Algebraic constructions in the category of vector bundles

The category of generalized Lie algebroids is presented. We obtain an exterior differential calculus for generalized Lie algebroids. In particular, we obtain similar results with the classical and modern results for Lie algebroids. So, a new result of Maurer-Cartan type is presented. Supposing that any vector subbundle of the pullback vector bundle of a generalized Lie algebroid is called interior differential system (IDS) for that generalized Lie algebroid, a theorem of Cartan type is obtained. Extending the classical notion of exterior differential system (EDS) to generalized Lie algebroids, a theorem of Cartan type is obtained. Using the theory of linear connections of Ehresmann type presented in the paper [1], the identities of Cartan and Bianchi type are presented.Comment: 29 page

Mechanical Systems in the Generalized Lie Algebroids Framework

\emph{Mechanical systems} called by use, \emph{mechanical}$\left(\rho ,\eta\right)$\emph{-systems, Lagrange mechanical}$\left(\rho ,\eta \right)$\emph{-systems} or \emph{Finsler mechanical}$\left(\rho ,\eta \right)$\emph{-systems} are presented. The canonical $\left(\rho ,\eta \right)$\emph{-}semi(spray) associated to a mechanical $\left(\rho ,\eta \right)$-system is obtained. New and important results are obtained in the particular case of Lie algebroids. The Lagrange mechanical $(\rho ,\eta)$% -systems are the spaces necessary to develop a new Lagrangian formalism. We obtain the $(\rho ,\eta)$-semispray associated to a regular Lagrangian $L$ and external force $F_{e}$ and we derive the equations of Euler-Lagrange type. So, a new solution for the Weinstein's Problem in the general framework of generalized Lie algebroids is presented.Comment: 43 pages International journal of Geometric Methods in Modern Physics, 2013. arXiv admin note: substantial text overlap with arXiv:1108.2844, arXiv:1007.1541, arXiv:1109.1242, arXiv:1101.0960, arXiv:1108.505

Superantigen architecture: Functional decoration on a conserved scaffold

A defining and consistent feature of the bacterial superantigens from Staphylococcus aureus and Streptococcus pyogenes is their strongly conserved three-dimensional structure. Structural studies to date show that the array of more than 280 amino acid sequences known for superantigens (SAgs) and staphylococcal superantigen-like (SSL) proteins all have the same fold-a structure in which the same three-dimensional arrangement of α-helices and β-sheets is traced by each amino acid sequence, with the same topology (for recent reviews, see references 29 and 43). A typical SAg structure comprises two domains-an N-terminal β -barrel domain called an OB-fold (4, 25) and a C-terminal β-grasp domain in which a long α-helix packs on to a mixed parallel and antiparallel β-sheet. These two domains are traversed by an α-helix that lies at the N terminus of the protein and packs against the β-grasp domain, thus linking the N- and C-terminal domains

Weyl's Theory in the Generalized Lie Algebroids Framework

The geometry of the Lie algebroid generalized tangent bundle of a generalized Lie algebroid is developed. Formulas of Ricci type and identities of Cartan and Bianchi type are presented. Introducing the notion of geodesic of a mechanical $\left( \rho ,\eta \right)$-system with respect to a $(\rho, \eta)$-spray, the Berwald $(\rho, \eta)$-derivative operator and its mixed curvature, we obtain main results to conceptualize the Weyl's method in this general framework. Finally, we obtain two new results of Weyl type for the geometry of mechanical $\left( \rho ,\eta \right)$-systems

Infinite stacking of alternating polyfluoroaryl rings and bromide anions

The crystal structure of 1-(4-bromo-2,3,5,6-tetrafluorophenyl)-3-benzylimidazolium bromide comprises columns of parallel bromotetrafluorophenyl rings with an interplanar distance of 6.936(6) Å separated by bromide anions

Expression and purification of an adenylation domain from a eukaryotic nonribosomal peptide synthetase: Using structural genomics tools for a challenging target

Nonribosomal peptide synthetases (NRPSs) are large multimodular and multidomain enzymes that are involved in synthesising an array of molecules that are important in human and animal health. NRPSs are found in both bacteria and fungi but most of the research to date has focused on the bacterial enzymes. This is largely due to the technical challenges in producing active fungal NRPSs, which stem from their large size and multidomain nature. In order to target fungal NRPS domains for biochemical and structural characterisation, we tackled this challenge by using the cloning and expression tools of structural genomics to screen the many variables that can influence the expression and purification of proteins. Using these tools we have screened 32 constructs containing 16 different fungal NRPS domains or domain combinations for expression and solubility. Two of these yielded soluble protein with one, the third adenylation domain of the SidN NRPS (SidNA3) from the grass endophyte Neotyphodium lolii, being tractable for purification using Ni-affinity resin. The initial purified protein exhibited poor solution behaviour but optimisation of the expression construct and the buffer conditions used for purification, resulted in stable recombinant protein suitable for biochemical characterisation, crystallisation and structure determination