Inverse methods in two-dimensional NMR spectral analysis

On the inversion of diffusion NMR data: Tikhonov regularization and optimal choice of the regularization parameter

The analysis of diffusion NMR data in terms of distributions of diffusion coefficients is hampered by the ill-posed nature of the required inverse Laplace transformation. Naïve approaches such as multiexponential fitting or standard least-squares algorithms are numerically unstable and often fail. This paper updates the CONTIN approach of the application of Tikhonov regularization to stabilise this numerical inversion problem and demonstrates two methods for automatically choosing the optimal value of the regularization parameter. These approaches are computationally efficient and easy to implement using standard matrix algebra techniques. Example analyses are presenting using both synthetic data and experimental results of diffusion NMR studies on the azo-dye sunset yellow and some polymer molecular weight reference standards.

Use of inverse theory algorithms in the analysis of biomembrane NMR data

Treating the analysis of experimental spectroscopic data as an inverse problem and using regularization techniques to obtain stable pseudoinverse solutions, allows access to previously unavailable level of spectroscopic detail. The data is mapped into an appropriate physically relevant parameter space, leading to better qualitative and quantitative understanding of the underlying physics, and in turn, to better and more detailed models. A brief survey of relevant inverse methods is illustrated by several successful applications to the analysis of nuclear magnetic resonance data, yielding new insight into the structure and dynamics of biomembrane lipids.

A DOQSY approach for the elucidation of torsion angle distributions in biopolymers: application to silk

Silk from the wild silkworm Samia cynthia ricini with a molecular mass of about 300kDa consists of alternating repeats of nano-crystalline poly-(Ala) and non-crystalline glycine-rich domains. The backbone torsion angles between pairs of these two amino acids is determined by DOQSY solid-state NMR spectroscopy: the alanine-rich domains are predominantly in a beta-sheet conformation, whereas the glycine-rich domains are found to be partially in an extended beta-sheet conformation and partially in an approximately 3(1)-helical conformation. In the cast film from liquid silk significantly different secondary structures were found: the alanine-rich domains are alpha-helical conformation, whereas the results for glycine-labelled sample are explained by a random-coil state. A detailed error analysis of the technique is presented.

Orientational deconvolution of two-dimensional static disorder by a Tikhonov regularized method for 2H solid state NMR of nano-tubular-oriented structures

A general trend of supramolecular chemistry is the building of mesoscopic-oriented nanotubes. When the typical radius of the channel almost fits the mean supramolecular cross-sectional radius, the guest supramolecule is ultraconfined in the channel. In that case, only rotational disorder around the channel axis is allowed. For sufficiently low temperatures, we expect this 2D disorder to be static on the NMR timescale, and it should reflect the local symmetry of the channels. In this article, we show that experiments performed with deuterium single crystal solid-state NMR as a function of rotation around the channel axis may lead to important information concerning the static orientational disorder of the confined supramolecules. Using an inversion method with Tikhonov regularization and a positivity constraint, that also takes into account of the nonideal pulse sequence response, the orientational probability density can be obtained from 1D experiments performed at different angles, even for significant disorder. As a first step, the method is validated on four different theoretical distributions. It is then applied to 2H NMR single crystal experiments performed on an archetype of parallel channels intergrowth compounds: selectively deuterated 1,10-decanedicarboxylic diacids in hydrogenated urea channels. The diacids form one-dimensional infinite hydrogen-bonded chains ultraconfined in urea linear channels.

Chemical shift correlations in disordered solids

We show how two-dimensional chemical shift conditional probability distributions can be extracted from experimental NMR correlation spectra of disordered solids. We show that transverse dephasing times are of central importance in determining the resolution (and sensitivity) of these probability distributions. These conditional probability distributions provide a new source of structural information characteristic of disordered solids, which is much more sensitive to structure than the individual-atom chemical shift distributions. The structural information contained in these distributions is clearly a potentially extremely rich source for understanding disorder. This is illustrated with examples of a phosphorus-containing organic compound and with a sample of disordered cellulose where the different structural allomorphs present are identified from the distributions.