsically disordered regions (IDRs) interspersed between folded domains-are generally characterized as having no persistent tertiary structure; instead they interconvert between a large number of different and often expanded structures. IDPs and IDRs are involved in an enormously wide range of biological functions and reveal novel mechanisms of interactions, and while they defy the common structure-function paradigm of folded proteins, their structural preferences and dynamics are important for their function. We here discuss open questions in the field of IDPs and IDRs, focusing on areas where machine learning and other computational methods play a role. We discuss computational methods aimed to predict transiently formed local and long-range structure, including methods for integrative structural biology. We discuss the many different ways in which IDPs and IDRs can bind to other molecules, both via short linear motifs, as well as in the formation of larger dynamic complexes such as biomolecular condensates. We discuss how experiments are providing insight into such complexes and may enable more accurate predictions. Finally, we discuss the role of IDPs in disease and how new methods are needed to interpret the mechanistic effects of genomic variants in IDPs.

Ubiquitin Interacting Motifs: Duality Between Structured and Disordered Motifs

Ubiquitin is a small protein at the heart of many cellular processes, and several different protein domains are known to recognize and bind ubiquitin. A common motif for interaction with ubiquitin is the Ubiquitin Interacting Motif (UIM), characterized by a conserved sequence signature and often found in multi-domain proteins. Multi-domain proteins with intrinsically disordered regions mediate interactions with multiple partners, orchestrating diverse pathways. Short linear motifs for binding are often embedded in these disordered regions and play crucial roles in modulating protein function. In this work, we investigated the structural propensities of UIMs using molecular dynamics simulations and NMR chemical shifts. Despite the structural portrait depicted by X-crystallography of stable helical structures, we show that UIMs feature both helical and intrinsically disordered conformations. Our results shed light on a new class of disordered UIMs. This group is here exemplified by the C-terminal domain of one isoform of ataxin-3 and a group of ubiquitin-specific proteases. Intriguingly, UIMs not only bind ubiquitin. They can be a recruitment point for other interactors, such as parkin and the heat shock protein Hsc70-4. Disordered UIMs can provide versatility and new functions to the client proteins, opening new directions for research on their interactome.

A novel approach for studying receptor-ligand interactions on living cells surface by using NUS/T1ρ-NMR methodologies combined with computational techniques: The RGDechi15D-αvβ5 integrin complex

Structural investigations of receptor-ligand interactions on living cells surface by high-resolution Nuclear Magnetic Resonance (NMR) are problematic due to their short lifetime, which often prevents the acquisition of experiments longer than few hours. To overcome these limitations, we developed an on-cell NMR-based approach for exploring the molecular determinants driving the receptor-ligand recognition mechanism under native conditions. Our method relies on the combination of high-resolution structural and dynamics NMR data with Molecular Dynamics simulations and Molecular Docking studies. The key point of our strategy is the use of Non Uniform Sampling (NUS) and T1ρ-NMR techniques to collect atomic-resolution structural and dynamics information on the receptor-ligand interactions with living cells, that can be used as conformational constraints in computational studies. In fact, the application of these two NMR methodologies allows to record spectra with high S/N ratio and resolution within the lifetime of cells. In particular, 2D NUS [¹H–¹H] trNOESY spectra are used to explore the ligand conformational changes induced by receptor binding; whereas T1ρ-based experiments are applied to characterize the ligand binding epitope by defining two parameters: T1ρ Attenuation factor and T1ρ Binding Effect. This approach has been tested to characterize the molecular determinants regulating the recognition mechanism of α_vβ₅-integrin by a selective cyclic binder peptide named RGDechi15D. Our data demonstrate that the developed strategy represents an alternative in-cell NMR tool for studying, at atomic resolution, receptor-ligand recognition mechanism on living cells surface. Additionally, our application may be extremely useful for screening of the interaction profiling of drugs with their therapeutic targets in their native cellular environment.

Informing NMR experiments with molecular dynamics simulations to characterize the dominant activated state of the KcsA ion channel

As the first potassium channel with an x-ray structure determined, and given its homology to eukaryotic channels, the pH-gated prokaryotic channel KcsA has been extensively studied. Nevertheless, questions related, in particular, to the allosteric coupling between its gates remain open. The many currently available x-ray crystallography structures appear to correspond to various stages of activation and inactivation, offering insights into the molecular basis of these mechanisms. Since these studies have required mutations, complexation with antibodies, and substitution of detergents in place of lipids, examining the channel under more native conditions is desirable. Solid-state nuclear magnetic resonance (SSNMR) can be used to study the wild-type protein under activating conditions (low pH), at room temperature, and in bacteriomimetic liposomes. In this work, we sought to structurally assign the activated state present in SSNMR experiments. We used a combination of molecular dynamics (MD) simulations, chemical shift prediction algorithms, and Bayesian inference techniques to determine which of the most plausible x-ray structures resolved to date best represents the activated state captured in SSNMR. We first identified specific nuclei with simulated NMR chemical shifts that differed significantly when comparing partially open vs fully open ensembles from MD simulations. The simulated NMR chemical shifts for those specific nuclei were then compared to experimental ones, revealing that the simulation of the partially open state was in good agreement with the SSNMR data. Nuclei that discriminate effectively between partially and fully open states belong to residues spread over the sequence and provide a molecular level description of the conformational change.

