Performance tuning non-uniform sampling for sensitivity enhancement of signal-limited biological NMR

Fisher information for smart sampling in time-domain spectroscopy

Time-domain spectroscopy encompasses a wide range of techniques, such as Fourier-transform infrared, pump-probe, Fourier-transform Raman, and two-dimensional electronic spectroscopies. These methods enable various applications, such as molecule characterization, excited state dynamics studies, or spectral classification. Typically, these techniques rarely use sampling schemes that exploit the prior knowledge scientists typically have before the actual experiment. Indeed, not all sampling coordinates carry the same amount of information, and a careful selection of the sampling points may notably affect the resulting performance. In this work, we rationalize, with examples, the various advantages of using an optimal sampling scheme tailored to the specific experimental characteristics and/or expected results. We show that using a sampling scheme optimizing the Fisher information minimizes the variance of the desired parameters. This can greatly improve, for example, spectral classifications and multidimensional spectroscopy. We demonstrate how smart sampling may reduce the acquisition time of an experiment by one to two orders of magnitude, while still providing a similar level of information.

Exploring the Higher Order Structure and Conformational Transitions in Insulin Microcrystalline Biopharmaceuticals by Proton-Detected Solid-State Nuclear Magnetic Resonance at Natural Abundance

The integrity of a higher order structure (HOS) is an essential requirement to ensure the efficacy, stability, and safety of protein therapeutics. Solution-state nuclear magnetic resonance (NMR) occupies a unique niche as one of the most promising methods to access atomic-level structural information on soluble biopharmaceutical formulations. Another major class of drugs is poorly soluble, such as microcrystalline suspensions, which poses significant challenges for the characterization of the active ingredient in its native state. Here, we have demonstrated a solid-state NMR method for HOS characterization of biopharmaceutical suspensions employing a selective excitation scheme under fast magic angle spinning (MAS). The applicability of the method is shown on commercial insulin suspensions at natural isotopic abundance. Selective excitation aided with proton detection and non-uniform sampling (NUS) provides improved sensitivity and resolution. The enhanced resolution enabled us to demonstrate the first experimental evidence of a phenol-escaping pathway in insulin, leading to conformational transitions to different hexameric states. This approach has the potential to serve as a valuable means for meticulously examining microcrystalline biopharmaceutical suspensions, which was previously not attainable in their native formulation states and can be seamlessly extended to other classes of biopharmaceuticals such as mAbs and other microcrystalline proteins.

14-3-3 interaction with phosphodiesterase 8A sustains PKA signaling and downregulates the MAPK pathway

The cAMP/PKA and mitogen-activated protein kinase (MAPK) signaling cascade control many cellular processes and are highly regulated for optimal cellular responses upon external stimuli. Phosphodiesterase 8A (PDE8A) is an important regulator that inhibits signaling via cAMP-dependent PKA by hydrolyzing intracellular cAMP pool. Conversely, PDE8A activates the MAPK pathway by protecting CRAF/Raf1 kinase from PKA-mediated inhibitory phosphorylation at Ser259 residue, a binding site of scaffold protein 14-3-3. It still remains enigmatic as to how the cross-talk involving PDE8A regulation influences cAMP/PKA and MAPK signaling pathways. Here, we report that PDE8A interacts with 14-3-3ζ in both yeast and mammalian system, and this interaction is enhanced upon the activation of PKA, which phosphorylates PDE8A's Ser359 residue. Biophysical characterization of phospho-Ser359 peptide with 14-3-3ζ protein further supports their interaction. Strikingly, 14-3-3ζ reduces the catalytic activity of PDE8A, which upregulates the cAMP/PKA pathway while the MAPK pathway is downregulated. Moreover, 14-3-3ζ in complex with PDE8A and cAMP-bound regulatory subunit of PKA, RIα, delays the deactivation of PKA signaling. Our results define 14-3-3ζ as a molecular switch that operates signaling between cAMP/PKA and MAPK by associating with PDE8A.

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.

Accelerating quantitative 13C NMR spectra using an EXtended ACquisition Time (EXACT) method

Accurate quantitative ¹³C NMR spectra can be accelerated by using EXACT (EXtended ACquisition Time) NMR methods which reduce Nuclear Overhauser Enhancement (NOE) during the FID. This allows 30-50% shorter experiment times to be used when achieving a given level of quantitative accuracy.

