Efficient and generalized processing of multidimensional NUS NMR data: the NESTA algorithm and comparison of regularization terms

SCREENES: Enhancing non-uniform sampling reconstruction for symmetrical NMR spectroscopy

BACKGROUND

Symmetrical NMR spectroscopy, such as Total Correlation Spectroscopy (TOCSY) and other homonuclear spectroscopy, displays symmetry in chemical shift but are generally not symmetrical in terms of intensity, which constitutes a pivotal branch of multidimensional NMR spectroscopy and offers a robust tool for elucidating the structures and dynamics of complex samples, particularly in the context of biological macromolecules. Non-Uniform Sampling (NUS) stands as a critical technique for accelerating multidimensional NMR experiments. However, symmetrical NMR spectroscopy inherently presents dynamic peak intensities, where cross peaks tend to be substantially weaker compared to diagonal peaks. Recovering these weaker cross peaks from NUS data poses a significant challenge, often resulting in compromised data quality.

RESULTS

We enhance the reconstruction quality of NUS symmetrical NMR spectroscopy based on the assumption that the asymmetry in intensity is mild. Regarding the sampling schedule, we employ the symmetrical sampling structure integrated with Poisson sampling schedule to enhance the efficiency of data acquisition. In term of the reconstruction algorithm, we propose the new method by incorporating hard and soft symmetrical constraints into our recently developed L1-norm-based Compressed Sensing (CS) method known as Sparse Complex-valued REconstruction Enabled by Newton method (SCREEN). Additionally, we propose a two-step reconstruction strategy that separately addresses diagonal and cross peaks. In this two-step strategy, cross peaks are effectively reconstructed by excluding the stronger diagonal peaks. Extensive experimental results validate the effectiveness of our proposed methodology.

SIGNIFICANCE

This method enhances the overall quality of the reconstructed NUS symmetrical NMR spectra, especially in terms of cross peaks, thereby enriching the interpretation of spectral information. Furthermore, it boosts the robustness towards regularization parameters, facilitating a user-friendly experience.

Efficient Access to Elusive 1D 13C NMR Spectra through Highly Resolved 1H, 13C-Long-Range Correlation Spectroscopy

A method for obtaining 1D 13C NMR spectra from natural products or metabolites using proton detection is described. The approach delivers singlets for every 13C signal without conducting any broadband 1H decoupling (CPD) and is based on calculating 13C projections from constant-time HMBC and conventional HSQC experiments, recorded at high digital resolution and processed to pure phases. Paramount to the proposed method is the implication of nonuniform sampling and echo processing. The echo processing produces phase-sensitive 2D CT-HMBC spectra with narrow 13C signal line shapes. Two simple HMBC pulse sequences are utilized with the suppression of homo- and heteronuclear couplings. Due to the removal of the 1H multiplet structure in F1 (no tilt at higher digital resolution), 13C singlets arise. An overall increase in 13C signal-to-noise (SINO) for all types of carbon multiplicities is observed, making the proposed technique superior compared to direct 13C excitation. For otherwise difficult-to-measure quaternary carbon atoms, a SINO enhancement of up to 6 and 12 depending on F1 resolution (3 and 6 Hz/point) is reported. Echo/anti-Echo signal detection cleans up the spectrum. Nonuniform sampling (NUS) lays the groundwork to significantly reduce the total acquisition time. Final 1D 13C projections are obtained by combining the 13C projection from CT HMBC and conventional HSQC. This orthogonal concept of combining the 13C projections from different spectra inherently minimizes the risk of missing 13C cross-peaks by inappropriate setting of long-range nJHC coupling delays and the shortcoming of T2 relaxations. The advantages and some limitations of the concept are discussed.

Exploring Sulfur Sites in Proteins via Triple-Resonance 1H-Detected 77Se NMR

NMR spectroscopy has been applied to virtually all sites within proteins and biomolecules; however, the observation of sulfur sites remains very challenging. Recent studies have examined 77Se as a replacement for sulfur and applied 77Se NMR in both the solution and solid states. As a spin-1/2 nuclide, 77Se is attractive as a probe of sulfur sites, and it has a very large chemical shift range (due to a large chemical shift anisotropy), which makes it potentially very sensitive to structural and/or binding interactions as well as dynamics. Despite being a spin-1/2 nuclide, there have been rather limited studies of 77Se, and the ability to use 1H-indirect detection has been sparse. Some examples exist, but in the absence of a directly bonded, nonexchangeable 1H, these have been largely limited to smaller molecules. We develop and illustrate approaches using double-labeling of 13C and 77Se in proteins that enable more sensitive triple-resonance schemes via multistep coherence transfers and 1H-detection. These methods require specialized hardware and decoupling schemes, which we developed and will be discussed.

Non-uniform sampling of similar NMR spectra and its application to studies of the interaction between alpha-synuclein and liposomes

The accelerated acquisition of multidimensional NMR spectra using sparse non-uniform sampling (NUS) has been widely adopted in recent years. The key concept in NUS is that a major part of the data is omitted during measurement, and then reconstructed using, for example, compressed sensing (CS) methods. CS requires spectra to be compressible, that is, they should contain relatively few "significant" points. The more compressible the spectrum, the fewer experimental NUS points needed in order for it to be accurately reconstructed. In this paper we show that the CS processing of similar spectra can be enhanced by reconstructing only the differences between them. Accurate reconstruction can be obtained at lower sampling levels as the difference is sparser than the spectrum itself. In many situations this method is superior to "conventional" compressed sensing. We exemplify the concept of "difference CS" with one such case-the study of alpha-synuclein binding to liposomes and its dependence on temperature. To obtain information on temperature-dependent transitions between different states, we need to acquire several dozen spectra at various temperatures, with and without the presence of liposomes. Our detailed investigation reveals that changes in the binding modes of the alpha-synuclein ensemble are not only temperature-dependent but also show non-linear behavior in their transitions. Our proposed CS processing approach dramatically reduces the number of NUS points required and thus significantly shortens the experimental time.

nus-tool: A unified program for generating and analyzing sample schedules for nonuniformly sampled NMR experiments

Increases in digital resolution achieved by high-field NMR require increases in spectral width. Additionally, the ability to resolve two overlapping peaks requires a sufficiently long acquisition time. These constraints combine, so that achieving high resolution spectra on high-field magnets requires long experiment times when employing uniform sampling and Fourier Transform processing. These limitations may be addressed by using nonuniform sampling (NUS), but the complexity of the parameter space across the variety of available NUS schemes greatly hinders the establishment of optimal approaches and best practices. We address these challenges with nus-tool, which is a software package for generating and analyzing NUS schedules. The nus-tool software internally implements random sampling and exponentially biased sampling. Through pre-configured plug-ins, it also provides access to quantile sampling and Poisson gap sampling. The software computes the relative sensitivity, mean evolution time, point spread function, and peak-to-sidelobe ratio; all of which can be determined for a candidate sample schedule prior to running an experiment to verify expected sensitivity, resolution, and artifact suppression. The nus-tool package is freely available on the NMRbox platform through an interactive GUI and via the command line, which is especially useful for scripted workflows that investigate the effectiveness of various NUS schemes.