Bcl-xL Dynamics under the Lens of Protein Structure Networks

Understanding the finely orchestrated interactions leading to or preventing programmed cell death (apoptosis) is of utmost importance in cancer research because the failure of these systems could eventually lead to the onset of the disease. In this regard, the maintenance of a delicate balance between the promoters and inhibitors of mitochondrial apoptosis is crucial, as demonstrated by the interplay among the Bcl-2 family members. In particular, B-cell lymphoma extra-large (Bcl-x_L) is a target of interest due to the forefront role of its dysfunctions in cancer development. Bcl-x_L prevents apoptosis by binding both the pro-apoptotic BH3-only proteins, like PUMA, and the noncanonical partners, such as p53, at different sites. An allosteric communication between the BH3-only protein binding pocket and the p53 binding site, mediating the release of p53 from Bcl-x_L upon PUMA binding, has been postulated and supported by nuclear magnetic resonance and other biophysical data. The molecular details of this mechanism, especially at the residue level, remain unclear. In this work, we investigated the distal communication between these two sites in Bcl-x_L in its free state and when bound to PUMA. We also evaluated how missense mutations of Bcl-x_L found in cancer samples might impair this communication and therefore the allosteric mechanism. We employed all-atom explicit solvent microsecond molecular dynamics simulations, analyzed through a Protein Structure Network approach and integrated with calculations of changes in free energies upon cancer-related mutations identified by genomics studies. We found a subset of candidate residues responsible for both maintaining protein stability and for conveying structural information between the two binding sites and hypothesized possible communication routes between specific residues at both sites.

Investigating Conformational Dynamics and Allostery in the p53 DNA-Binding Domain Using Molecular Simulations

The p53 tumor suppressor is a multifaceted context-dependent protein, which is involved in multiple cellular pathways, with the ability to either keep the cells alive or to kill them through mechanisms such as apoptosis. To complicate this picture, cancer cells that express mutant p53 becomes addicted to the mutant activity, so that the mutant variant features a myriad of gain-of-function activities, opening different venues for therapy. This makes essential to think outside the box and apply new approaches to the study of p53 structure-(mis)function relationship to find new critical components of its pathway or to understand how known parts are interconnected, compete, or cooperate. In this context, I will here illustrate how to integrate different computational methods to the identification of possible allosteric effects transmitted from the DNA binding interface of p53 to regions for cofactor recruitment. The protocol can be extended to any other cases of study. Indeed, it does not necessarily apply only to the study of DNA-induced effects, but more broadly to the investigation of long-range effects induced by a biological partner that binds to a biomolecule of interest.

Review and Prospect: Deep Learning in Nuclear Magnetic Resonance Spectroscopy

Since the concept of deep learning (DL) was formally proposed in 2006, it has had a major impact on academic research and industry. Nowadays, DL provides an unprecedented way to analyze and process data with demonstrated great results in computer vision, medical imaging, natural language processing, and so forth. Herein, applications of DL in NMR spectroscopy are summarized, and a perspective for DL as an entirely new approach that is likely to transform NMR spectroscopy into a much more efficient and powerful technique in chemistry and life sciences is outlined.

Structure and Dynamics in the ATG8 Family From Experimental to Computational Techniques

Autophagy is a conserved and essential intracellular mechanism for the removal of damaged components. Since autophagy deregulation is linked to different kinds of pathologies, it is fundamental to gain knowledge on the fine molecular and structural details related to the core proteins of the autophagy machinery. Among these, the family of human ATG8 proteins plays a central role in recruiting other proteins to the different membrane structures involved in the autophagic pathway. Several experimental structures are available for the members of the ATG8 family alone or in complex with their different biological partners, including disordered regions of proteins containing a short linear motif called LC3 interacting motif. Recently, the first structural details of the interaction of ATG8 proteins with biological membranes came into light. The availability of structural data for human ATG8 proteins has been paving the way for studies on their structure-function-dynamic relationship using biomolecular simulations. Experimental and computational structural biology can help to address several outstanding questions on the mechanism of human ATG8 proteins, including their specificity toward different interactors, their association with membranes, the heterogeneity of their conformational ensemble, and their regulation by post-translational modifications. We here summarize the main results collected so far and discuss the future perspectives within the field and the knowledge gaps. Our review can serve as a roadmap for future structural and dynamics studies of the ATG8 family members in health and disease.

