A Monte Carlo/simulated annealing algorithm for sequential resonance assignment in solid state NMR of uniformly labeled proteins with magic-angle spinning

ASAP: An automatic sequential assignment program for congested multidimensional solid state NMR spectra

Accurate signal assignments can be challenging for congested solid-state NMR (ssNMR) spectra. We describe an automatic sequential assignment program (ASAP) to partially overcome this challenge. ASAP takes three input files: the residue type assignments (RTAs) determined from the better-resolved NCACX spectrum, the full peak list of the NCOCX spectrum, and the protein sequence. It integrates our auto-residue type assignment strategy (ARTIST) with the Monte Carlo simulated annealing (MCSA) algorithm to overcome the hurdle for accurate signal assignments caused by incomplete side-chain resonances and spectral congestion. Combined, ASAP demonstrates robust performance and accelerates signal assignments of large proteins (>200 residues) that lack crystalline order.

Structure of Amyloid Peptide Ribbons Characterized by Electron Microscopy, Atomic Force Microscopy, and Solid-State Nuclear Magnetic Resonance

Polypeptides often self-assemble to form amyloid fibrils, which contain cross-β structural motifs and are typically 5-15 nm in width and micrometers in length. In many cases, short segments of longer amyloid-forming protein or peptide sequences also form cross-β assemblies but with distinctive ribbon-like morphologies that are characterized by a well-defined thickness (on the order of 5 nm) in one lateral dimension and a variable width (typically 10-100 nm) in the other. Here, we use a novel combination of data from solid-state nuclear magnetic resonance (ssNMR), dark-field transmission electron microscopy (TEM), atomic force microscopy (AFM), and cryogenic electron microscopy (cryoEM) to investigate the structures within amyloid ribbons formed by residues 14-23 and residues 11-25 of the Alzheimer's disease-associated amyloid-β peptide (Aβ14-23 and Aβ11-25). The ssNMR data indicate antiparallel β-sheets with specific registries of intermolecular hydrogen bonds. Mass-per-area values are derived from dark-field TEM data. The ribbon thickness is determined from AFM images. For Aβ14-23 ribbons, averaged cryoEM images show a periodic spacing of β-sheets. The combined data support structures in which the amyloid ribbon growth direction is the direction of intermolecular hydrogen bonds between β-strands, the ribbon thickness corresponds to the width of one β-sheet (i.e., approximately the length of one molecule), and the variable ribbon width is a variable multiple of the thickness of one β-sheet (i.e., a multiple of the repeat distance in a stack of β-sheets). This architecture for a cross-β assembly may generally exist within amyloid ribbons.

Solid-state NMR studies of amyloids

Amyloids have special structural properties and are involved in many aspects of biological function. In particular, amyloids are the cause or hallmarks of a group of notorious and incurable neurodegenerative diseases. The extraordinary high molecular weight and aggregation states of amyloids have posed a challenge for researchers studying them. Solid-state NMR (SSNMR) has been extensively applied to study the structures and dynamics of amyloids for the past 20 or more years and brought us tremendous progress in understanding their structure and related diseases. These studies, at the same time, helped to push SSNMR technical developments in sensitivity and resolution. In this review, some interesting research studies and important technical developments are highlighted to give the reader an overview of the current state of this field.

Liquid Droplet Aging and Seeded Fibril Formation of the Cytotoxic Granule Associated RNA Binding Protein TIA1 Low Complexity Domain

Protein domains biased toward a few amino acid types are vital for the formation of biomolecular condensates in living cells. These membraneless compartments are formed by molecules exhibiting a range of molecular motions and structural order. Missense mutations increase condensate persistence lifetimes or structural order, properties that are thought to underlie pathological protein aggregation. In the context of stress granules associated with neurodegenerative diseases, this process involves the rigidification of protein liquid droplets into β-strand rich protein fibrils. Here, we characterize the molecular mechanism underlying the rigidification of liquid droplets for the low complexity domain of the Cytotoxic granule associated RNA binding protein TIA1 (TIA1) stress granule protein and the influence of a disease mutation linked to neurodegenerative diseases. A seeding procedure and solid state nuclear magnetic resonance measurements show that the low complexity domain converges on a β-strand rich fibril conformation composed of 21% of the sequence. Additional solid state nuclear magnetic resonance measurements and difference spectroscopy show that aged liquid droplets of wild type and a proline-to-leucine mutant low complexity domain are composed of fibril assemblies that are conformationally heterogeneous and structurally distinct from the seeded fibril preparation. Regarding low complexity domains, our data support the functional template-driven formation of conformationally homogeneous structures, that rigidification of liquid droplets into conformationally heterogenous structures promotes pathological interactions, and that the effect of disease mutations is more nuanced than increasing thermodynamic stability or increasing β-strand structure content.

Identification of the Rigid Core for Aged Liquid Droplets of an RNA-Binding Protein Low Complexity Domain

The biomolecular condensation of proteins with low complexity sequences plays a functional role in RNA metabolism and a pathogenic role in neurodegenerative diseases. The formation of dynamic liquid droplets brings biomolecules together to achieve complex cellular functions. The rigidification of liquid droplets into β-strand-rich hydrogel structures composed of protein fibrils is thought to be purely pathological in nature. However, low complexity sequences often harbor multiple fibril-prone regions with delicately balanced functional and pathological interactions. Here, we investigate the maturation of liquid droplets formed by the low complexity domain of the TAR DNA-binding protein 43 (TDP-43). Solid state nuclear magnetic resonance measurements on the aged liquid droplets identify residues 365-400 as the structured core, which are squarely outside the region between residues 311-360 thought to be most important for pathological fibril formation and aggregation. The results of this study suggest that multiple segments of this low complexity domain are prone to form fibrils and that stabilization of β-strand-rich structure in one segment precludes the other region from adopting a rigid fibril structure.