Structural Plasticity of Pioneer Factor Sox2 and DNA Bendability Modulate Nucleosome Engagement and Sox2-Oct4 Synergism

Pioneer transcription factors (pTFs) can bind directly to silent chromatin and promote vital transcriptional programs. Here, by integrating high-resolution nuclear magnetic resonance (NMR) spectroscopy with biochemistry, we reveal new structural and mechanistic insights into the interaction of pluripotency pTFs and functional partners Sox2 and Oct4 with nucleosomes. We find that the affinity and conformation of Sox2 for solvent-exposed nucleosome sites depend strongly on their position and DNA sequence. Sox2, which is partially disordered but becomes structured upon DNA binding and bending, forms a super-stable nucleosome complex at superhelical location +5 (SHL+5) with similar affinity and conformation to that with naked DNA. However, at suboptimal internal and end-positioned sites where DNA may be harder to deform, Sox2 favors partially unfolded and more dynamic states that are encoded in its intrinsic flexibility. Importantly, Sox2 structure and DNA bending can be stabilized by synergistic Oct4 binding, but only on adjacent motifs near the nucleosome edge and with the full Oct4 DNA-binding domain. Further mutational studies reveal that strategically impaired Sox2 folding is coupled to reduced DNA bending and inhibits nucleosome binding and Sox2-Oct4 cooperation, while increased nucleosomal DNA flexibility enhances Sox2 association. Together, our findings fit a model where the site-specific DNA bending propensity and structural plasticity of Sox2 govern distinct modes of nucleosome engagement and modulate Sox2-Oct4 synergism. The principles outlined here can potentially guide pTF site selection in the genome and facilitate interaction with other chromatin factors or chromatin opening in vivo.

Clustered sparsity and Poisson-gap sampling

Non-uniform sampling (NUS) is a popular way of reducing the amount of time taken by multidimensional NMR experiments. Among the various non-uniform sampling schemes that exist, the Poisson-gap (PG) schedules are particularly popular, especially when combined with compressed-sensing (CS) reconstruction of missing data points. However, the use of PG is based mainly on practical experience and has not, as yet, been explained in terms of CS theory. Moreover, an apparent contradiction exists between the reported effectiveness of PG and CS theory, which states that a "flat" pseudo-random generator is the best way to generate sampling schedules in order to reconstruct sparse spectra. In this paper we explain how, and in what situations, PG reveals its superior features in NMR spectroscopy. We support our theoretical considerations with simulations and analyses of experimental data from the Biological Magnetic Resonance Bank (BMRB). Our analyses reveal a previously unnoticed feature of many NMR spectra that explains the success of "blue-noise" schedules, such as PG. We call this feature "clustered sparsity". This refers to the fact that the peaks in NMR spectra are not just sparse but often form clusters in the indirect dimension, and PG is particularly suited to deal with such situations. Additionally, we discuss why denser sampling in the initial and final parts of the clustered signal may be useful.

NUScon: a community-driven platform for quantitative evaluation of nonuniform sampling in NMR

Although the concepts of nonuniform sampling (NUS​​​​​​​) and non-Fourier spectral reconstruction in multidimensional NMR began to emerge 4 decades ago , it is only relatively recently that NUS has become more commonplace. Advantages of NUS include the ability to tailor experiments to reduce data collection time and to improve spectral quality, whether through detection of closely spaced peaks (i.e., "resolution") or peaks of weak intensity (i.e., "sensitivity"). Wider adoption of these methods is the result of improvements in computational performance, a growing abundance and flexibility of software, support from NMR spectrometer vendors, and the increased data sampling demands imposed by higher magnetic fields. However, the identification of best practices still remains a significant and unmet challenge. Unlike the discrete Fourier transform, non-Fourier methods used to reconstruct spectra from NUS data are nonlinear, depend on the complexity and nature of the signals, and lack quantitative or formal theory describing their performance. Seemingly subtle algorithmic differences may lead to significant variabilities in spectral qualities and artifacts. A community-based critical assessment of NUS challenge problems has been initiated, called the "Nonuniform Sampling Contest" (NUScon), with the objective of determining best practices for processing and analyzing NUS experiments. We address this objective by constructing challenges from NMR experiments that we inject with synthetic signals, and we process these challenges using workflows submitted by the community. In the initial rounds of NUScon our aim is to establish objective criteria for evaluating the quality of spectral reconstructions. We present here a software package for performing the quantitative analyses, and we present the results from the first two rounds of NUScon. We discuss the challenges that remain and present a roadmap for continued community-driven development with the ultimate aim of providing best practices in this rapidly evolving field. The NUScon software package and all data from evaluating the challenge problems are hosted on the NMRbox platform.

Non-uniform sampling for NOESY? A case study on spiramycin

To date, most nuclear magnetic resonance (NMR)-based 3-D structure determinations of both small molecules and of biopolymers utilize the nuclear Overhauser effect (NOE) via NOESY spectra. The acquisition of high-quality NOESY spectra is a prerequisite for quantitative analysis providing accurate interatomic distances. As the acquisition of NOE build-ups is time-consuming, acceleration of the process by the use of non-uniform sampling (NUS) may seem beneficial; however, the quantitativity of NOESY spectra acquired with NUS has not yet been validated. Herein, NOESY spectra with various extents of NUS have been recorded, artificial NUS spectra with two different sampling schemes created, and by using two different NUS reconstruction algorithms the influence of NUS on the data quality was evaluated. Using statistical analyses, NUS is demonstrated to influence the accuracy of quantitative NOE experiments. The NOE-based distances show an increased error as the sampling density decreases. Weak NOE signals are affected more severely by NUS than more intense ones. The application of NUS with NOESY comes at two major costs: the interatomic distances are determined with lower accuracy and long-range correlations are lost.

Conserved allosteric ensembles in disordered proteins using TROSY/anti-TROSY R2-filtered spectroscopy

Defining the role of intrinsic disorder in proteins in the myriad of biological processes with which it is involved represents a significant goal in modern biophysics. Toward this end, NMR is uniquely suited for molecular studies of dynamic and disordered regions, but studying these regions in concert with their more structured domains and binding partners presents spectroscopic challenges. Here, we investigate the interactions between the structured and disordered regions of the human glucocorticoid receptor (GR). To do this, we developed an NMR strategy that relies on a novel relaxation filter for the simultaneous study of structured and unstructured regions. Using this approach, we conducted a comparative analysis of three translational isoforms of GR containing a folded DNA-binding domain (DBD) and two disordered regions that flank the DBD, one of which varies in size in the different isoforms. Notably, we were able to assign resonances that had previously been inaccessible because of the spectral complexity of the translational isoforms, which in turn allowed us to 1) identify a region of the structured DBD that undergoes significant changes in the local chemical environment in the presence of the disordered region and 2) determine differences in the conformational ensembles of the disordered regions of the translational isoforms. Furthermore, an ensemble-based thermodynamic analysis of the isoforms reveals conserved patterns of stability within the N-terminal domain of GR that persist despite low sequence conservation. These studies provide an avenue for further investigations of the mechanistic underpinnings of the functional relevance of the translational isoforms of GR while also providing a general NMR strategy for studying systems containing both structured and disordered regions.