Accelerating prediction of chemical shift of protein structures on GPUs: Using OpenACC

Experimental chemical shifts (CS) from solution and solid state magic-angle-spinning nuclear magnetic resonance (NMR) spectra provide atomic level information for each amino acid within a protein or protein complex. However, structure determination of large complexes and assemblies based on NMR data alone remains challenging due to the complexity of the calculations. Here, we present a hardware accelerated strategy for the estimation of NMR chemical-shifts of large macromolecular complexes based on the previously published PPM_One software. The original code was not viable for computing large complexes, with our largest dataset taking approximately 14 hours to complete. Our results show that serial code refactoring and parallel acceleration brought down the time taken of the software running on an NVIDIA Volta 100 (V100) Graphic Processing Unit (GPU) to 46.71 seconds for our largest dataset of 11.3 million atoms. We use OpenACC, a directive-based programming model for porting the application to a heterogeneous system consisting of x86 processors and NVIDIA GPUs. Finally, we demonstrate the feasibility of our approach in systems of increasing complexity ranging from 100K to 11.3M atoms.

Nuclear magnetic resonance (NMR) spectroscopy yields chemical shifts (CSs) which reveal chemical details of the environment of an atom in a protein. Computer estimation of CSs require the calculation of several contributing terms including interatomic distances, ring current effects and the formation of hydrogen bonds. Here, taking advantage of graphic processing units (GPUs), the estimation of chemical shifts are accelerated thus enabling the determination of the CSs for large systems, encompassing millions of atoms. The rapid determination of CSs enables the use of CS-based validation for other molecular dynamics computations.

Accurate prediction of chemical shifts for aqueous protein structure on "Real World" data

Here we report a new machine learning algorithm for protein chemical shift prediction that outperforms existing chemical shift calculators on realistic data that is not heavily curated, nor eliminates test predictions ad hoc. Our UCBShift predictor implements two modules: a transfer prediction module that employs both sequence and structural alignment to select reference candidates for experimental chemical shift replication, and a redesigned machine learning module based on random forest regression which utilizes more, and more carefully curated, feature extracted data. When combined together, this new predictor achieves state-of-the-art accuracy for predicting chemical shifts on a randomly selected dataset without careful curation, with root-mean-square errors of 0.31 ppm for amide hydrogens, 0.19 ppm for Hα, 0.84 ppm for C', 0.81 ppm for Cα, 1.00 ppm for Cβ, and 1.81 ppm for N. When similar sequences or structurally related proteins are available, UCBShift shows superior native state selection from misfolded decoy sets compared to SPARTA+ and SHIFTX2, and even without homology we exceed current prediction accuracy of all other popular chemical shift predictors.

Molecular Dynamics model of peptide-protein conjugation: case study of covalent complex between Sos1 peptide and N-terminal SH3 domain from Grb2

We have investigated covalent conjugation of VPPPVPPRRRX′ peptide (where X′ denotes N^ε-chloroacetyl lysine) to N-terminal SH3 domain from adapter protein Grb2. Our experimental results confirmed that the peptide first binds to the SH3 domain noncovalently before establishing a covalent linkage through reaction of X′ with the target cysteine residue C32. We have also confirmed that this reaction involves a thiolate-anion form of C32 and follows the S_N2 mechanism. For this system, we have developed a new MD-based protocol to model the formation of covalent conjugate. The simulation starts with the known coordinates of the noncovalent complex. When two reactive groups come into contact during the course of the simulation, the reaction is initiated. The reaction is modeled via gradual interpolation between the two sets of force field parameters that are representative of the noncovalent and covalent complexes. The simulation proceeds smoothly, with no appreciable perturbations to temperature, pressure or volume, and results in a high-quality MD model of the covalent complex. The validity of this model is confirmed using the experimental chemical shift data. The new MD-based approach offers a valuable tool to explore the mechanics of protein-peptide conjugation and build accurate models of covalent complexes.

Bayesian-Maximum-Entropy Reweighting of IDP Ensembles Based on NMR Chemical Shifts

Bayesian and Maximum Entropy approaches allow for a statistically sound and systematic fitting of experimental and computational data. Unfortunately, assessing the relative confidence in these two types of data remains difficult as several steps add unknown error. Here we propose the use of a validation-set method to determine the balance, and thus the amount of fitting. We apply the method to synthetic NMR chemical shift data of an intrinsically disordered protein. We show that the method gives consistent results even when other methods to assess the amount of fitting cannot be applied. Finally, we also describe how the errors in the chemical shift predictor can lead to an incorrect fitting and how using secondary chemical shifts could alleviate this problem.

Side chain to main chain hydrogen bonds stabilize a polyglutamine helix in a transcription factor

Polyglutamine (polyQ) tracts are regions of low sequence complexity frequently found in transcription factors. Tract length often correlates with transcriptional activity and expansion beyond specific thresholds in certain human proteins is the cause of polyQ disorders. To study the structural basis of the association between tract length, transcriptional activity and disease, we addressed how the conformation of the polyQ tract of the androgen receptor, associated with spinobulbar muscular atrophy (SBMA), depends on its length. Here we report that this sequence folds into a helical structure stabilized by unconventional hydrogen bonds between glutamine side chains and main chain carbonyl groups, and that its helicity directly correlates with tract length. These unusual hydrogen bonds are bifurcate with the conventional hydrogen bonds stabilizing α-helices. Our findings suggest a plausible rationale for the association between polyQ tract length and androgen receptor transcriptional activity and have implications for establishing the mechanistic basis of SBMA.