Solid-state NMR spectroscopy

Solid-state nuclear magnetic resonance (NMR) spectroscopy is an atomic-level method used to determine the chemical structure, three-dimensional structure, and dynamics of solids and semi-solids. This Primer summarizes the basic principles of NMR as applied to the wide range of solid systems. The fundamental nuclear spin interactions and the effects of magnetic fields and radiofrequency pulses on nuclear spins are the same as in liquid-state NMR. However, because of the anisotropy of the interactions in the solid state, the majority of high-resolution solid-state NMR spectra is measured under magic-angle spinning (MAS), which has profound effects on the types of radiofrequency pulse sequences required to extract structural and dynamical information. We describe the most common MAS NMR experiments and data analysis approaches for investigating biological macromolecules, organic materials, and inorganic solids. Continuing development of sensitivity-enhancement approaches, including 1H-detected fast MAS experiments, dynamic nuclear polarization, and experiments tailored to ultrahigh magnetic fields, is described. We highlight recent applications of solid-state NMR to biological and materials chemistry. The Primer ends with a discussion of current limitations of NMR to study solids, and points to future avenues of development to further enhance the capabilities of this sophisticated spectroscopy for new applications.

A Slice-based 13C-detected NMR Spin System Forming and Resonance Assignment Method

Nuclear magnetic resonance (NMR) spectroscopy is attracting more attention in the field of computational structural biology. Till recently, ¹H-detected experiments are the dominant NMR technique used due to the high sensitivity of ¹H nuclei. However, the current availability of high magnetic fields and cryogenically cooled probe heads allow researchers to overcome the low sensitivity of ¹³C nuclei. Consequently, ¹³C-detected experiments have become a popular technique in different NMR applications especially resonance assignment and structure determination of large proteins. In this paper, we propose the first spin system forming method for ¹³C-detected NMR spectra. Our method is able to accurately form spin systems based on as few as two ¹³C-detected spectra, CBCACON, and CBCANCO. Our method picks slices from the more trusted spectrum and uses them as feedback to direct the slice picking in the less trusted one. This feedback leads to picking the accurate slices that consequently helps to form better spin systems. We tested our method on a real dataset of 'Ubiquitin' and a benchmark simulated dataset consisting of 12 proteins. We fed our spin systems as inputs to a genetic algorithm to generate the chemical shift assignment, and obtained 92 percent correct chemical shift assignment for Ubiquitin. For the simulated dataset, we obtained an average recall of 86 percent and an average precision of 88 percent. Finally, our chemical shift assignment of Ubiquitin was given as an input to CS-ROSETTA server that generated structures close to the experimentally determined structure.

Automated assignment of NMR spectra of macroscopically oriented proteins using simulated annealing

An automated technique for the sequential assignment of NMR backbone resonances of oriented protein samples has been developed and tested based on ¹⁵N-¹⁵N homonuclear exchange and spin-exchanged separated local-field spectra. By treating the experimental spectral intensity as a pseudopotential, the Monte-Carlo Simulated Annealing algorithm has been employed to seek lowest-energy assignment solutions over a large sampling space where direct enumeration would be unfeasible. The determined sequential assignments have been scored based on the positions of the crosspeaks resulting from the possible orders for the main peaks. This approach is versatile in terms of the parameters that can be specified to achieve the best-fit result. At a minimum the algorithm requires a continuous segment of the main-peak chemical shifts obtained from a uniformly labeled sample and a spin-exchanged experimental spectrum represented as a 2D matrix array. With selective labeling experiments, groups of chemical shifts corresponding to specific locations in the protein backbone can be fixed, thereby decreasing the sampling space. The output from the program consists of a list of top-score main peak assignments, which can be subjected to further scoring criteria until a consensus solution is found. The algorithm has first been tested on a synthetic spectrum with randomly generated chemical shifts and dipolar couplings for the main peaks. The original assignments have been successfully recovered for as many as 100 main peaks when residue-type information was used even in the presence of substantial spectral peak overlap. The algorithm was then applied to assigning two sets of experimental spectra to recover and confirm the previously established assignments in an automated fashion. For the 20-residue transmembrane domain of Pf1 coat protein reconstituted in magnetically aligned bicelles, the original assignment by Park et al. (2010) was recovered by the automated algorithm with additional input from 5 selectively labeled amino acid spectra. The second case considered was the 46 residue Pf1 bacteriophage from Thiriot et al. (2005) and Knox et al. (2010), of which 38 residues were fit. Automated fitting resulted in several possible assignments but not exactly the original assignment. By using a post-fitting filtering procedure based on the number of missed cross peaks and Pf1 helical structure, a consensus spectroscopic assignment is proposed covering 84% of the original assignment. While the automated assignment works best in spectra with well-resolved crosspeaks, it also tolerates substantial spectral crowding to yield reasonable assignments in the cases where ambiguity and degeneracy of possible assignment solutions are inevitable.

