Nonuniform sampling and maximum entropy reconstruction applied to the accurate measurement of residual dipolar couplings

A fast approach to 3D HSQC-based spectroscopy based on a Fourier phase encoding of pre-targeted resonances

Multidimensional Nuclear Magnetic Resonance (NMR) provides a unique window into structure and dynamics at an atomic level. Traditionally, given the scan-by-scan time modulation involved in these experiments, the duration of nD NMR increases exponentially with spectral dimensionality. In addition, acquisition times increase as the number of spectral elements being sought in each indirect domain - given by the ratio between the spectral bandwidth being targeted and the resolution desired. These long sampling times can be substantially reduced by exploiting information that is often available from lower-dimensionality acquisitions. This work presents a novel approach that exploits previous 2D information to speed up the acquisition of 3D spectra, based on what we denote as a Time-Optimized FouriEr Encoding (TOFEE) of pre-targeted peaks. Such 3D TOFEE experiments, which present points in common with Hadamard-encoded 3D acquisitions, do not necessarily require more scans than their 2D counterparts. This is here demonstrated based on extensions of 2D Heteronuclear Single-quantum Coherence (HSQC) experiments, to 3D HSQC-TOCSY or 3D HSQC-NOESY acquisitions. The theoretical basis of this new approach is given, and experimental demonstrations are presented on small molecule and protein-based model systems.

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

Non-uniform sampling (NUS) has been established as a route to obtaining true sensitivity enhancements when recording indirect dimensions of decaying signals in the same total experimental time as traditional uniform incrementation of the indirect evolution period. Theory and experiments have shown that NUS can yield up to two-fold improvements in the intrinsic signal-to-noise ratio (SNR) of each dimension, while even conservative protocols can yield 20-40% improvements in the intrinsic SNR of NMR data. Applications of biological NMR that can benefit from these improvements are emerging, and in this work we develop some practical aspects of applying NUS nD-NMR to studies that approach the traditional detection limit of nD-NMR spectroscopy. Conditions for obtaining high NUS sensitivity enhancements are considered here in the context of enabling (1)H,(15)N-HSQC experiments on natural abundance protein samples and (1)H,(13)C-HMBC experiments on a challenging natural product. Through systematic studies we arrive at more precise guidelines to contrast sensitivity enhancements with reduced line shape constraints, and report an alternative sampling density based on a quarter-wave sinusoidal distribution that returns the highest fidelity we have seen to date in line shapes obtained by maximum entropy processing of non-uniformly sampled data.

Non-uniform sampling in EPR – optimizing data acquisition for HYSCORE spectroscopy

Non-uniformly sampled HYSCORE data combined with maximum entropy reconstruction can shorten experimental times by approximately an order of magnitude.

On the role of NMR spectroscopy for characterization of antimicrobial peptides

Antimicrobial peptides (AMPs) provide a primordial source of immunity, conferring upon eukaryotic cells resistance against bacteria, protozoa, and viruses. Despite a few examples of anionic peptides, AMPs are usually relatively short positively charged polypeptides, consisting of a dozen to about a hundred amino acids, and exhibiting amphipathic character. Despite significant differences in their primary and secondary structures, all AMPs discovered to date share the ability to interact with cellular membranes, thereby affecting bilayer stability, disrupting membrane organization, and/or forming well-defined pores. AMPs selectively target infectious agents without being susceptible to any of the common pathways by which these acquire resistance, thereby making AMPs prime candidates to provide therapeutic alternatives to conventional drugs. However, the mechanisms of AMP actions are still a matter of intense debate. The structure-function paradigm suggests that a better understanding of how AMPs elicit their biological functions could result from atomic resolution studies of peptide-lipid interactions. In contrast, more strict thermodynamic views preclude any roles for three-dimensional structures. Indeed, the design of selective AMPs based solely on structural parameters has been challenging. In this chapter, we will focus on selected AMPs for which studies on the corresponding AMP-lipid interactions have helped reach an understanding of how AMP effects are mediated. We will emphasize the roles of both liquid- and solid-state NMR spectroscopy for elucidating the mechanisms of action of AMPs.

Speeding up the measurement of one-bond scalar (1J) and residual dipolar couplings (1D) by using non-uniform sampling (NUS)

The accurate and precise measurement of one-bond scalar and residual dipolar coupling (RDC) constants is of prime importance to be able to use RDCs for structure determination. If coupling constants are to be extracted from the indirect dimension of HSQC spectra a significant saving of measurement time can be achieved by non-uniform sampling (NUS). Coupling constants can either be obtained with the same precision as in traditionally acquired spectra in a fraction of the measurement time or the precision can be significantly improved if the same amount of measurement time as for traditionally acquired spectra is invested. The application of NUS for the measurement of (1)J (scalar coupling constants) and (1)T (total couplings constants) from different kinds of ω(1)-coupled spectra (including also J-scaled ones) is examined in detail and the possible gains in time or resolution are discussed. When using the newly proposed compressed sensing (CS) algorithm for processing, the quality of the spectra is comparable to the traditionally sampled ones.