Software for reconstruction of nonuniformly sampled NMR data

Nonuniform sampling (NUS) of multidimensional NMR experiments is a powerful tool to obtain high-resolution spectra with less instrument time. With NUS, only a subset of the points needed for conventional Fourier transformation is recorded, and sophisticated algorithms are needed to reconstruct the missing data points. During the last decade, several software packages implementing the reconstruction algorithms have emerged and been refined and now result in spectra of almost similar quality as spectra from conventionally recorded and processed data. However, from the number of literature references to the reconstruction methods, many more multidimensional NMR spectra could presumably be recorded with NUS. To help researchers considering to start using NUS for their NMR experiments, we here review 13 different reconstruction methods found in five software packages (CambridgeCS, hmsIST, MddNMR, NESTA-NMR, and SMILE). We have compared how the methods run with the provided example scripts for reconstructing a nonuniform sampled three-dimensional ¹⁵ N-NOESY-HSQC at sampling densities from 5% to 50%. Overall, the spectra are all of similar quality above 20% sampling density. Thus, without any particular knowledge about the details of the reconstruction algorithms, significant reduction in the experiment time can be achieved. Below 20% sampling density, the intensities of particular weak peaks start being affected. MddNMR's IST with virtual echo and the SMILE algorithms still reproduced the spectra with the highest accuracy of peak intensities.

Temperature as an Extra Dimension in Multidimensional Protein NMR Spectroscopy

NMR spectroscopy is a particularly informative method for studying protein structures and dynamics in solution; however, it is also one of the most time-consuming. Modern approaches to biomolecular NMR spectroscopy are based on lengthy multidimensional experiments, the duration of which grows exponentially with the number of dimensions. The experimental time may even be several days in the case of 3D and 4D spectra. Moreover, the experiment often has to be repeated under several different conditions, for example, to measure the temperature-dependent effects in a spectrum (temperature coefficients (TCs)). Herein, a new approach that involves joint sampling of indirect evolution times and temperature is proposed. This allows TCs to be measured through 3D spectra in even less time than that needed to acquire a single spectrum by using the conventional approach. Two signal processing methods that are complementary, in terms of sensitivity and resolution, 1) dividing data into overlapping subsets followed by compressed sensing reconstruction, and 2) treating the complete data set with a variant of the Radon transform, are proposed. The temperature-swept 3D HNCO spectra of two intrinsically disordered proteins, osteopontin and CD44 cytoplasmic tail, show that this new approach makes it possible to determine TCs and their non-linearities effectively. Non-linearities, which indicate the presence of a compact state, are particularly interesting. The complete package of data acquisition and processing software for this new approach are provided.

Principal component analysis for automated classification of 2D spectra and interferograms of protein therapeutics: influence of noise, reconstruction details, and data preparation

Protein therapeutics have numerous critical quality attributes (CQA) that must be evaluated to ensure safety and efficacy, including the requirement to adopt and retain the correct three-dimensional fold without forming unintended aggregates. Therefore, the ability to monitor protein higher order structure (HOS) can be valuable throughout the lifecycle of a protein therapeutic, from development to manufacture. 2D NMR has been introduced as a robust and precise tool to assess the HOS of a protein biotherapeutic. A common use case is to decide whether two groups of spectra are substantially different, as an indicator of difference in HOS. We demonstrate a quantitative use of principal component analysis (PCA) scores to perform this decision-making, and demonstrate the effect of acquisition and processing details on class separation using samples of NISTmAb monoclonal antibody Reference Material subjected to two different oxidative stress protocols. The work introduces an approach to computing similarity from PCA scores based upon the technique of histogram intersection, a method originally developed for retrieval of images from large databases. Results show that class separation can be robust with respect to random noise, reconstruction method, and analysis region selection. By contrast, details such as baseline distortion can have a pronounced effect, and so must be controlled carefully. Since the classification approach can be performed without the need to identify peaks, results suggest that it is possible to use even more efficient measurement strategies that do not produce spectra that can be analyzed visually, but nevertheless allow useful decision-making that is objective and automated.

Non-Uniform Sampling in NMR Spectroscopy and the Preservation of Spectral Knowledge in the Time and Frequency Domains

The increased sensitivity under weighted non-uniform sampling (NUS) is demonstrated and quantified using Monte Carlo simulations of nuclear magnetic resonance (NMR) time- and frequency-domain signals. The concept of spectral knowledge is introduced and shown to be superior to the frequency-domain signal-to-noise ratio for assessing the quality of NMR data. Two methods for rigorously preserving spectral knowledge and the time-domain NUS knowledge enhancement upon transformation to the frequency domain are demonstrated, both theoretically and numerically. The first, non-uniform weighted sampling using consistent root-mean-square noise, is applicable to data sampled on the Nyquist grid, whereas the second, the block Fourier transform using consistent root-mean-square noise, can be used to transform time-domain data acquired with arbitrary, off-grid NUS.

Backbone Hydrogen Bond Energies in Membrane Proteins Are Insensitive to Large Changes in Local Water Concentration

A hallmark feature of biological lipid bilayer structure is a depth-dependent polarity gradient largely resulting from the change in water concentration over the angstrom length scale. This gradient is particularly steep as it crosses the membrane interfacial regions where the water concentration drops at least a million-fold along the direction of the bilayer normal. Although local water content is often assumed to be a major determinant of membrane protein stability, the effect of the water-induced polarity gradient upon backbone hydrogen bond strength has not been systematically investigated. We addressed this question by measuring the free energy change for a number of backbone hydrogen bonds in the transmembrane protein OmpW. These values were obtained at 33 backbone amides from hydrogen/deuterium fractionation factors by nuclear magnetic resonance spectroscopy. We surprisingly found that OmpW backbone hydrogen bond energies do not vary over a wide range of water concentrations that are characteristic of the solvation environment in the bilayer interfacial region. We validated the interpretation of our results by determining the hydrodynamic and solvation properties of our OmpW-micelle complex using analytical ultracentrifugation and molecular dynamics simulations. The magnitudes of the backbone hydrogen bond free energy changes in our study are comparable to those observed in water-soluble proteins, the H-segment of the leader peptidase helix used in the von Heijne and White biological scale experiments, and several interfacial peptides. Our results agree with those reported for the transmembrane α-helical portion of the amyloid precursor protein after the latter values were adjusted for kinetic isotope effects. Overall, our work suggests that backbone hydrogen bonds provide modest thermodynamic stability to membrane protein structures and that many amides are unaffected by dehydration within the bilayer.