Solid-state MAS NMR resonance assignment methods for proteins

The prerequisite to structural or functional studies of proteins by NMR is generally the assignment of resonances. Since the first assignment of proteins by solid-state MAS NMR was conducted almost two decades ago, a wide variety of different pulse sequences and methods have been proposed and continue to be developed. Traditionally, a variety of 2D and 3D ¹³C-detected experiments have been used for the assignment of backbone and side-chain ¹³C and ¹⁵N resonances. These methods have found widespread use across the field. But as the hardware has changed and higher spinning frequencies and magnetic fields are becoming available, the ability to use direct proton detection is opening up a new set of assignment methods based on triple-resonance experiments. This review describes solid-state MAS NMR assignment methods using carbon detection and proton detection at different deuteration levels. The use of different isotopic labelling schemes as an aid to assignment in difficult cases is discussed as well as the increasing number of software packages that support manual and automated resonance assignment.

Detecting and accounting for multiple sources of positional variance in peak list registration analysis and spin system grouping

Peak lists derived from nuclear magnetic resonance (NMR) spectra are commonly used as input data for a variety of computer assisted and automated analyses. These include automated protein resonance assignment and protein structure calculation software tools. Prior to these analyses, peak lists must be aligned to each other and sets of related peaks must be grouped based on common chemical shift dimensions. Even when programs can perform peak grouping, they require the user to provide uniform match tolerances or use default values. However, peak grouping is further complicated by multiple sources of variance in peak position limiting the effectiveness of grouping methods that utilize uniform match tolerances. In addition, no method currently exists for deriving peak positional variances from single peak lists for grouping peaks into spin systems, i.e. spin system grouping within a single peak list. Therefore, we developed a complementary pair of peak list registration analysis and spin system grouping algorithms designed to overcome these limitations. We have implemented these algorithms into an approach that can identify multiple dimension-specific positional variances that exist in a single peak list and group peaks from a single peak list into spin systems. The resulting software tools generate a variety of useful statistics on both a single peak list and pairwise peak list alignment, especially for quality assessment of peak list datasets. We used a range of low and high quality experimental solution NMR and solid-state NMR peak lists to assess performance of our registration analysis and grouping algorithms. Analyses show that an algorithm using a single iteration and uniform match tolerances approach is only able to recover from 50 to 80% of the spin systems due to the presence of multiple sources of variance. Our algorithm recovers additional spin systems by reevaluating match tolerances in multiple iterations. To facilitate evaluation of the algorithms, we developed a peak list simulator within our nmrstarlib package that generates user-defined assigned peak lists from a given BMRB entry or database of entries. In addition, over 100,000 simulated peak lists with one or two sources of variance were generated to evaluate the performance and robustness of these new registration analysis and peak grouping algorithms.

Total lineshape analysis of high-resolution NMR spectra powered by simulated annealing

The novel algorithm for a total lineshape analysis of high-resolution NMR spectra has been developed. A global optimization by simulated annealing has been applied that has allowed to overcome the main trouble of common approaches which had frequently returned solutions for local minima rather than for global ones. The algorithm has been verified for the four-spin test systems ABCD, and has been successfully used for analysis of experimental NMR spectra of proline. The approach has allowed to avoid a sophisticated manual setup of initial parameters and to conduct the analysis of complicated high-resolution NMR spectra nearly automatically.

Cellulose Structural Polymorphism in Plant Primary Cell Walls Investigated by High-Field 2D Solid-State NMR Spectroscopy and Density Functional Theory Calculations

The native cellulose of bacterial, algal, and animal origins has been well studied structurally using X-ray and neutron diffraction and solid-state NMR spectroscopy, and is known to consist of varying proportions of two allomorphs, Iα and Iβ, which differ in hydrogen bonding, chain packing, and local conformation. In comparison, cellulose structure in plant primary cell walls is much less understood because plant cellulose has lower crystallinity and extensive interactions with matrix polysaccharides. Here we have combined two-dimensional magic-angle-spinning (MAS) solid-state nuclear magnetic resonance (solid-state NMR) spectroscopy at high magnetic fields with density functional theory (DFT) calculations to obtain detailed information about the structural polymorphism and spatial distributions of plant primary-wall cellulose. 2D (13)C-(13)C correlation spectra of uniformly (13)C-labeled cell walls of several model plants resolved seven sets of cellulose chemical shifts. Among these, five sets (denoted a-e) belong to cellulose in the interior of the microfibril while two sets (f and g) can be assigned to surface cellulose. Importantly, most of the interior cellulose (13)C chemical shifts differ significantly from the (13)C chemical shifts of the Iα and Iβ allomorphs, indicating that plant primary-wall cellulose has different conformations, packing, and hydrogen bonding from celluloses of other organisms. 2D (13)C-(13)C correlation experiments with long mixing times and with water polarization transfer revealed the spatial distributions and matrix-polysaccharide interactions of these cellulose structures. Celluloses f and g are well mixed chains on the microfibril surface, celluloses a and b are interior chains that are in molecular contact with the surface chains, while cellulose c resides in the core of the microfibril, outside spin diffusion contact with the surface. Interestingly, cellulose d, whose chemical shifts differ most significantly from those of bacterial, algal, and animal cellulose, interacts with hemicellulose, is poorly hydrated, and is targeted by the protein expansin during wall loosening. To obtain information about the C6 hydroxymethyl conformation of these plant celluloses, we carried out DFT calculations of (13)C chemical shifts, using the Iα and Iβ crystal structures as templates and varying the C5-C6 torsion angle. Comparison with the experimental chemical shifts suggests that all interior cellulose favor the tg conformation, but cellulose d also has a similar propensity to adopt the gt conformation. These results indicate that cellulose in plant primary cell walls, due to their interactions with matrix polysaccharides, and has polymorphic structures that are not a simple superposition of the Iα and Iβ allomorphs, thus distinguishing them from bacterial and animal celluloses.