Rapid quantitative 1H–13C two-dimensional NMR with high precision

Two dimensional (2D) ¹H–¹³C heteronuclear single-quantum correlation (HSQC) spectroscopy has recently been proposed for quantitative determination of typical linear low density polyethylene (LLDPE) with high accuracy. It requires highly precise measurement to achieve further reliable quantification. In this context, this paper aims at determining conditions that allow the achievement of high precision. On the basis of the optimized parameters, two time-saving strategies, nonuniform sampling (NUS) and band-selective HSQC are evaluated on model polyolefins in terms of repeatability. Precision better than 0.3% and 5% for ethylene content (E mol%) and 1-hexene content (H mol%) of the model poly(ethylene-co-1-hexene)s are obtained with 50% NUS or band-selective HSQC. Moreover, dramatic precision enhancements can be achieved with the combination of band-selective HSQC and 50% NUS, in which repeatabilities better than 0.15% and 2.5% for E mol% and H mol% are observed. The experiment times are reduced to about 0.5 h. These methods open important perspectives for rapid, precise and accurate quantitative analysis of complex polymers.

Precision better than 2.5% can be achieved with the combination of band-selective HSQC and 50% NUS in 0.5 h.

Nonuniformly sampled exclusively-13 C/15 N 4D solid-state NMR experiments: Assignment and characterization of IKe phage capsid

An important step in the process of protein research by NMR is the assignment of chemical shifts. In the coat protein of IKe bacteriophage, there are 53 residues making up a long helix resulting in relatively high spectral ambiguity. Assignment thus requires the collection of a set of three-dimensional (3D) experiments and the preparation of sparsely labeled samples. Increasing the dimensionality can facilitate fast and reliable assignment of IKe and of larger proteins. Recent progress in nonuniform sampling techniques made the application of multidimensional NMR solid-state experiments beyond 3D more practical. 4D ¹ H-detected experiments have been demonstrated in high-fields and at spinning speeds of 60 kHz and higher but are not practical at spinning speeds of 10-20 kHz for fully protonated proteins. Here, we demonstrate the applicability of a nonuniformly sampled 4D ¹³ C/¹⁵ N-only correlation experiment performed at a moderate field of 14.1 T, which can incorporate sufficiently long acquisition periods in all dimensions. We show how a single CANCOCX experiment, supported by several 2D carbon-based correlation experiments, is utilized for the assignment of heteronuclei in the coat protein of the IKe bacteriophage. One sparsely labeled sample was used to validate sidechain assignment of several hydrophobic-residue sidechains. A comparison to solution NMR studies of isolated IKe coat proteins embedded in micelles points to key residues involved in structural rearrangement of the capsid upon assembly of the virus. The benefits of 4D to a quicker assignment are discussed, and the method may prove useful for studying proteins at relatively low fields.

Developing nonuniform sampling strategies to improve sensitivity and resolution in 1,1-ADEQUATE experiments

Nonuniform sampling (NUS) strategies are developed for acquiring highly resolved 1,1-ADEQUATE spectra, in both conventional and homodecoupled (HD) variants with improved sensitivity. Specifically, the quantile-directed and Poisson gap methods were critically compared for distributing the samples nonuniformly, and the quantile schedules were further optimized for weighting. Both maximum entropy and iterative soft thresholding spectral estimation algorithms were evaluated. All NUS approaches were robust when the degree of data reduction is moderate, on the order of a 50% reduction of sampling points. Further sampling reduction by NUS is facilitated by using weighted schedules designed by the quantile method, which also suppresses sampling noise well. Seed independence and the ability to specify the sample weighting in quantile scheduling are important in optimizing NUS for 1,1-ADEQUATE data acquisition. Using NUS yields an improvement in sensitivity, while also making longer evolution times accessible that would be difficult or impractical to attain by uniform sampling. Theoretical predictions for the sensitivity enhancements in these experiments are in the range of 5-20%; NUS is shown to disambiguate weak signals, reveal some ⁿ J_CC correlations obscured by noise, and improve signal strength relative to uniform sampling in the same experimental time. This work presents sample schedule development for applying NUS to challenging experiments. The schedules developed here are made available for general use and should facilitate the broader utilization of ADEQUATE experiments (including 1,1-, 1,n-, and HD- variants) for challenging structure elucidation problems.

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.