Amino-acid selective isotope labeling enables simultaneous overlapping signal decomposition and information extraction from NMR spectra

Signal overlapping is a major bottleneck for protein NMR analysis. We propose a new method, stable-isotope-assisted parameter extraction (SiPex), to resolve overlapping signals by a combination of amino-acid selective isotope labeling (AASIL) and tensor decomposition. The basic idea of Sipex is that overlapping signals can be decomposed with the help of intensity patterns derived from quantitative fractional AASIL, which also provides amino-acid information. In SiPex, spectra for protein characterization, such as ¹⁵N relaxation measurements, are assembled with those for amino-acid information to form a four-order tensor, where the intensity patterns from AASIL contribute to high decomposition performance even if the signals share similar chemical shift values or characterization profiles, such as relaxation curves. The loading vectors of each decomposed component, corresponding to an amide group, represent both the amino-acid and relaxation information. This information link provides an alternative protein analysis method that does not require "assignments" in a general sense; i.e., chemical shift determinations, since the amino-acid information for some of the residues allows unambiguous assignment according to the dual selective labeling. SiPex can also decompose signals in time-domain raw data without Fourier transform, even in non-uniformly sampled data without spectral reconstruction. These features of SiPex should expand biological NMR applications by overcoming their overlapping and assignment problems.

Fast time-resolved NMR with non-uniform sampling

NMR spectroscopy is a versatile tool for studying time-dependent processes: chemical reactions, phase transitions or macromolecular structure changes. However, time-resolved NMR is usually based on the simplest among available techniques - one-dimensional spectra serving as "snapshots" of the studied process. One of the reasons is that multidimensional experiments are very time-expensive due to costly sampling of evolution time space. In this review we summarize efforts to alleviate the problem of limited applicability of multidimensional NMR in time-resolved studies. We focus on techniques based on sparse or non-uniform sampling (NUS), which lead to experimental time reduction by omitting a significant part of the data during measurement and reconstructing it mathematically, adopting certain assumptions about the spectrum. NUS spectra are faster to acquire than conventional ones and thus better suited to the role of "snapshots", but still suffer from non-stationarity of the signal i.e. amplitude and frequency variations within a dataset. We discuss in detail how these instabilities affect the spectra, and what are the optimal ways of sampling the non-stationary FID signal. Finally, we discuss related areas of NMR where serial experiments are exploited and how they can benefit from the same NUS-based approaches.

Non-uniform HYSCORE: Measurement, processing and analysis with Hyscorean

Non-uniform sampling (NUS) provides a considerable reduction of measurement time especially for multi-dimensional experiments. This comes at the cost of additional signal processing steps to reconstruct the complete signal from the experimental data points. Despite being routinely employed in NMR for many experiments, EPR applications have not benefited from NUS due to the lack of a straightforward implementation to perform NUS in common commercial spectrometers. In this work we present a novel method to perform NUS HYSCORE experiments on commercial Bruker EPR spectrometers, along with a benchmark of modern reconstruction methods, and new processing software tools for NUS HYSCORE signals. All of this comes in the form of a free-software package: Hyscorean. Experimental NUS spectra are measured and processed with this package using different reconstruction methods and compared to their uniform sampled counterparts, thereby showcasing the method's potential for EPR spectroscopy.

Replacement of the heme axial lysine as a test of conformational adaptability in the truncated hemoglobin THB1

Amino acid replacement is a useful strategy to assess the roles of axial heme ligands in the function of native heme proteins. THB1, the protein product of the Chlamydomonas reinhardtii THB1 gene, is a group 1 truncated hemoglobin that uses a lysine residue in the E helix (Lys53, at position E10 by reference to myoglobin) as an iron ligand at neutral pH. Phylogenetic evidence shows that many homologous proteins have a histidine, methionine or arginine at the same position. In THB1, these amino acids would each be expected to convey distinct reactive properties if replacing the native lysine as an axial ligand. To explore the ability of the group 1 truncated Hb fold to support alternative ligation schemes and distal pocket conformations, the properties of the THB1 variants K53A as a control, K53H, K53M, and K53R were investigated by electronic absorption, EPR, and NMR spectroscopies. We found that His53 is capable of heme ligation in both the Fe(III) and Fe(II) states, that Met53 can coordinate only in the Fe(II) state, and that Arg53 stabilizes a hydroxide ligand in the Fe(III) state. The data illustrate that the group 1 truncated Hb fold can tolerate diverse rearrangement of the heme environment and has a strong tendency to use two protein side chains as iron ligands despite accompanying structural perturbations. Access to various redox pairs and different responses to pH make this protein an excellent test case for energetic and dynamic studies of heme ligation.

Replacement of the Distal Histidine Reveals a Noncanonical Heme Binding Site in a 2-on-2 Hemoglobin

Heme ligation in hemoglobin is typically assumed by the "proximal" histidine. Hydrophobic contacts, ionic interactions, and the ligation bond secure the heme between two α-helices denoted E and F. Across the hemoglobin superfamily, several proteins also use a "distal" histidine, making the native state a bis-histidine complex. The group 1 truncated hemoglobin from Synechocystis sp. PCC 6803, GlbN, is one such bis-histidine protein. Ferric GlbN, in which the distal histidine (His46 or E10) has been replaced with a leucine, though expected to bind a water molecule and yield a high-spin iron complex at neutral pH, has low-spin spectral properties. Here, we applied nuclear magnetic resonance and electronic absorption spectroscopic methods to GlbN modified with heme and amino acid replacements to identify the distal ligand in H46L GlbN. We found that His117, a residue located in the C-terminal portion of the protein and on the proximal side of the heme, is responsible for the formation of an alternative bis-histidine complex. Simultaneous coordination by His70 and His117 situates the heme in a binding site different from the canonical site. This new holoprotein form is achieved with only local conformational changes. Heme affinity in the alternative site is weaker than in the normal site, likely because of strained coordination and a reduced number of specific heme-protein interactions. The observation of an unconventional heme binding site has important implications for the interpretation of mutagenesis results and globin homology modeling.

XLSY: Extra-Large NMR Spectroscopy

NMR studies of intrinsically disordered proteins and other complex biomolecular systems require spectra with the highest resolution and dimensionality. An efficient approach, extra‐large NMR spectroscopy, is presented for experimental data collection, reconstruction, and handling of very large NMR spectra by a combination of the radial and non‐uniform sampling, a new processing algorithm, and rigorous statistical validation. We demonstrate the first high‐quality reconstruction of a full seven‐dimensional HNCOCACONH and two five‐dimensional HACACONH and HN(CA)CONH experiments for a representative intrinsically disordered protein α‐synuclein. XLSY will significantly enhance the NMR toolbox in challenging biomolecular studies.