Polyglutamine (polyQ) tracts are low-complexity regions and their expansion is linked to certain neurodegenerative diseases. Here the authors combine experimental and computational approaches to find that the length of the androgen receptor polyQ tract correlates with its helicity and show that the polyQ helical structure is stabilized by hydrogen bonds between the Gln side chains and main chain carbonyl groups.

NMR Resonance Assignment Methodology: Characterizing Large Sparsely Labeled Glycoproteins

Characterization of proteins using NMR methods begins with assignment of resonances to specific residues. This is usually accomplished using sequential connectivities between nuclear pairs in proteins uniformly labeled with NMR active isotopes. This becomes impractical for larger proteins, and especially for proteins that are best expressed in mammalian cells, including glycoproteins. Here an alternate protocol for the assignment of NMR resonances of sparsely labeled proteins, namely, the ones labeled with a single amino acid type, or a limited subset of types, isotopically enriched with ¹⁵N or ¹³C, is described. The protocol is based on comparison of data collected using extensions of simple two-dimensional NMR experiments (correlated chemical shifts, nuclear Overhauser effects, residual dipolar couplings) to predictions from molecular dynamics trajectories that begin with known protein structures. Optimal pairing of predicted and experimental values is facilitated by a software package that employs a genetic algorithm, ASSIGN_SLP_MD. The approach is applied to the 36-kDa luminal domain of the sialyltransferase, rST6Gal1, in which all phenylalanines are labeled with ¹⁵N, and the results are validated by elimination of resonances via single-point mutations of selected phenylalanines to tyrosines. Assignment allows the use of previously published paramagnetic relaxation enhancements to evaluate placement of a substrate analog in the active site of this protein. The protocol will open the way to structural characterization of the many glycosylated and other proteins that are best expressed in mammalian cells.

Probing the functional conformations of an atypical proline-rich fusion peptide

Simulations confirm a propensity for extended and solvent exposed conformations of the p15 fusion peptide capable of membrane targeting.

Characterization of intrinsically disordered proteins and their dynamic complexes: From in vitro to cell-like environments

Over the last two decades, it has become increasingly clear that a large fraction of the human proteome is intrinsically disordered or contains disordered segments of significant length. These intrinsically disordered proteins (IDPs) play important regulatory roles throughout biology, underlining the importance of understanding their conformational behavior and interaction mechanisms at the molecular level. Here we review recent progress in the NMR characterization of the structure and dynamics of IDPs in various functional states and environments. We describe the complementarity of different NMR parameters for quantifying the conformational propensities of IDPs in their isolated and phosphorylated states, and we discuss the challenges associated with obtaining structural models of dynamic protein-protein complexes involving IDPs. In addition, we review recent progress in understanding the conformational behavior of IDPs in cell-like environments such as in the presence of crowding agents, in membrane-less organelles and in the complex environment of the human cell.

Molecular dynamics ensemble refinement of the heterogeneous native state of NCBD using chemical shifts and NOEs

Many proteins display complex dynamical properties that are often intimately linked to their biological functions. As the native state of a protein is best described as an ensemble of conformations, it is important to be able to generate models of native state ensembles with high accuracy. Due to limitations in sampling efficiency and force field accuracy it is, however, challenging to obtain accurate ensembles of protein conformations by the use of molecular simulations alone. Here we show that dynamic ensemble refinement, which combines an accurate atomistic force field with commonly available nuclear magnetic resonance (NMR) chemical shifts and NOEs, can provide a detailed and accurate description of the conformational ensemble of the native state of a highly dynamic protein. As both NOEs and chemical shifts are averaged on timescales up to milliseconds, the resulting ensembles reflect the structural heterogeneity that goes beyond that probed, e.g., by NMR relaxation order parameters. We selected the small protein domain NCBD as object of our study since this protein, which has been characterized experimentally in substantial detail, displays a rich and complex dynamical behaviour. In particular, the protein has been described as having a molten-globule like structure, but with a relatively rigid core. Our approach allowed us to describe the conformational dynamics of NCBD in solution, and to probe the structural heterogeneity resulting from both short- and long-timescale dynamics by the calculation of order parameters on different time scales. These results illustrate the usefulness of our approach since they show that NCBD is rather rigid on the nanosecond timescale, but interconverts within a broader ensemble on longer timescales, thus enabling the derivation of a coherent set of conclusions from various NMR experiments on this protein, which could otherwise appear in contradiction with each other.

