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.

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.

Anomalous amide proton chemical shifts as signatures of hydrogen bonding to aromatic sidechains.

Hydrogen bonding between an amide group and the p-π cloud of an aromatic ring was first identified in a protein in the 1980s. Subsequent surveys of high-resolution X-ray crystal structures found multiple instances, but their preponderance was determined to be infrequent. Hydrogen atoms participating in a hydrogen bond to the p-π cloud of an aromatic ring are expected to experience an upfield chemical shift arising from a shielding ring current shift. We surveyed the Biological Magnetic Resonance Data Bank for amide hydrogens exhibiting unusual shifts as well as corroborating nuclear Overhauser effects between the amide protons and ring protons. We found evidence that Trp residues are more likely to be involved in p-π hydrogen bonds than other aromatic amino acids, whereas His residues are more likely to be involved in in-plane hydrogen bonds, with a ring nitrogen acting as the hydrogen acceptor. The p-π hydrogen bonds may be more abundant than previously believed. The inclusion in NMR structure refinement protocols of shift effects in amide protons from aromatic sidechains, or explicit hydrogen bond restraints between amides and aromatic rings, could improve the local accuracy of sidechain orientations in solution NMR protein structures, but their impact on global accuracy is likely be limited.

Merging NMR Data and Computation Facilitates Data-Centered Research.

The Biological Magnetic Resonance Data Bank (BMRB) has served the NMR structural biology community for 40 years, and has been instrumental in the development of many widely-used tools. It fosters the reuse of data resources in structural biology by embodying the FAIR data principles (Findable, Accessible, Inter-operable, and Re-usable). NMRbox is less than a decade old, but complements BMRB by providing NMR software and high-performance computing resources, facilitating the reuse of software resources. BMRB and NMRbox both facilitate reproducible research. NMRbox also fosters the development and deployment of complex meta-software. Combining BMRB and NMRbox helps speed and simplify workflows that utilize BMRB, and enables facile federation of BMRB with other data repositories. Utilization of BMRB and NMRbox in tandem will enable additional advances, such as machine learning, that are poised to become increasingly powerful.

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.

mol2sphere: spherical decomposition of multi-domain molecules for visualization and coarse grained spatial modeling.

Motivation: Proteins, especially those involved in signaling pathways are composed of functional modules connected by linker domains with varying degrees of flexibility. To understand the structure-function relationships in these macromolecules, it is helpful to visualize the geometric arrangement of domains. Furthermore, accurate spatial representation of domain structure is necessary for coarse-grain models of the multi-molecular interactions that comprise signaling pathways. Results: We introduce a new tool, mol2sphere, that transforms the atomistic structure of a macromolecule into a series of linked spheres corresponding to domains. It does this with a k-means clustering algorithm. It may be used for visualization or for coarse grain modeling and simulation. Availability and implementation: PyMOL plugin, source, and documentation.https://nmrbox.org/registry/mol2sphere. SpringSaLaD executables and documentation: http://vcell.org/ssalad, SpringSaLaD v.2 source: https://github.com/jmasison/SpringSaLaD.

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.

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.

Robust and transferable quantification of NMR spectral quality using IROC analysis.

Non-Fourier methods are increasingly utilized in NMR spectroscopy because of their ability to handle nonuniformly-sampled data. However, non-Fourier methods present unique challenges due to their nonlinearity, which can produce nonrandom noise and render conventional metrics for spectral quality such as signal-to-noise ratio unreliable. The lack of robust and transferable metrics (i.e. applicable to methods exhibiting different nonlinearities) has hampered comparison of non-Fourier methods and nonuniform sampling schemes, preventing the identification of best practices. We describe a novel method, in situ receiver operating characteristic analysis (IROC), for characterizing spectral quality based on the Receiver Operating Characteristic curve. IROC utilizes synthetic signals added to empirical data as "ground truth", and provides several robust scalar-valued metrics for spectral quality. This approach avoids problems posed by nonlinear spectral estimates, and provides a versatile quantitative means of characterizing many aspects of spectral quality. We demonstrate applications to parameter optimization in Fourier and non-Fourier spectral estimation, critical comparison of different methods for spectrum analysis, and optimization of nonuniform sampling schemes. The approach will accelerate the discovery of optimal approaches to nonuniform sampling experiment design and non-Fourier spectrum analysis for multidimensional NMR.

NMRbox: A Resource for Biomolecular NMR Computation.