Non-Uniform and Absolute Minimal Sampling for High-Throughput Multidimensional NMR Applications

Many biomolecular NMR applications can benefit from the faster acquisition of multidimensional NMR data with high resolution and their automated analysis and interpretation. In recent years, a number of non-uniform sampling (NUS) approaches have been introduced for the reconstruction of multidimensional NMR spectra, such as compressed sensing, thereby bypassing traditional Fourier-transform processing. Such approaches are applicable to both biomacromolecules and small molecules and their complex mixtures and can be combined with homonuclear decoupling (pure shift) and covariance processing. For homonuclear 2D TOCSY experiments, absolute minimal sampling (AMS) permits the drastic shortening of measurement times necessary for high-throughput applications for identification and quantification of components in complex biological mixtures in the field of metabolomics. Such TOCSY spectra can be comprehensively represented by graphic theoretical maximal cliques for the identification of entire spin systems and their subsequent query against NMR databases. Integration of these methods in webservers permits the rapid and reliable identification of mixture components. Recent progress is reviewed in this Minireview.

Structural and functional analysis of Dickkopf 4 (Dkk4): New insights into Dkk evolution and regulation of Wnt signaling by Dkk and Kremen proteins

Dickkopf (Dkk) family proteins are important regulators of Wnt signaling pathways, which play key roles in many essential biological processes. Here, we report the first detailed structural and dynamics study of a full-length mature Dkk protein (Dkk4, residues 19–224), including determination of the first atomic-resolution structure for the N-terminal cysteine-rich domain (CRD1) conserved among Dkk proteins. We discovered that CRD1 has significant structural homology to the Dkk C-terminal cysteine-rich domain (CRD2), pointing to multiple gene duplication events during Dkk family evolution. We also show that Dkk4 consists of two independent folded domains (CRD1 and CRD2) joined by a highly flexible, nonstructured linker. Similarly, the N-terminal region preceding CRD1 and containing a highly conserved NXI(R/K) sequence motif was shown to be dynamic and highly flexible. We demonstrate that Dkk4 CRD2 mediates high-affinity binding to both the E1E2 region of low-density lipoprotein receptor–related protein 6 (LRP6 E1E2) and the Kremen1 (Krm1) extracellular domain. In contrast, the N-terminal region alone bound with only moderate affinity to LRP6 E1E2, consistent with binding via the conserved NXI(R/K) motif, but did not interact with Krm proteins. We also confirmed that Dkk and Krm family proteins function synergistically to inhibit Wnt signaling. Insights provided by our integrated structural, dynamics, interaction, and functional studies have allowed us to refine the model of synergistic regulation of Wnt signaling by Dkk proteins. Our results indicate the potential for the formation of a diverse range of ternary complexes comprising Dkk, Krm, and LRP5/6 proteins, allowing fine-tuning of Wnt-dependent signaling.

ISCU(M108I) and ISCU(D39V) Differ from Wild-Type ISCU in Their Failure To Form Cysteine Desulfurase Complexes Containing Both Frataxin and Ferredoxin

Whereas iron-sulfur (Fe-S) cluster assembly on the wild-type scaffold protein ISCU, as catalyzed by the human cysteine desulfurase complex (NIA)2, exhibits a requirement for frataxin (FXN), in yeast, ISCU variant M108I has been shown to bypass the FXN requirement. Wild-type ISCU populates two interconverting conformational states: one structured and one dynamically disordered. We show here that variants ISCU(M108I) and ISCU(D39V) of human ISCU populate only the structured state. We have compared the properties of ISCU, ISCU(M108I), and ISCU(D39V), with and without FXN, in both the cysteine desulfurase step of Fe-S cluster assembly and the overall Fe-S cluster assembly reaction catalyzed by (NIA)2. In the cysteine desulfurase step with dithiothreitol (DTT) as the reductant, FXN was found to stimulate cysteine desulfurase activity with both the wild-type and structured variants, although the effect was less prominent with ISCU(D39V) than with the wild-type or ISCU(M108I). In overall Fe-S cluster assembly, frataxin was found to stimulate cluster assembly with both the wild-type and structured variants when the reductant was DTT; however, with the physiological reductant, reduced ferredoxin 2 (rdFDX2), FXN stimulated the reaction with wild-type ISCU but not with either ISCU(M108I) or ISCU(D39V). Nuclear magnetic resonance titration experiments revealed that wild-type ISCU, FXN, and rdFDX2 all bind to (NIA)2. However, when ISCU was replaced by the fully structured variant ISCU(M108I), the addition of rdFDX2 to the [NIA-ISCU(M108I)-FXN]2 complex led to the release of FXN. Thus, the displacement of FXN by rdFDX2 explains the failure of FXN to stimulate Fe-S cluster assembly on ISCU(M108I).

From Raw Data to Protein Backbone Chemical Shifts Using NMRFx Processing and NMRViewJ Analysis

Assignment of the chemical shifts of the backbone atoms (HN, N, CA, CB, and C) of proteins is often a prerequisite to using NMR information in the study of proteins. These chemical shifts and their perturbations are the basis for the analysis of protein dynamics, ligand binding, and backbone conformation. They are generally assigned prior to full side-chain assignments and the determination of the complete three-dimensional molecular structure. This chapter describes the use of two software packages, NMRFx Processor and NMRViewJ, in going from raw NMR data to backbone assignments. The step-by-step procedure describes processing of the data and the use of manual and automated features of the RunAbout tool in NMRViewJ to perform the assignments.

Solution NMR views of dynamical ordering of biomacromolecules

BACKGROUND

To understand the mechanisms related to the 'dynamical ordering' of macromolecules and biological systems, it is crucial to monitor, in detail, molecular interactions and their dynamics across multiple timescales. Solution nuclear magnetic resonance (NMR) spectroscopy is an ideal tool that can investigate biophysical events at the atomic level, in near-physiological buffer solutions, or even inside cells.

SCOPE OF REVIEW

In the past several decades, progress in solution NMR has significantly contributed to the elucidation of three-dimensional structures, the understanding of conformational motions, and the underlying thermodynamic and kinetic properties of biomacromolecules. This review discusses recent methodological development of NMR, their applications and some of the remaining challenges.

MAJOR CONCLUSIONS

Although a major drawback of NMR is its difficulty in studying the dynamical ordering of larger biomolecular systems, current technologies have achieved considerable success in the structural analysis of substantially large proteins and biomolecular complexes over 1MDa and have characterised a wide range of timescales across which biomolecular motion exists. While NMR is well suited to obtain local structure information in detail, it contributes valuable and unique information within hybrid approaches that combine complementary methodologies, including solution scattering and microscopic techniques.

GENERAL SIGNIFICANCE

For living systems, the dynamic assembly and disassembly of macromolecular complexes is of utmost importance for cellular homeostasis and, if dysregulated, implied in human disease. It is thus instructive for the advancement of the study of the dynamical ordering to discuss the potential possibilities of solution NMR spectroscopy and its applications. This article is part of a Special Issue entitled "Biophysical Exploration of Dynamical Ordering of Biomolecular Systems" edited by Dr. Koichi Kato.