Measuring the signs of the methyl 1H chemical shift differences between major and 'invisible' minor protein conformational states using methyl 1H multi-quantum spectroscopy

Carr-Purcell-Meiboom-Gill (CPMG) type relaxation dispersion experiments are now routinely used to characterise protein conformational dynamics that occurs on the μs to millisecond (ms) timescale between a visible major state and 'invisible' minor states. The exchange rate(s) ([Formula: see text]), population(s) of the minor state(s) and the absolute value of the chemical shift difference [Formula: see text] (ppm) between different exchanging states can be extracted from the CPMG data. However the sign of [Formula: see text] that is required to reconstruct the spectrum of the 'invisible' minor state(s) cannot be obtained from CPMG data alone. Building upon the recently developed triple quantum (TQ) methyl [Formula: see text] CPMG experiment (Yuwen in Angew Chem 55:11490-11494, 2016) we have developed pulse sequences that use carbon detection to generate and evolve single quantum (SQ), double quantum (DQ) and TQ coherences from methyl protons in the indirect dimension to measure the chemical exchange-induced shifts of the SQ, DQ and TQ coherences from which the sign of [Formula: see text] is readily obtained for two state exchange. Further a combined analysis of the CPMG data and the difference in exchange induced shifts between the SQ and DQ resonances and between the SQ and TQ resonances improves the estimates of exchange parameters like the population of the minor state. We demonstrate the use of these experiments on two proteins undergoing exchange: (1) the ~ 18 kDa cavity mutant of T4 Lysozyme ([Formula: see text]) and (2) the [Formula: see text] kDa Peripheral Sub-unit Binding Domain (PSBD) from the acetyl transferase of Bacillus stearothermophilus ([Formula: see text]).

The PROSECCO server for chemical shift predictions in ordered and disordered proteins

The chemical shifts measured in solution-state and solid-state nuclear magnetic resonance (NMR) are powerful probes of the structure and dynamics of protein molecules. The exploitation of chemical shifts requires methods to correlate these data with the protein structures and sequences. We present here an approach to calculate accurate chemical shifts in both ordered and disordered proteins using exclusively the information contained in their sequences. Our sequence-based approach, protein sequences and chemical shift correlations (PROSECCO), achieves the accuracy of the most advanced structure-based methods in the characterization of chemical shifts of folded proteins and improves the state of the art in the study of disordered proteins. Our analyses revealed fundamental insights on the structural information carried by NMR chemical shifts of structured and unstructured protein states.

Unraveling the meaning of chemical shifts in protein NMR

Chemical shifts are among the most informative parameters in protein NMR. They provide wealth of information about protein secondary and tertiary structure, protein flexibility, and protein-ligand binding. In this report, we review the progress in interpreting and utilizing protein chemical shifts that has occurred over the past 25years, with a particular focus on the large body of work arising from our group and other Canadian NMR laboratories. More specifically, this review focuses on describing, assessing, and providing some historical context for various chemical shift-based methods to: (1) determine protein secondary and super-secondary structure; (2) derive protein torsion angles; (3) assess protein flexibility; (4) predict residue accessible surface area; (5) refine 3D protein structures; (6) determine 3D protein structures and (7) characterize intrinsically disordered proteins. This review also briefly covers some of the methods that we previously developed to predict chemical shifts from 3D protein structures and/or protein sequence data. It is hoped that this review will help to increase awareness of the considerable utility of NMR chemical shifts in structural biology and facilitate more widespread adoption of chemical-shift based methods by the NMR spectroscopists, structural biologists, protein biophysicists, and biochemists worldwide. This article is part of a Special Issue entitled: Biophysics in Canada, edited by Lewis Kay, John Baenziger, Albert Berghuis and Peter Tieleman.

CryoEM Structure Refinement by Integrating NMR Chemical Shifts with Molecular Dynamics Simulations

Single particle cryoEM has emerged as a powerful method for structure determination of proteins and complexes, complementing X-ray crystallography and NMR spectroscopy. Yet, for many systems, the resolution of cryoEM density map has been limited to 4-6 Å, which only allows for resolving bulky amino acids side chains, thus hindering accurate model building from the density map. On the other hand, experimental chemical shifts (CS) from solution and solid state MAS NMR spectra provide atomic level data for each amino acid within a molecule or a complex; however, structure determination of large complexes and assemblies based on NMR data alone remains challenging. Here, we present a novel integrated strategy to combine the highly complementary experimental data from cryoEM and NMR computationally by molecular dynamics simulations to derive an atomistic model, which is not attainable by either approach alone. We use the HIV-1 capsid protein (CA) C-terminal domain as well as the large capsid assembly to demonstrate the feasibility of this approach, termed NMR CS-biased cryoEM structure refinement.

DNA-binding protects p53 from interactions with cofactors involved in transcription-independent functions

Binding-induced conformational changes of a protein at regions distant from the binding site may play crucial roles in protein function and regulation. The p53 tumour suppressor is an example of such an allosterically regulated protein. Little is known, however, about how DNA binding can affect distal sites for transcription factors. Furthermore, the molecular details of how a local perturbation is transmitted through a protein structure are generally elusive and occur on timescales hard to explore by simulations. Thus, we employed state-of-the-art enhanced sampling atomistic simulations to unveil DNA-induced effects on p53 structure and dynamics that modulate the recruitment of cofactors and the impact of phosphorylation at Ser215. We show that DNA interaction promotes a conformational change in a region 3 nm away from the DNA binding site. Specifically, binding to DNA increases the population of an occluded minor state at this distal site by more than 4-fold, whereas phosphorylation traps the protein in its major state. In the minor conformation, the interface of p53 that binds biological partners related to p53 transcription-independent functions is not accessible. Significantly, our study reveals a mechanism of DNA-mediated protection of p53 from interactions with partners involved in the p53 transcription-independent signalling. This also suggests that conformational dynamics is tightly related to p53 signalling.

