Deciphering protein dynamics from NMR data using explicit structure sampling and selection

The pathogen-encoded signalling receptor Tir exploits host-like intrinsic disorder for infection

The translocated intimin receptor (Tir) is an essential type III secretion system (T3SS) effector of attaching and effacing pathogens contributing to the global foodborne disease burden. Tir acts as a cell-surface receptor in host cells, rewiring intracellular processes by targeting multiple host proteins. We investigated the molecular basis for Tir's binding diversity in signalling, finding that Tir is a disordered protein with host-like binding motifs. Unexpectedly, also are several other T3SS effectors. By an integrative approach, we reveal that Tir dimerises via an antiparallel OB-fold within a highly disordered N-terminal cytosolic domain. Also, it has a long disordered C-terminal cytosolic domain partially structured at host-like motifs that bind lipids. Membrane affinity depends on lipid composition and phosphorylation, highlighting a previously unrecognised host interaction impacting Tir-induced actin polymerisation and cell death. Furthermore, multi-site tyrosine phosphorylation enables Tir to engage host SH2 domains in a multivalent fuzzy complex, consistent with Tir's scaffolding role and binding promiscuity. Our findings provide insights into the intracellular Tir domains, highlighting the ability of T3SS effectors to exploit host-like protein disorder as a strategy for host evasion.

An RNA excited conformational state at atomic resolution

Sparse and short-lived excited RNA conformational states are essential players in cell physiology, disease, and therapeutic development, yet determining their 3D structures remains challenging. Combining mutagenesis, NMR spectroscopy, and computational modeling, we determined the 3D structural ensemble formed by a short-lived (lifetime ~2.1 ms) lowly-populated (~0.4%) conformational state in HIV-1 TAR RNA. Through a strand register shift, the excited conformational state completely remodels the 3D structure of the ground state (RMSD from the ground state = 7.2 ± 0.9 Å), forming a surprisingly more ordered conformational ensemble rich in non-canonical mismatches. The structure impedes the formation of the motifs recognized by Tat and the super elongation complex, explaining why this alternative TAR conformation cannot activate HIV-1 transcription. The ability to determine the 3D structures of fleeting RNA states using the presented methodology holds great promise for our understanding of RNA biology, disease mechanisms, and the development of RNA-targeting therapeutics.

Kinetic Resolution of the Atomic 3D Structures Formed by Ground and Excited Conformational States in an RNA Dynamic Ensemble

Knowing the 3D structures formed by the various conformations populating the RNA free-energy landscape, their relative abundance, and kinetic interconversion rates is required to obtain a quantitative and predictive understanding of how RNAs fold and function at the atomic level. While methods integrating ensemble-averaged experimental data with computational modeling are helping define the most abundant conformations in RNA ensembles, elucidating their kinetic rates of interconversion and determining the 3D structures of sparsely populated short-lived RNA excited conformational states (ESs) remains challenging. Here, we developed an approach integrating Rosetta-FARFAR RNA structure prediction with NMR residual dipolar couplings and relaxation dispersion that simultaneously determines the 3D structures formed by the ground-state (GS) and ES subensembles, their relative abundance, and kinetic rates of interconversion. The approach is demonstrated on HIV-1 TAR, whose six-nucleotide apical loop was previously shown to form a sparsely populated (∼13%) short-lived (lifetime ∼ 45 μs) ES. In the GS, the apical loop forms a broad distribution of open conformations interconverting on the pico-to-nanosecond time scale. Most residues are unpaired and preorganized to bind the Tat-superelongation protein complex. The apical loop zips up in the ES, forming a narrow distribution of closed conformations, which sequester critical residues required for protein recognition. Our work introduces an approach for determining the 3D ensemble models formed by sparsely populated RNA conformational states, provides a rare atomic view of an RNA ES, and kinetically resolves the atomic 3D structures of RNA conformational substates, interchanging on time scales spanning 6 orders of magnitude, from picoseconds to microseconds.

Reweighting methods for elucidation of conformation ensembles of proteins

Proteins are inherently dynamic macromolecules that exist in equilibrium among multiple conformational states, and motions of protein backbone and side chains are fundamental to biological function. The ability to characterize the conformational landscape is particularly important for intrinsically disordered proteins, multidomain proteins, and weakly bound complexes, where single-structure representations are inadequate. As the focus of structural biology shifts from relatively rigid macromolecules toward larger and more complex systems and molecular assemblies, there is a need for structural approaches that can paint a more realistic picture of such conformationally heterogeneous systems. Here, we review reweighting methods for elucidation of structural ensembles based on experimental data, with the focus on applications to multidomain proteins.

Interdomain Dynamics via Paramagnetic NMR on the Highly Flexible Complex Calmodulin/Munc13-1

Paramagnetic NMR constraints are very useful to study protein interdomain motion, but their interpretation is not always straightforward. On the example of the particularly flexible complex Calmodulin/Munc13-1, we present a new approach to characterize this motion with pseudocontact shifts and residual dipolar couplings. Using molecular mechanics, we sampled the conformational space of the complex and used a genetic algorithm to find ensembles that are in agreement with the data. We used the Bayesian information criterion to determine the ideal ensemble size. This way, we were able to make an accurate, unambiguous, reproducible model of the interdomain motion of Calmodulin/Munc13-1 without prior knowledge about the domain orientation from crystallography.

Protein Dynamics to Define and Refine Disordered Protein Ensembles

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

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.

Developments in solution-state NMR yield broader and deeper views of the dynamic ensembles of nucleic acids

Nucleic acids do not fold into a single conformation, and dynamic ensembles are needed to describe their propensities to cycle between different conformations when performing cellular functions. We review recent advances in solution-state nuclear magnetic resonance (NMR) methods and their integration with computational techniques that are improving the ability to probe the dynamic ensembles of DNA and RNA. These include computational approaches for predicting chemical shifts from structure and generating conformational libraries from sequence, measurements of exact nuclear Overhauser effects, development of new probes to study chemical exchange using relaxation dispersion, faster and more sensitive real-time NMR techniques, and new NMR approaches to tackle large nucleic acid assemblies. We discuss how these advances are leading to new mechanistic insights into gene expression and regulation.