The influence of the probability density function on spectral quality in nonuniformly sampled multidimensional NMR

The goal of nonuniform sampling (NUS) is to select a subset of free induction decays (FIDs) from the conventional, uniform grid in a manner that sufficiently samples short evolution times needed for improved sensitivity and long evolution times needed for enhanced resolution. In addition to specifying the number of FIDs to be collected from a uniform grid, NUS schemes also specify the distribution of the selected FIDs, which directly impacts sampling-induced artifacts. Sampling schemes typically address these heuristic guidelines by utilizing a probability density function (PDF) to bias the distribution of sampled evolution times. Given this common approach, schemes differentiate themselves by how the evolution times are distributed within the envelope of the PDF. Here, we employ maximum entropy reconstruction and utilize in situ receiver operating characteristic (IROC) to conduct a critical comparison of the sensitivity and resolution that can be achieved by three types of biased sampling schemes: exponential (PDF is exponentially decaying), Poisson-gap (PDF derived from a sine function), and quantile-directed (PDF defined by simple polynomial decay). This methodology reveals practical insights and trends regarding how the sampling schemes and bias can provide the highest sensitivity and resolution for two nonuniformly sampled dimensions in a three-dimensional biomolecular NMR experiment. The IROC analysis circumvents the limitations of common metrics when used with nonlinear spectral estimation (a characteristic of all methods used with NUS) by quantifying the spectral quality via synthetic signals that are added to the empirical dataset. Recovery of these synthetic signals provides a proxy for the quality of the empirical portion of the spectrum. The central finding is that differences in spectral quality are primarily driven by the strength of bias in the PDF. In addition, a sampling coverage threshold is observed that appears to be connected to the dependence of each NUS method on its random seed. The differences between sampling schemes and biases are most relevant below 20% coverage where seed-dependence is high, whereas at higher coverages, the performance metrics for all of the sampling schemes begin to converge and approach a seed-independent regime. The results presented here show that aggressive sampling at low coverage can produce high-quality spectra by employing a sampling scheme that adheres to a decaying PDF with a bias to a broad range of short evolution times and includes relatively few FIDs at long evolution times.

2D J-correlated proton NMR experiments for structural fingerprinting of biotherapeutics

The higher order structure (HOS) of protein therapeutics is essential for drug safety and efficacy and can be evaluated by two-dimensional (2D) nuclear magnetic resonance (NMR) spectroscopy at atomic resolution. ¹Hn-¹⁵N amide correlated and ¹H-¹³C methyl correlated NMR spectroscopies at natural isotopic abundance have been demonstrated as feasible on protein therapeutics as large as monoclonal antibodies and show great promise for use in establishing drug substance structural consistency across manufacturing changes and in comparing a biosimilar to an originator reference product. Spectral fingerprints from ¹Hn-¹Hα correlations acquired using 2D homonuclear proton-proton J-correlated NMR experiments provide a complementary approach for high-resolution assessment of the HOS of lower molecular weight (<25 kDa) protein therapeutics. Here, we evaluate different pulse sequences (COSY, TOCSY and TACSY) used to generate proton-proton J-correlated NMR spectral fingerprints and appraise the performance of each method for application to protein therapeutic HOS assessment and comparability.

Optimizing the transformation of HYSCORE data using the maximum entropy algorithm

Non-uniform sampling (NUS) in combination with the Maximum Entropy (MaxEnt) algorithm as applied to multi-dimensional NMR data has been thoroughly investigated and the NUS approach shown to provide significant sensitivity improvements as compared to methods using uniformly sampled (US) data and the discrete Fourier transform (DFT). Hyperfine sublevel correlation (HYSCORE) is a standard pulse EPR experiment that can potentially benefit greatly from this approach, but the data present unique challenges as compared to NMR. HYSCORE data typically exhibit a very large range of peak intensities, signals are in the form of irregularly shaped ridges with variable intensities, and time traces are generally truncated to save measurement time. MaxEnt has the advantageous properties that it does not require US data, dampens weak signals (noise) and does not suffer from windowing artifacts due to truncation of the time traces. Critical to the success of the MaxEnt algorithm is the choice of the two input parameters aim and def which describe the data noise and contribution of entropy in the optimization, respectively. In this paper we expand our preliminary study on the application of MaxEnt to the reconstruction of HYSCORE spectra to include a detailed analysis on sensitivity to detect weak peaks, investigate the non-linearity of the transformation and ascertain if it can be characterized by the introduction of synthetic peaks, and define a general range for the choice of aim and def. Furthermore, the ability of the MaxEnt method to remove windowing artefacts in uniformly sampled truncated HYSCORE data is described.