Deterministic schedules for robust and reproducible non-uniform sampling in multidimensional NMR

We show that a simple, general, and easily reproducible method for generating non-uniform sampling (NUS) schedules preserves the benefits of random sampling, including inherently reduced sampling artifacts, while removing the pitfalls associated with choosing an arbitrary seed. Sampling schedules are generated from a discrete cumulative distribution function (CDF) that closely fits the continuous CDF of the desired probability density function. We compare random and deterministic sampling using a Gaussian probability density function applied to 2D HSQC spectra. Data are processed using the previously published method of Spectroscopy by Integration of Frequency and Time domain data (SIFT). NUS spectra from deterministic sampling schedules were found to be at least as good as those from random schedules at the SIFT critical sampling density, and significantly better at half that sampling density. The method can be applied to any probability density function and generalized to greater than two dimensions.

Sensitivity enhancement for maximally resolved two-dimensional NMR by nonuniform sampling

Resolving NMR signals which are separated in frequency on the order of their line widths requires obtaining the time domain free induction decay for a maximum time tmax = πT2 , where T2 is the transverse relaxation time of the given signals. Unfortunately, samples acquired beyond ∼1.26T2 contribute more noise than signal to the data; and samples in the range of about (0.75-1.26)× T2 have a negligible effect on the signal-to-noise ratio (SNR). Therefore, one must sacrifice SNR to reach evolution times of πT2 . One can preserve resolution in a shorter total experimental time by selecting a reduced set of samples from the Nyquist grid according to an exponential probability density which is on the order of the T2 of the signals. This practice is widely termed nonuniform sampling (NUS). We derive analytic theory for the enhancement of the intrinsic SNR of NUS time domain data compared with uniformly sampled data when the total experimental times are equivalent. This theory is general for any tmax and exponential weighting and is further carefully validated with simulations. Enhancements of SNR in the time domain on the order of twofold are routinely available when tmax ∼ πT2 and are reflected in the subsequent maximum entropy reconstructed spectra. SNR enhancement by NUS is demonstrated to be helpful in enabling the acquisition of HMQC spectra of dilute bile salts in which high resolution in the indirect carbon dimension is required.

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.

Maximum Entropy Spectral Reconstruction of Non-Uniformly Sampled Data

The time required to complete a multidimensional NMR experiment is directly proportional to the number of evolution times sampled in the indirect dimensions. A consequence when utilizing conventional methods of data acquisition and spectrum analysis is that resolution in the indirect dimensions is frequently sample-limited. The problem becomes more acute at very high magnetic fields, where increased chemical shift dispersion requires shorter time increments to avoid aliasing. It has long been recognized that a way to avoid this limitation is to utilize methods of spectrum analysis that do not require data to be sampled at uniform intervals, permitting the collection of data at long evolution times requisite for high resolution without requiring collection of data at all intervening multiples of the sampling interval. Several promising methods have evolved that are seemingly quite different, yet can be shown to yield similar results when applied to similar sampling strategies, emphasizing the importance of the choice of samples, regardless of the technique used to compute the spectrum. Maximum entropy (MaxEnt) reconstruction is a very general method for spectrum analysis of non-uniformly sampled data (NUS), and because it can be used with essentially arbitrary sampling strategies and makes no assumptions about the nature of the signal, it provides a convenient basis for exploring the influence of the choice of samples on spectral quality. In this article we use this versatility of MaxEnt reconstruction to compare different approaches to NUS in multidimensional NMR and suggest strategies for improving spectral quality by careful choice of sample times.

An entropy-based approach for testing genetic epistasis underlying complex diseases

The genetic basis of complex diseases is expected to be highly heterogeneous, with complex interactions among multiple disease loci and environment factors. Due to the multi-dimensional property of interactions among large number of genetic loci, efficient statistical approach has not been well developed to handle the high-order epistatic complexity. In this article, we introduce a new approach for testing genetic epistasis in multiple loci using an entropy-based statistic for a case-only design. The entropy-based statistic asymptotically follows a chi(2) distribution. Computer simulations show that the entropy-based approach has better control of type I error and higher power compared to the standard chi(2) test. Motivated by a schizophrenia data set, we propose a method for measuring and testing the relative entropy of a clinical phenotype, through which one can test the contribution or interaction of multiple disease loci to a clinical phenotype. A sequential forward selection procedure is proposed to construct a genetic interaction network which is illustrated through a tree-based diagram. The network information clearly shows the relative importance of a set of genetic loci on a clinical phenotype. To show the utility of the new entropy-based approach, it is applied to analyze two real data sets, a schizophrenia data set and a published malaria data set. Our approach provides a fast and testable framework for genetic epistasis study in a case-only design.