Amyloid Oligomers: A Joint Experimental/Computational Perspective on Alzheimer's Disease, Parkinson's Disease, Type II Diabetes, and Amyotrophic Lateral Sclerosis

Protein misfolding and aggregation is observed in many amyloidogenic diseases affecting either the central nervous system or a variety of peripheral tissues. Structural and dynamic characterization of all species along the pathways from monomers to fibrils is challenging by experimental and computational means because they involve intrinsically disordered proteins in most diseases. Yet understanding how amyloid species become toxic is the challenge in developing a treatment for these diseases. Here we review what computer, in vitro, in vivo, and pharmacological experiments tell us about the accumulation and deposition of the oligomers of the (Aβ, tau), α-synuclein, IAPP, and superoxide dismutase 1 proteins, which have been the mainstream concept underlying Alzheimer's disease (AD), Parkinson's disease (PD), type II diabetes (T2D), and amyotrophic lateral sclerosis (ALS) research, respectively, for many years.

Modeling of Hidden Structures Using Sparse Chemical Shift Data from NMR Relaxation Dispersion

NMR relaxation dispersion measurements report on conformational changes occurring on the μs-ms timescale. Chemical shift information derived from relaxation dispersion can be used to generate structural models of weakly populated alternative conformational states. Current methods to obtain such models rely on determining the signs of chemical shift changes between the conformational states, which are difficult to obtain in many situations. Here, we use a "sample and select" method to generate relevant structural models of alternative conformations of the C-terminal-associated region of Escherichia coli dihydrofolate reductase (DHFR), using only unsigned chemical shift changes for backbone amides and carbonyls (¹H, ¹⁵N, and ¹³C'). We find that CS-Rosetta sampling with unsigned chemical shift changes generates a diversity of structures that are sufficient to characterize a minor conformational state of the C-terminal region of DHFR. The excited state differs from the ground state by a change in secondary structure, consistent with previous predictions from chemical shift hypersurfaces and validated by the x-ray structure of a partially humanized mutant of E. coli DHFR (N23PP/G51PEKN). The results demonstrate that the combination of fragment modeling with sparse chemical shift data can determine the structure of an alternative conformation of DHFR sampled on the μs-ms timescale. Such methods will be useful for characterizing alternative states, which can potentially be used for in silico drug screening, as well as contributing to understanding the role of minor states in biology and molecular evolution.

Rapid and accurate determination of atomistic RNA dynamic ensemble models using NMR and structure prediction

Biomolecules form dynamic ensembles of many inter-converting conformations which are key for understanding how they fold and function. However, determining ensembles is challenging because the information required to specify atomic structures for thousands of conformations far exceeds that of experimental measurements. We addressed this data gap and dramatically simplified and accelerated RNA ensemble determination by using structure prediction tools that leverage the growing database of RNA structures to generate a conformation library. Refinement of this library with NMR residual dipolar couplings provided an atomistic ensemble model for HIV-1 TAR, and the model accuracy was independently supported by comparisons to quantum-mechanical calculations of NMR chemical shifts, comparison to a crystal structure of a substate, and through designed ensemble redistribution via atomic mutagenesis. Applications to TAR bulge variants and more complex tertiary RNAs support the generality of this approach and the potential to make the determination of atomic-resolution RNA ensembles routine.

Determining dynamic ensembles of biomolecules is still challenging. Here the authors present an approach for rapid RNA ensemble determination that combines RNA structure prediction tools and NMR residual dipolar coupling data and use it to determine atomistic ensemble models for a variety of RNAs.

Experimentally-driven protein structure modeling

Revolutions in natural and exact sciences started at the dawn of last century have led to the explosion of theoretical, experimental, and computational approaches to determine structures of molecules, complexes, as well as their rich conformational dynamics. Since different experimental methods produce information that is attributed to specific time and length scales, corresponding computational methods have to be tailored to these scales and experiments. These methods can be then combined and integrated in scales, hence producing a fuller picture of molecular structure and motion from the "puzzle pieces" offered by various experiments. Here, we describe a number of computational approaches to utilize experimental data to glance into structure of proteins and understand their dynamics. We will also discuss the limitations and the resolution of the constraints-based modeling approaches. SIGNIFICANCE: Experimentally-driven computational structure modeling and determination is a rapidly evolving alternative to traditional approaches for molecular structure determination. These new hybrid experimental-computational approaches are proving to be a powerful microscope to glance into the structural features of intrinsically or partially disordered proteins, dynamics of molecules and complexes. In this review, we describe various approaches in the field of experimentally-driven computational structure modeling.

How to learn from inconsistencies: Integrating molecular simulations with experimental data

Molecular simulations and biophysical experiments can be used to provide independent and complementary insights into the molecular origin of biological processes. A particularly useful strategy is to use molecular simulations as a modeling tool to interpret experimental measurements, and to use experimental data to refine our biophysical models. Thus, explicit integration and synergy between molecular simulations and experiments is fundamental for furthering our understanding of biological processes. This is especially true in the case where discrepancies between measured and simulated observables emerge. In this chapter, we provide an overview of some of the core ideas behind methods that were developed to improve the consistency between experimental information and numerical predictions. We distinguish between situations where experiments are used to refine our understanding and models of specific systems, and situations where experiments are used more generally to refine transferable models. We discuss different philosophies and attempt to unify them in a single framework. Until now, such integration between experiments and simulations have mostly been applied to equilibrium data, and we discuss more recent developments aimed to analyze time-dependent or time-resolved data.