Framework for and evaluation of bursts in random sampling of multidimensional NMR experiments

The grouping of data in bursts, also referred to as clusters, spikes or clumps, is a common phenomenon in stochastic sampling. There have been several reports that suggest that in NMR, the presence of such bursts is beneficial to spectral reconstruction where data are sampled nonuniformly. In this work, we seek to define a mode of sampling that produces bursts of randomly distributed data in a controlled manner. An algorithm is described for achieving this where the burst length and its uniformity is controlled - we refer to this type of sampling mode as clustered sampling. Measures are introduced for assessing the "burstiness" of nonuniformly sampled data in multiple dimensions and properties of the point-spread-function of these schedules are assessed. The clustered sampling method is applied to samples drawn from an exponentially weighted distribution either distributed randomly or pseudo-randomly by use of a jittering algorithm. The results reveal that bursts introduce characteristic sampling artifacts that are shifted to low frequencies (red shifted), with respect to the signal frequency, and that they produce artifact-reduced regions at frequencies related to the burst length. This observation is contrary to that observed for sampling methods that seek to evenly distribute NUS data, such as jittered or Poisson sampling. Extensive evaluation of simulated data with comparable inherent sensitivity, reveals that at high sampling coverage (25% in 1D), the distribution of the data has little impact on common spectral quality measures. Application of the introduced clustered sampling method to an experimental 3D NOESY experiment showed results consistent with that found for the simulated 1D data. However, in the extremes of very sparse sampling, the results suggest that there may be some advantages associated with incorporation of bursts in nonuniform sampling. The tools and theory presented will serve as a starting point to further explore this novel mode of sampling in NMR.

Nonuniform sampling in multidimensional NMR for improving spectral sensitivity

The development of multidimensional NMR spectroscopy enabled an explosion of structural and dynamical investigations on proteins and other biomacromolecules. Practical limitations on data sampling, based on the Jeener paradigm of parametric sampling of indirect time domains, have long placed limits on resolution in the corresponding frequency dimensions. The emergence of nonuniform sampling (NUS) in indirect time dimensions circumvents those limitations, affording high resolution spectra from short data records collected in practically realized measurement times. In addition to substantially improved resolution, NUS can also be exploited to improve sensitivity, with gains comparable to those obtained using cryogenically cooled probes. We describe a general approach for acquiring and processing multidimensional NUS NMR data for improving sensitivity.

Nonuniform sampling by quantiles

A flexible strategy for choosing samples nonuniformly from a Nyquist grid using the concept of statistical quantiles is presented for broad classes of NMR experimentation. Quantile-directed scheduling is intuitive and flexible for any weighting function, promotes reproducibility and seed independence, and is generalizable to multiple dimensions. In brief, weighting functions are divided into regions of equal probability, which define the samples to be acquired. Quantile scheduling therefore achieves close adherence to a probability distribution function, thereby minimizing gaps for any given degree of subsampling of the Nyquist grid. A characteristic of quantile scheduling is that one-dimensional, weighted NUS schedules are deterministic, however higher dimensional schedules are similar within a user-specified jittering parameter. To develop unweighted sampling, we investigated the minimum jitter needed to disrupt subharmonic tracts, and show that this criterion can be met in many cases by jittering within 25-50% of the subharmonic gap. For nD-NUS, three supplemental components to choosing samples by quantiles are proposed in this work: (i) forcing the corner samples to ensure sampling to specified maximum values in indirect evolution times, (ii) providing an option to triangular backfill sampling schedules to promote dense/uniform tracts at the beginning of signal evolution periods, and (iii) providing an option to force the edges of nD-NUS schedules to be identical to the 1D quantiles. Quantile-directed scheduling meets the diverse needs of current NUS experimentation, but can also be used for future NUS implementations such as off-grid NUS and more. A computer program implementing these principles (a.k.a. QSched) in 1D- and 2D-NUS is available under the general public license.

Practical Nonuniform Sampling and Non-Fourier Spectral Reconstruction for Multidimensional NMR

A general approach to accelerating multidimensional NMR experiments via nonuniform sampling and maximum entropy spectral reconstruction was first demonstrated by Laue and colleagues in 1987. Following decades of continual improvements involving dozens of software packages for non-Fourier spectral analysis and many different schemes for nonuniform sampling, we still lack a clear consensus on best practices for sampling or spectral reconstruction, and programs for processing nonuniformly sampled data are not particularly user-friendly. Nevertheless, it is possible to discern conservative and general guidelines for nonuniform sampling and spectral reconstruction. Here, we describe a robust semi-automated workflow that employs these guidelines for simplifying the selection of a sampling schedule and the processing of the resulting nonuniformly sampled multidimensional NMR data. Our approach is based on NMRbox, a shared platform for NMR software that facilitates workflow development and execution, and enables rapid comparison of alternate approaches.

