Extracting Ramachandran torsional angle distributions from 2D NMR data using Tikhonov regularization /

Solid state nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for studying structural and dynamical properties of disordered and partially ordered materials, such as glasses, polymers, liquid crystals, and biological materials. In particular, twodimensional( 2D) NMR methods such as ^^C-^^C correlation spectroscopy under the magicangle- spinning (MAS) conditions have been used to measure structural constraints on the secondary structure of proteins and polypeptides. Amyloid fibrils implicated in a broad class of diseases such as Alzheimer's are known to contain a particular repeating structural motif, called a /5-sheet. However, the details of such structures are poorly understood, primarily because the structural constraints extracted from the 2D NMR data in the form of the so-called Ramachandran (backbone torsion) angle distributions, g{^,'4)), are strongly model-dependent. Inverse theory methods are used to extract Ramachandran angle distributions from a set of 2D MAS and constant-time double-quantum-filtered dipolar recoupling (CTDQFD) data. This is a vastly underdetermined problem, and the stability of the inverse mapping is problematic. Tikhonov regularization is a well-known method of improving the stability of the inverse; in this work it is extended to use a new regularization functional based on the Laplacian rather than on the norm of the function itself. In this way, one makes use of the inherently two-dimensional nature of the underlying Ramachandran maps. In addition, a modification of the existing numerical procedure is performed, as appropriate for an underdetermined inverse problem. Stability of the algorithm with respect to the signal-to-noise (S/N) ratio is examined using a simulated data set. The results show excellent convergence to the true angle distribution function g{(j),ii) for the S/N ratio above 100.

Simultaneous extraction of order parameters and orientational distribution fuctions from 31[superscript]P NMR spectra of magnetically partially oriented phospholipid bilayers

Order parameter profiles extracted from the NMR spectra of model membranes are a valuable source of information about their structure and molecular motions. To al1alyze powder spectra the de-Pake-ing (numerical deconvolution) ~echnique can be used, but it assumes a random (spherical) dist.ribution of orientations in the sample. Multilamellar vesicles are known to deform and orient in the strong magnetic fields of NMR magnets, producing non-spherical orientation distributions. A recently developed technique for simultaneously extracting the anisotropies of the system as well as the orientation distributions is applied to the analysis of partially magnetically oriented 31p NMR spectra of phospholipids. A mixture of synthetic lipids, POPE and POPG, is analyzed to measure distortion of multilamellar vesicles in a magnetic field. In the analysis three models describing the shape of the distorted vesicles are examined. Ellipsoids of rotation with a semiaxis ratio of about 1.14 are found to provide a good approximation of the shape of the distorted vesicles. This is in reasonable agreement with published experimental work. All three models yield clearly non-spherical orientational distributions, as well as a precise measure of the anisotropy of the chemical shift. Noise in the experimental data prevented the analysis from concluding which of the three models is the best approximation. A discretization scheme for finding stability in the algorithm is outlined

Solid state NMR chemical shifts as an alternative to diffraction data in the determination of SIC polytypic structures

Silicon carbide, which has many polytypic modifications of a very simple and very symmetric structure, is an excellent model system for exploring, the relationship between chemical shift, long-range dipolar shielding, and crystal structure in network solids. A simple McConnell equation treatment of bond anisotropy effects in a poly type predicts chemical shifts for silicon and carbon sites which agree well with the experiment, provided that contributions from bonds up to 100 A are included in the calculation. The calculated chemical shifts depend on three factors: the layer stacking sequence, electrical centre of gravity, and the spacings between silicon and carbon layers. The assignment of peaks to lattice sites is proved possible for three polytypes (6H, 15R, and 3C). The fact that the calculated chemical shifts are very sensitive to layer spacings provides us a potential way to detennine and refine a crystal structure. In this work, the layer spacings of 6H SiC have been calculated and are within X-ray standard deviations. Under this premise, the layer spacings of 15R have been detennined. 29Si and 13C single crystal nmr studies of 6H SiC polytype indicate that all silicons and carbons are magnetically anisotropic. The relationship between a magnetic shielding tensor component and layer spacings has been derived. The comparisons between experimental and semi-empirical chemical shielding tensor components indicate that the paramagnetic shielding of silicon should be included in the single crystal chemical shift calculation.

Half-sandwich silane complexes of ruthenium and iron : synthesis, structure and application to catalysis

The present thesis describes syntheses, structural studies, and catalytic reactivity of new non-classical silane complexes of ruthenium and iron. The ruthenium complexes CpRu(PPri3)CI(T]2-HSiR3) (1) (SiR3 = SiCh (a), SiClzMe (b), SiCIMe2 (c), SiH2Ph (d), SiMe2Ph (e» were prepared by reactions of the new unsaturated complex CpRu(PPri3)CI with silanes. According to NMR studies and X-ray analyses, the complexes la-c exhibit unusual simultaneous Si··· H and Si··· CI-Ru interactions. The complex CpRu(PPri3)CI was also used for the preparation of the first examples of late transition metal agostic silylamido complexes CpRu(PPri3)(N(T]2-HSiMe2)R) (2) (R= Ar or But), which were characterized by NMR spectroscopy. The iron complexes CpFe(PMePri2)H2(SiR3) (3) (SiR3 = SiCh (a), SiClzMe (b), SiCIMe2 (c), SiH2Ph (d), SiMe2Ph (e» were synthesized by the reaction of the new borohydride iron complex CpFe(PMePri2)(B~) with silanes in the presence NEt3. The complexes 3 exhibit unprecedented two simultaneous and equivalent Si··· H interactions, which was confirmed by X-ray analyses and DFT calculations. A series of cationic ruthenium complexes [CpRu(PR3)(CH3CN)(112-HSiR'3)]BAF (PR3 = PPri 3 (4), PPh3 (5); SiR'3 = SiCh (a), SiClzMe (b), SiClMe2 (c), SiH2Ph (d), SiMe2Ph (e» was obtained by substitution of one of the labile acetonitrile ligands in [CpRu(PR3)(CH3CNh]BAF with sHanes. Analogous complexes [TpRu(PR3)(CH3CN)(T]2 -HSiR' 3)]BAF (5) were obtained by the reaction of TpRu(PR3)(CH3CN)CI with LiBAF in the presence of silanes. The complexes 4-5 were characterized by NMR spectroscopy, and the observed coupling constants J(Si-H) allowed us to estimate the extent of Si-H bond activation in these compounds. The catalytic activity in hydrosilylation reactions of all of the above complexes was examined. The most promising results were achieved with the cationic ruthenium precatalyst [CpRu(PPri3)(CH3CN)2t (6). Complex 6 shows good to excellent catalytic activity in the hydrosilylation of carbonyls, dehydrogenative coupling of silanes with alcohols, amines, acids, and reduction of acid chlorides. We also discovered very selective reduction of nitriles and pyridines into the corresponding N-silyl imines and l,4-dihydropyridines, respectively, at room temperature with the possibility of catalyst recycling. These chemoselective catalytic methods have no analogues in the literature. The reactions were proposed to proceed via an ionic mechanism with intermediate formation of the silane a-complexes 4.