Determination of protein backbone structure using only residual dipolar couplings

Recent Advances in NMR Protein Structure Prediction with ROSETTA

Nuclear magnetic resonance (NMR) spectroscopy is a powerful method for studying the structure and dynamics of proteins in their native state. For high-resolution NMR structure determination, the collection of a rich restraint dataset is necessary. This can be difficult to achieve for proteins with high molecular weight or a complex architecture. Computational modeling techniques can complement sparse NMR datasets (<1 restraint per residue) with additional structural information to elucidate protein structures in these difficult cases. The Rosetta software for protein structure modeling and design is used by structural biologists for structure determination tasks in which limited experimental data is available. This review gives an overview of the computational protocols available in the Rosetta framework for modeling protein structures from NMR data. We explain the computational algorithms used for the integration of different NMR data types in Rosetta. We also highlight new developments, including modeling tools for data from paramagnetic NMR and hydrogen-deuterium exchange, as well as chemical shifts in CS-Rosetta. Furthermore, strategies are discussed to complement and improve structure predictions made by the current state-of-the-art AlphaFold2 program using NMR-guided Rosetta modeling.

REDCRAFT: A computational platform using residual dipolar coupling NMR data for determining structures of perdeuterated proteins in solution

Nuclear Magnetic Resonance (NMR) spectroscopy is one of the three primary experimental means of characterizing macromolecular structures, including protein structures. Structure determination by solution NMR spectroscopy has traditionally relied heavily on distance restraints derived from nuclear Overhauser effect (NOE) measurements. While structure determination of proteins from NOE-based restraints is well understood and broadly used, structure determination from Residual Dipolar Couplings (RDCs) is relatively less well developed. Here, we describe the new features of the protein structure modeling program REDCRAFT and focus on the new Adaptive Decimation (AD) feature. The AD plays a critical role in improving the robustness of REDCRAFT to missing or noisy data, while allowing structure determination of larger proteins from less data. In this report we demonstrate the successful application of REDCRAFT in structure determination of proteins ranging in size from 50 to 145 residues using experimentally collected data, and of larger proteins (145 to 573 residues) using simulated RDC data. In both cases, REDCRAFT uses only RDC data that can be collected from perdeuterated proteins. Finally, we compare the accuracy of structure determination from RDCs alone with traditional NOE-based methods for the structurally novel PF.2048.1 protein. The RDC-based structure of PF.2048.1 exhibited 1.0 Å BB-RMSD with respect to a high-quality NOE-based structure. Although optimal strategies would include using RDC data together with chemical shift, NOE, and other NMR data, these studies provide proof-of-principle for robust structure determination of largely-perdeuterated proteins from RDC data alone using REDCRAFT.

Residual Dipolar Couplings have the potential to improve the accuracy and reduce the time needed to characterize protein structures. In addition, RDC data have been demonstrated to concurrently elucidate structure of proteins, provide assignment of resonances, and characterize the internal dynamics of proteins. Given all the advantages associated with the study of proteins from RDC data, based on the statistics provided by the Protein Databank (PDB), surprisingly only 124 proteins (out of nearly 150,000 proteins) have utilized RDCs as part of their structure determination. Even a smaller subset of these proteins (approximately 7) have utilized RDCs as the primary source of data for structure determination. One key factor in the use of RDCs is the challenging computational and analytical aspects of this source of data. In this report, we demonstrate the success of the REDCRAFT software package in structure determination of proteins using RDC data that can be collected from small and large proteins in a routine fashion. REDCRAFT accomplishes the challenging task of structure determination from RDCs by introducing a unique search and optimization technique that is both robust and computationally tractable. Structure determination from routinely collectable RDC data using REDCRAFT can complement existing methods to provide faster and more accurate studies of larger and more complex protein structures by NMR spectroscopy in solution state.

Increased usability, algorithmic improvements and incorporation of data mining for structure calculation of proteins with REDCRAFT software package

Background

Traditional approaches to elucidation of protein structures by Nuclear Magnetic Resonance spectroscopy (NMR) rely on distance restraints also known as Nuclear Overhauser effects (NOEs). The use of NOEs as the primary source of structure determination by NMR spectroscopy is time consuming and expensive. Residual Dipolar Couplings (RDCs) have become an alternate approach for structure calculation by NMR spectroscopy. In previous works, the software package REDCRAFT has been presented as a means of harnessing the information containing in RDCs for structure calculation of proteins. However, to meet its full potential, several improvements to REDCRAFT must be made.

Results

In this work, we present improvements to REDCRAFT that include increased usability, better interoperability, and a more robust core algorithm. We have demonstrated the impact of the improved core algorithm in the successful folding of the protein 1A1Z with as high as ±4 Hz of added error. The REDCRAFT computed structure from the highly corrupted data exhibited less than 1.0 Å with respect to the X-ray structure. We have also demonstrated the interoperability of REDCRAFT in a few instances including with PDBMine to reduce the amount of required data in successful folding of proteins to unprecedented levels. Here we have demonstrated the successful folding of the protein 1D3Z (to within 2.4 Å of the X-ray structure) using only N-H RDCs from one alignment medium.

Conclusions

The additional GUI features of REDCRAFT combined with the NEF compliance have significantly increased the flexibility and usability of this software package. The improvements of the core algorithm have substantially improved the robustness of REDCRAFT in utilizing less experimental data both in quality and quantity.