Molecular Dynamics Simulations of 441 Two-Residue Peptides in Aqueous Solution: Conformational Preferences and Neighboring Residue Effects with the Amber ff99SB-ildn-NMR Force Field

Understanding the intrinsic conformational preferences of amino acids and the extent to which they are modulated by neighboring residues is a key issue for developing predictive models of protein folding and stability. Here we present the results of 441 independent explicit-solvent MD simulations of all possible two-residue peptides that contain the 20 standard amino acids with histidine modeled in both its neutral and protonated states. (3)J(HNHα) coupling constants and δ(Hα) chemical shifts calculated from the MD simulations correlate quite well with recently published experimental measurements for a corresponding set of two-residue peptides. Neighboring residue effects (NREs) on the average (3)J(HNHα) and δ(Hα) values of adjacent residues are also reasonably well reproduced, with the large NREs exerted experimentally by aromatic residues, in particular, being accurately captured. NREs on the secondary structure preferences of adjacent amino acids have been computed and compared with corresponding effects observed in a coil library and the average β-turn preferences of all amino acid types have been determined. Finally, the intrinsic conformational preferences of histidine, and its NREs on the conformational preferences of adjacent residues, are both shown to be strongly affected by the protonation state of the imidazole ring.

Decoding the Mobility and Time Scales of Protein Loops

The flexible nature of protein loops and the time scales of their dynamics are critical for many biologically important events at the molecular level, such as protein interaction and recognition processes. In order to obtain a predictive understanding of the dynamic properties of loops, 500 ns molecular dynamics (MD) computer simulations of 38 different proteins were performed and validated using NMR chemical shifts. A total of 169 loops were analyzed and classified into three types, namely fast loops with correlation times <10 ns, slow loops with correlation times between 10 and 500 ns, and loops that are static over the course of the whole trajectory. Chemical and biophysical loop descriptors, such as amino-acid sequence, average 3D structure, charge distribution, hydrophobicity, and local contacts were used to develop and parametrize the ToeLoop algorithm for the prediction of the flexibility and motional time scale of every protein loop, which is also implemented as a public Web server (http://spin.ccic.ohio-state.edu/index.php/loop). The results demonstrate that loop dynamics with their time scales can be predicted rapidly with reasonable accuracy, which will allow the screening of average protein structures to help better understand the various roles loops can play in the context of protein-protein interactions and binding.

Concurrent Increases and Decreases in Local Stability and Conformational Heterogeneity in Cu, Zn Superoxide Dismutase Variants Revealed by Temperature-Dependence of Amide Chemical Shifts

The chemical shifts of backbone amide protons in proteins are sensitive reporters of local structural stability and conformational heterogeneity, which can be determined from their readily measured linear and nonlinear temperature-dependences, respectively. Here we report analyses of amide proton temperature-dependences for native dimeric Cu, Zn superoxide dismutase (holo pWT SOD1) and structurally diverse mutant SOD1s associated with amyotrophic lateral sclerosis (ALS). Holo pWT SOD1 loses structure with temperature first at its periphery and, while having extremely high global stability, nevertheless exhibits extensive conformational heterogeneity, with ∼1 in 5 residues showing evidence for population of low energy alternative states. The holo G93A and E100G ALS mutants have moderately decreased global stability, whereas V148I is slightly stabilized. Comparison of the holo mutants as well as the marginally stable immature monomeric unmetalated and disulfide-reduced (apo(2SH)) pWT with holo pWT shows that changes in the local structural stability of individual amides vary greatly, with average changes corresponding to differences in global protein stability measured by differential scanning calorimetry. Mutants also exhibit altered conformational heterogeneity compared to pWT. Strikingly, substantial increases as well as decreases in local stability and conformational heterogeneity occur, in particular upon maturation and for G93A. Thus, the temperature-dependence of amide shifts for SOD1 variants is a rich source of information on the location and extent of perturbation of structure upon covalent changes and ligand binding. The implications for potential mechanisms of toxic misfolding of SOD1 in disease and for general aspects of protein energetics, including entropy-enthalpy compensation, are discussed.

A systematic study on RNA NMR chemical shift calculation based on the automated fragmentation QM/MM approach

¹H, ¹³C and ¹⁵N NMR chemical shift calculations on RNAs were performed using the automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach.