What NMR can do in the biopharmaceutical industry

Nuclear magnetic resonance (NMR) spectroscopy has a unique capability to probe the primary and higher order molecular structure and the structural dynamics of biomolecules at an atomic resolution, and this capability has been greatly fortified over the last five decades by an astonishing NMR instrumental and methodological development. Because of these factors, NMR has become a primary tool for the structure investigation of biomolecules, spawning a whole scientific subfield dedicated to the subject. This role of NMR is by now well established and broadly appreciated, especially in the context of academic research dealing with proteins that are purified and isotope-labeled in order to facilitate the necessary sophisticated multidimensional NMR measurements. However, the more recent industrial development, manufacturing, and quality control of biopharmaceuticals provide a different framework for NMR. For example, protein drug substances are not isotope-labeled and are present in a medium of excipients, which make structural NMR measurements much more difficult. On the other hand, biotechnology involves many other analytical requirements that can be efficiently addressed by NMR. In this respect the scope and limitations of NMR are less well understood. Having the non-expert reader in mind, herein we wish to highlight the ways in which modern NMR can effectively support biotechnological developments. Our focus will be on biosimilar proteins, pointing out certain cases where its use is probably essential. Based partly on literature data, and partly on our own hands-on experience, this paper is intended to be a guide for choosing the proper NMR approach for analytical questions concerning the structural comparability of therapeutic proteins, monitoring technology-related impurities, protein quantification, analysis of spent media, identification of extractable and leachable components, etc. Also, we focus on critical considerations, particularly those coming from drug authority guidelines, which limit the use of the well-established NMR tools in everyday practice.

Efficient assignment and NMR analysis of an intact virus using sequential side-chain correlations and DNP sensitization

An experimental strategy has been developed to increase the efficiency of dynamic nuclear polarization (DNP) in solid-state NMR studies. The method makes assignments simpler, faster, and more reliable via sequential correlations of both side-chain and Cα resonances. The approach is particularly suited to complex biomolecules and systems with significant chemical-shift degeneracy. It was designed to overcome the spectral congestion and line broadening that occur due to sample freezing at the cryogenic temperatures required for DNP. Nonuniform sampling (NUS) is incorporated to achieve time-efficient collection of multidimensional data. Additionally, fast (25 kHz) magic-angle spinning (MAS) provides optimal sensitivity and resolution. Data collected in <1 wk produced a virtually complete de novo assignment of the coat protein of Pf1 virus. The peak positions and linewidths for samples near 100 K are perturbed relative to those near 273 K. These temperature-induced perturbations are strongly correlated with hydration surfaces.

Application of 2D-NMR with room temperature NMR probes for the assessment of the higher order structure of filgrastim

The higher order structure (HOS) of biotherapeutics is a critical quality attribute that can be evaluated by nuclear magnetic resonance (NMR) spectroscopy at atomic resolution. NMR spectral mapping of HOS can be used to establish HOS consistency of a biologic across manufacturing changes or to compare a biosimilar to an innovator reference product. A previous inter-laboratory study performed using filgrastim drug products demonstrated that two-dimensional (2D)-NMR ¹H^N-¹⁵N^H heteronuclear correlation spectroscopy is a highly robust and precise method for mapping the HOS of biologic drugs at natural abundance using high sensitivity NMR 'cold probes.' Here, the applicability of the 2D-NMR method to fingerprint the HOS of filgrastim products is demonstrated using lower sensitivity, room temperature NMR probes. Combined chemical shift deviation and principal component analysis are used to illustrate the performance and inter-laboratory precision of the 2D-NMR method when implemented on room temperature probes.

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.

A new approach to the optimisation of non-uniform sampling schedules for use in the rapid acquisition of 2D NMR spectra of small molecules

Non-uniform sampling allows the routine, rapid acquisition of 2D NMR data. When the number of points in the NUS schedule is low, the quality of the data obtained is very dependent of the schedule used. A simple proceedure for finding optimium schedules has been developed and is demonstrated for the multiplicity edited HSQC experiment.

