Concepts in Magnetic Resonance Part A最新文献

Nuclear magnetic resonance (NMR) spectroscopy is widely used across the physical, chemical, and biological sciences. A core component of NMR studies is multidimensional experiments, which enable correlation of properties from one or more NMR-active nuclei. In high-resolution biomolecular NMR, common nuclei are ¹H, ¹⁵N, and ¹³C, and triple resonance experiments using these three nuclei form the backbone of NMR structural studies. In other fields, a range of other nuclei may be used. Multidimensional NMR experiments provide unparalleled information content, but this comes at the price of long experiment times required to achieve the necessary resolution and sensitivity. Non-uniform sampling (NUS) techniques to reduce the required data sampling have existed for many decades. Recently, such techniques have received heightened interest due to the development of compressed sensing (CS) methods for reconstructing spectra from such NUS datasets. When applied jointly, these methods provide a powerful approach to dramatically improve the resolution of spectra per time unit and under suitable conditions can also lead to signal-to-noise ratio improvements. In this review, we explore the basis of NUS approaches, the fundamental features of NUS reconstruction using CS and applications based on CS approaches including the benefits of expanding the repertoire of biomolecular NMR experiments into higher dimensions. We discuss some of the recent algorithms and software packages and provide practical tips for recording and processing NUS data by CS.

Protein nuclear magnetic resonance (NMR) assignment can be a tedious and error-prone process, and it is often a limiting factor in biomolecular NMR studies. Challenges are exacerbated in larger proteins, disordered proteins, and often alpha-helical proteins, owing to an increase in spectral complexity and frequency degeneracies. Here, several multidimensional spectra must be inspected and compared in an iterative manner before resonances can be assigned with confidence. Over the last 2 decades, covariance NMR has evolved to become applicable to protein multidimensional spectra. The method, previously used to generate new correlations from spectra of small organic molecules, can now be used to recast assignment procedures as mathematical operations on NMR spectra. These operations result in multidimensional correlation maps combining all information from input spectra and providing direct correlations between moieties that would otherwise be compared indirectly through reporter nuclei. Thus, resonances of sequential residues can be identified and side-chain signals can be assigned by visual inspection of 4D arrays. This review highlights advances in covariance NMR that permitted to generate reliable 4D arrays and describes how these arrays can be obtained from conventional NMR spectra.

NMR measurements are often performed in a serial manner, that is, the acquisition of an FID signal is repeated under various conditions, either controlled (as temperature or pH changes) or uncontrolled (as reaction progress). The traditional approach to process “serial” data is to perform the Fourier transform of each FID in a series. However, it suffers from several problems, in particular, from the need to sample full Nyquist grid and reach a sufficient signal-to-noise ratio in each separate spectrum. The problems become particularly cumbersome in the case of multidimensional signals, where sampling is costly and sensitivity is an issue. Over the years, several methods of alternative, “joint” processing of FID series have been proposed. In this paper, we discuss the principles of some of them: Accordion Spectroscopy, Multidimensional Decomposition, Radon transform, a combination of Compressed Sensing and the Laplace transform. According to our knowledge, this is the first review on serial NMR data processing approaches. The reader is provided with MATLAB scripts allowing to perform simulations and processing using these algorithms.

Determination of the distribution of magnetic resonance (MR) transverse relaxation times is emerging as an important method for materials characterization, including assessment of tissue pathology in biomedicine. These distributions are obtained from the inverse Laplace transform (ILT) of multiexponential decay data. Stabilization of this classically ill-posed problem is most commonly attempted using Tikhonov regularization with an L₂ penalty term. However, with the availability of convex optimization algorithms and recognition of the importance of sparsity in model reconstruction, there has been increasing interest in alternative penalties. The L₁ penalty enforces a greater degree of sparsity than L₂, and so may be suitable for highly localized relaxation time distributions. In addition, L_p penalties, 1 < p < 2, and the elastic net (EN) penalty, defined as a linear combination of L₁ and L₂ penalties, may be appropriate for distributions consisting of both narrow and broad components. We evaluate the L₁, L₂, L_p, and EN penalties for model relaxation time distributions consisting of two Gaussian peaks. For distributions with narrow Gaussian peaks, the L₁ penalty works well to maintain sparsity and promote resolution, while the conventional L₂ penalty performs best for distributions with broader peaks. Finally, the L_p and EN penalties do in fact outperform the L₁ and L₂ penalties for distributions with components of unequal widths. These findings serve as indicators of appropriate regularization in the typical situation in which the experimentalist has a priori knowledge of the general characteristics of the underlying relaxation time distribution. Our findings can be applied to both the recovery of T₂ distributions from spin echo decay data as well as distributions of other MR parameters, such as apparent diffusion constant, from their multiexponential decay signals.

The historical evolution of sparse sampling methods in multidimensional NMR is important for understanding them in the context of developments outside of NMR. This brief, anecdotal history provides context, but also points to potential sources of insights into sparse sampling that have yet to be utilized in NMR. Advances in sparse sampling for multidimensional NMR represent a confluence of many disparate threads.

Nonuniform sampling (NUS) offers NMR spectroscopists a means of accelerating data collection and increasing spectral quality in multidimensional (nD) experiments. The data from NUS experiments are incomplete by design, and must be reconstructed prior to use. While most existing reconstruction techniques compute point estimates of the true signal, Bayesian statistics offers a means of estimating posterior distributions over the signal, which enable more rigorous quantitation and uncertainty estimation. In this article, we describe the variational approach to approximating Bayesian posterior distributions, and illustrate how it can be applied to extend existing results from Bayesian spectrum analysis and compressed sensing. The new NUS reconstruction algorithms resulting from variational Bayes are computationally efficient, and offer new insights into the concepts of spectral sparsity and optimal sampling in NMR experiments.

The starting point of all NMR experiments is a spin polarization which develops when we place the sample in static magnetic field B₀. There are excess of spins aligned along B₀ (spin up with lower energy) than spins aligned opposite (spin down with higher energy) to the field B₀. A natural question is what is the source of this excess spin polarization because relaxation mechanisms can flip a up spin to a down spin and vice-versa. The answer lies in the density of states. When a molecule with spin down flips to spin up it loses energy. This energy goes into increasing the kinetic energy of the molecule in the gas/solution phase. At this increased kinetic energy, there are more rotational-translational states accessible to the molecule than at lower energy. This increases the probability the molecule will spend in spin up state (higher kinetic energy state). This is the source of excess polarization. In this article, we use an argument based on equipartition of energy to explicitly count the excess states that become accessible to the molecule when its spin is flipped from down to up. Using this counting, we derive the familiar Boltzmann distribution of the ratio of up vs down spins. Although prima facie, there is nothing new in this article, we find the mode counting argument for excess states interesting. Furthermore, the article stresses the fact that spin polarization arises from higher density of states at increased kinetic energy of molecules.