On the relation between rotation increments in different tangent spaces

In computational mechanics, finite rotations are often represented by rotation vectors. Rotation vector increments corresponding to different tangent: spaces are generally related by a linear operator, known as the tangential transformation T. In this note, we derive the higher order terms that are usually left out in linear relation. The exact nonlinear relation is also presented. Errors via the linearized T are numerically estimated. While the concept of T arises out of the nonlinear characteristics of the rotation manifold, it has been derived via tensor analysis in the context of computational mechanics (Cardona and Geradin, 1988). We investigate the operator T from a Lie group perspective, which provides a better insight and a 1-1 correspondence between approaches based on tensor analysis and the standard matrix Lie group theory. (C) 2010 Elsevier Ltd. All rights reserved.

Identification and characterization of a library of microheterogeneous cyclohexa-depsipeptides from the fungus

Ten new cyclic hexadepsipeptides, six isariins and four isaridins, from the fungus Isaria have been identified and characterized by high-performance liquid chromatography, coupled to tandem electrospray ionization mass spectrometry (LC-ESIMS/MS). The isariins possess a beta-hydroxy acid residue and five alpha-amino acids, while isaridins contain a beta-amino acid, an alpha-hydroxy acid, and four alpha-amino acids. One- and two-dimensional NMR spectroscopy confirmed the chemical identity of some of the isariin fractions. Mass spectral fragmentation patterns of [M + H](+) ions reveal clear diagnostic fragment ions for the isariins and isaridins. Previously described cyclic depsipeptides, isarfelins from Isaria felina (Guo, Y. X.; Liu, Q. H.; Ng, T. B.; Wang H. X. Peptides 2005, 26, 2384), are now reassigned as members of the isaridin family. Examination of isaridin sequences revealed significant similarities with cyclic hexadepsipeptides such as destruxins and roseotoxins. The structure of an isariin (isariin A) investigated by NMR spectroscopy indicated the presence of a hybrid alpha beta C-11 turn, formed by the beta-hydroxy acid and glycine residues and a (D)Leu-(L)Ala type II' beta-turn. Additionally, the inhibitory effect of isariins and an isaridin on the intra-erythrocytic growth of Plasmodium falciparum is presented.