Enhancing NMR derived ensembles with kinetics on multiple timescales

Nuclear magnetic resonance (NMR) has the unique advantage of elucidating the structure and dynamics of biomolecules in solution at physiological temperatures, where they are in constant movement on timescales from picoseconds to milliseconds. Such motions have been shown to be critical for enzyme catalysis, allosteric regulation, and molecular recognition. With NMR being particularly sensitive to these timescales, detailed information about the kinetics can be acquired. However, nearly all methods of NMR-based biomolecular structure determination neglect kinetics, which introduces a large approximation to the underlying physics, limiting both structural resolution and the ability to accurately determine molecular flexibility. Here we present the Kinetic Ensemble approach that uses a hierarchy of interconversion rates between a set of ensemble members to rigorously calculate Nuclear Overhauser Effect (NOE) intensities. It can be used to simultaneously refine both temporal and structural coordinates. By generalizing ideas from the extended model free approach, the method can analyze the amplitudes and kinetics of motions anywhere along the backbone or side chains. Furthermore, analysis of a large set of crystal structures suggests that NOE data contains a surprising amount of high-resolution information that is better modeled using our approach. The Kinetic Ensemble approach provides the means to unify numerous types of experiments under a single quantitative framework and more fully characterize and exploit kinetically distinct protein states. While we apply the approach here to the protein ubiquitin and cross validate it with previously derived datasets, the approach can be applied to any protein for which NOE data is available.

Integrative Approaches in Structural Biology: A More Complete Picture from the Combination of Individual Techniques

With the recent technological and computational advancements, structural biology has begun to tackle more and more difficult questions, including complex biochemical pathways and transient interactions among macromolecules. This has demonstrated that, to approach the complexity of biology, one single technique is largely insufficient and unable to yield thorough answers, whereas integrated approaches have been more and more adopted with successful results. Traditional structural techniques (X-ray crystallography and Nuclear Magnetic Resonance (NMR)) and the emerging ones (cryo-electron microscopy (cryo-EM), Small Angle X-ray Scattering (SAXS)), together with molecular modeling, have pros and cons which very nicely complement one another. In this review, three examples of synergistic approaches chosen from our previous research will be revisited. The first shows how the joint use of both solution and solid-state NMR (SSNMR), X-ray crystallography, and cryo-EM is crucial to elucidate the structure of polyethylene glycol (PEG)ylated asparaginase, which would not be obtainable through any of the techniques taken alone. The second deals with the integrated use of NMR, X-ray crystallography, and SAXS in order to elucidate the catalytic mechanism of an enzyme that is based on the flexibility of the enzyme itself. The third one shows how it is possible to put together experimental data from X-ray crystallography and NMR restraints in order to refine a protein model in order to obtain a structure which simultaneously satisfies both experimental datasets and is therefore closer to the ‘real structure’.

An arsenal of methods for the experimental characterization of intrinsically disordered proteins - How to choose and combine them?

In this review, we detail the most common experimental approaches to assess and characterize protein intrinsic structural disorder, with the notable exception of NMR and EPR spectroscopy, two ideally suited approaches that will be described in depth in two other reviews within this special issue. We discuss the advantages, the limitations, as well as the caveats of the various methods. We also describe less common and more demanding approaches that enable achieving further insights into the conformational properties of IDPs. Finally, we present recent developments that have enabled assessment of structural disorder in living cells, and discuss the currently available methods to model IDPs as conformational ensembles.

Limits in accuracy and a strategy of RNA structure prediction using experimental information

RNA structural complexity and flexibility present a challenge for computational modeling efforts. Experimental information and bioinformatics data can be used as restraints to improve the accuracy of RNA tertiary structure prediction. Regarding utilization of restraints, the fundamental questions are: (i) What is the limit in prediction accuracy that one can achieve with arbitrary number of restraints? (ii) Is there a strategy for selection of the minimal number of restraints that would result in the best structural model? We address the first question by testing the limits in prediction accuracy using native contacts as restraints. To address the second question, we develop an algorithm based on the distance variation allowed by secondary structure (DVASS), which ranks restraints according to their importance to RNA tertiary structure prediction. We find that due to kinetic traps, the greatest improvement in the structure prediction accuracy is achieved when we utilize only 40-60% of the total number of native contacts as restraints. When the restraints are sorted by DVASS algorithm, using only the first 20% ranked restraints can greatly improve the prediction accuracy. Our findings suggest that only a limited number of strategically selected distance restraints can significantly assist in RNA structure modeling.

Determination of Structural Ensembles of Flexible Molecules in Solution from NMR Data Undergoing Spin Diffusion

Spin diffusion is a formidable problem when interpreting NMR data of chemical compounds. We developed a method to reconstruct the conformational ensemble of flexible molecules displaying spin diffusion, which minimizes the subjective bias in the interpretation of experimental data and which can be used routinely to obtain sets of structures with the correct thermodynamic weights. We showed in the case of a flexible molecule that the correct conformational ensemble is quite different from that obtained with standard methods.