Conformationally selective multidimensional chemical shift ranges in proteins from a PACSY database purged using intrinsic quality criteria

We have determined refined multidimensional chemical shift ranges for intra-residue correlations ((13)C-(13)C, (15)N-(13)C, etc.) in proteins, which can be used to gain type-assignment and/or secondary-structure information from experimental NMR spectra. The chemical-shift ranges are the result of a statistical analysis of the PACSY database of >3000 proteins with 3D structures (1,200,207 (13)C chemical shifts and >3 million chemical shifts in total); these data were originally derived from the Biological Magnetic Resonance Data Bank. Using relatively simple non-parametric statistics to find peak maxima in the distributions of helix, sheet, coil and turn chemical shifts, and without the use of limited "hand-picked" data sets, we show that ~94% of the (13)C NMR data and almost all (15)N data are quite accurately referenced and assigned, with smaller standard deviations (0.2 and 0.8 ppm, respectively) than recognized previously. On the other hand, approximately 6% of the (13)C chemical shift data in the PACSY database are shown to be clearly misreferenced, mostly by ca. -2.4 ppm. The removal of the misreferenced data and other outliers by this purging by intrinsic quality criteria (PIQC) allows for reliable identification of secondary maxima in the two-dimensional chemical-shift distributions already pre-separated by secondary structure. We demonstrate that some of these correspond to specific regions in the Ramachandran plot, including left-handed helix dihedral angles, reflect unusual hydrogen bonding, or are due to the influence of a following proline residue. With appropriate smoothing, significantly more tightly defined chemical shift ranges are obtained for each amino acid type in the different secondary structures. These chemical shift ranges, which may be defined at any statistical threshold, can be used for amino-acid type assignment and secondary-structure analysis of chemical shifts from intra-residue cross peaks by inspection or by using a provided command-line Python script (PLUQin), which should be useful in protein structure determination. The refined chemical shift distributions are utilized in a simple quality test (SQAT) that should be applied to new protein NMR data before deposition in a databank, and they could benefit many other chemical-shift based tools.

Aromatic spectral editing techniques for magic-angle-spinning solid-state NMR spectroscopy of uniformly (13)C-labeled proteins

The four aromatic amino acids in proteins, namely histidine, phenylalanine, tyrosine, and tryptophan, have strongly overlapping (13)C chemical shift ranges between 100 and 160ppm, and have so far been largely neglected in solid-state NMR determination of protein structures. Yet aromatic residues play important roles in biology through π-π and cation-π interactions. To better resolve and assign aromatic residues' (13)C signals in magic-angle-spinning (MAS) solid-state NMR spectra, we introduce two spectral editing techniques. The first method uses gated (1)H decoupling in a proton-driven spin-diffusion (PDSD) experiment to remove all protonated (13)C signals and retain only non-protonated carbon signals in the aromatic region of the (13)C spectra. The second technique uses chemical shift filters and (1)H-(13)C dipolar dephasing to selectively detect the Cα, Cβ and CO cross peaks of aromatic residues while suppressing the signals of all aliphatic residues. We demonstrate these two techniques on amino acids, a model peptide, and the microcrystalline protein GB1, and show that they significantly simplify the 2D NMR spectra and both reveal and permit the ready assignment of the aromatic residues' signals.

Successive Stages of Amyloid-β Self-Assembly Characterized by Solid-State Nuclear Magnetic Resonance with Dynamic Nuclear Polarization

Self-assembly of amyloid-β (Aβ) peptides in human brain tissue leads to neurodegeneration in Alzheimer's disease (AD). Amyloid fibrils, whose structures have been extensively characterized by solid state nuclear magnetic resonance (ssNMR) and other methods, are the thermodynamic end point of Aβ self-assembly. Oligomeric and protofibrillar assemblies, whose structures are less well-understood, are also observed as intermediates in the assembly process in vitro and have been implicated as important neurotoxic species in AD. We report experiments in which the structural evolution of 40-residue Aβ (Aβ40) is monitored by ssNMR measurements on frozen solutions prepared at four successive stages of the self-assembly process. Measurements on transient intermediates are enabled by ssNMR signal enhancements from dynamic nuclear polarization (DNP) at temperatures below 30 K. DNP-enhanced ssNMR data reveal a monotonic increase in conformational order from an initial state comprised primarily of monomers and small oligomers in solution at high pH, to larger oligomers near neutral pH, to metastable protofibrils, and finally to fibrils. Surprisingly, the predominant molecular conformation, indicated by (13)C NMR chemical shifts and by side chain contacts between F19 and L34 residues, is qualitatively similar at all stages. However, the in-register parallel β-sheet supramolecular structure, indicated by intermolecular (13)C spin polarization transfers, does not develop before the fibril stage. This work represents the first application of DNP-enhanced ssNMR to the characterization of peptide or protein self-assembly intermediates.

On the problem of resonance assignments in solid state NMR of uniformly ¹⁵N,¹³C-labeled proteins

Determination of accurate resonance assignments from multidimensional chemical shift correlation spectra is one of the major problems in biomolecular solid state NMR, particularly for relative large proteins with less-than-ideal NMR linewidths. This article investigates the difficulty of resonance assignment, using a computational Monte Carlo/simulated annealing (MCSA) algorithm to search for assignments from artificial three-dimensional spectra that are constructed from the reported isotropic (15)N and (13)C chemical shifts of two proteins whose structures have been determined by solution NMR methods. The results demonstrate how assignment simulations can provide new insights into factors that affect the assignment process, which can then help guide the design of experimental strategies. Specifically, simulations are performed for the catalytic domain of SrtC (147 residues, primarily β-sheet secondary structure) and the N-terminal domain of MLKL (166 residues, primarily α-helical secondary structure). Assuming unambiguous residue-type assignments and four ideal three-dimensional data sets (NCACX, NCOCX, CONCA, and CANCA), uncertainties in chemical shifts must be less than 0.4 ppm for assignments for SrtC to be unique, and less than 0.2 ppm for MLKL. Eliminating CANCA data has no significant effect, but additionally eliminating CONCA data leads to more stringent requirements for chemical shift precision. Introducing moderate ambiguities in residue-type assignments does not have a significant effect.