HERMES - A Software Tool for the Prediction and Analysis of Magnetic-Field-Induced Residual Dipolar Couplings in Nucleic Acids

Field-Induced Residual Dipolar Couplings (fiRDC) are a valuable source of long-range information on structure of nucleic acids (NA) in solution. A web application (HERMES) was developed for structure-based prediction and analysis of the (fiRDCs) in NA. fiRDC prediction is based on input 3D model structure(s) of NA and a built-in library of nucleobase-specific magnetic susceptibility tensors and reference geometries. HERMES allows three basic applications: (i) the prediction of fiRDCs for a given structural model of NAs, (ii) the validation of experimental or modeled NA structures using experimentally derived fiRDCs, and (iii) assessment of the oligomeric state of the NA fragment and/or the identification of a molecular NA model that is consistent with experimentally derived fiRDC data. Additionally, the program's built-in routine for rigid body modeling allows the evaluation of relative orientation of domains within NA that is in agreement with experimental fiRDCs.

Paramagnetic NMR Spectroscopy Is a Tool to Address Reactivity, Structure, and Protein–Protein Interactions of Metalloproteins: The Case of Iron–Sulfur Proteins

The study of cellular machineries responsible for the iron–sulfur (Fe–S) cluster biogenesis has led to the identification of a large number of proteins, whose importance for life is documented by an increasing number of diseases linked to them. The labile nature of Fe–S clusters and the transient protein–protein interactions, occurring during the various steps of the maturation process, make their structural characterization in solution particularly difficult. Paramagnetic nuclear magnetic resonance (NMR) has been used for decades to characterize chemical composition, magnetic coupling, and the electronic structure of Fe–S clusters in proteins; it represents, therefore, a powerful tool to study the protein–protein interaction networks of proteins involving into iron–sulfur cluster biogenesis. The optimization of the various NMR experiments with respect to the hyperfine interaction will be summarized here in the form of a protocol; recently developed experiments for measuring longitudinal and transverse nuclear relaxation rates in highly paramagnetic systems will be also reviewed. Finally, we will address the use of extrinsic paramagnetic centers covalently bound to diamagnetic proteins, which contributed over the last twenty years to promote the applications of paramagnetic NMR well beyond the structural biology of metalloproteins.

Structural Characterization of N-WASP Domain V Using MD Simulations with NMR and SAXS Data

Because of their large conformational heterogeneity, structural characterization of intrinsically disordered proteins (IDPs) is very challenging using classical experimental methods alone. In this study, we use NMR and small-angle x-ray scattering (SAXS) data with multiple molecular dynamics (MD) simulations to describe the conformational ensemble of the fully disordered verprolin homology domain of the neural Aldrich syndrome protein involved in the regulation of actin polymerization. First, we studied several back-calculation software of SAXS scattering intensity and optimized the adjustable parameters to accurately calculate the SAXS intensity from an atomic structure. We also identified the most appropriate force fields for MD simulations of this IDP. Then, we analyzed four conformational ensembles of neural Aldrich syndrome protein verprolin homology domain, two generated with the program flexible-meccano with or without NMR-derived information as input and two others generated by MD simulations with two different force fields. These four conformational ensembles were compared to available NMR and SAXS data for validation. We found that MD simulations with the AMBER-03w force field and the TIP4P/2005s water model are able to correctly describe the conformational ensemble of this 67-residue IDP at both local and global level.

Determination of the conformational states of strychnine in solution using NMR residual dipolar couplings in a tensor-free approach

Small molecules with rotatable bonds can occupy different conformational states in solution as a consequence of their thermal fluctuations. The accurate determination of the structures of such states, as well as of their statistical weights, has been challenging because of the technical difficulties in extracting information from experimental measurements, which are normally averaged over the conformational space available. Here, to achieve this objective, we present an approach based on a recently proposed tensor-free method for incorporating NMR residual dipolar couplings as structural restraints in replica-averaged molecular dynamics simulations. This approach enables the information provided by the experimental data to be used in the spirit of the maximum entropy principle to determine the structural ensembles of small molecules. Furthermore, in order to enhance the sampling of the conformational space we incorporated the metadynamics method in the simulations. We illustrate the method in the case of strychnine, determining the three major conformational states of this small molecule and their associated occupation probabilities.

Perspectives on paramagnetic NMR from a life sciences infrastructure

The effects arising in NMR spectroscopy because of the presence of unpaired electrons, collectively referred to as "paramagnetic NMR" have attracted increasing attention over the last decades. From the standpoint of the structural and mechanistic biology, paramagnetic NMR provides long range restraints that can be used to assess the accuracy of crystal structures in solution and to improve them by simultaneous refinements through NMR and X-ray data. These restraints also provide information on structure rearrangements and conformational variability in biomolecular systems. Theoretical improvements in quantum chemistry calculations can nowadays allow for accurate calculations of the paramagnetic data from a molecular structural model, thus providing a tool to refine the metal coordination environment by matching the paramagnetic effects observed far away from the metal. Furthermore, the availability of an improved technology (higher fields and faster magic angle spinning) has promoted paramagnetic NMR applications in the fast-growing area of biomolecular solid-state NMR. Major improvements in dynamic nuclear polarization have been recently achieved, especially through the exploitation of the Overhauser effect occurring through the contact-driven relaxation mechanism: the very large enhancement of the ¹³C signal observed in a variety of liquid organic compounds at high fields is expected to open up new perspectives for applications of solution NMR.