Computational Probing of Watson-Crick/Hoogsteen Breathing in a DNA Duplex Containing N1-Methylated Adenine

DNA breathing is a local conformational fluctuation spontaneously occurring in double-stranded DNAs. In particular, the possibility of individual base pairs (bps) in duplex DNA to flip between alternate bp modes, i.e., Watson-Crick (WC)-like and Hoogsteen (HG)-like, at relevant time scales has impacted DNA research fields for many years. In this study, to computationally probe effects of chemical modification on the DNA breathing, we present a free energy landscape of spontaneous thermal transitions between WC and HG bps in a free DNA duplex containing N1-methylated adenine (m1A). For the current free energy computation, a variant of well-tempered metadynamics simulation was extensively performed for a total of 40 μs to produce free energy surfaces. The free energy profile indicated that, upon the chemical modification of adenine, the HG bp (m1A·T) was located in the most favorable conformation (96.7%); however, the canonical WC bp (m1A·T) was distorted into two WC-like bps of WC* (2.8%) and WC** (0.5%). The conformational exchange between these two minor WC-like bps occurs with the first hundred nanoseconds. The transition between WC-like and HG bp features multiple transition pathways displaying various extents of base flipping in combination with glycosidic rotation. Analysis of the simulated ensemble showed that the m1A-induced changes of the backbone and sugar pucker were in a reasonable agreement with previous results inferred from NMR experiments. Also, this study revealed that the formation of the stable HG bp upon the mutation alters the characteristics of dynamic fluctuations of the neighboring WC residues of m1A. We expect this simulation approach to be a robust computational scheme to complement and guide future high-resolution experiments on many outstanding issues of duplex DNA breathing.

SAXS-guided Enhanced Unbiased Sampling for Structure Determination of Proteins and Complexes

Molecular simulations can be utilized to predict protein structure ensembles and dynamics, though sufficient sampling of molecular ensembles and identification of key biologically relevant conformations remains challenging. Low-resolution experimental techniques provide valuable structural information on biomolecule at near-native conditions, which are often combined with molecular simulations to determine and refine protein structural ensembles. In this study, we demonstrate how small angle x-ray scattering (SAXS) information can be incorporated in Markov state model-based adaptive sampling strategy to enhance time efficiency of unbiased MD simulations and identify functionally relevant conformations of proteins and complexes. Our results show that using SAXS data combined with additional information, such as thermodynamics and distance restraints, we are able to distinguish otherwise degenerate structures due to the inherent ambiguity of SAXS pattern. We further demonstrate that adaptive sampling guided by SAXS and hybrid information can significantly reduce the computation time required to discover target structures. Overall, our findings demonstrate the potential of this hybrid approach in predicting near-native structures of proteins and complexes. Other low-resolution experimental information can be incorporated in a similar manner to collectively enhance unbiased sampling and improve the accuracy of structure prediction from simulation.

Conformational states of Zika virus non-structural protein 3 determined by molecular dynamics simulations with small-angle X-Ray scattering data

Zika virus (ZIKV) has become a great public health emergency. Its non-structural protein 3 (NS3) is a key enzyme in viral replication and has been considered as a potential therapeutic target. A conformational characterization of ZIKV NS3 is critical for a comprehensive understanding of its molecular interactions and functions. However, the high conformational flexibility of solution NS3 obstacles the structural characterization of NS3 solely from the experimental observable that averages over its heterogeneous conformations. Here, we employed replica exchange with solute tempering (REST) method to simulate the di-domain protein ZIKV NS3. Three independent MD simulations identified a conserved conformational ensemble of NS3, consisting of a major conformational state and several minor states from compact to loose conformations. The major state agrees well with the scattering profile from small-angle X-ray scattering (SAXS) experiments. Moreover, the simulated ensemble is supported by a direct data-fitting result that requires both short- and long-range structural contacts to recover the experimental data. We discussed the interplay between simulation and experiment in ensemble construction of flexible biomolecules and shed light on the physically derived conformational ensembles.

Investigating energy-based pool structure selection in the structure ensemble modeling with experimental distance constraints: The example from a multidomain protein Pub1

The structural variations of multidomain proteins with flexible parts mediate many biological processes, and a structure ensemble can be determined by selecting a weighted combination of representative structures from a simulated structure pool, producing the best fit to experimental constraints such as interatomic distance. In this study, a hybrid structure-based and physics-based atomistic force field with an efficient sampling strategy is adopted to simulate a model di-domain protein against experimental paramagnetic relaxation enhancement (PRE) data that correspond to distance constraints. The molecular dynamics simulations produce a wide range of conformations depicted on a protein energy landscape. Subsequently, a conformational ensemble recovered with low-energy structures and the minimum-size restraint is identified in good agreement with experimental PRE rates, and the result is also supported by chemical shift perturbations and small-angle X-ray scattering data. It is illustrated that the regularizations of energy and ensemble-size prevent an arbitrary interpretation of protein conformations. Moreover, energy is found to serve as a critical control to refine the structure pool and prevent data overfitting, because the absence of energy regularization exposes ensemble construction to the noise from high-energy structures and causes a more ambiguous representation of protein conformations. Finally, we perform structure-ensemble optimizations with a topology-based structure pool, to enhance the understanding on the ensemble results from different sources of pool candidates.

Solving protein structures using short-distance cross-linking constraints as a guide for discrete molecular dynamics simulations

We present an integrated experimental and computational approach for de novo protein structure determination in which short-distance cross-linking data are incorporated into rapid discrete molecular dynamics (DMD) simulations as constraints, reducing the conformational space and achieving the correct protein folding on practical time scales. We tested our approach on myoglobin and FK506 binding protein-models for α helix-rich and β sheet-rich proteins, respectively-and found that the lowest-energy structures obtained were in agreement with the crystal structure, hydrogen-deuterium exchange, surface modification, and long-distance cross-linking validation data. Our approach is readily applicable to other proteins with unknown structures.

Insights into Watson-Crick/Hoogsteen breathing dynamics and damage repair from the solution structure and dynamic ensemble of DNA duplexes containing m1A

In the canonical DNA double helix, Watson-Crick (WC) base pairs (bps) exist in dynamic equilibrium with sparsely populated (∼0.02-0.4%) and short-lived (lifetimes ∼0.2-2.5 ms) Hoogsteen (HG) bps. To gain insights into transient HG bps, we used solution-state nuclear magnetic resonance spectroscopy, including measurements of residual dipolar couplings and molecular dynamics simulations, to examine how a single HG bp trapped using the N1-methylated adenine (m1A) lesion affects the structural and dynamic properties of two duplexes. The solution structure and dynamic ensembles of the duplexes reveals that in both cases, m1A forms a m1A•T HG bp, which is accompanied by local and global structural and dynamic perturbations in the double helix. These include a bias toward the BI backbone conformation; sugar repuckering, major-groove directed kinking (∼9°); and local melting of neighboring WC bps. These results provide atomic insights into WC/HG breathing dynamics in unmodified DNA duplexes as well as identify structural and dynamic signatures that could play roles in m1A recognition and repair.