MAS NMR of HIV-1 protein assemblies

The negative global impact of the AIDS pandemic is well known. In this perspective article, the utility of magic angle spinning (MAS) NMR spectroscopy to answer pressing questions related to the structure and dynamics of HIV-1 protein assemblies is examined. In recent years, MAS NMR has undergone major technological developments enabling studies of large viral assemblies. We discuss some of these evolving methods and technologies and provide a perspective on the current state of MAS NMR as applied to the investigations into structure and dynamics of HIV-1 assemblies of CA capsid protein and of Gag maturation intermediates.

Median Modified Wiener Filter for nonlinear adaptive spatial denoising of protein NMR multidimensional spectra

Denoising multidimensional NMR-spectra is a fundamental step in NMR protein structure determination. The state-of-the-art method uses wavelet-denoising, which may suffer when applied to non-stationary signals affected by Gaussian-white-noise mixed with strong impulsive artifacts, like those in multi-dimensional NMR-spectra. Regrettably, Wavelet's performance depends on a combinatorial search of wavelet shapes and parameters; and multi-dimensional extension of wavelet-denoising is highly non-trivial, which hampers its application to multidimensional NMR-spectra. Here, we endorse a diverse philosophy of denoising NMR-spectra: less is more! We consider spatial filters that have only one parameter to tune: the window-size. We propose, for the first time, the 3D extension of the median-modified-Wiener-filter (MMWF), an adaptive variant of the median-filter, and also its novel variation named MMWF*. We test the proposed filters and the Wiener-filter, an adaptive variant of the mean-filter, on a benchmark set that contains 16 two-dimensional and three-dimensional NMR-spectra extracted from eight proteins. Our results demonstrate that the adaptive spatial filters significantly outperform their non-adaptive versions. The performance of the new MMWF* on 2D/3D-spectra is even better than wavelet-denoising. Noticeably, MMWF* produces stable high performance almost invariant for diverse window-size settings: this signifies a consistent advantage in the implementation of automatic pipelines for protein NMR-spectra analysis.

VirtualSpectrum, a tool for simulating peak list for multi-dimensional NMR spectra

NMR spectroscopy is a widely used technique for characterizing the structure and dynamics of macromolecules. Often large amounts of NMR data are required to characterize the structure of proteins. To save valuable time and resources on data acquisition, simulated data is useful in the developmental phase, for data analysis, and for comparison with experimental data. However, existing tools for this purpose can be difficult to use, are sometimes specialized for certain types of molecules or spectra, or produce too idealized data. Here we present a fast, flexible and robust tool, VirtualSpectrum, for generating peak lists for most multi-dimensional NMR experiments for both liquid and solid state NMR. It is possible to tune the quality of the generated peak lists to include sources of artifacts from peak overlap, noise and missing signals. VirtualSpectrum uses an analytic expression to represent the spectrum and derive the peak positions, seamlessly handling overlap between signals. We demonstrate our tool by comparing simulated and experimental spectra for different multi-dimensional NMR spectra and analyzing systematically three cases where overlap between peaks is particularly relevant; solid state NMR data, liquid state NMR homonuclear (1)H and (15)N-edited spectra, and 2D/3D heteronuclear correlation spectra of unstructured proteins. We analyze the impact of protein size and secondary structure on peak overlap and on the accuracy of structure determination based on data of different qualities simulated by VirtualSpectrum.

An automated framework for NMR resonance assignment through simultaneous slice picking and spin system forming

Despite significant advances in automated nuclear magnetic resonance-based protein structure determination, the high numbers of false positives and false negatives among the peaks selected by fully automated methods remain a problem. These false positives and negatives impair the performance of resonance assignment methods. One of the main reasons for this problem is that the computational research community often considers peak picking and resonance assignment to be two separate problems, whereas spectroscopists use expert knowledge to pick peaks and assign their resonances at the same time. We propose a novel framework that simultaneously conducts slice picking and spin system forming, an essential step in resonance assignment. Our framework then employs a genetic algorithm, directed by both connectivity information and amino acid typing information from the spin systems, to assign the spin systems to residues. The inputs to our framework can be as few as two commonly used spectra, i.e., CBCA(CO)NH and HNCACB. Different from the existing peak picking and resonance assignment methods that treat peaks as the units, our method is based on 'slices', which are one-dimensional vectors in three-dimensional spectra that correspond to certain ([Formula: see text]) values. Experimental results on both benchmark simulated data sets and four real protein data sets demonstrate that our method significantly outperforms the state-of-the-art methods while using a less number of spectra than those methods. Our method is freely available at http://sfb.kaust.edu.sa/Pages/Software.aspx.