A Set of Efficient nD NMR Protocols for Resonance Assignments of Intrinsically Disordered Proteins

The RF pulse scheme RN[N-CA HEHAHA]NH, which provides a convenient approach to the acquisition of different multidimensional chemical shift correlation NMR spectra leading to backbone resonance assignments, including those of the proline residues of intrinsically disordered proteins (IDPs), is experimentally demonstrated. Depending on the type of correlation data required, the method involves the generation of in-phase ((15) N)(x) magnetisation via different magnetisation transfer pathways such as H→N→CO→N, HA→CA→CO→N, H→N→CA→N and H→CA→N, the subsequent application of (15) N-(13) C(α) heteronuclear Hartmann-Hahn mixing over a period of ≈100 ms, chemical-shift labelling of relevant nuclei before and after the heteronuclear mixing step and amide proton detection in the acquisition dimension. It makes use of the favourable relaxation properties of IDPs and the presence of (1) JCαN and (2) JCαN couplings to achieve efficient correlation of the backbone resonances of each amino acid residue "i" with the backbone amide resonances of residues "i-1" and "i+1". It can be implemented in a straightforward way through simple modifications of the RF pulse schemes commonly employed in protein NMR studies. The efficacy of the approach is demonstrated using a uniformly ((15) N,(13) C) labelled sample of α-synuclein. The different possibilities for obtaining the amino-acid-type information, simultaneously with the connectivity data between the backbone resonances of sequentially neighbouring residues, have also been outlined.

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.

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.

Application of Natural Isotopic Abundance ¹H-¹³C- and ¹H-¹⁵N-Correlated Two-Dimensional NMR for Evaluation of the Structure of Protein Therapeutics

Methods for characterizing the higher-order structure of protein therapeutics are in great demand for establishing consistency in drug manufacturing, for detecting drug product variations resulting from modifications in the manufacturing process, and for comparing a biosimilar to an innovator reference product. In principle, solution NMR can provide a robust approach for characterization of the conformation(s) of protein therapeutics in formulation at atomic resolution. However, molecular weight limitations and the perceived need for stable isotope labeling have to date limited its practical applications in the biopharmaceutical industry. Advances in NMR magnet and console technologies, cryogenically cooled probes, and new rapid acquisition methodologies, particularly selective optimized flip-angle short transient pulse schemes and nonuniform sampling, have greatly ameliorated these limitations. Here, we describe experimental methods for the collection and analysis of 2D (1)H(N)-(15)N-amide- and (1)H-(13)C-methyl-correlated spectra applied to protein drug products at natural isotopic abundance, including representatives from the rapidly growing class of monoclonal antibody (mAb) therapeutics. Practical aspects of experimental setup and data acquisition for both standard and rapid acquisition NMR techniques are described. Furthermore, strategies for the statistical comparison of 2D (1)H(N)-(15)N-amide- and (1)H-(13)C-methyl-correlated spectra are detailed.

Fast acquisition of multidimensional NMR spectra of solids and mesophases using alternative sampling methods

Unique information about the atom-level structure and dynamics of solids and mesophases can be obtained by the use of multidimensional nuclear magnetic resonance (NMR) experiments. Nevertheless, the acquisition of these experiments often requires long acquisition times. We review here alternative sampling methods, which have been proposed to circumvent this issue in the case of solids and mesophases. Compared to the spectra of solutions, those of solids and mesophases present some specificities because they usually display lower signal-to-noise ratios, non-Lorentzian line shapes, lower spectral resolutions and wider spectral widths. We highlight herein the advantages and limitations of these alternative sampling methods. A first route to accelerate the acquisition time of multidimensional NMR spectra consists in the use of sparse sampling schemes, such as truncated, radial or random sampling ones. These sparsely sampled datasets are generally processed by reconstruction methods differing from the Discrete Fourier Transform (DFT). A host of non-DFT methods have been applied for solids and mesophases, including the G-matrix Fourier transform, the linear least-square procedures, the covariance transform, the maximum entropy and the compressed sensing. A second class of alternative sampling consists in departing from the Jeener paradigm for multidimensional NMR experiments. These non-Jeener methods include Hadamard spectroscopy as well as spatial or orientational encoding of the evolution frequencies. The increasing number of high field NMR magnets and the development of techniques to enhance NMR sensitivity will contribute to widen the use of these alternative sampling methods for the study of solids and mesophases in the coming years.