Autofocusing imaging system based on laser ranging and a retina-like sample

A novel autofocusing method combining active and passive techniques is proposed to improve autofocusing performance. The proposed method is divided into coarse and fine autofocusing stages. First, a laser ranging finder viewed as the active technique is used to obtain a reasonable initial position of the compensating lens group during the coarse autofocusing stage. Second, a retina-like sampling method is used to decrease the volume of processing data during the fine autofocusing stage. We developed a prototype and performed comparative experiments using different targets based on the proposed method and the traditional passive method (TPM). Under optical power of 9×, the TPM consumed 2.5 s, while the proposed method performed at 1.3 s. The comparative experiments also showed that the proposed method exhibited a better anti-interference property than the traditional method.

Interpolating and extrapolating with hmsIST: seeking a tmax for optimal sensitivity, resolution and frequency accuracy

Non-Uniform Sampling has the potential to exploit the optimal resolution of high-field NMR instruments. This is not possible in 3D and 4D NMR experiments when using traditional uniform sampling due to the long overall measurement time. Nominally, uniformly sampled time domain data acquired to a maximum evolution time t_max can be extended to high resolution via a virtual maximum evolution time t*_max while extrapolating with linear prediction or iterative soft thresholding (IST). At the high resolution obtainable with extrapolation of US data, however, the accuracy of peak positions is compromised as observed when comparing inter- and intra-residue peaks in a 3D HNCA experiment. However, the accuracy of peak positions is largely improved by spreading the same number of acquired time domain data points non-uniformly over a larger evolution time to an optimal t_max followed by extrapolation to a total t*_max and processing the data with an appropriate reconstruction method, such as hmsIST. To explore the optimum value of experimentally measured t_max to be reached non-uniformly with a given number of sampling points we have created test situations of time-equivalent experiments and evaluate sensitivity and accuracy of peak positions. Here we use signal-to-maximum-noise ratio as the decisive measure of sensitivity. We find that both sensitivity and resolution are optimal when PoissonGap sampling to a t_max of about ½*T₂^*. Digital resolution is further enhanced by extrapolating the range of acquired time domain data to 2*T₂^* but without measuring experimental points beyond ½*T₂^*.

Joint non-uniform sampling of all incremented time delays for quicker acquisition in protein relaxation studies

NMR relaxometry plays crucial role in studies of protein dynamics. The measurement of longitudinal and transverse relaxation rates of [Formula: see text]N is the main source of information on backbone motions. However, even the most basic approach exploiting a series of [Formula: see text]N HSQC spectra can require several hours of measurement time. Standard non-uniform sampling (NUS), i.e. random under-sampling of indirect time domain, typically cannot reduce this by more than 2-4[Formula: see text] due to relatively low "compressibility" of these spectra. In this paper we propose an extension of NUS to relaxation delays. The two-dimensional space of [Formula: see text]/[Formula: see text] is sampled in a way similar to NUS of [Formula: see text]/[Formula: see text] domain in 3D spectra. The signal is also processed in a way similar to that known from 3D NUS spectra i.e. using one of the most popular compressed sensing algorithms, iterative soft thresholding. The 2D Fourier transform matrix is replaced with mixed inverse Laplace-Fourier transform matrix. The peak positions in resulting 3D spectrum are characterized by two frequency coordinates and relaxation rate and thus no additional fitting of exponential curves is required. The method is tested on three globular proteins, providing satisfactory results in a time corresponding to acquisition of two conventional [Formula: see text]N HSQC spectra.

Pitfalls in compressed sensing reconstruction and how to avoid them

Multidimensional NMR can provide unmatched spectral resolution, which is crucial when dealing with samples of biological macromolecules. The resolution, however, comes at the high price of long experimental time. Non-uniform sampling (NUS) of the evolution time domain allows to suppress this limitation by sampling only a small fraction of the data, but requires sophisticated algorithms to reconstruct omitted data points. A significant group of such algorithms known as compressed sensing (CS) is based on the assumption of sparsity of a reconstructed spectrum. Several papers on the application of CS in multidimensional NMR have been published in the last years, and the developed methods have been implemented in most spectral processing software. However, the publications rarely show the cases when NUS reconstruction does not work perfectly or explain how to solve the problem. On the other hand, every-day users of NUS develop their rules-of-thumb, which help to set up the processing in an optimal way, but often without a deeper insight. In this paper, we discuss several sources of problems faced in CS reconstructions: low sampling level, missassumption of spectral sparsity, wrong stopping criterion and attempts to extrapolate the signal too much. As an appendix, we provide MATLAB codes of several CS algorithms used in NMR. We hope that this work will explain the mechanism of NUS reconstructions and help readers to set up acquisition and processing parameters. Also, we believe that it might be helpful for algorithm developers.

Sparse multidimensional iterative lineshape-enhanced (SMILE) reconstruction of both non-uniformly sampled and conventional NMR data

Implementation of a new algorithm, SMILE, is described for reconstruction of non-uniformly sampled two-, three- and four-dimensional NMR data, which takes advantage of the known phases of the NMR spectrum and the exponential decay of underlying time domain signals. The method is very robust with respect to the chosen sampling protocol and, in its default mode, also extends the truncated time domain signals by a modest amount of non-sampled zeros. SMILE can likewise be used to extend conventional uniformly sampled data, as an effective multidimensional alternative to linear prediction. The program is provided as a plug-in to the widely used NMRPipe software suite, and can be used with default parameters for mainstream application, or with user control over the iterative process to possibly further improve reconstruction quality and to lower the demand on computational resources. For large data sets, the method is robust and demonstrated for sparsities down to ca 1%, and final all-real spectral sizes as large as 300 Gb. Comparison between fully sampled, conventionally processed spectra and randomly selected NUS subsets of this data shows that the reconstruction quality approaches the theoretical limit in terms of peak position fidelity and intensity. SMILE essentially removes the noise-like appearance associated with the point-spread function of signals that are a default of five-fold above the noise level, but impacts the actual thermal noise in the NMR spectra only minimally. Therefore, the appearance and interpretation of SMILE-reconstructed spectra is very similar to that of fully sampled spectra generated by Fourier transformation.

Human Mitochondrial Ferredoxin 1 (FDX1) and Ferredoxin 2 (FDX2) Both Bind Cysteine Desulfurase and Donate Electrons for Iron-Sulfur Cluster Biosynthesis

Ferredoxins play an important role as an electron donor in iron-sulfur (Fe-S) cluster biosynthesis. Two ferredoxins, human mitochondrial ferredoxin 1 (FDX1) and human mitochondrial ferredoxin 2 (FDX2), are present in the matrix of human mitochondria. Conflicting results have been reported regarding their respective function in mitochondrial iron-sulfur cluster biogenesis. We report here biophysical studies of the interaction of these two ferredoxins with other proteins involved in mitochondrial iron-sulfur cluster assembly. Results from nuclear magnetic resonance spectroscopy show that both FDX1 and FDX2 (in both their reduced and oxidized states) interact with the protein complex responsible for cluster assembly, which contains cysteine desulfurase (NFS1), ISD11 (also known as LYRM4), and acyl carrier protein (Acp). In all cases, ferredoxin residues close to the Fe-S cluster are involved in the interaction with this complex. Isothermal titration calorimetry results showed that FDX2 binds more tightly to the cysteine desulfurase complex than FDX1 does. The reduced form of each ferredoxin became oxidized in the presence of the cysteine desulfurase complex when l-cysteine was added, leading to its conversion to l-alanine and the generation of sulfide. In an in vitro reaction, the reduced form of each ferredoxin was found to support Fe-S cluster assembly on ISCU; the rate of cluster assembly was faster with FDX2 than with FDX1. Taken together, these results show that both FDX1 and FDX2 can function in Fe-S cluster assembly in vitro.