Automated robust and accurate assignment of protein resonances for solid state NMR

The process of resonance assignment represents a time-consuming and potentially error-prone bottleneck in structural studies of proteins by solid-state NMR (ssNMR). Software for the automation of this process is therefore of high interest. Procedures developed through the last decades for solution-state NMR are not directly applicable for ssNMR due to the inherently lower data quality caused by lower sensitivity and broader lines, leading to overlap between peaks. Recently, the first efforts towards procedures specifically aimed for ssNMR have been realized (Schmidt et al. in J Biomol NMR 56(3):243-254, 2013). Here we present a robust automatic method, which can accurately assign protein resonances using peak lists from a small set of simple 2D and 3D ssNMR experiments, applicable in cases with low sensitivity. The method is demonstrated on three uniformly (13)C, (15)N labeled biomolecules with different challenges on the assignments. In particular, for the immunoglobulin binding domain B1 of streptococcal protein G automatic assignment shows 100% accuracy for the backbone resonances and 91.8% when including all side chain carbons. It is demonstrated, by using a procedure for generating artificial spectra with increasing line widths, that our method, GAMES_ASSIGN can handle a significant amount of overlapping peaks in the assignment. The impact of including different ssNMR experiments is evaluated as well.

Resonance assignment of the NMR spectra of disordered proteins using a multi-objective non-dominated sorting genetic algorithm

A multi-objective genetic algorithm is introduced to predict the assignment of protein solid-state NMR (SSNMR) spectra with partial resonance overlap and missing peaks due to broad linewidths, molecular motion, and low sensitivity. This non-dominated sorting genetic algorithm II (NSGA-II) aims to identify all possible assignments that are consistent with the spectra and to compare the relative merit of these assignments. Our approach is modeled after the recently introduced Monte-Carlo simulated-annealing (MC/SA) protocol, with the key difference that NSGA-II simultaneously optimizes multiple assignment objectives instead of searching for possible assignments based on a single composite score. The multiple objectives include maximizing the number of consistently assigned peaks between multiple spectra ("good connections"), maximizing the number of used peaks, minimizing the number of inconsistently assigned peaks between spectra ("bad connections"), and minimizing the number of assigned peaks that have no matching peaks in the other spectra ("edges"). Using six SSNMR protein chemical shift datasets with varying levels of imperfection that was introduced by peak deletion, random chemical shift changes, and manual peak picking of spectra with moderately broad linewidths, we show that the NSGA-II algorithm produces a large number of valid and good assignments rapidly. For high-quality chemical shift peak lists, NSGA-II and MC/SA perform similarly well. However, when the peak lists contain many missing peaks that are uncorrelated between different spectra and have chemical shift deviations between spectra, the modified NSGA-II produces a larger number of valid solutions than MC/SA, and is more effective at distinguishing good from mediocre assignments by avoiding the hazard of suboptimal weighting factors for the various objectives. These two advantages, namely diversity and better evaluation, lead to a higher probability of predicting the correct assignment for a larger number of residues. On the other hand, when there are multiple equally good assignments that are significantly different from each other, the modified NSGA-II is less efficient than MC/SA in finding all the solutions. This problem is solved by a combined NSGA-II/MC algorithm, which appears to have the advantages of both NSGA-II and MC/SA. This combination algorithm is robust for the three most difficult chemical shift datasets examined here and is expected to give the highest-quality de novo assignment of challenging protein NMR spectra.

Automated solid-state NMR resonance assignment of protein microcrystals and amyloids

Solid-state NMR is an emerging structure determination technique for crystalline and non-crystalline protein assemblies, e.g., amyloids. Resonance assignment constitutes the first and often very time-consuming step to a structure. We present ssFLYA, a generally applicable algorithm for automatic assignment of protein solid-state NMR spectra. Application to microcrystals of ubiquitin and the Ure2 prion C-terminal domain, as well as amyloids of HET-s(218-289) and α-synuclein yielded 88-97 % correctness for the backbone and side-chain assignments that are classified as self-consistent by the algorithm, and 77-90 % correctness if also assignments classified as tentative by the algorithm are included.

Practical use of chemical shift databases for protein solid-state NMR: 2D chemical shift maps and amino-acid assignment with secondary-structure information

We introduce a Python-based program that utilizes the large database of (13)C and (15)N chemical shifts in the Biological Magnetic Resonance Bank to rapidly predict the amino acid type and secondary structure from correlated chemical shifts. The program, called PACSYlite Unified Query (PLUQ), is designed to help assign peaks obtained from 2D (13)C-(13)C, (15)N-(13)C, or 3D (15)N-(13)C-(13)C magic-angle-spinning correlation spectra. We show secondary-structure specific 2D (13)C-(13)C correlation maps of all twenty amino acids, constructed from a chemical shift database of 262,209 residues. The maps reveal interesting conformation-dependent chemical shift distributions and facilitate searching of correlation peaks during amino-acid type assignment. Based on these correlations, PLUQ outputs the most likely amino acid types and the associated secondary structures from inputs of experimental chemical shifts. We test the assignment accuracy using four high-quality protein structures. Based on only the Cα and Cβ chemical shifts, the highest-ranked PLUQ assignments were 40-60 % correct in both the amino-acid type and the secondary structure. For three input chemical shifts (CO-Cα-Cβ or N-Cα-Cβ), the first-ranked assignments were correct for 60 % of the residues, while within the top three predictions, the correct assignments were found for 80 % of the residues. PLUQ and the chemical shift maps are expected to be useful at the first stage of sequential assignment, for combination with automated sequential assignment programs, and for highly disordered proteins for which secondary structure analysis is the main goal of structure determination.