Block-restraining of residual dipolar couplings to allow fluctuating relative alignments of molecular subdomains

Residual dipolar couplings (RDCs), unlike most other types of NMR observables, provide orientational information, reporting on the alignment of inter-spin vectors (ISVs) relative to the magnetic field. A great challenge in using experimental RDCs to restrain molecular dynamics (MD) simulations is how to represent this alignment. An alignment tensor is often used to parameterise the contribution of molecular alignment to the angular dependence of RDCs. All ISVs that share the same tensor have fixed relative alignment, i.e. if just one tensor is used, the molecule is internally rigid. Here we propose and illustrate a method for subdividing molecules into individually aligned blocks during MD simulations restrained to fit RDCs. This allows the relative orientation of each block to vary during the simulation, which in turn ensures that the internal structure of each block is more realistically reproduced.

Structure Calculation and Reconstruction of Discrete-State Dynamics from Residual Dipolar Couplings

Residual dipolar couplings (RDCs) acquired by nuclear magnetic resonance (NMR) spectroscopy are an indispensable source of information in investigation of molecular structures and dynamics. Here, we present a comprehensive strategy for structure calculation and reconstruction of discrete-state dynamics from RDC data that is based on the singular value decomposition (SVD) method of order tensor estimation. In addition to structure determination, we provide a mechanism of producing an ensemble of conformations for the dynamical regions of a protein from RDC data. The developed methodology has been tested on simulated RDC data with ±1 Hz of error from an 83 residue α protein (PDB ID 1A1Z ) and a 213 residue α/β protein DGCR8 (PDB ID 2YT4 ). In nearly all instances, our method reproduced the structure of the protein including the conformational ensemble to within less than 2 Å. On the basis of our investigations, arc motions with more than 30° of rotation are identified as internal dynamics and are reconstructed with sufficient accuracy. Furthermore, states with relative occupancies above 20% are consistently recognized and reconstructed successfully. Arc motions with a magnitude of 15° or relative occupancy of less than 10% are consistently unrecognizable as dynamical regions within the context of ±1 Hz of error.

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.

Improvements to REDCRAFT: a software tool for simultaneous characterization of protein backbone structure and dynamics from residual dipolar couplings

Within the past two decades, there has been an increase in the acquisition of residual dipolar couplings (RDC) for investigations of biomolecular structures. Their use however is still not as widely adopted as the traditional methods of structure determination by NMR, despite their potential for extending the limits in studies that examine both the structure and dynamics of biomolecules. This is in part due to the difficulties associated with the analysis of this information-rich data type. The software analysis tool REDCRAFT was previously introduced to address some of these challenges. Here we describe and evaluate a number of additional features that have been incorporated in order to extend its computational and analytical capabilities. REDCRAFT's more traditional enhancements integrate a modified steric collision term, as well as structural refinement in the rotamer space. Other, non-traditional improvements include: the filtering of viable structures based on relative order tensor estimates, decimation of the conformational space based on structural similarity, and forward/reverse folding of proteins. Utilizing REDCRAFT's newest features we demonstrate de-novo folding of proteins 1D3Z and 1P7E to within less than 1.6 Å of the corresponding X-ray structures, using as many as four RDCs per residue and as little as two RDCs per residue, in two alignment media. We also show the successful folding of a structure to less than 1.6 Å of the X-ray structure using {C(i-1)-N(i), N(i)-H(i), and C(i-1)-H(i)} RDCs in one alignment medium, and only {N(i)-H(i)} in the second alignment medium (a set of data which can be collected on deuterated samples). The program is available for download from our website at http://ifestos.cse.sc.edu .

A tensor-free method for the structural and dynamical refinement of proteins using residual dipolar couplings

Residual dipolar couplings (RDCs) are parameters measured in nuclear magnetic resonance spectroscopy that can provide exquisitely detailed information about the structure and dynamics of biological macromolecules. We describe here a method of using RDCs for the structural and dynamical refinement of proteins that is based on the observation that the RDC between two atomic nuclei depends directly on the angle ϑ between the internuclear vector and the external magnetic field. For every pair of nuclei for which an RDC is available experimentally, we introduce a structural restraint to minimize the deviation from the value of the angle ϑ derived from the measured RDC and that calculated in the refinement protocol. As each restraint involves only the calculation of the angle ϑ of the corresponding internuclear vector, the method does not require the definition of an overall alignment tensor to describe the preferred orientation of the protein with respect to the alignment medium. Application to the case of ubiquitin demonstrates that this method enables an accurate refinement of the structure and dynamics of this protein to be obtained.

Dynafold: a dynamic programming approach to protein backbone structure determination from minimal sets of Residual Dipolar Couplings

Residual Dipolar Couplings (RDCs) are a source of NMR data that can provide a powerful set of constraints on the orientation of inter-nuclear vectors, and are quickly becoming a larger part of the experimental toolset for molecular biologists. However, few reliable protocols exist for the determination of protein backbone structures from small sets of RDCs. DynaFold is a new dynamic programming algorithm designed specifically for this task, using minimal sets of RDCs collected in multiple alignment media. DynaFold was first tested utilizing synthetic data generated for the N--H , C(α)--H(α), and C--N vectors of 1BRF, 1F53, 110M, and 3LAY proteins, with up to ±1 Hz error in three alignment media, and was able to produce structures with less than 1.9 Å of the original structures. DynaFold was then tested using experimental data, obtained from the Biological Magnetic Resonance Bank, for proteins PDBID:1P7E and 1D3Z using RDC data from two alignment media. This exercise yielded structures within 1.0 Å of their respective published structures in segments with high data density, and less than 1.9 Å over the entire protein. The same sets of RDC data were also used in comparisons with traditional methods for analysis of RDCs, which failed to match the accuracy of DynaFold's approach to structure determination.