Advances in computation have been enabling many recent advances in biomolecular applications of NMR. Due to the wide diversity of applications of NMR, the number and variety of software packages for processing and analyzing NMR data is quite large, with labs relying on dozens, if not hundreds of software packages. Discovery, acquisition, installation, and maintenance of all these packages is a burdensome task. Because the majority of software packages originate in academic labs, persistence of the software is compromised when developers graduate, funding ceases, or investigators turn to other projects. To simplify access to and use of biomolecular NMR software, foster persistence, and enhance reproducibility of computational workflows, we have developed NMRbox, a shared resource for NMR software and computation. NMRbox employs virtualization to provide a comprehensive software environment preconfigured with hundreds of software packages, available as a downloadable virtual machine or as a Platform-as-a-Service supported by a dedicated compute cloud. Ongoing development includes a metadata harvester to regularize, annotate, and preserve workflows and facilitate and enhance data depositions to BioMagResBank, and tools for Bayesian inference to enhance the robustness and extensibility of computational analyses. In addition to facilitating use and preservation of the rich and dynamic software environment for biomolecular NMR, NMRbox fosters the development and deployment of a new class of metasoftware packages. NMRbox is freely available to not-for-profit users.

Correction: Sparse sampling methods in multidimensional NMR.

Correction for 'Sparse sampling methods in multidimensional NMR' by Mehdi Mobli et al., Phys. Chem. Chem. Phys., 2012, 14, 10835-10843.

Beyond cones: an improved model of whisker bending based on measured mechanics and tapering.

The sense of touch is represented by neural activity patterns evoked by mechanosensory input forces. The rodent whisker system is exceptional for studying the neurophysiology of touch in part because these forces can be precisely computed from video of whisker deformation. We evaluate the accuracy of a standard model of whisker bending, which assumes quasi-static dynamics and a linearly tapered conical profile, using controlled whisker deflections. We find significant discrepancies between model and experiment: real whiskers bend more than predicted upon contact at locations in the middle of the whisker and less at distal locations. Thus whiskers behave as if their stiffness near the base and near the tip is larger than expected for a homogeneous cone. We assess whether contact direction, friction, inhomogeneous elasticity, whisker orientation, or nonconical shape could explain these deviations. We show that a thin-middle taper of mouse whisker shape accounts for the majority of this behavior. This taper is conserved across rows and columns of the whisker array. The taper has a large effect on the touch-evoked forces and the ease with which whiskers slip past objects, which are key drivers of neural activity in tactile object localization and identification. This holds for orientations with intrinsic whisker curvature pointed toward, away from, or down from objects, validating two-dimensional models of simple whisker-object interactions. The precision of computational models relating sensory input forces to neural activity patterns can be quantitatively enhanced by taking thin-middle taper into account with a simple corrective function that we provide.

Nonuniform sampling of hypercomplex multidimensional NMR experiments: Dimensionality, quadrature phase and randomization.

Nonuniform sampling (NUS) in multidimensional NMR permits the exploration of higher dimensional experiments and longer evolution times than the Nyquist Theorem practically allows for uniformly sampled experiments. However, the spectra of NUS data include sampling-induced artifacts and may be subject to distortions imposed by sparse data reconstruction techniques, issues not encountered with the discrete Fourier transform (DFT) applied to uniformly sampled data. The characterization of these NUS-induced artifacts allows for more informed sample schedule design and improved spectral quality. The DFT-Convolution Theorem, via the point-spread function (PSF) for a given sampling scheme, provides a useful framework for exploring the nature of NUS sampling artifacts. In this work, we analyze the PSFs for a set of specially constructed NUS schemes to quantify the interplay between randomization and dimensionality for reducing artifacts relative to uniformly undersampled controls. In particular, we find a synergistic relationship between the indirect time dimensions and the "quadrature phase dimension" (i.e. the hypercomplex components collected for quadrature detection). The quadrature phase dimension provides additional degrees of freedom that enable partial-component NUS (collecting a subset of quadrature components) to further reduce sampling-induced aliases relative to traditional full-component NUS (collecting all quadrature components). The efficacy of artifact reduction is exponentially related to the dimensionality of the sample space. Our results quantify the utility of partial-component NUS as an additional means for introducing decoherence into sampling schemes and reducing sampling artifacts in high dimensional experiments.

Comprehensive bioimaging with fluorinated nanoparticles using breathable liquids.

