(1)H and (13)C NMR studies of asymmetrically substituted bis- and tris-Tröger's bases

The (1)H and (13)C NMR spectra of two stereoisomeric bis-Tr?ger's bases and four stereoisomeric tris-Tr?ger's bases asymmetrically substituted on the external aromatic rings were recorded and the corresponding signals assigned. The relative configuration of the stereogenic units has been unequivocally determined on the basis of homoallylic couplings and NOE experiments.     

Demixing of severely overlapped H NMR resonances and interpretation of anomalous intensity pattern of dipolar coupled A3 spins in a weakly aligning medium

The increasing scientific and industrial interest towards metabonomics takes advantage from the high qualitative and quantitative information level of nuclear magnetic resonance (NMR) spectroscopy. However, several chemical and physical factors can affect the absolute and the relative position of an NMR signal and it is not always possible or desirable to eliminate these effects a priori. To remove misalignment of NMR signals a posteriori, several algorithms have been proposed in the literature. The icoshift program presented here is an open source and highly efficient program designed for solving signal alignment problems in metabonomic NMR data analysis. The icoshift algorithm is based on correlation shifting of spectral intervals and employs an FFT engine that aligns all spectra simultaneously. The algorithm is demonstrated to be faster than similar methods found in the literature making full-resolution alignment of large datasets feasible and thus avoiding down-sampling steps such as binning. The algorithm uses missing values as a filling alternative in order to avoid spectral artifacts at the segment boundaries. The algorithm is made open source and the Matlab code including documentation can be downloaded from www.models.life.ku.dk.     

Connectivity of a general class of inhomogeneous random digraphs

We study a family of directed random graphs whose arcs are sampled independently of each other, and are present in the graph with a probability that depends on the attributes of the vertices involved. In particular, this family of models includes as special cases the directed versions of the Erd?s‐Rényi model, graphs with given expected degrees, the generalized random graph, and the Poissonian random graph. We establish a phase transition for the existence of a giant strongly connected component and provide some other basic properties, including the limiting joint distribution of the degrees and the mean number of arcs. In particular, we show that by choosing the joint distribution of the vertex attributes according to a multivariate regularly varying distribution, one can obtain scale‐free graphs with arbitrary in‐degree/out‐degree dependence.     

The multicomponent discrete equation hierarchy with variable spectral parameters and a new integrable coupling system

This Letter reports on a study of the multicomponent discrete integrable equation hierarchy with variable spectral parameters. An instance of new multicomponent lattice equation is obtained. Correspondingly, a feasible way to construct the integrable couplings is presented. It indicates that the study of integrable couplings using the block matrix-form of Lie algebra is an important and effective method.     

Complete (1)H NMR spectral fingerprint of huperzine A

Complete analysis of the (1)H NMR spectrum of huperzine A, 1-amino-13-ethylidene-11-methyl-6-aza-tricyclo[7.3.1.0(2, 7)]trideca-2(7),3,10-trien-5-one, a Lycopodium alkaloid and anti-Alzheimer drug lead containing an ABCD(E)(MN)(OP)X(3)Y(3)-type system of 15 nonexchangeable proton spins, is reported for the first time, and earlier assignments are corrected. The complete (1)H parameter set of 11 chemical shifts clarifies the diastereotopism of both methylene groups, and provides a total of 38 observed H,H-couplings including 31 long-range ((4-6)J) connectivities. The NMR data is consistent with the comparatively rigid alicyclic backbone predicted by molecular mechanics calculations, and forms the basis for (1)H NMR fingerprint analysis for the purpose of dereplication, purity analysis, and elucidation of structural analogs.     

SESAME-HSQC for simultaneous measurement of NH and CH scalar and residual dipolar couplings

We present a novel pulse sequence, SESAME-HSQC, for the simultaneous measurement of several NH and CH scalar and residual dipolar couplings in double labeled proteins. The proposed Spin-statE Selective All Multiplicity Edited (SESAME)-HSQC combines gradient selected and sensitivity enhanced (15)N- and constant-time (13)C-HSQC experiments with the recently introduced spin-state selective method (Nolis et al., J. Magn. Reson. 180 (2006) 39-50) for measuring couplings simultaneously at amide and aliphatic regions. Excellent resolution and high sensitivity is warranted by removing all coupling interactions during the indirectly detected t(1) period, and by employing pulsed field gradients for coherence selection and utilizing coherence order selective spin-state selection. The scalar and residual dipolar couplings can be readily measured from a two-dimensional (15)N/(13)C-HSQC spectrum without additional spectral crowding. SESAME-HSQC can be used for epitope mapping by observing chemical shift changes in both amide and aliphatic regions. Simultaneously, potential conversion in protein conformation can be probed by analyzing changes in residual dipolar couplings induced by ligand binding. The pulse sequence is experimentally verified with a sample of (15)N/(13)C enriched human ubiquitin. The internuclear vector directions determined from the residual dipolar couplings are found to be in excellent correlation with those predicted from ubiquitin's refined solution structure.     

An Investigation of Poly(dimethylsiloxane) Chain Dynamics and Order in Its Inclusion Compound with γ‐Cyclodextrin by Fast‐MAS Solid‐State NMR Spectroscopy

The dynamics of poly(dimethylsiloxane) in its inclusion compound with γ‐cyclodextrin are elucidated using modern fast‐MAS solid‐state NMR techniques. Measurements of methyl ¹H–¹H and ¹H–¹³C dipolar coupling constants indicate that the polymer undergoes a uniform motion, rendering all methyl groups equivalent. The dynamics of the Si—C bond is characterized by either a dynamic order parameter of S = 0.72, or, assuming a stably rotating helical structure, an inclination angle of 73° relative to the rotation axis.     

Two new integrable couplings of the soliton hierarchies with self-consistent sources

A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with sl(4) has been presented (Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6613). Based on this method, we construct two integrable couplings of the soliton hierarchy with self-consistent sources by using the loop algebra sl(4). In this paper, we also point out that there are some errors in these references and we have corrected these errors and set up new formula. The method can be generalized to other soliton hierarchy with self-consistent sources.