Modeling helical proteins using residual dipolar couplings, sparse long-range distance constraints and a simple residue-based force field

We present a fast and simple protocol to obtain moderate-resolution backbone structures of helical proteins. This approach utilizes a combination of sparse backbone NMR data (residual dipolar couplings and paramagnetic relaxation enhancements) or EPR data with a residue-based force field and Monte Carlo/simulated annealing protocol to explore the folding energy landscape of helical proteins. By using only backbone NMR data, which are relatively easy to collect and analyze, and strategically placed spin relaxation probes, we show that it is possible to obtain protein structures with correct helical topology and backbone RMS deviations well below 4 Å. This approach offers promising alternatives for the structural determination of proteins in which nuclear Overha-user effect data are difficult or impossible to assign and produces initial models that will speed up the high-resolution structure determination by NMR spectroscopy.

Three-dimensional protein fold determination from backbone amide pseudocontact shifts generated by lanthanide tags at multiple sites

Site-specific attachment of paramagnetic lanthanide ions to a protein generates pseudocontact shifts (PCS) in the nuclear magnetic resonance (NMR) spectra of the protein that are easily measured as changes in chemical shifts. By labeling the protein with lanthanide tags at four different sites, PCSs are observed for most amide protons and accurate information is obtained about their coordinates in three-dimensional space. The approach is demonstrated with the chaperone ERp29, for which large differences have been reported between X-ray and NMR structures of the C-terminal domain, ERp29-C. The results unambiguously show that the structure of rat ERp29-C in solution is similar to the crystal structure of human ERp29-C. PCSs of backbone amides were the only structural restraints required. Because these can be measured for more dilute protein solutions than other NMR restraints, the approach greatly widens the range of proteins amenable to structural studies in solution.

Residual dipolar couplings measured in unfolded proteins are sensitive to amino-acid-specific geometries as well as local conformational sampling

Many functional proteins do not have well defined folded structures. In recent years, both experimental and computational approaches have been developed to study the conformational behaviour of this type of protein. It has been shown previously that experimental RDCs (residual dipolar couplings) can be used to study the backbone sampling of disordered proteins in some detail. In these studies, the backbone structure was modelled using a common geometry for all amino acids. In the present paper, we demonstrate that experimental RDCs are also sensitive to the specific geometry of each amino acid as defined by energy-minimized internal co-ordinates. We have modified the FM (flexible-Meccano) algorithm that constructs conformational ensembles on the basis of a statistical coil model, to account for these differences. The modified algorithm inherits the advantages of the FM algorithm to efficiently sample the potential energy landscape for coil conformations. The specific geometries incorporated in the new algorithm result in a better reproduction of experimental RDCs and are generally applicable for further studies to characterize the conformational properties of intrinsically disordered proteins. In addition, the internal-co-ordinate-based algorithm is an order of magnitude more efficient, and facilitates side-chain construction, surface osmolyte simulation, spin-label distribution sampling and proline cis/trans isomer simulation.

Flexible-meccano: a tool for the generation of explicit ensemble descriptions of intrinsically disordered proteins and their associated experimental observables

MOTIVATION

Intrinsically disordered proteins (IDPs) represent a significant fraction of the human proteome. The classical structure function paradigm that has successfully underpinned our understanding of molecular biology breaks down when considering proteins that have no stable tertiary structure in their functional form. One convenient approach is to describe the protein in terms of an equilibrium of rapidly inter-converting conformers. Currently, tools to generate such ensemble descriptions are extremely rare, and poorly adapted to the prediction of experimental data.

RESULTS

We present flexible-meccano-a highly efficient algorithm that generates ensembles of molecules, on the basis of amino acid-specific conformational potentials and volume exclusion. Conformational sampling depends uniquely on the primary sequence, with the possibility of introducing additional local or long-range conformational propensities at an amino acid-specific resolution. The algorithm can also be used to calculate expected values of experimental parameters measured at atomic or molecular resolution, such as nuclear magnetic resonance (NMR) and small angle scattering, respectively. We envisage that flexible-meccano will be useful for researchers who wish to compare experimental data with those expected from a fully disordered protein, researchers who see experimental evidence of deviation from 'random coil' behaviour in their protein, or researchers who are interested in working with a broad ensemble of conformers representing the flexibility of the IDP of interest.

AVAILABILITY

A fully documented multi-platform executable is provided, with examples, at http://www.ibs.fr/science-213/scientific-output/software/flexible-meccano/

CONTACT

martin.blackledge@ibs.fr.

Blind testing of routine, fully automated determination of protein structures from NMR data

The protocols currently used for protein structure determination by nuclear magnetic resonance (NMR) depend on the determination of a large number of upper distance limits for proton-proton pairs. Typically, this task is performed manually by an experienced researcher rather than automatically by using a specific computer program. To assess whether it is indeed possible to generate in a fully automated manner NMR structures adequate for deposition in the Protein Data Bank, we gathered 10 experimental data sets with unassigned nuclear Overhauser effect spectroscopy (NOESY) peak lists for various proteins of unknown structure, computed structures for each of them using different, fully automatic programs, and compared the results to each other and to the manually solved reference structures that were not available at the time the data were provided. This constitutes a stringent "blind" assessment similar to the CASP and CAPRI initiatives. This study demonstrates the feasibility of routine, fully automated protein structure determination by NMR.

