Fast quantitative 2D NMR for metabolomics and lipidomics: A tutorial

Nuclear magnetic resonance (NMR) is a well-known analytical technique for the analysis of complex mixtures. Its quantitative capability makes it ideally suited to metabolomics or lipidomics studies involving large sample collections of complex biological samples. To overcome the ubiquitous limitation of spectral overcrowding when recording 1D NMR spectra on such samples, the acquisition of 2D NMR spectra allows a better separation between overlapped resonances while yielding accurate quantitative data when appropriate analytical protocols are implemented. Moreover, the experiment duration can be considerably reduced by applying fast acquisition methods. Here, we describe the general workflow to acquire fast quantitative 2D NMR spectra in the "omics" context. It is illustrated on three representative and complementary experiments: UF COSY, ZF-TOCSY with nonuniform sampling, and HSQC with nonuniform sampling. After giving some details and recommendations on how to apply this protocol, its implementation in the case of targeted and untargeted metabolomics/lipidomics studies is described.

Rapid maximum likelihood ancestral state reconstruction of continuous characters: A rerooting-free algorithm

Ancestral state reconstruction is a method used to study the evolutionary trajectories of quantitative characters on phylogenies. Although efficient methods for univariate ancestral state reconstruction under a Brownian motion model have been described for at least 25 years, to date no generalization has been described to allow more complex evolutionary models, such as multivariate trait evolution, non-Brownian models, missing data, and within-species variation. Furthermore, even for simple univariate Brownian motion models, most phylogenetic comparative R packages compute ancestral states via inefficient tree rerooting and full tree traversals at each tree node, making ancestral state reconstruction extremely time-consuming for large phylogenies. Here, a computationally efficient method for fast maximum likelihood ancestral state reconstruction of continuous characters is described. The algorithm has linear complexity relative to the number of species and outperforms the fastest existing R implementations by several orders of magnitude. The described algorithm is capable of performing ancestral state reconstruction on a 1,000,000-species phylogeny in fewer than 2 s using a standard laptop, whereas the next fastest R implementation would take several days to complete. The method is generalizable to more complex evolutionary models, such as phylogenetic regression, within-species variation, non-Brownian evolutionary models, and multivariate trait evolution. Because this method enables fast repeated computations on phylogenies of virtually any size, implementation of the described algorithm can drastically alleviate the computational burden of many otherwise prohibitively time-consuming tasks requiring reconstruction of ancestral states, such as phylogenetic imputation of missing data, bootstrapping procedures, Expectation-Maximization algorithms, and Bayesian estimation. The described ancestral state reconstruction algorithm is implemented in the Rphylopars functions anc.recon and phylopars.

A double-Fourier approach to enhance the efficiency of the indirect domain sampling in 2D NMR

The relatively long times that may be involved in high-resolution two-dimensional nuclear magnetic resonance (2D NMR) have stimulated the search for alternative schemes to collect these data. Particularly onerous situations arise when both high-resolution and large spectral widths are sought along the indirect domain. Strategies proposed for dealing with such cases include folding-over procedures, Hadamard encoding, and nonlinear data sampling. This communication discusses an alternative strategy, which exploits a partial prior knowledge regarding the position of the NMR resonances along the indirect domain together with customized excitations for every particular t1 increment, to achieve an optimal sampling in terms of resolution and bandwidth. On the basis of such optimized encoding of the indirect-domain evolution, which can easily be coped with by modern spectrometers, it becomes possible to maximize the resolution of fine structures without compromising on the spectral bandwidths. The processing of the resulting data along the indirect domain is based on the use of two serially applied discrete Fourier transforms; one to distinguish the main bands in the spectrum and the other to resolve the latter's fine features. A number of simple heteronuclear correlation experiments illustrating the significant acquisition time savings and simultaneous improvements in resolution that can be achieved with the resulting double-Fourier encoding procedure are illustrated.