(1)H(N), (13)C, and (15)N resonance assignments of the CDTb-interacting domain (CDTaBID) from the Clostridium difficile binary toxin catalytic component (CDTa, residues 1-221)

Once considered a relatively harmless bacterium, Clostridium difficile has become a major concern for healthcare facilities, now the most commonly reported hospital-acquired pathogen. C. difficile infection (CDI) is usually contracted when the normal gut microbiome is compromised by antibiotic therapy, allowing the opportunistic pathogen to grow and produce its toxins. The severity of infection ranges from watery diarrhea and abdominal cramping to pseudomembranous colitis, sepsis, or death. The past decade has seen a marked increase in the frequency and severity of CDI among industrialized nations owing directly to the emergence of a highly virulent C. difficile strain, NAP1. Along with the large Clostridial toxins expressed by non-epidemic strains, C. difficile NAP1 produces a binary toxin, C. difficile transferase (CDT). As the name suggests, CDT is a two-component toxin comprised of an ADP-ribosyltransferase (ART) component (CDTa) and a cell-binding/translocation component (CDTb) that function to destabilize the host cytoskeleton by covalent modification of actin monomers. Central to the mechanism of binary toxin-induced pathogenicity is the formation of CDTa/CDTb complexes at the cell surface. From the perspective of CDTa, this interaction is mediated by the N-terminal domain (residues 1-215) and is spatially and functionally independent of ART activity, which is located in the C-terminal domain (residues 216-420). Here we report the (1)H(N), (13)C, and (15)N backbone resonance assignments of a 221 amino acid, ~26 kDa N-terminal CDTb-interacting domain (CDTaBID) construct by heteronuclear NMR spectroscopy. These NMR assignments represent the first component coordination domain for a family of Clostridium or Bacillus species harboring ART activity. Our assignments lay the foundation for detailed solution state characterization of structure-function relationships, toxin complex formation, and NMR-based drug discovery efforts.

Subrandom methods for multidimensional nonuniform sampling

Methods of nonuniform sampling that utilize pseudorandom number sequences to select points from a weighted Nyquist grid are commonplace in biomolecular NMR studies, due to the beneficial incoherence introduced by pseudorandom sampling. However, these methods require the specification of a non-arbitrary seed number in order to initialize a pseudorandom number generator. Because the performance of pseudorandom sampling schedules can substantially vary based on seed number, this can complicate the task of routine data collection. Approaches such as jittered sampling and stochastic gap sampling are effective at reducing random seed dependence of nonuniform sampling schedules, but still require the specification of a seed number. This work formalizes the use of subrandom number sequences in nonuniform sampling as a means of seed-independent sampling, and compares the performance of three subrandom methods to their pseudorandom counterparts using commonly applied schedule performance metrics. Reconstruction results using experimental datasets are also provided to validate claims made using these performance metrics.

NMRFx Processor: a cross-platform NMR data processing program

NMRFx Processor is a new program for the processing of NMR data. Written in the Java programming language, NMRFx Processor is a cross-platform application and runs on Linux, Mac OS X and Windows operating systems. The application can be run in both a graphical user interface (GUI) mode and from the command line. Processing scripts are written in the Python programming language and executed so that the low-level Java commands are automatically run in parallel on computers with multiple cores or CPUs. Processing scripts can be generated automatically from the parameters of NMR experiments or interactively constructed in the GUI. A wide variety of processing operations are provided, including methods for processing of non-uniformly sampled datasets using iterative soft thresholding. The interactive GUI also enables the use of the program as an educational tool for teaching basic and advanced techniques in NMR data analysis.

Accurate determination of rates from non-uniformly sampled relaxation data

The application of non-uniform sampling (NUS) to relaxation experiments traditionally used to characterize the fast internal motion of proteins is quantitatively examined. Experimentally acquired Poisson-gap sampled data reconstructed with iterative soft thresholding are compared to regular sequentially sampled (RSS) data. Using ubiquitin as a model system, it is shown that 25 % sampling is sufficient for the determination of quantitatively accurate relaxation rates. When the sampling density is fixed at 25 %, the accuracy of rates is shown to increase sharply with the total number of sampled points until eventually converging near the inherent reproducibility of the experiment. Perhaps contrary to some expectations, it is found that accurate peak height reconstruction is not required for the determination of accurate rates. Instead, inaccuracies in rates arise from inconsistencies in reconstruction across the relaxation series that primarily manifest as a non-linearity in the recovered peak height. This indicates that the performance of an NUS relaxation experiment cannot be predicted from comparison of peak heights using a single RSS reference spectrum. The generality of these findings was assessed using three alternative reconstruction algorithms, eight different relaxation measurements, and three additional proteins that exhibit varying degrees of spectral complexity. From these data, it is revealed that non-linearity in peak height reconstruction across the relaxation series is strongly correlated with errors in NUS-derived relaxation rates. Importantly, it is shown that this correlation can be exploited to reliably predict the performance of an NUS-relaxation experiment by using three or more RSS reference planes from the relaxation series. The RSS reference time points can also serve to provide estimates of the uncertainty of the sampled intensity, which for a typical relaxation times series incurs no penalty in total acquisition time.

The AUDANA algorithm for automated protein 3D structure determination from NMR NOE data

We introduce AUDANA (Automated Database-Assisted NOE Assignment), an algorithm for determining three-dimensional structures of proteins from NMR data that automates the assignment of 3D-NOE spectra, generates distance constraints, and conducts iterative high temperature molecular dynamics and simulated annealing. The protein sequence, chemical shift assignments, and NOE spectra are the only required inputs. Distance constraints generated automatically from ambiguously assigned NOE peaks are validated during the structure calculation against information from an enlarged version of the freely available PACSY database that incorporates information on protein structures deposited in the Protein Data Bank (PDB). This approach yields robust sets of distance constraints and 3D structures. We evaluated the performance of AUDANA with input data for 14 proteins ranging in size from 6 to 25 kDa that had 27-98 % sequence identity to proteins in the database. In all cases, the automatically calculated 3D structures passed stringent validation tests. Structures were determined with and without database support. In 9/14 cases, database support improved the agreement with manually determined structures in the PDB and in 11/14 cases, database support lowered the r.m.s.d. of the family of 20 structural models.