An improved algorithm for MFR fragment assembly

A method for generating protein backbone models from backbone only NMR data is presented, which is based on molecular fragment replacement (MFR). In a first step, the PDB database is mined for homologous peptide fragments using experimental backbone-only data i.e. backbone chemical shifts (CS) and residual dipolar couplings (RDC). Second, this fragment library is refined against the experimental restraints. Finally, the fragments are assembled into a protein backbone fold using a rigid body docking algorithm using the RDCs as restraints. For improved performance, backbone nuclear Overhauser effects (NOEs) may be included at that stage. Compared to previous implementations of MFR-derived structure determination protocols this model-building algorithm offers improved stability and reliability. Furthermore, relative to CS-ROSETTA based methods, it provides faster performance and straightforward implementation with the option to easily include further types of restraints and additional energy terms.

Towards the physical basis of how intrinsic disorder mediates protein function

Intrinsically disordered proteins (IDPs) are an important class of functional proteins that is highly prevalent in biology and has broad association with human diseases. In contrast to structured proteins, free IDPs exist as heterogeneous and dynamical conformational ensembles under physiological conditions. Many concepts have been discussed on how such intrinsic disorder may provide crucial functional advantages, particularly in cellular signaling and regulation. Establishing the physical basis of these proposed phenomena requires not only detailed characterization of the disordered conformational ensembles, but also mechanistic understanding of the roles of various ensemble properties in IDP interaction and regulation. Here, we review the experimental and computational approaches that may be integrated to address many important challenges of establishing a "structural" basis of IDP function, and discuss some of the key emerging ideas on how the conformational ensembles of IDPs may mediate function, especially in coupled binding and folding interactions.

Rapid measurement of residual dipolar couplings for fast fold elucidation of proteins

It has been demonstrated that protein folds can be determined using appropriate computational protocols with NMR chemical shifts as the sole source of experimental restraints. While such approaches are very promising they still suffer from low convergence resulting in long computation times to achieve accurate results. Here we present a suite of time- and sensitivity optimized NMR experiments for rapid measurement of up to six RDCs per residue. Including such an RDC data set, measured in less than 24 h on a single aligned protein sample, greatly improves convergence of the Rosetta-NMR protocol, allowing for overnight fold calculation of small proteins. We demonstrate the performance of our fast fold calculation approach for ubiquitin as a test case, and for two RNA-binding domains of the plant protein HYL1. Structure calculations based on simulated RDC data highlight the importance of an accurate and precise set of several complementary RDCs as additional input restraints for high-quality de novo structure determination.

A Bayesian approach for determining protein side-chain rotamer conformations using unassigned NOE data

A major bottleneck in protein structure determination via nuclear magnetic resonance (NMR) is the lengthy and laborious process of assigning resonances and nuclear Overhauser effect (NOE) cross peaks. Recent studies have shown that accurate backbone folds can be determined using sparse NMR data, such as residual dipolar couplings (RDCs) or backbone chemical shifts. This opens a question of whether we can also determine the accurate protein side-chain conformations using sparse or unassigned NMR data. We attack this question by using unassigned nuclear Overhauser effect spectroscopy (NOESY) data, which records the through-space dipolar interactions between protons nearby in three-dimensional (3D) space. We propose a Bayesian approach with a Markov random field (MRF) model to integrate the likelihood function derived from observed experimental data, with prior information (i.e., empirical molecular mechanics energies) about the protein structures. We unify the side-chain structure prediction problem with the side-chain structure determination problem using unassigned NMR data, and apply the deterministic dead-end elimination (DEE) and A* search algorithms to provably find the global optimum solution that maximizes the posterior probability. We employ a Hausdorff-based measure to derive the likelihood of a rotamer or a pairwise rotamer interaction from unassigned NOESY data. In addition, we apply a systematic and rigorous approach to estimate the experimental noise in NMR data, which also determines the weighting factor of the data term in the scoring function derived from the Bayesian framework. We tested our approach on real NMR data of three proteins: the FF Domain 2 of human transcription elongation factor CA150 (FF2), the B1 domain of Protein G (GB1), and human ubiquitin. The promising results indicate that our algorithm can be applied in high-resolution protein structure determination. Since our approach does not require any NOE assignment, it can accelerate the NMR structure determination process.

Searching and optimizing structure ensembles for complex flexible sugars

NMR restrictions are suitable to specify the geometry of a molecule when a single well-defined global free energy minimum exists that is significantly lower than other local minima. Carbohydrates are quite flexible, and therefore, NMR observables do not always correlate with a single conformer but instead with an ensemble of low free energy conformers that can be accessed by thermal fluctuations. In this communication, we describe a novel procedure to identify and weight the contribution to the ensemble of local minima conformers based on comparison to residual dipolar couplings (RDCs) or other NMR observables, such as scalar couplings. A genetic algorithm is implemented to globally minimize the R factor comparing calculated RDCs to experiment. This is done by optimizing the weights of different conformers derived from the exhaustive local minima conformational search program, fast sugar structure prediction software (FSPS). We apply this framework to six human milk sugars, LND-1, LNF-1, LNF-2, LNF-3, LNnT, and LNT, and are able to determine corresponding population weights for the ensemble of conformers. Interestingly, our results indicate that in all cases the RDCs can be well represented by only a few most important conformers. This confirms that several, but not all of the glycosidic linkages in histo-blood group "epitopes" are quite rigid.