A critical assessment of methods to recover information from averaged data

Conformational heterogeneity is key to the function of many biomacromolecules, but only a few groups have tried to characterize it until recently. Now, thanks to the increased throughput of experimental data and the increased computational power, the problem of the characterization of protein structural variability has become more and more popular. Several groups have devoted their efforts in trying to create quantitative, reliable and accurate protocols for extracting such information from averaged data. We analyze here different approaches, discussing strengths and weaknesses of each. All approaches can roughly be clustered into two groups: those satisfying the maximum entropy principle and those recovering ensembles composed of a restricted number of molecular conformations. In the first case, the solution focuses on the features that are common to all the infinite solutions satisfying the experimental data; in the second case, the reconstructed ensemble shows the conformational regions where a large probability can be placed. The upper limits for conformational probabilities (MaxOcc) can also be calculated. We also give an overview of the mainstream experimental observables, with considerations on the assumptions underlying their usage.

Principles of protein structural ensemble determination

The biological functions of protein molecules are intimately dependent on their conformational dynamics. This aspect is particularly evident for disordered proteins, which constitute perhaps one-third of the human proteome. Therefore, structural ensembles often offer more useful representations of proteins than individual conformations. Here, we describe how the well-established principles of protein structure determination should be extended to the case of protein structural ensembles determination. These principles concern primarily how to deal with conformationally heterogeneous states, and with experimental measurements that are averaged over such states and affected by a variety of errors. We first review the growing literature of recent methods that combine experimental and computational information to model structural ensembles, highlighting their similarities and differences. We then address some conceptual problems in the determination of structural ensembles and define future goals towards the establishment of objective criteria for the comparison, validation, visualization and dissemination of such ensembles.

Predicting protein backbone chemical shifts from Cα coordinates: extracting high resolution experimental observables from low resolution models

Given the demonstrated utility of coarse-grained modeling and simulations approaches in studying protein structure and dynamics, developing methods that allow experimental observables to be directly recovered from coarse-grained models is of great importance. In this work, we develop one such method that enables protein backbone chemical shifts (¹HN, ¹Hα, ¹³Cα, ¹³C, ¹³Cβ, and ¹⁵N) to be predicted from Cα coordinates. We show that our Cα-based method, LARMOR^Cα, predicts backbone chemical shifts with comparable accuracy to some all-atom approaches. More importantly, we demonstrate that LARMOR^Cα predicted chemical shifts are able to resolve native structure from decoy pools that contain both native and non-native models, and so it is sensitive to protein structure. As an application, we use LARMOR^Cα to characterize the transient state of the fast-folding protein gpW using recently published NMR relaxation dispersion derived backbone chemical shifts. The model we obtain is consistent with the previously proposed model based on independent analysis of the chemical shift dispersion pattern of the transient state. We anticipate that LARMOR^Cα will find utility as a tool that enables important protein conformational substates to be identified by “parsing” trajectories and ensembles generated using coarse-grained modeling and simulations.

Comprehensive structural and dynamical view of an unfolded protein from the combination of single-molecule FRET, NMR, and SAXS

The properties of unfolded proteins are essential both for the mechanisms of protein folding and for the function of the large group of intrinsically disordered proteins. However, the detailed structural and dynamical characterization of these highly dynamic and conformationally heterogeneous ensembles has remained challenging. Here we combine and compare three of the leading techniques for the investigation of unfolded proteins, NMR spectroscopy (NMR), small-angle X-ray scattering (SAXS), and single-molecule Förster resonance energy transfer (FRET), with the goal of quantitatively testing their consistency and complementarity and for obtaining a comprehensive view of the unfolded-state ensemble. Using unfolded ubiquitin as a test case, we find that its average dimensions derived from FRET and from structural ensembles calculated using the program X-PLOR-NIH based on NMR and SAXS restraints agree remarkably well; even the shapes of the underlying intramolecular distance distributions are in good agreement, attesting to the reliability of the approaches. The NMR-based results provide a highly sensitive way of quantifying residual structure in the unfolded state. FRET-based nanosecond fluorescence correlation spectroscopy allows long-range distances and chain dynamics to be probed in a time range inaccessible by NMR. The combined techniques thus provide a way of optimally using the complementarity of the available methods for a quantitative structural and dynamical description of unfolded proteins both at the global and the local level.

Constructing Structure Ensembles of Intrinsically Disordered Proteins from Chemical Shift Data

Modeling the structural ensemble of intrinsically disordered proteins (IDPs), which lack fixed structures, is essential in understanding their cellular functions and revealing their regulation mechanisms in signaling pathways of related diseases (e.g., cancers and neurodegenerative disorders). Though the ensemble concept has been widely believed to be the most accurate way to depict 3D structures of IDPs, few of the traditional ensemble-based approaches effectively address the degeneracy problem that occurs when multiple solutions are consistent with experimental data and is the main challenge in the IDP ensemble construction task. In this article, based on a predefined conformational library, we formalize the structure ensemble construction problem into a least squares framework, which provides the optimal solution when the data constraints outnumber unknown variables. To deal with the degeneracy problem, we further propose a regularized regression approach based on the elastic net technique with the assumption that the weights to be estimated for individual structures in the ensemble are sparse. We have validated our methods through a reference ensemble approach as well as by testing the real biological data of three proteins, including alpha-synuclein, the translocation domain of Colocin N, and the K18 domain of Tau protein.

