Importance of time-ordered non-uniform sampling of multi-dimensional NMR spectra of Aβ1-42 peptide under aggregating conditions

Although the order of the time steps in which the non-uniform sampling (NUS) schedule is implemented when acquiring multi-dimensional NMR spectra is of limited importance when sample conditions remain unchanged over the course of the experiment, it is shown to have major impact when samples are unstable. In the latter case, time-ordering of the NUS data points by the normalized radial length yields a reduction of sampling artifacts, regardless of the spectral reconstruction algorithm. The disadvantage of time-ordered NUS sampling is that halting the experiment prior to its completion will result in lower spectral resolution, rather than a sparser data matrix. Alternatively, digitally correcting for sample decay prior to reconstruction of randomly ordered NUS data points can mitigate reconstruction artifacts, at the cost of somewhat lower sensitivity. Application of these sampling schemes to the Alzheimer's amyloid beta (Aβ1-42) peptide at an elevated concentration, low temperature, and 3 kbar of pressure, where approximately 75% of the peptide reverts to an NMR-invisible state during the collection of a 3D 15N-separated NOESY spectrum, highlights the improvement in artifact suppression and reveals weak medium-range NOE contacts in several regions, including the C-terminal region of the peptide.

Sparse multidimensional iterative lineshape-enhanced (SMILE) reconstruction of both non-uniformly sampled and conventional NMR data

Implementation of a new algorithm, SMILE, is described for reconstruction of non-uniformly sampled two-, three- and four-dimensional NMR data, which takes advantage of the known phases of the NMR spectrum and the exponential decay of underlying time domain signals. The method is very robust with respect to the chosen sampling protocol and, in its default mode, also extends the truncated time domain signals by a modest amount of non-sampled zeros. SMILE can likewise be used to extend conventional uniformly sampled data, as an effective multidimensional alternative to linear prediction. The program is provided as a plug-in to the widely used NMRPipe software suite, and can be used with default parameters for mainstream application, or with user control over the iterative process to possibly further improve reconstruction quality and to lower the demand on computational resources. For large data sets, the method is robust and demonstrated for sparsities down to ca 1%, and final all-real spectral sizes as large as 300 Gb. Comparison between fully sampled, conventionally processed spectra and randomly selected NUS subsets of this data shows that the reconstruction quality approaches the theoretical limit in terms of peak position fidelity and intensity. SMILE essentially removes the noise-like appearance associated with the point-spread function of signals that are a default of five-fold above the noise level, but impacts the actual thermal noise in the NMR spectra only minimally. Therefore, the appearance and interpretation of SMILE-reconstructed spectra is very similar to that of fully sampled spectra generated by Fourier transformation.

A practical guide and power analysis for GLMMs: detecting among treatment variation in random effects

In ecology and evolution generalized linear mixed models (GLMMs) are becoming increasingly used to test for differences in variation by treatment at multiple hierarchical levels. Yet, the specific sampling schemes that optimize the power of an experiment to detect differences in random effects by treatment/group remain unknown. In this paper we develop a blueprint for conducting power analyses for GLMMs focusing on detecting differences in variance by treatment. We present parameterization and power analyses for random-intercepts and random-slopes GLMMs because of their generality as focal parameters for most applications and because of their immediate applicability to emerging questions in the field of behavioral ecology. We focus on the extreme case of hierarchically structured binomial data, though the framework presented here generalizes easily to any error distribution model. First, we determine the optimal ratio of individuals to repeated measures within individuals that maximizes power to detect differences by treatment in among-individual variation in intercept, among-individual variation in slope, and within-individual variation in intercept. Second, we explore how power to detect differences in target variance parameters is affected by total variation. Our results indicate heterogeneity in power across ratios of individuals to repeated measures with an optimal ratio determined by both the target variance parameter and total sample size. Additionally, power to detect each variance parameter was low overall (in most cases >1,000 total observations per treatment needed to achieve 80% power) and decreased with increasing variance in non-target random effects. With growing interest in variance as the parameter of inquiry, these power analyses provide a crucial component for designing experiments focused on detecting differences in variance. We hope to inspire novel experimental designs in ecology and evolution investigating the causes and implications of individual-level phenotypic variance, such as the adaptive significance of within-individual variation.