Resolution-enhanced 2D NMR of complex mixtures by non-uniform sampling

NMR is a powerful tool for the analysis of complex mixtures and the identification of individual components. Two-dimensional (2D) NMR potentially offers a wealth of information, but resolution is often sacrificed in order to contain experimental times. We explore the use of non-uniform sampling (NUS) to increase substantially the resolution of 2D NMR spectra of complex mixtures of small molecules, with no increase in experimental time. Two common pulse sequences for metabolomics applications are analysed, HSQC and TOCSY. Specific attention is paid to sensitivity in resolution-enhanced NUS spectra, using the signal-to-maximum-noise ratio as a metric. With a careful choice of sampling schedule and reconstruction algorithm, resolution in the (13) C dimension for HSQC is increased by a factor of at least 32, with no loss in sensitivity and no spurious peaks. For TOCSY, multiplets can be resolved in the indirect dimension in a reasonable experimental time. These properties should increase the usefulness of 2D NMR for metabolomics applications by, for example, increasing the chances of metabolite identification.

HN-NCA heteronuclear TOCSY-NH experiment for (1)H(N) and (15)N sequential correlations in ((13)C, (15)N) labelled intrinsically disordered proteins

A simple triple resonance NMR experiment that leads to the correlation of the backbone amide resonances of each amino acid residue 'i' with that of residues 'i-1' and 'i+1' in ((13)C, (15)N) labelled intrinsically disordered proteins (IDPs) is presented. The experimental scheme, {HN-NCA heteronuclear TOCSY-NH}, exploits the favourable relaxation properties of IDPs and the presence of (1) J CαN and (2) J CαN couplings to transfer the (15)N x magnetisation from amino acid residue 'i' to adjacent residues via the application of a band-selective (15)N-(13)C(α) heteronuclear cross-polarisation sequence of ~100 ms duration. Employing non-uniform sampling in the indirect dimensions, the efficacy of the approach has been demonstrated by the acquisition of 3D HNN chemical shift correlation spectra of α-synuclein. The experimental performance of the RF pulse sequence has been compared with that of the conventional INEPT-based HN(CA)NH pulse scheme. As the availability of data from both the HCCNH and HNN experiments will make it possible to use the information extracted from one experiment to simplify the analysis of the data of the other and lead to a robust approach for unambiguous backbone and side-chain resonance assignments, a time-saving strategy for the simultaneous collection of HCCNH and HNN data is also described.

Dereplication: racing to speed up the natural products discovery process

Covering: 1993-2014 (July)To alleviate the dereplication holdup, which is a major bottleneck in natural products discovery, scientists have been conducting their research efforts to add tools to their "bag of tricks" aiming to achieve faster, more accurate and efficient ways to accelerate the pace of the drug discovery process. Consequently dereplication has become a hot topic presenting a huge publication boom since 2012, blending multidisciplinary fields in new ways that provide important conceptual and/or methodological advances, opening up pioneering research prospects in this field.

Reducing seed dependent variability of non-uniformly sampled multidimensional NMR data

The application of NMR spectroscopy to study the structure, dynamics and function of macromolecules requires the acquisition of several multidimensional spectra. The one-dimensional NMR time-response from the spectrometer is extended to additional dimensions by introducing incremented delays in the experiment that cause oscillation of the signal along "indirect" dimensions. For a given dimension the delay is incremented at twice the rate of the maximum frequency (Nyquist rate). To achieve high-resolution requires acquisition of long data records sampled at the Nyquist rate. This is typically a prohibitive step due to time constraints, resulting in sub-optimal data records to the detriment of subsequent analyses. The multidimensional NMR spectrum itself is typically sparse, and it has been shown that in such cases it is possible to use non-Fourier methods to reconstruct a high-resolution multidimensional spectrum from a random subset of non-uniformly sampled (NUS) data. For a given acquisition time, NUS has the potential to improve the sensitivity and resolution of a multidimensional spectrum, compared to traditional uniform sampling. The improvements in sensitivity and/or resolution achieved by NUS are heavily dependent on the distribution of points in the random subset acquired. Typically, random points are selected from a probability density function (PDF) weighted according to the NMR signal envelope. In extreme cases as little as 1% of the data is subsampled. The heavy under-sampling can result in poor reproducibility, i.e. when two experiments are carried out where the same number of random samples is selected from the same PDF but using different random seeds. Here, a jittered sampling approach is introduced that is shown to improve random seed dependent reproducibility of multidimensional spectra generated from NUS data, compared to commonly applied NUS methods. It is shown that this is achieved due to the low variability of the inherent sensitivity of the random subset chosen from a given PDF. Finally, it is demonstrated that metrics used to find optimal NUS distributions are heavily dependent on the inherent sensitivity of the random subset, and such optimisation is therefore less critical when using the proposed sampling scheme.