Dynamic Protein Interaction Networks and New Structural Paradigms in Signaling

Understanding signaling and other complex biological processes requires elucidating the critical roles of intrinsically disordered proteins (IDPs) and regions (IDRs), which represent ∼30% of the proteome and enable unique regulatory mechanisms. In this review, we describe the structural heterogeneity of disordered proteins that underpins these mechanisms and the latest progress in obtaining structural descriptions of conformational ensembles of disordered proteins that are needed for linking structure and dynamics to function. We describe the diverse interactions of IDPs that can have unusual characteristics such as "ultrasensitivity" and "regulated folding and unfolding". We also summarize the mounting data showing that large-scale assembly and protein phase separation occurs within a variety of signaling complexes and cellular structures. In addition, we discuss efforts to therapeutically target disordered proteins with small molecules. Overall, we interpret the remodeling of disordered state ensembles due to binding and post-translational modifications within an expanded framework for allostery that provides significant insights into how disordered proteins transmit biological information.

Controlling Allosteric Networks in Proteins

Allosteric transition, defined as conformational changes induced by ligand binding, is one of the fundamental properties of proteins. Allostery has been observed and characterized in many proteins, and has been recently utilized to control protein function via regulation of protein activity. Here, we review the physical and evolutionary origin of protein allostery, as well as its importance to protein regulation, drug discovery, and biological processes in living systems. We describe recently developed approaches to identify allosteric pathways, connected sets of pairwise interactions that are responsible for propagation of conformational change from the ligand-binding site to a distal functional site. We then present experimental and computational protein engineering approaches for control of protein function by modulation of allosteric sites. As an example of application of these approaches, we describe a synergistic computational and experimental approach to rescue the cystic-fibrosis-associated protein cystic fibrosis transmembrane conductance regulator, which upon deletion of a single residue misfolds and causes disease. This example demonstrates the power of allosteric manipulation in proteins to both elucidate mechanisms of molecular function and to develop therapeutic strategies that rescue those functions. Allosteric control of proteins provides a tool to shine a light on the complex cascades of cellular processes and facilitate unprecedented interrogation of biological systems.

How to tackle protein structural data from solution and solid state: An integrated approach

Long-range NMR restraints, such as diamagnetic residual dipolar couplings and paramagnetic data, can be used to determine 3D structures of macromolecules. They are also used to monitor, and potentially to improve, the accuracy of a macromolecular structure in solution by validating or "correcting" a crystal model. Since crystal structures suffer from crystal packing forces they may not be accurate models for the macromolecular structures in solution. However, the presence of real differences should be tested for by simultaneous refinement of the structure using both crystal and solution NMR data. To achieve this, the program REFMAC5 from CCP4 was modified to allow the simultaneous use of X-ray crystallographic and paramagnetic NMR data and/or diamagnetic residual dipolar couplings. Inconsistencies between crystal structures and solution NMR data, if any, may be due either to structural rearrangements occurring on passing from the solution to solid state, or to a greater degree of conformational heterogeneity in solution with respect to the crystal. In the case of multidomain proteins, paramagnetic restraints can provide the correct mutual orientations and positions of domains in solution, as well as information on the conformational variability experienced by the macromolecule.

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.

Modulating RNA Alignment Using Directional Dynamic Kinks: Application in Determining an Atomic-Resolution Ensemble for a Hairpin using NMR Residual Dipolar Couplings

Approaches that combine experimental data and computational molecular dynamics (MD) to determine atomic resolution ensembles of biomolecules require the measurement of abundant experimental data. NMR residual dipolar couplings (RDCs) carry rich dynamics information, however, difficulties in modulating overall alignment of nucleic acids have limited the ability to fully extract this information. We present a strategy for modulating RNA alignment that is based on introducing variable dynamic kinks in terminal helices. With this strategy, we measured seven sets of RDCs in a cUUCGg apical loop and used this rich data set to test the accuracy of an 0.8 μs MD simulation computed using the Amber ff10 force field as well as to determine an atomic resolution ensemble. The MD-generated ensemble quantitatively reproduces the measured RDCs, but selection of a sub-ensemble was required to satisfy the RDCs within error. The largest discrepancies between the RDC-selected and MD-generated ensembles are observed for the most flexible loop residues and backbone angles connecting the loop to the helix, with the RDC-selected ensemble resulting in more uniform dynamics. Comparison of the RDC-selected ensemble with NMR spin relaxation data suggests that the dynamics occurs on the ps-ns time scales as verified by measurements of R(1ρ) relaxation-dispersion data. The RDC-satisfying ensemble samples many conformations adopted by the hairpin in crystal structures indicating that intrinsic plasticity may play important roles in conformational adaptation. The approach presented here can be applied to test nucleic acid force fields and to characterize dynamics in diverse RNA motifs at atomic resolution.

Unveiling Inherent Degeneracies in Determining Population-Weighted Ensembles of Interdomain Orientational Distributions Using NMR Residual Dipolar Couplings: Application to RNA Helix Junction Helix Motifs