Advances in automated NMR protein structure determination

Around half of all protein structures solved nowadays using solution-state nuclear magnetic resonance (NMR) spectroscopy have been because of automated data analysis. The pervasiveness of computational approaches in general hides, however, a more nuanced view in which the full variety and richness of the field appears. This review is structured around a comparison of methods associated with three NMR observables: classical nuclear Overhauser effect (NOE) constraint gathering in contrast with more recent chemical shift and residual dipole coupling (RDC) based protocols. In each case, the emphasis is placed on the latest research, covering mainly the past 5 years. By describing both general concepts and representative programs, the objective is to map out a field in which--through the very profusion of approaches--it is all too easy to lose one's bearings.

NMR spectroscopy to study the dynamics and interactions of CFTR

The cystic fibrosis transmembrane conductance regulator (CFTR) is a multi-domain membrane chloride channel whose activity is regulated by ATP at two nucleotide-binding domains (NBD1 and NBD2) and by phosphorylation of the regulatory (R) region. The NBDs and the R region have functionally relevant motions that are critical for channel gating. Nuclear magnetic resonance (NMR) spectroscopy is a highly useful technique for obtaining information on the structure and interactions of CFTR and is extremely powerful for probing dynamics. NMR approaches for studying CFTR are reviewed, using our previous NBD1 and the R region results to provide examples. These NMR data are yielding insights into the dynamic properties and interactions that facilitate normal CFTR regulation as well as pathological effects of mutations, including the most common disease mutant, deletion of F508 in NBD1.

Intrinsically disordered proteins in a physics-based world

Intrinsically disordered proteins (IDPs) are a newly recognized class of functional proteins that rely on a lack of stable structure for function. They are highly prevalent in biology, play fundamental roles, and are extensively involved in human diseases. For signaling and regulation, IDPs often fold into stable structures upon binding to specific targets. The mechanisms of these coupled binding and folding processes are of significant importance because they underlie the organization of regulatory networks that dictate various aspects of cellular decision-making. This review first discusses the challenge in detailed experimental characterization of these heterogeneous and dynamics proteins and the unique and exciting opportunity for physics-based modeling to make crucial contributions, and then summarizes key lessons from recent de novo simulations of the structure and interactions of several regulatory IDPs.

Simultaneous structure and dynamics of a membrane protein using REDCRAFT: membrane-bound form of Pf1 coat protein

A strategy for simultaneous study of the structure and internal dynamics of a membrane protein is described using the REDCRAFT algorithm. The membrane-bound form of the Pf1 major coat protein (mbPf1) was used as an example. First, synthetic data is utilized to validate the simultaneous study of structure and dynamics with REDCRAFT using dihedral restraints and backbone N-H RDCs from two different alignments. Subsequently, the validated analysis is applied to experimental data and confirms that REDCRAFT produces meaningful structures from sparse RDC data. Furthermore, simulated data from a two-state jump motion is used to illustrate the necessity for simultaneous consideration of structure and dynamics. Disregarding internal dynamics during the course of structure determination is shown to produce an average-state that is not related to the two intermediate states. During the analysis of RDC data from the dynamic model, REDCRAFT appropriately identifies the region separating the static and dynamic domains of the protein. Finally, analysis of experimental data strongly suggests the existence of internal motion between the amphipathic and the transmembrane helices of the membrane-bound form of the protein. The ability to perform fragmented structure determination of each domain without a priori assumption of the order tensors allows an independent determination of the order tensors, which yields a more comprehensive description of protein structure and dynamics and is particularly relevant to the study of membrane proteins.

Rapid global structure determination of large RNA and RNA complexes using NMR and small-angle X-ray scattering

Among the greatest advances in biology today are the discoveries of various roles played by RNA in biological processes. However, despite significant advances in RNA structure determination using X-ray crystallography [1] and solution NMR [2-4], the number of bona fide RNA structures is very limited, in comparison with the growing number of known functional RNAs. This is because of great difficulty in growing crystals or/and obtaining phase information, and severe size constraints on structure determination by solution NMR spectroscopy. Clearly, there is an acute need for new methodologies for RNA structure determination. The prevailing approach for structure determination of RNA in solution is a "bottom-up" approach that was basically transplanted from the approach used for determining protein structures, despite vast differences in both structural features and chemical compositions between these two types of biomacromolecules. In this chapter, we describe a new method, which has been reported recently, for rapid global structure determination of RNAs using solution-based NMR spectroscopy and small-angle X-ray scattering. The method treats duplexes as major building blocks of RNA structures. By determining the global orientations of the duplexes and the overall shape, the global structure of an RNA can be constructed and further regularized using Xplor-NIH. The utility of the method was demonstrated in global structure determination of two RNAs, a 71-nt and 102-nt RNAs with an estimated backbone RMSD ∼3.0Å. The global structure opens door to high-resolution structure determination in solution.