Fluorocarbons are lipophobic and non-polar molecules that exhibit remarkable biocompatibility, with applications in liquid ventilation and synthetic blood. The unique properties of these compounds have also enabled mass spectrometry imaging of tissues where the fluorocarbons act as a Teflon-like coating for nanostructured surfaces to assist in desorption/ionization. Here we report fluorinated gold nanoparticles (f-AuNPs) designed to facilitate nanostructure imaging mass spectrometry. Irradiation of f-AuNPs results in the release of the fluorocarbon ligands providing a driving force for analyte desorption. The f-AuNPs allow for the mass spectrometry analysis of both lipophilic and polar (central carbon) metabolites. An important property of AuNPs is that they also act as contrast agents for X-ray microtomography and electron microscopy, a feature we have exploited by infusing f-AuNPs into tissue via fluorocarbon liquids to facilitate multimodal (molecular and anatomical) imaging.

Nonuniform sampling and maximum entropy reconstruction in multidimensional NMR.

NMR spectroscopy is one of the most powerful and versatile analytic tools available to chemists. The discrete Fourier transform (DFT) played a seminal role in the development of modern NMR, including the multidimensional methods that are essential for characterizing complex biomolecules. However, it suffers from well-known limitations: chiefly the difficulty in obtaining high-resolution spectral estimates from short data records. Because the time required to perform an experiment is proportional to the number of data samples, this problem imposes a sampling burden for multidimensional NMR experiments. At high magnetic field, where spectral dispersion is greatest, the problem becomes particularly acute. Consequently multidimensional NMR experiments that rely on the DFT must either sacrifice resolution in order to be completed in reasonable time or use inordinate amounts of time to achieve the potential resolution afforded by high-field magnets. Maximum entropy (MaxEnt) reconstruction is a non-Fourier method of spectrum analysis that can provide high-resolution spectral estimates from short data records. It can also be used with nonuniformly sampled data sets. Since resolution is substantially determined by the largest evolution time sampled, nonuniform sampling enables high resolution while avoiding the need to uniformly sample at large numbers of evolution times. The Nyquist sampling theorem does not apply to nonuniformly sampled data, and artifacts that occur with the use of nonuniform sampling can be viewed as frequency-aliased signals. Strategies for suppressing nonuniform sampling artifacts include the careful design of the sampling scheme and special methods for computing the spectrum. Researchers now routinely report that they can complete an N-dimensional NMR experiment 3(N-1) times faster (a 3D experiment in one ninth of the time). As a result, high-resolution three- and four-dimensional experiments that were prohibitively time consuming are now practical. Conversely, tailored sampling in the indirect dimensions has led to improved sensitivity. Further advances in nonuniform sampling strategies could enable further reductions in sampling requirements for high resolution NMR spectra, and the combination of these strategies with robust non-Fourier methods of spectrum analysis (such as MaxEnt) represent a profound change in the way researchers conduct multidimensional experiments. The potential benefits will enable more advanced applications of multidimensional NMR spectroscopy to study biological macromolecules, metabolomics, natural products, dynamic systems, and other areas where resolution, sensitivity, or experiment time are limiting. Just as the development of multidimensional NMR methods presaged multidimensional methods in other areas of spectroscopy, we anticipate that nonuniform sampling approaches will find applications in other forms of spectroscopy.

Formalism for hypercomplex multidimensional NMR employing partial-component subsampling.

Multidimensional NMR spectroscopy typically employs phase-sensitive detection, which results in hypercomplex data (and spectra) when utilized in more than one dimension. Nonuniform sampling approaches have become commonplace in multidimensional NMR, enabling dramatic reductions in experiment time, increases in sensitivity and/or increases in resolution. In order to utilize nonuniform sampling optimally, it is necessary to characterize the relationship between the spectrum of a uniformly sampled data set and the spectrum of a subsampled data set. In this work we construct an algebra of hypercomplex numbers suitable for representing multidimensional NMR data along with partial-component nonuniform sampling (i.e. the hypercomplex components of data points are subsampled). This formalism leads to a modified DFT-Convolution relationship involving a partial-component, hypercomplex point-spread function set. The framework presented here is essential for the continued development and appropriate characterization of partial-component nonuniform sampling.

Sparse sampling methods in multidimensional NMR.