A growing number of studies employ time-averaged experimental data to determine dynamic ensembles of biomolecules. While it is well-known that different ensembles can satisfy experimental data to within error, the extent and nature of these degeneracies, and their impact on the accuracy of the ensemble determination remains poorly understood. Here, we use simulations and a recently introduced metric for assessing ensemble similarity to explore degeneracies in determining ensembles using NMR residual dipolar couplings (RDCs) with specific application to A-form helices in RNA. Various target ensembles were constructed representing different domain-domain orientational distributions that are confined to a topologically restricted (<10%) conformational space. Five independent sets of ensemble averaged RDCs were then computed for each target ensemble and a "sample and select" scheme used to identify degenerate ensembles that satisfy RDCs to within experimental uncertainty. We find that ensembles with different ensemble sizes and that can differ significantly from the target ensemble (by as much as ∑Ω ∼ 0.4 where ∑Ω varies between 0 and 1 for maximum and minimum ensemble similarity, respectively) can satisfy the ensemble averaged RDCs. These deviations increase with the number of unique conformers and breadth of the target distribution, and result in significant uncertainty in determining conformational entropy (as large as 5 kcal/mol at T = 298 K). Nevertheless, the RDC-degenerate ensembles are biased toward populated regions of the target ensemble, and capture other essential features of the distribution, including the shape. Our results identify ensemble size as a major source of uncertainty in determining ensembles and suggest that NMR interactions such as RDCs and spin relaxation, on their own, do not carry the necessary information needed to determine conformational entropy at a useful level of precision. The framework introduced here provides a general approach for exploring degeneracies in ensemble determination for different types of experimental data.

Information content of long-range NMR data for the characterization of conformational heterogeneity

Long-range NMR data, namely residual dipolar couplings (RDCs) from external alignment and paramagnetic data, are becoming increasingly popular for the characterization of conformational heterogeneity of multidomain biomacromolecules and protein complexes. The question addressed here is how much information is contained in these averaged data. We have analyzed and compared the information content of conformationally averaged RDCs caused by steric alignment and of both RDCs and pseudocontact shifts caused by paramagnetic alignment, and found that, despite the substantial differences, they contain a similar amount of information. Furthermore, using several synthetic tests we find that both sets of data are equally good towards recovering the major state(s) in conformational distributions.

NMR studies of dynamic biomolecular conformational ensembles

Multidimensional heteronuclear NMR approaches can provide nearly complete sequential signal assignments of isotopically enriched biomolecules. The availability of assignments together with measurements of spin relaxation rates, residual spin interactions, J-couplings and chemical shifts provides information at atomic resolution about internal dynamics on timescales ranging from ps to ms, both in solution and in the solid state. However, due to the complexity of biomolecules, it is not possible to extract a unique atomic-resolution description of biomolecular motions even from extensive NMR data when many conformations are sampled on multiple timescales. For this reason, powerful computational approaches are increasingly applied to large NMR data sets to elucidate conformational ensembles sampled by biomolecules. In the past decade, considerable attention has been directed at an important class of biomolecules that function by binding to a wide variety of target molecules. Questions of current interest are: "Does the free biomolecule sample a conformational ensemble that encompasses the conformations found when it binds to various targets; and if so, on what time scale is the ensemble sampled?" This article reviews recent efforts to answer these questions, with a focus on comparing ensembles obtained for the same biomolecules by different investigators. A detailed comparison of results obtained is provided for three biomolecules: ubiquitin, calmodulin and the HIV-1 trans-activation response RNA.

Recovering a representative conformational ensemble from underdetermined macromolecular structural data

Structural analysis of proteins and nucleic acids is complicated by their inherent flexibility, conferred, for example, by linkers between their contiguous domains. Therefore, the macromolecule needs to be represented by an ensemble of conformations instead of a single conformation. Determining this ensemble is challenging because the experimental data are a convoluted average of contributions from multiple conformations. As the number of the ensemble degrees of freedom generally greatly exceeds the number of independent observables, directly deconvolving experimental data into a representative ensemble is an ill-posed problem. Recent developments in sparse approximations and compressive sensing have demonstrated that useful information can be recovered from underdetermined (ill-posed) systems of linear equations by using sparsity regularization. Inspired by these advances, we designed the Sparse Ensemble Selection (SES) method for recovering multiple conformations from a limited number of observations. SES is more general and accurate than previously published minimum-ensemble methods, and we use it to obtain representative conformational ensembles of Lys48-linked diubiquitin, characterized by the residual dipolar coupling data measured at several pH conditions. These representative ensembles are validated against NMR chemical shift perturbation data and compared to maximum-entropy results. The SES method reproduced and quantified the previously observed pH dependence of the major conformation of Lys48-linked diubiquitin, and revealed lesser-populated conformations that are preorganized for binding known diubiquitin receptors, thus providing insights into possible mechanisms of receptor recognition by polyubiquitin. SES is applicable to any experimental observables that can be expressed as a weighted linear combination of data for individual states.

Insights into domain-domain motions in proteins and RNA from solution NMR

Many multidomain proteins and ribonucleic acids consist of domains that autonomously fold and that are linked together by flexible junctions. This architectural design allows domains to sample a wide range of positions with respect to one another, yet do so in a way that retains structural specificity, since the number of sampled conformations remains extremely small compared to the total conformations that would be sampled if the domains were connected by an infinitely long linker. This “tuned” flexibility in interdomain conformation is in turn used in many biochemical processes.

There is great interest in characterizing the dynamic properties of multidomain systems, and moving beyond conventional descriptions in terms of static structures, toward the characterization of population-weighted ensembles describing a distribution of many conformations sampled in solution. There is also great interest in understanding the design principles and underlying physical and chemical interactions that specify the nature of interdomain flexibility. NMR spectroscopy is one of the most powerful techniques for characterizing motions in complex biomolecules and has contributed greatly toward our basic understanding of dynamics in proteins and nucleic acids and its role in folding, recognition, and signaling.

Here, we review methods that have been developed in our laboratories to address these challenges. Our approaches are based on the ability of one domain of the molecule to self-align in a magnetic field, or to dominate the overall orientation of the molecule, so that the conformational freedom of other domains can be assessed by their degree of alignment induced by the aligned part. In turn, this self-alignment ability can be intrinsic or can be caused by tagging appropriate constructs to the molecule of interest. In general, self-alignment is due to magnetic susceptibility anisotropy. Nucleic acids with elongated helices have this feature, as well as several paramagnetic metal centers that can be found in, or attached to, a protein domain.