High-resolution protein structure determination starting with a global fold calculated from exact solutions to the RDC equations

We present a novel structure determination approach that exploits the global orientational restraints from RDCs to resolve ambiguous NOE assignments. Unlike traditional approaches that bootstrap the initial fold from ambiguous NOE assignments, we start by using RDCs to compute accurate secondary structure element (SSE) backbones at the beginning of structure calculation. Our structure determination package, called RDC-PANDA: (RDC-based SSE PAcking with NOEs for Structure Determination and NOE Assignment), consists of three modules: (1) RDC-EXACT: ; (2) PACKER: ; and (3) HANA: (HAusdorff-based NOE Assignment). RDC-EXACT: computes the global optimal solution of backbone dihedral angles for each secondary structure element by exactly solving a system of quartic RDC equations derived by Wang and Donald (Proceedings of the IEEE computational systems bioinformatics conference (CSB), Stanford, CA, 2004a; J Biomol NMR 29(3):223-242, 2004b), and systematically searching over the roots, each of which is a backbone dihedral varphi- or psi-angle consistent with the RDC data. Using a small number of unambiguous inter-SSE NOEs extracted using only chemical shift information, PACKER: performs a systematic search for the core structure, including all SSE backbone conformations. HANA: uses a Hausdorff-based scoring function to measure the similarity between the experimental spectra and the back-computed NOE pattern for each side-chain from a statistically-diverse rotamer library, and drives the selection of optimal position-specific rotamers for filtering ambiguous NOE assignments. Finally, a local minimization approach is used to compute the loops and refine side-chain conformations by fixing the core structure as a rigid body while allowing movement of loops and side-chains. RDC-PANDA: was applied to NMR data for the FF Domain 2 of human transcription elongation factor CA150 (RNA polymerase II C-terminal domain interacting protein), human ubiquitin, the ubiquitin-binding zinc finger domain of the human Y-family DNA polymerase Eta (pol eta UBZ), and the human Set2-Rpb1 interacting domain (hSRI). These results demonstrated the efficiency and accuracy of our algorithm, and show that RDC-PANDA: can be successfully applied for high-resolution protein structure determination using only a limited set of NMR data by first computing RDC-defined backbones.

Probing mutation-induced structural perturbations by refinement against residual dipolar couplings: application to the U4 spliceosomal RNP complex

Confident interpretation of biochemical experiments performed with mutated proteins relies on verification of the integrity of the mutant structures. We present a simple and rapid refinement protocol for comparing the structures of mutated and wild-type proteins. Our approach involves measurement of residual dipolar couplings, and only requires assignment of the backbone resonances of the mutant species. We demonstrate application of the protocol to a mutant of the 15.5K protein, a core component of the U4 spliceosomal ribonucleoprotein (RNP) complex. Confirmation of the unperturbed structure of the mutated protein prompted re-examination of a previous mutagenesis study and indicated that the interpretation of mutant binding affinities in terms of direct interfacial contacts should be applied with caution.

Efficient and accurate estimation of relative order tensors from lambda-maps

The rapid increase in the availability of RDC data from multiple alignment media in recent years has necessitated the development of more sophisticated analyses that extract the RDC data's full information content. This article presents an analysis of the distribution of RDCs from two media (2D-RDC data), using the information obtained from a lambda-map. This article also introduces an efficient algorithm, which leverages these findings to extract the order tensors for each alignment medium using unassigned RDC data in the absence of any structural information. The results of applying this 2D-RDC analysis method to synthetic and experimental data are reported in this article. The relative order tensor estimates obtained from the 2D-RDC analysis are compared to order tensors obtained from the program REDCAT after using assignment and structural information. The final comparisons indicate that the relative order tensors estimated from the unassigned 2D-RDC method very closely match the results from methods that require assignment and structural information. The presented method is successful even in cases with small datasets. The results of analyzing experimental RDC data for the protein 1P7E are presented to demonstrate the potential of the presented work in accurately estimating the principal order parameters from RDC data that incompletely sample the RDC space. In addition to the new algorithm, a discussion of the uniqueness of the solutions is presented; no more than two clusters of distinct solutions have been shown to satisfy each lambda-map.

16-fold degeneracy of peptide plane orientations from residual dipolar couplings: analytical treatment and implications for protein structure determination

Residual dipolar couplings (RDCs) measured for internally rigid molecular fragments provide important information about the relative orientations of these fragments. Dependent on the symmetry of the alignment tensor and the symmetry of the molecular fragment, however, there generally exist more than one solution for the fragment orientation consistent with the measured RDCs. Analytical solutions are presented that describe the complete set of orientations of internally rigid fragments that are consistent with multiple dipolar couplings measured in a single alignment medium that is rhombic. For the first time, it is shown that, for a planar fragment such as the peptide plane, there generally exist 16 different solutions with their analytical expressions presented explicitly. The presence of these solutions is shown to be highly relevant for standard structure determination protocols using RDCs to refine molecular structures. In particular, when using standard protein structure refinement with RDCs that were measured in a single alignment medium as constraints, it is found that often more than one of the peptide plane solutions is physically viable; i.e., despite being consistent with measured RDCs, the local backbone structure can be incorrect. On the basis of experimental and simulated examples, it is rationalized why protein structures that are refined against RDCs measured in a single medium can have lower resolution (precision) than one would expect on the basis of the experimental accuracy of the RDCs. Conditions are discussed under which the correct solution can be identified.

Estimation of relative order tensors, and reconstruction of vectors in space using unassigned RDC data and its application

Advances in NMR instrumentation and pulse sequence design have resulted in easier acquisition of Residual Dipolar Coupling (RDC) data. However, computational and theoretical analysis of this type of data has continued to challenge the international community of investigators because of their complexity and rich information content. Contemporary use of RDC data has required a-priori assignment, which significantly increases the overall cost of structural analysis. This article introduces a novel algorithm that utilizes unassigned RDC data acquired from multiple alignment media (nD-RDC, n3) for simultaneous extraction of the relative order tensor matrices and reconstruction of the interacting vectors in space. Estimation of the relative order tensors and reconstruction of the interacting vectors can be invaluable in a number of endeavors. An example application has been presented where the reconstructed vectors have been used to quantify the fitness of a template protein structure to the unknown protein structure. This work has other important direct applications such as verification of the novelty of an unknown protein and validation of the accuracy of an available protein structure model in drug design. More importantly, the presented work has the potential to bridge the gap between experimental and computational methods of structure determination.