Artifacts in time-resolved NUS: A case study of NOE build-up curves from 2D NOESY

Multidimensional NMR spectroscopy requires time-consuming sampling of indirect dimensions and so is usually used to study stable samples. However, dynamically changing compounds or their mixtures commonly occur in problems of natural science. Monitoring them requires the use multidimensional NMR in a time-resolved manner - in other words, a series of quick spectra must be acquired at different points in time. Among the many solutions that have been proposed to achieve this goal, time-resolved non-uniform sampling (TR-NUS) is one of the simplest. In a TR-NUS experiment, the signal is sampled using a shuffled random schedule and then divided into overlapping subsets. These subsets are then processed using one of the NUS reconstruction methods, for example compressed sensing (CS). The resulting stack of spectra forms a temporal "pseudo-dimension" that shows the changes caused by the process occurring in the sample. CS enables the use of small subsets of data, which minimizes the averaging of the effects studied. Yet, even within these limited timeframes, the sample undergoes certain changes. In this paper we discuss the effect of varying signal amplitude in a TR-NUS experiment. Our theoretical calculations show that the variations within the subsets lead to t1-noise, which is dependent on the rate of change of the signal amplitude. We verify these predictions experimentally. As a model case we choose a novel 2D TR-NOESY experiment in which mixing time is varied in parallel with shuffled NUS in the indirect dimension. The experiment, performed on a sample of strychnine, provides a near-continuous NOE build-up curve, whose shape closely reflects the t1-noise level. 2D TR-NOESY reduces the measurement time compared to the conventional approach and makes it possible to verify the theoretical predictions about signal variations during TR-NUS.

Convex accelerated maximum entropy reconstruction

Maximum entropy (MaxEnt) spectral reconstruction methods provide a powerful framework for spectral estimation of nonuniformly sampled datasets. Many methods exist within this framework, usually defined based on the magnitude of a Lagrange multiplier in the MaxEnt objective function. An algorithm is presented here that utilizes accelerated first-order convex optimization techniques to rapidly and reliably reconstruct nonuniformly sampled NMR datasets using the principle of maximum entropy. This algorithm - called CAMERA for Convex Accelerated Maximum Entropy Reconstruction Algorithm - is a new approach to spectral reconstruction that exhibits fast, tunable convergence in both constant-aim and constant-lambda modes. A high-performance, open source NMR data processing tool is described that implements CAMERA, and brief comparisons to existing reconstruction methods are made on several example spectra.

Rpn1 provides adjacent receptor sites for substrate binding and deubiquitination by the proteasome

Hundreds of pathways for degradation converge at ubiquitin recognition by a proteasome. Here, we found that the five known proteasomal ubiquitin receptors in yeast are collectively nonessential for ubiquitin recognition and identified a sixth receptor, Rpn1. A site ( T1: ) in the Rpn1 toroid recognized ubiquitin and ubiquitin-like ( UBL: ) domains of substrate shuttling factors. T1 structures with monoubiquitin or lysine 48 diubiquitin show three neighboring outer helices engaging two ubiquitins. T1 contributes a distinct substrate-binding pathway with preference for lysine 48-linked chains. Proximal to T1 within the Rpn1 toroid is a second UBL-binding site ( T2: ) that assists in ubiquitin chain disassembly, by binding the UBL of deubiquitinating enzyme Ubp6. Thus, a two-site recognition domain intrinsic to the proteasome uses distinct ubiquitin-fold ligands to assemble substrates, shuttling factors, and a deubiquitinating enzyme.

Deterministic multidimensional nonuniform gap sampling

Born from empirical observations in nonuniformly sampled multidimensional NMR data relating to gaps between sampled points, the Poisson-gap sampling method has enjoyed widespread use in biomolecular NMR. While the majority of nonuniform sampling schemes are fully randomly drawn from probability densities that vary over a Nyquist grid, the Poisson-gap scheme employs constrained random deviates to minimize the gaps between sampled grid points. We describe a deterministic gap sampling method, based on the average behavior of Poisson-gap sampling, which performs comparably to its random counterpart with the additional benefit of completely deterministic behavior. We also introduce a general algorithm for multidimensional nonuniform sampling based on a gap equation, and apply it to yield a deterministic sampling scheme that combines burst-mode sampling features with those of Poisson-gap schemes. Finally, we derive a relationship between stochastic gap equations and the expectation value of their sampling probability densities.

NMRFAM-SDF: a protein structure determination framework

The computationally demanding nature of automated NMR structure determination necessitates a delicate balancing of factors that include the time complexity of data collection, the computational complexity of chemical shift assignments, and selection of proper optimization steps. During the past two decades the computational and algorithmic aspects of several discrete steps of the process have been addressed. Although no single comprehensive solution has emerged, the incorporation of a validation protocol has gained recognition as a necessary step for a robust automated approach. The need for validation becomes even more pronounced in cases of proteins with higher structural complexity, where potentially larger errors generated at each step can propagate and accumulate in the process of structure calculation, thereby significantly degrading the efficacy of any software framework. This paper introduces a complete framework for protein structure determination with NMR--from data acquisition to the structure determination. The aim is twofold: to simplify the structure determination process for non-NMR experts whenever feasible, while maintaining flexibility by providing a set of modules that validate each step, and to enable the assessment of error propagations. This framework, called NMRFAM-SDF (NMRFAM-Structure Determination Framework), and its various components are available for download from the NMRFAM website (http://nmrfam.wisc.edu/software.htm).

Sensitivity of nonuniform sampling NMR

Many information-rich multidimensional experiments in nuclear magnetic resonance spectroscopy can benefit from a signal-to-noise ratio (SNR) enhancement of up to about 2-fold if a decaying signal in an indirect dimension is sampled with nonconsecutive increments, termed nonuniform sampling (NUS). This work provides formal theoretical results and applications to resolve major questions about the scope of the NUS enhancement. First, we introduce the NUS Sensitivity Theorem in which any decreasing sampling density applied to any exponentially decaying signal always results in higher sensitivity (SNR per square root of measurement time) than uniform sampling (US). Several cases will illustrate this theorem and show that even conservative applications of NUS improve sensitivity by useful amounts. Next, we turn to a serious limitation of uniform sampling: the SNR by US decreases for extending evolution times, and thus total experimental times, beyond 1.26T2 (T2 = signal decay constant). Thus, SNR and resolution cannot be simultaneously improved by extending US beyond 1.26T2. We find that NUS can eliminate this constraint, and we introduce the matched NUS SNR Theorem: an exponential sampling density matched to the signal decay always improves the SNR with additional evolution time. Though proved for a specific case, broader classes of NUS densities also improve SNR with evolution time. Applications of these theoretical results are given for a soluble plant natural product and a solid tripeptide (u-(13)C,(15)N-MLF). These formal results clearly demonstrate the inadequacies of applying US to decaying signals in indirect nD-NMR dimensions, supporting a broader adoption of NUS.