Measuring similarity between dynamic ensembles of biomolecules

We present a simple and general approach termed REsemble for quantifying population overlap and structural similarity between ensembles. This approach captures improvements in the quality of ensembles determined using increasing input experimental data--improvements that go undetected when conventional methods for comparing ensembles are used--and reveals unexpected similarities between RNA ensembles determined using NMR and molecular dynamics simulations.

Computational approaches to mapping allosteric pathways

Allosteric signaling occurs when chemical and/or physical changes at an allosteric site alter the activity of a primary orthosteric site often many Ångströms distant. A number of recently developed computational techniques, including dynamical network analysis, novel topological and molecular dynamics methods, and hybrids of these methods, are useful for elucidating allosteric signaling pathways at the atomistic level. No single method prevails as best to identify allosteric signal propagation path(s), rather each has particular strengths in characterizing signals that occur over specific timescale ranges and magnitudes of conformational fluctuation. With continued improvement in accuracy and predictive power, these computational techniques aim to become useful drug discovery tools that will allow researchers to identify allostery critical residues for subsequent pharmacological targeting.

Advances in the determination of nucleic acid conformational ensembles

Conformational changes in nucleic acids play a key role in the way genetic information is stored, transferred, and processed in living cells. Here, we describe new approaches that employ a broad range of experimental data, including NMR-derived chemical shifts and residual dipolar couplings, small-angle X-ray scattering, and computational approaches such as molecular dynamics simulations to determine ensembles of DNA and RNA at atomic resolution. We review the complementary information that can be obtained from diverse sets of data and the various methods that have been developed to combine these data with computational methods to construct ensembles and assess their uncertainty. We conclude by surveying RNA and DNA ensembles determined using these methods, highlighting the unique physical and functional insights obtained so far.

NMR studies of nucleic acid dynamics

Nucleic acid structures have to satisfy two diametrically opposite requirements; on one hand they have to adopt well-defined 3D structures that can be specifically recognized by proteins; on the other hand, their structures must be sufficiently flexible to undergo very large conformational changes that are required during key biochemical processes, including replication, transcription, and translation. How do nucleic acids introduce flexibility into their 3D structure without losing biological specificity? Here, I describe the development and application of NMR spectroscopic techniques in my laboratory for characterizing the dynamic properties of nucleic acids that tightly integrate a broad set of NMR measurements, including residual dipolar couplings, spin relaxation, and relaxation dispersion with sample engineering and computational approaches. This approach allowed us to obtain fundamental new insights into directional flexibility in nucleic acids that enable their structures to change in a very specific functional manner.

Inference of structure ensembles of flexible biomolecules from sparse, averaged data

We present the theoretical foundations of a general principle to infer structure ensembles of flexible biomolecules from spatially and temporally averaged data obtained in biophysical experiments. The central idea is to compute the Kullback-Leibler optimal modification of a given prior distribution with respect to the experimental data and its uncertainty. This principle generalizes the successful inferential structure determination method and recently proposed maximum entropy methods. Tractability of the protocol is demonstrated through the analysis of simulated nuclear magnetic resonance spectroscopy data of a small peptide.

A general method for constructing atomic-resolution RNA ensembles using NMR residual dipolar couplings: the basis for interhelical motions revealed

The ability to modulate alignment and measure multiple independent sets of NMR residual dipolar couplings (RDCs) has made it possible to characterize internal motions in proteins at atomic resolution and with time scale sensitivity ranging from picoseconds up to milliseconds. The application of such methods to the study of RNA dynamics, however, remains fundamentally limited by the inability to modulate alignment and by strong couplings between internal and overall motions that complicate the quantitative interpretation of RDCs. Here, we address this problem by showing that RNA alignment can be generally modulated, in a controlled manner, by variable elongation of A-form helices and that the information contained within the measured RDCs can be extracted even in the presence of strong couplings between motions and overall alignment via structure-based prediction of alignment. Using this approach, four RDC data sets, and a broad conformational pool obtained from a 8.2 μs molecular dynamics simulation, we successfully construct and validate an atomic resolution ensemble of human immunodeficiency virus type I transactivation response element RNA. This ensemble reveals local motions in and around the bulge involving changes in stacking and hydrogen-bonding interactions, which are undetectable by traditional spin relaxation and drive global changes in interhelical orientation. This new approach broadens the scope of using RDCs in characterizing the dynamics of nucleic acids.

Utility of 1H NMR chemical shifts in determining RNA structure and dynamics

The development of methods for predicting NMR chemical shifts with high accuracy and speed is increasingly allowing use of these abundant, readily accessible measurements in determining the structure and dynamics of proteins. For nucleic acids, however, despite the availability of semiempirical methods for predicting (1)H chemical shifts, their use in determining the structure and dynamics has not yet been examined. Here, we show that (1)H chemical shifts offer powerful restraints for RNA structure determination, allowing discrimination of native structure from non-native states to within 2-4 Å, and <3 Å when highly flexible residues are ignored. Theoretical simulations shows that although (1)H chemical shifts can provide valuable information for constructing RNA dynamic ensembles, large uncertainties in the chemical shift predictions and inherent degeneracies lead to higher uncertainties as compared to residual dipolar couplings.

Understanding biomolecular motion, recognition, and allostery by use of conformational ensembles

We review the role conformational ensembles can play in the analysis of biomolecular dynamics, molecular recognition, and allostery. We introduce currently available methods for generating ensembles of biomolecules and illustrate their application with relevant examples from the literature. We show how, for binding, conformational ensembles provide a way of distinguishing the competing models of induced fit and conformational selection. For allostery we review the classic models and show how conformational ensembles can play a role in unravelling the intricate pathways of communication that enable allostery to occur. Finally, we discuss the limitations of conformational ensembles and highlight some potential applications for the future.