Protocol To Make Protein NMR Structures Amenable to Stable Long Time Scale Molecular Dynamics Simulations

A robust protocol for the treatment of NMR protein structures is presented that makes them amenable to long time scale molecular dynamics (MD) simulations that are stable. The protocol embeds an NMR structure in a native low energy region of the recently developed ff99SB_φψ(g24;CS) molecular mechanics force field. Extended MD trajectories that start from these structures show good consistency with proton-proton nuclear Overhauser effect data, and they reproduce NMR chemical shift data better than the original NMR structures as is demonstrated for four protein systems. Moreover, for all proteins studied here the simulations spontaneously approach the X-ray crystal structures, thereby improving the effective resolution of the initial structural models.

Investigating protein conformational energy landscapes and atomic resolution dynamics from NMR dipolar couplings: a review

Nuclear magnetic resonance spectroscopy is exquisitely sensitive to protein dynamics. In particular inter-nuclear dipolar couplings, that become measurable in solution when the protein is dissolved in a dilute liquid crystalline solution, report on all conformations sampled up to millisecond timescales. As such they provide the opportunity to describe the Boltzmann distribution present in solution at atomic resolution, and thereby to map the conformational energy landscape in unprecedented detail. The development of analytical methods and approaches based on numerical simulation and their application to numerous biologically important systems is presented.

AFNMR: automated fragmentation quantum mechanical calculation of NMR chemical shifts for biomolecules

We evaluate the performance of the automated fragmentation quantum mechanics/molecular mechanics approach (AF-QM/MM) on the calculation of protein and nucleic acid NMR chemical shifts. The AF-QM/MM approach models solvent effects implicitly through a set of surface charges computed using the Poisson-Boltzmann equation, and it can also be combined with an explicit solvent model through the placement of water molecules in the first solvation shell around the solute; the latter substantially improves the accuracy of chemical shift prediction of protons involved in hydrogen bonding with solvent. We also compare the performance of AF-QM/MM on proteins and nucleic acids with two leading empirical chemical shift prediction programs SHIFTS and SHIFTX2. Although the empirical programs outperform AF-QM/MM in predicting chemical shifts, the differences are in some cases small, and the latter can be applied to chemical shifts on biomolecules which are outside the training set employed by the empirical programs, such as structures containing ligands, metal centers, and non-standard residues. The AF-QM/MM described here is implemented in version 5 of the SHIFTS software, and is fully automated, so that only a structure in PDB format is required as input.

A Semiautomated Assignment Protocol for Methyl Group Side Chains in Large Proteins

The developments of biosynthetic specific labeling strategies for side-chain methyl groups have allowed structural and dynamic characterization of very large proteins and protein complexes. However, the assignment of the methyl-group resonances remains an Achilles' heel for NMR, as the experiments designed to correlate side chains to the protein backbone become rather insensitive with the increase of the transverse relaxation rates. In this chapter, we outline a semiempirical approach to assign the resonances of methyl-group side chains in large proteins. This method requires a crystal structure or an NMR ensemble of conformers as an input, together with NMR data sets such as nuclear Overhauser effects (NOEs) and paramagnetic relaxation enhancements (PREs), to be implemented in a computational protocol that provides a probabilistic assignment of methyl-group resonances. As an example, we report the protocol used in our laboratory to assign the side chains of the 42-kDa catalytic subunit of the cAMP-dependent protein kinase A. Although we emphasize the labeling of isoleucine, leucine, and valine residues, this method is applicable to other methyl group side chains such as those of alanine, methionine, and threonine, as well as reductively methylated cysteine side chains.

Mechanisms of amyloid formation revealed by solution NMR

Amyloid fibrils are proteinaceous elongated aggregates involved in more than fifty human diseases. Recent advances in electron microscopy and solid state NMR have allowed the characterization of fibril structures to different extents of refinement. However, structural details about the mechanism of fibril formation remain relatively poorly defined. This is mainly due to the complex, heterogeneous and transient nature of the species responsible for assembly; properties that make them difficult to detect and characterize in structural detail using biophysical techniques. The ability of solution NMR spectroscopy to investigate exchange between multiple protein states, to characterize transient and low-population species, and to study high molecular weight assemblies, render NMR an invaluable technique for studies of amyloid assembly. In this article we review state-of-the-art solution NMR methods for investigations of: (a) protein dynamics that lead to the formation of aggregation-prone species; (b) amyloidogenic intrinsically disordered proteins; and (c) protein-protein interactions on pathway to fibril formation. Together, these topics highlight the power and potential of NMR to provide atomic level information about the molecular mechanisms of one of the most fascinating problems in structural biology.

PPM_One: a static protein structure based chemical shift predictor

We mined the most recent editions of the BioMagResDataBank and the protein data bank to parametrize a new empirical knowledge-based chemical shift predictor of protein backbone atoms using either a linear or an artificial neural network model. The resulting chemical shift predictor PPM_One accepts a single static 3D structure as input and emulates the effect of local protein dynamics via interatomic steric contacts. Furthermore, the chemical shift prediction was extended to most side-chain protons and it is found that the prediction accuracy is at a level allowing an independent assessment of stereospecific assignments. For a previously established set of test proteins some overall improvement was achieved over current top-performing chemical shift prediction programs.