Recent advances in computational methods for nuclear magnetic resonance data processing

Although three-dimensional protein structure determination using nuclear magnetic resonance (NMR) spectroscopy is a computationally costly and tedious process that would benefit from advanced computational techniques, it has not garnered much research attention from specialists in bioinformatics and computational biology. In this paper, we review recent advances in computational methods for NMR protein structure determination. We summarize the advantages of and bottlenecks in the existing methods and outline some open problems in the field. We also discuss current trends in NMR technology development and suggest directions for research on future computational methods for NMR.

Improved chemical shift prediction by Rosetta conformational sampling

Chemical shift frequencies represent a time-average of all the conformational states populated by a protein. Thus, chemical shift prediction programs based on sequence and database analysis yield higher accuracy for rigid rather than flexible protein segments. Here we show that the prediction accuracy can be significantly improved by averaging over an ensemble of structures, predicted solely from amino acid sequence with the Rosetta program. This approach to chemical shift and structure prediction has the potential to be useful for guiding resonance assignments, especially in solid-state NMR structural studies of membrane proteins in proteoliposomes.

Restraints on backbone conformations in solid state NMR studies of uniformly labeled proteins from quantitative amide 15N-15N and carbonyl 13C-13C dipolar recoupling data

Recent structural studies of uniformly (15)N, (13)C-labeled proteins by solid state nuclear magnetic resonance (NMR) rely principally on two sources of structural restraints: (i) restraints on backbone conformation from isotropic (15)N and (13)C chemical shifts, based on empirical correlations between chemical shifts and backbone torsion angles; (ii) restraints on inter-residue proximities from qualitative measurements of internuclear dipole-dipole couplings, detected as the presence or absence of inter-residue crosspeaks in multidimensional spectra. We show that site-specific dipole-dipole couplings among (15)N-labeled backbone amide sites and among (13)C-labeled backbone carbonyl sites can be measured quantitatively in uniformly-labeled proteins, using dipolar recoupling techniques that we call (15)N-BARE and (13)C-BARE (BAckbone REcoupling), and that the resulting data represent a new source of restraints on backbone conformation. (15)N-BARE and (13)C-BARE data can be incorporated into structural modeling calculations as potential energy surfaces, which are derived from comparisons between experimental (15)N and (13)C signal decay curves, extracted from crosspeak intensities in series of two-dimensional spectra, with numerical simulations of the (15)N-BARE and (13)C-BARE measurements. We demonstrate this approach through experiments on microcrystalline, uniformly (15)N, (13)C-labeled protein GB1. Results for GB1 show that (15)N-BARE and (13)C-BARE restraints are complementary to restraints from chemical shifts and inter-residue crosspeaks, improving both the precision and the accuracy of calculated structures.

VITAL NMR: using chemical shift derived secondary structure information for a limited set of amino acids to assess homology model accuracy

Homology modeling is a powerful tool for predicting protein structures, whose success depends on obtaining a reasonable alignment between a given structural template and the protein sequence being analyzed. In order to leverage greater predictive power for proteins with few structural templates, we have developed a method to rank homology models based upon their compliance to secondary structure derived from experimental solid-state NMR (SSNMR) data. Such data is obtainable in a rapid manner by simple SSNMR experiments (e.g., (13)C-(13)C 2D correlation spectra). To test our homology model scoring procedure for various amino acid labeling schemes, we generated a library of 7,474 homology models for 22 protein targets culled from the TALOS+/SPARTA+ training set of protein structures. Using subsets of amino acids that are plausibly assigned by SSNMR, we discovered that pairs of the residues Val, Ile, Thr, Ala and Leu (VITAL) emulate an ideal dataset where all residues are site specifically assigned. Scoring the models with a predicted VITAL site-specific dataset and calculating secondary structure with the Chemical Shift Index resulted in a Pearson correlation coefficient (-0.75) commensurate to the control (-0.77), where secondary structure was scored site specifically for all amino acids (ALL 20) using STRIDE. This method promises to accelerate structure procurement by SSNMR for proteins with unknown folds through guiding the selection of remotely homologous protein templates and assessing model quality.

Magic angle spinning solid-state NMR experiments for structural characterization of proteins

Solid-state nuclear magnetic resonance (SSNMR) has become a prominent method in biology and is suitable for the characterization of insoluble proteins and protein aggregates such as amyloid fibrils, membrane-lipid complexes, and precipitated proteins. Often, the initial and the most critical step is to obtain spectroscopic assignments, that is, to determine chemical shifts of individual atoms. The procedures for SSNMR spectroscopic assignments are now well established for small microcrystalline proteins, where high signal-to-noise can be obtained. The sensitivity of the experiments and spectral resolution decrease with the increasing molecular weight, which makes setting SSNMR experiments in large proteins a much more challenging and demanding procedure. Here, we describe the protocol for the most common set of 3D magic angle spinning (MAS) SSNMR experiments. While the procedures described in the text are well known to SSNMR practitioners, we hope they will be of interest to scientists interested in extending their repertoire of biophysical techniques.

A software framework for analysing solid-state MAS NMR data

Solid-state magic-angle-spinning (MAS) NMR of proteins has undergone many rapid methodological developments in recent years, enabling detailed studies of protein structure, function and dynamics. Software development, however, has not kept pace with these advances and data analysis is mostly performed using tools developed for solution NMR which do not directly address solid-state specific issues. Here we present additions to the CcpNmr Analysis software package which enable easier identification of spinning side bands, straightforward analysis of double quantum spectra, automatic consideration of non-uniform labelling schemes, as well as extension of other existing features to the needs of solid-state MAS data. To underpin this, we have updated and extended the CCPN data model and experiment descriptions to include transfer types and nomenclature appropriate for solid-state NMR experiments, as well as a set of experiment prototypes covering the experiments commonly employed by solid-sate MAS protein NMR spectroscopists. This work not only improves solid-state MAS NMR data analysis but provides a platform for anyone who uses the CCPN data model for programming, data transfer, or data archival involving solid-state MAS NMR data.