Structural biology by NMR: structure, dynamics, and interactions

The function of bio-macromolecules is determined by both their 3D structure and conformational dynamics. These molecules are inherently flexible systems displaying a broad range of dynamics on time-scales from picoseconds to seconds. Nuclear Magnetic Resonance (NMR) spectroscopy has emerged as the method of choice for studying both protein structure and dynamics in solution. Typically, NMR experiments are sensitive both to structural features and to dynamics, and hence the measured data contain information on both. Despite major progress in both experimental approaches and computational methods, obtaining a consistent view of structure and dynamics from experimental NMR data remains a challenge. Molecular dynamics simulations have emerged as an indispensable tool in the analysis of NMR data.

De novo determination of internuclear vector orientations from residual dipolar couplings measured in three independent alignment media

The straightforward interpretation of solution state residual dipolar couplings (RDCs) in terms of internuclear vector orientations generally requires prior knowledge of the alignment tensor, which in turn is normally estimated using a structural model. We have developed a protocol which allows the requirement for prior structural knowledge to be dispensed with as long as RDC measurements can be made in three independent alignment media. This approach, called Rigid Structure from Dipolar Couplings (RSDC), allows vector orientations and alignment tensors to be determined de novo from just three independent sets of RDCs. It is shown that complications arising from the existence of multiple solutions can be overcome by careful consideration of alignment tensor magnitudes in addition to the agreement between measured and calculated RDCs. Extensive simulations as well applications to the proteins ubiquitin and Staphylococcal protein GB1 demonstrate that this method can provide robust determinations of alignment tensors and amide N-H bond orientations often with better than 10 degrees accuracy, even in the presence of modest levels of internal dynamics.

REDCRAFT: a tool for simultaneous characterization of protein backbone structure and motion from RDC data

REDCRAFT, a new open source software tool that accommodates the analysis of RDC data for simultaneous structure and dynamics characterization of proteins is presented in this article. Simultaneous consideration of structure and motion is believed to be necessary for accurate representation of the solution-state of a protein. REDCRAFT is designed to primarily utilize RDC data from multiple alignment media in two stages. During Stage-I, a list of possible torsion angles joining any two neighboring peptide planes is ranked based on their fitness to experimental constraints; in Stage-II, a dipeptide fragment is extended by addition of one peptide plane at a time. The algorithm adopted by REDCRAFT is very efficient and can produce a structure for an 80 residue protein within two hours on a typical desktop computer. REDCRAFT exhibits robustness with respect to noise and missing data. REDCRAFT describes the overall alignment of the molecule in the form of an order tensor matrix and is capable of identifying peptide fragments with internal dynamics. Identification of the location of internal motion will permit a more accurate structural representation. Experimental data from two proteins as well as simulated data are presented to illustrate the capabilities of REDCRAFT in both structure determination and identification of the dynamical regions.

A unifying probabilistic framework for analyzing residual dipolar couplings

Residual dipolar couplings provide complementary information to the nuclear Overhauser effect measurements that are traditionally used in biomolecular structure determination by NMR. In a de novo structure determination, however, lack of knowledge about the degree and orientation of molecular alignment complicates the analysis of dipolar coupling data. We present a probabilistic framework for analyzing residual dipolar couplings and demonstrate that it is possible to estimate the atomic coordinates, the complete molecular alignment tensor, and the error of the couplings simultaneously. As a by-product, we also obtain estimates of the uncertainty in the coordinates and the alignment tensor. We show that our approach encompasses existing methods for determining the alignment tensor as special cases, including least squares estimation, histogram fitting, and elimination of an explicit alignment tensor in the restraint energy.

Simultaneous definition of high resolution protein structure and backbone conformational dynamics using NMR residual dipolar couplings

Despite the importance of molecular dynamics for biological activity, most approaches to protein structure determination, whether based on crystallographic or solution studies, propose three-dimensional atomic representations of a single configuration that take no account of conformational fluctuation. Non-averaged anisotropic NMR interactions, such as residual dipolar couplings, that become measurable under conditions of weak alignment, provide sensitive probes of both molecular structure and dynamics. Residual dipolar couplings are becoming increasingly powerful for the study of proteins in solution. In this minireview we present their use for the simultaneous determination of protein structure and dynamics.

Periodicity, planarity, and pixel (3P): a program using the intrinsic residual dipolar coupling periodicity-to-peptide plane correlation and phi/psi angles to derive protein backbone structures

We present a detailed description of a theory and a program called 3P. "3P" stands for periodicity, planarity, and pixel. The 3P program is based on the intrinsic periodic correlations between residual dipolar couplings (RDCs) and in-plane internuclear vectors, and between RDCs and the orientation of peptide planes relative to an alignment tensor. The program extracts accurate rhombic, axial components of the alignment tensor without explicit coordinates, and discrete peptide plane orientations, which are utilized in combination with readily available phi/psi angles to determine the three-dimensional backbone structures of proteins. The 3P program uses one alignment tensor. We demonstrate the utility and robustness of the program, using both experimental and synthetic data sets, which were added with different levels of noise or were incomplete. The program is interfaced to Xplor-NIH via a "3P" module and is available to the public. The limitations and differences between our program and existing methods are also discussed.