Integrating atomistic molecular dynamics simulations, experiments, and network analysis to study protein dynamics: strength in unity

In the last years, we have been observing remarkable improvements in the field of protein dynamics. Indeed, we can now study protein dynamics in atomistic details over several timescales with a rich portfolio of experimental and computational techniques. On one side, this provides us with the possibility to validate simulation methods and physical models against a broad range of experimental observables. On the other side, it also allows a complementary and comprehensive view on protein structure and dynamics. What is needed now is a better understanding of the link between the dynamic properties that we observe and the functional properties of these important cellular machines. To make progresses in this direction, we need to improve the physical models used to describe proteins and solvent in molecular dynamics, as well as to strengthen the integration of experiments and simulations to overcome their own limitations. Moreover, now that we have the means to study protein dynamics in great details, we need new tools to understand the information embedded in the protein ensembles and in their dynamic signature. With this aim in mind, we should enrich the current tools for analysis of biomolecular simulations with attention to the effects that can be propagated over long distances and are often associated to important biological functions. In this context, approaches inspired by network analysis can make an important contribution to the analysis of molecular dynamics simulations.

Reliable resonance assignments of selected residues of proteins with known structure based on empirical NMR chemical shift prediction

A robust NMR resonance assignment method is introduced for proteins whose 3D structure has previously been determined by X-ray crystallography. The goal of the method is to obtain a subset of correct assignments from a parsimonious set of 3D NMR experiments of (15)N, (13)C labeled proteins. Chemical shifts of sequential residue pairs are predicted from static protein structures using PPM_One, which are then compared with the corresponding experimental shifts. Globally optimized weighted matching identifies the assignments that are robust with respect to small changes in NMR cross-peak positions. The method, termed PASSPORT, is demonstrated for 4 proteins with 100-250 amino acids using 3D NHCA and a 3D CBCA(CO)NH experiments as input producing correct assignments with high reliability for 22% of the residues. The method, which works best for Gly, Ala, Ser, and Thr residues, provides assignments that serve as anchor points for additional assignments by both manual and semi-automated methods or they can be directly used for further studies, e.g. on ligand binding, protein dynamics, or post-translational modification, such as phosphorylation.

Ensemble MD simulations restrained via crystallographic data: accurate structure leads to accurate dynamics

Currently, the best existing molecular dynamics (MD) force fields cannot accurately reproduce the global free-energy minimum which realizes the experimental protein structure. As a result, long MD trajectories tend to drift away from the starting coordinates (e.g., crystallographic structures). To address this problem, we have devised a new simulation strategy aimed at protein crystals. An MD simulation of protein crystal is essentially an ensemble simulation involving multiple protein molecules in a crystal unit cell (or a block of unit cells). To ensure that average protein coordinates remain correct during the simulation, we introduced crystallography-based restraints into the MD protocol. Because these restraints are aimed at the ensemble-average structure, they have only minimal impact on conformational dynamics of the individual protein molecules. So long as the average structure remains reasonable, the proteins move in a native-like fashion as dictated by the original force field. To validate this approach, we have used the data from solid-state NMR spectroscopy, which is the orthogonal experimental technique uniquely sensitive to protein local dynamics. The new method has been tested on the well-established model protein, ubiquitin. The ensemble-restrained MD simulations produced lower crystallographic R factors than conventional simulations; they also led to more accurate predictions for crystallographic temperature factors, solid-state chemical shifts, and backbone order parameters. The predictions for (15) N R1 relaxation rates are at least as accurate as those obtained from conventional simulations. Taken together, these results suggest that the presented trajectories may be among the most realistic protein MD simulations ever reported. In this context, the ensemble restraints based on high-resolution crystallographic data can be viewed as protein-specific empirical corrections to the standard force fields.

Bayesian energy landscape tilting: towards concordant models of molecular ensembles

Predicting biological structure has remained challenging for systems such as disordered proteins that take on myriad conformations. Hybrid simulation/experiment strategies have been undermined by difficulties in evaluating errors from computational model inaccuracies and data uncertainties. Building on recent proposals from maximum entropy theory and nonequilibrium thermodynamics, we address these issues through a Bayesian energy landscape tilting (BELT) scheme for computing Bayesian hyperensembles over conformational ensembles. BELT uses Markov chain Monte Carlo to directly sample maximum-entropy conformational ensembles consistent with a set of input experimental observables. To test this framework, we apply BELT to model trialanine, starting from disagreeing simulations with the force fields ff96, ff99, ff99sbnmr-ildn, CHARMM27, and OPLS-AA. BELT incorporation of limited chemical shift and (3)J measurements gives convergent values of the peptide's α, β, and PPII conformational populations in all cases. As a test of predictive power, all five BELT hyperensembles recover set-aside measurements not used in the fitting and report accurate errors, even when starting from highly inaccurate simulations. BELT's principled framework thus enables practical predictions for complex biomolecular systems from discordant simulations and sparse data.