Although the discrete Fourier transform played an enabling role in the development of modern NMR spectroscopy, it suffers from a well-known difficulty providing high-resolution spectra from short data records. In multidimensional NMR experiments, so-called indirect time dimensions are sampled parametrically, with each instance of evolution times along the indirect dimensions sampled via separate one-dimensional experiments. The time required to conduct multidimensional experiments is directly proportional to the number of indirect evolution times sampled. Despite remarkable advances in resolution with increasing magnetic field strength, multiple dimensions remain essential for resolving individual resonances in NMR spectra of biological macromolecues. Conventional Fourier-based methods of spectrum analysis limit the resolution that can be practically achieved in the indirect dimensions. Nonuniform or sparse data collection strategies, together with suitable non-Fourier methods of spectrum analysis, enable high-resolution multidimensional spectra to be obtained. Although some of these approaches were first employed in NMR more than two decades ago, it is only relatively recently that they have been widely adopted. Here we describe the current practice of sparse sampling methods and prospects for further development of the approach to improve resolution and sensitivity and shorten experiment time in multidimensional NMR. While sparse sampling is particularly promising for multidimensional NMR, the basic principles could apply to other forms of multidimensional spectroscopy.

Data sampling in multidimensional NMR: fundamentals and strategies.

Beginning with the introduction of Fourier Transform NMR by Ernst and Anderson in 1966, time domain measurement of the impulse response (free induction decay) consisted of sampling the signal at a series of discrete intervals. For compatibility with the discrete Fourier transform, 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 were already well understood, and 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 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. In this chapter we review the fundamentals of uniform and nonuniform sampling methods in one- and multidimensional NMR.

Random phase detection in multidimensional NMR.

Despite advances in resolution accompanying the development of high-field superconducting magnets, biomolecular applications of NMR require multiple dimensions in order to resolve individual resonances, and the achievable resolution is typically limited by practical constraints on measuring time. In addition to the need for measuring long evolution times to obtain high resolution, the need to distinguish the sign of the frequency constrains the ability to shorten measuring times. Sign discrimination is typically accomplished by sampling the signal with two different receiver phases or by selecting a reference frequency outside the range of frequencies spanned by the signal and then sampling at a higher rate. In the parametrically sampled (indirect) time dimensions of multidimensional NMR experiments, either method imposes an additional factor of 2 sampling burden for each dimension. We demonstrate that by using a single detector phase at each time sample point, but randomly altering the phase for different points, the sign ambiguity that attends fixed single-phase detection is resolved. Random phase detection enables a reduction in experiment time by a factor of 2 for each indirect dimension, amounting to a factor of 8 for a four-dimensional experiment, albeit at the cost of introducing sampling artifacts. Alternatively, for fixed measuring time, random phase detection can be used to double resolution in each indirect dimension. Random phase detection is complementary to nonuniform sampling methods, and their combination offers the potential for additional benefits. In addition to applications in biomolecular NMR, random phase detection could be useful in magnetic resonance imaging and other signal processing contexts.

Knowledge-based nonuniform sampling in multidimensional NMR.

The full resolution afforded by high-field magnets is rarely realized in the indirect dimensions of multidimensional NMR experiments because of the time cost of uniformly sampling to long evolution times. Emerging methods utilizing nonuniform sampling (NUS) enable high resolution along indirect dimensions by sampling long evolution times without sampling at every multiple of the Nyquist sampling interval. While the earliest NUS approaches matched the decay of sampling density to the decay of the signal envelope, recent approaches based on coupled evolution times attempt to optimize sampling by choosing projection angles that increase the likelihood of resolving closely-spaced resonances. These approaches employ knowledge about chemical shifts to predict optimal projection angles, whereas prior applications of tailored sampling employed only knowledge of the decay rate. In this work we adapt the matched filter approach as a general strategy for knowledge-based nonuniform sampling that can exploit prior knowledge about chemical shifts and is not restricted to sampling projections. Based on several measures of performance, we find that exponentially weighted random sampling (envelope matched sampling) performs better than shift-based sampling (beat matched sampling). While shift-based sampling can yield small advantages in sensitivity, the gains are generally outweighed by diminished robustness. Our observation that more robust sampling schemes are only slightly less sensitive than schemes highly optimized using prior knowledge about chemical shifts has broad implications for any multidimensional NMR study employing NUS. The results derived from simulated data are demonstrated with a sample application to PfPMT, the phosphoethanolamine methyltransferase of the human malaria parasite Plasmodium falciparum.