Segmental polymorphism in a functional amyloid

Although amyloid fibrils are generally considered to be causative or contributing agents in amyloid diseases, several amyloid fibrils are also believed to have biological functions. Among these are fibrils formed by Pmel17 within melanosomes, which act as a template for melanin deposition. We use solid-state NMR to show that the molecular structures of fibrils formed by the 130-residue pseudo-repeat domain Pmel17:RPT are polymorphic even within the biologically relevant pH range. Thus, biological function in amyloid fibrils does not necessarily imply a unique molecular structure. Solid-state NMR spectra of three Pmel17:RPT polymorphs show that in all cases, only a subset (~30%) of the full amino acid sequence contributes to the immobilized fibril core. Although the repetitive nature of the sequence and incomplete spectral resolution prevent the determination of unique chemical shift assignments from two- and three-dimensional solid-state NMR spectra, we use a Monte Carlo assignment algorithm to identify protein segments that are present in or absent from the fibril core. The results show that the identity of the core-forming segments varies from one polymorph to another, a phenomenon known as segmental polymorphism.

A general Monte Carlo/simulated annealing algorithm for resonance assignment in NMR of uniformly labeled biopolymers

We describe a general computational approach to site-specific resonance assignments in multidimensional NMR studies of uniformly (15)N,(13)C-labeled biopolymers, based on a simple Monte Carlo/simulated annealing (MCSA) algorithm contained in the program MCASSIGN2. Input to MCASSIGN2 includes lists of multidimensional signals in the NMR spectra with their possible residue-type assignments (which need not be unique), the biopolymer sequence, and a table that describes the connections that relate one signal list to another. As output, MCASSIGN2 produces a high-scoring sequential assignment of the multidimensional signals, using a score function that rewards good connections (i.e., agreement between relevant sets of chemical shifts in different signal lists) and penalizes bad connections, unassigned signals, and assignment gaps. Examination of a set of high-scoring assignments from a large number of independent runs allows one to determine whether a unique assignment exists for the entire sequence or parts thereof. We demonstrate the MCSA algorithm using two-dimensional (2D) and three-dimensional (3D) solid state NMR spectra of several model protein samples (α-spectrin SH3 domain and protein G/B1 microcrystals, HET-s(218-289) fibrils), obtained with magic-angle spinning and standard polarization transfer techniques. The MCSA algorithm and MCASSIGN2 program can accommodate arbitrary combinations of NMR spectra with arbitrary dimensionality, and can therefore be applied in many areas of solid state and solution NMR.

The α-helical C-terminal domain of full-length recombinant PrP converts to an in-register parallel β-sheet structure in PrP fibrils: evidence from solid state nuclear magnetic resonance

We report the results of solid state nuclear magnetic resonance (NMR) measurements on amyloid fibrils formed by the full-length prion protein PrP (residues 23−231, Syrian hamster sequence). Measurements of intermolecular 13C−13C dipole−dipole couplings in selectively carbonyl-labeled samples indicate that β-sheets in these fibrils have an in-register parallel structure, as previously observed in amyloid fibrils associated with Alzheimer’s disease and type 2 diabetes and in yeast prion fibrils. Two-dimensional 13C−13C and 15N−13C solid state NMR spectra of a uniformly 15N- and 13C-labeled sample indicate that a relatively small fraction of the full sequence, localized to the C-terminal end, forms the structurally ordered, immobilized core. Although unique site-specific assignments of the solid state NMR signals cannot be obtained from these spectra, analysis with a Monte Carlo/simulated annealing algorithm suggests that the core is comprised primarily of residues in the 173−224 range. These results are consistent with earlier electron paramagnetic resonance studies of fibrils formed by residues 90−231 of the human PrP sequence, formed under somewhat different conditions [Cobb, N. J., Sonnichsen, F. D., McHaourab, H., and Surewicz, W. K. (2007) Proc. Natl. Acad. Sci. U.S.A. 104, 18946−18951], suggesting that an in-register parallel β-sheet structure formed by the C-terminal end may be a general feature of PrP fibrils prepared in vitro.

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.

Solid-state NMR studies of amyloid fibril structure

Current interest in amyloid fibrils stems from their involvement in neurodegenerative and other diseases and from their role as an alternative structural state for many peptides and proteins. Solid-state nuclear magnetic resonance (NMR) methods have the unique capability of providing detailed structural constraints for amyloid fibrils, sufficient for the development of full molecular models. In this article, recent progress in the application of solid-state NMR to fibrils associated with Alzheimer's disease, prion fibrils, and related systems is reviewed, along with relevant developments in solid-state NMR techniques and technology.

Solid-state NMR techniques for the structural determination of amyloid fibrils

This review discusses the solid-state NMR techniques developed for the study of amyloid fibrils. Literature up to the end of 2010 has been surveyed and the materials are organized according to five categories, viz. homonuclear dipolar recoupling and polarization transfer via J-coupling, heteronuclear dipolar recoupling, correlation spectroscopy, recoupling of chemical shift anisotropy, and tensor correlation. Our emphasis is on the NMR techniques and their practical aspects. The biological implications of the results obtained for amyloid fibrils are only briefly discussed. Our main objective is to showcase the power of NMR in the study of biological unoriented solids.