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.

Mapping monoclonal antibody structure by 2D 13C NMR at natural abundance

Monoclonal antibodies (mAbs) represent an important and rapidly growing class of biotherapeutics. Correct folding of a mAb is critical for drug efficacy, while misfolding can impact safety by eliciting unwanted immune or other off-target responses. Robust methods are therefore needed for the precise measurement of mAb structure for drug quality assessment and comparability. To date, the perception in the field has been that NMR could not be applied practically to mAbs due to the size (∼150 kDa) and complexity of these molecules, as well as the insensitivity of the method. The feasibility of applying NMR methods to stable isotope-labeled, protease-cleaved, mAb domains (Fab and Fc) has been demonstrated from both E. coli and Chinese hamster ovaries (CHO) cell expression platforms; however, isotopic labeling is not typically available when analyzing drug products. Here, we address the issue of feasibility of NMR-based mapping of mAb structure by demonstrating for the first time the application of a 2D (13)C NMR methyl fingerprint method for structural mapping of an intact mAb at natural isotopic abundance. Further, we show that 2D (13)C NMR spectra of protease-cleaved Fc and Fab fragments can provide accurate reporters on the domain structures that can be mapped directly to the intact mAb. Through combined use of rapid acquisition and nonuniform sampling techniques, we show that these Fab and Fc fingerprint spectra can be rapidly acquired in as short as approximately 30 min.

Nonuniform sampling and non-Fourier signal processing methods in multidimensional NMR

Beginning with the introduction of Fourier Transform NMR by Ernst and Anderson in 1966, time domain measurement of the impulse response (the free induction decay, FID) consisted of sampling the signal at a series of discrete intervals. For compatibility with the discrete Fourier transform (DFT), the intervals are kept uniform, and the Nyquist theorem dictates the largest value of the interval sufficient to avoid aliasing. With the proposal by Jeener of parametric sampling along an indirect time dimension, extension to multidimensional experiments employed the same sampling techniques used in one dimension, similarly subject to the Nyquist condition and suitable for processing via the discrete Fourier transform. The challenges of obtaining high-resolution spectral estimates from short data records using the DFT were already well understood, however. Despite techniques such as linear prediction extrapolation, the achievable resolution in the indirect dimensions is limited by practical constraints on measuring time. The advent of non-Fourier methods of spectrum analysis capable of processing nonuniformly sampled data has led to an explosion in the development of novel sampling strategies that avoid the limits on resolution and measurement time imposed by uniform sampling. The first part of this review discusses the many approaches to data sampling in multidimensional NMR, the second part highlights commonly used methods for signal processing of such data, and the review concludes with a discussion of other approaches to speeding up data acquisition in NMR.

Nonuniform sampling and non-Fourier signal processing methods in multidimensional NMR

Beginning with the introduction of Fourier Transform NMR by Ernst and Anderson in 1966, time domain measurement of the impulse response (the free induction decay, FID) consisted of sampling the signal at a series of discrete intervals. For compatibility with the discrete Fourier transform (DFT), the intervals are kept uniform, and the Nyquist theorem dictates the largest value of the interval sufficient to avoid aliasing. With the proposal by Jeener of parametric sampling along an indirect time dimension, extension to multidimensional experiments employed the same sampling techniques used in one dimension, similarly subject to the Nyquist condition and suitable for processing via the discrete Fourier transform. The challenges of obtaining high-resolution spectral estimates from short data records using the DFT were already well understood, however. Despite techniques such as linear prediction extrapolation, the achievable resolution in the indirect dimensions is limited by practical constraints on measuring time. The advent of non-Fourier methods of spectrum analysis capable of processing nonuniformly sampled data has led to an explosion in the development of novel sampling strategies that avoid the limits on resolution and measurement time imposed by uniform sampling. The first part of this review discusses the many approaches to data sampling in multidimensional NMR, the second part highlights commonly used methods for signal processing of such data, and the review concludes with a discussion of other approaches to speeding up data acquisition in NMR.