Mahalanobis distance correlation: A novel approach for quantitating changes in multidimensional NMR spectra in biological applications.

We present here a novel protocol for quantitating changes in the NMR spectra, which is based on Mahalanobis statistics. In a two dimensional NMR spectrum, the various peaks are taken to represent a distribution, and the two chemical shifts along the orthogonal axes and the peak intensities constitute three observables. All these observables vary in a correlated manner. Taking account of these, the Mahalanobis distance (MD) reflects the distance of any chosen peak from the centre of the distribution. For quantitating changes in a particular spectrum (say A) with N peaks (altered protein NMR spectrum) with respect to a reference spectrum (say B) with M peaks (original protein NMR spectrum), a composite spectrum with N + M peaks is generated. A one-to-one correspondence between N MD values considering all the N peaks in A and the same N peaks in the composite spectrum (A + B) is calculated. The MD distance of corresponding peaks in two different distributions can be correlated to assess the changes in the spectra during the course of a biological phenomenon, or as a result of biomolecular interactions. We have demonstrated these ideas, first, using the 1H-15N HSQC spectrum of Ubiquitin, and then application of these has been demonstrated for monitoring progression of fibrillation of the protein α-Synuclein, in absence and presence of safranal, a known inhibitor of fibrillation of the protein. The method is in general applicable to multidimensional NMR spectra, does not require extensive data collection, and allows quantitative assessment of spectral changes via a single parameter. We believe that the method will have wide ranging applications to monitor many biological phenomena, and will also be useful in an industrial environment for mass comparison of molecules in a rapid manner.

Brownian motion, spin diffusion and protein structure determination in solution.

This paper presents my recollections on the development of protein structure determination by NMR in solution from 1968 to 1992. The key to success was to identify NMR-accessible parameters that unambiguously determine the spatial arrangement of polypeptide chains. Inspired by work with cyclopeptides, model considerations showed that enforcing short non-bonding interatomic distances imposes «ring closure conditions¼ on polypeptide chains. Given that distances are scalar parameters, this indicated an avenue for studies of proteins in solution, i.e., under the regime of stochastic rotational and translational motions at frequencies in the nanosecond range (Brownian motion), where sharp pictures could not be obtained by photography-related methods. Later-on, we used distance geometry calculations with sets of inter-atomic distances derived from protein crystal structures to confirm that measurements of short proton-proton distances could provide atomic-resolution structures of globular proteins. During the years 1976-1984 the following four lines of research then led to protein structure determination by NMR in solution. First, the development of NMR experiments enabling the use of the nuclear Overhauser effect (NOE) for measurements of interatomic distances between pairs of hydrogen atoms in proteins. Second, obtaining sequence-specific resonance assignment solved the "phase problem" for protein structure determination by NMR. Third, generating and programming novel distance geometry algorithms enabled the calculation of atomic-resolution protein structures from limited sets of distance constraints measured by NMR. Fourth, the introduction of two-dimensional NMR provided greatly improved spectral resolution of the complex spectra of proteins as well as efficient delineation of scalar and dipole-dipole 1H-1H connectivities, thus making protein structure determination in solution viable and attractive.

A general strategy for the structural determination of carbohydrates by multi-dimensional NMR spectroscopies.

Two-dimensional NMR spectroscopies are one of the most frequently used techniques for the structural determination of carbohydrates. However, the data analysis is challenging because of the signal overlap in the 1H homonuclear correlation spectra. We attempted to explore a general strategy for the structural determination of carbohydrates by combined multi-dimensional spectroscopies. The strategy was applied to a human milk oligosaccharide lacto-N-difucohexaose I, that has been previously studied by conventional two-dimensional NMR spectroscopy. Assignment of the intra-residue resonances of the hexasaccharide using the three-dimensional spectrum was straightforward. Consequently, data analysis of the multi-dimensional spectra was significantly simplified, leading to a quicker determination of the intra- and inter-residue connections in the hexasaccharide. Application of the NMR strategy to chondroitin sulfate from bovine cartilage revealed two repeating disaccharide regions of the A and C units of chondroitin sulfate, indicating the high potential of this technique for the structural determination of complex polysaccharides.

NMR application in unconventional shale reservoirs - A new porous media research frontier.

Unconventional shale reservoirs have greatly contributed to the recent surge in petroleum production in the United States and are expected to lead the US oil production to a historical high in 2018. The complexity of the rocks and fluids in these reservoirs presents a significant challenge to the traditional approaches to the evaluation of geological formations due to the low porosity, permeability, complex lithology and fluid composition. NMR has emerged as the key measurement for evaluating these reservoirs, for quantifying their petrophysical parameters, fluid properties, and determining productivity. Measurement of the T1/T2 ratio by 2D NMR has been found to be critical for identifying the fluid composition of kerogen, bitumen, light/heavy oils, gases and brine in these formations. This paper will first provide a brief review of the theories of relaxation, measurement methods, and data inversion techniques and then will discuss several examples of applications of these NMR methods for understanding various aspects of the unconventional reservoirs. At the end, we will briefly discuss a few other topics, which are still in their developmental stages, such as solid state NMR, and their potential applications for shale rock evaluation.

INFOS: spectrum fitting software for NMR analysis.

Software for fitting of NMR spectra in MATLAB is presented. Spectra are fitted in the frequency domain, using Fourier transformed lineshapes, which are derived using the experimental acquisition and processing parameters. This yields more accurate fits compared to common fitting methods that use Lorentzian or Gaussian functions. Furthermore, a very time-efficient algorithm for calculating and fitting spectra has been developed. The software also performs initial peak picking, followed by subsequent fitting and refinement of the peak list, by iteratively adding and removing peaks to improve the overall fit. Estimation of error on fitting parameters is performed using a Monte-Carlo approach. Many fitting options allow the software to be flexible enough for a wide array of applications, while still being straightforward to set up with minimal user input.

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.

Toward optimal-resolution NMR of intrinsically disordered proteins.

Proteins, which, in their native conditions, sample a multitude of distinct conformational states characterized by high spatiotemporal heterogeneity, most often termed as intrinsically disordered proteins (IDPs), have become a target of broad interest over the past 15years. With the growing evidence of their important roles in fundamental cellular processes, there is an urgent need to characterize the conformational behavior of IDPs at the highest possible level. The unique feature of NMR spectroscopy in the context of IDPs is its ability to supply details of their structural and temporal alterations at atomic-level resolution. Here, we briefly review recently proposed NMR-based strategies to characterize transient states populated by IDPs and summarize the latest achievements and future prospects in methodological development. Because low chemical shift dispersion represents the major obstacle encountered when studying IDPs by nuclear magnetic resonance, particular attention is paid to techniques allowing one to approach the physical limits of attainable resolution.