Synthetic UDP-furanoses as potent inhibitors of mycobacterial galactan biogenesis

UDP-galactofuranose (UDP-Galf) is a substrate for two types of enzymes, UDP-galactopyranose mutase and galactofuranosyltransferases, which are present in many pathogenic organisms but absent from mammals. In particular, these enzymes are involved in the biosynthesis of cell wall galactan, a polymer essential for the survival of the causative agent of tuberculosis, Mycobacterium tuberculosis. We describe here the synthesis of derivatives of UDP-Galf modified at C-5 and C-6 using a chemoenzymatic route. In cell-free assays, these compounds prevented the formation of mycobacterial galactan, via the production of short "dead-end" intermediates resulting from their incorporation into the growing oligosaccharide chain. Modified UDP-furanoses thus constitute novel probes for the study of the two classes of enzymes involved in mycobacterial galactan assembly, and studies with these compounds may ultimately facilitate the future development of new therapeutic agents against tuberculosis.     

Breather Solutions in Periodic Media

For nonlinear wave equations existence proofs for breathers are very rare. In the spatially homogeneous case up to rescaling the sine-Gordon equation \({\partial^2_t u = \partial^2_x u - \sin (u)}\) is the only nonlinear wave equation which is known to possess breather solutions. For nonlinear wave equations in periodic media no examples of breather solutions have been known so far. Using spatial dynamics, center manifold theory and bifurcation theory for periodic systems we construct for the first time such time periodic solutions of finite energy for a nonlinear wave equation

$ s(x) \partial^2_t u(x,t) = \partial^2_x u(x,t) - q(x) u(x,t)+ r(x)u(x,t)^3, $

with spatially periodic coefficients s, q, and r on the real axis. Such breather solutions play an important role in theoretical scenarios where photonic crystals are used as optical storage.

     

Validity of the KdV equation for the modulation of periodic traveling waves in the NLS equation

Bethuel et al.  and  and Chiron and Rousset [3] gave very nice proofs of the fact that slow modulations in time and space of periodic wave trains of the NLS equation can approximately be described via solutions of the KdV equation associated with the wave train. Here we give a much shorter proof of a slightly weaker result avoiding the very detailed and fine analysis of ,  and . Our error estimates are based on a suitable choice of polar coordinates, a Cauchy–Kowalevskaya-like method, and energy estimates.     

Algebraic properties of classes of path ideals of posets

We consider path ideals associated to special classes of posets such as tree posets and cycles. We express their property of being sequentially Cohen–Macaulay in terms of the underlying poset. Moreover, monomial ideals, which arise in algebraic statistics from the Luce-decomposable model and the ascending model, can be viewed as path ideals of certain posets. We study invariants of these so-called Luce-decomposable monomial ideals and ascending ideals for diamond posets and products of chains. In particular, for these classes of posets, we explicitly compute their Krull dimension, their projective dimension, their Castelnuovo–Mumford regularity and their Betti numbers.     

Numerical test of Born–Oppenheimer approximation in chaotic systems

We study the validity of the Born–Oppenheimer approximation in chaotic dynamics. Using numerical solutions of autonomous Fermi accelerators, we show that the general adiabatic conditions can be interpreted as the narrowness of the chaotic region in phase space.     

Asymmetric benzoin reaction catalyzed by benzoylformate decarboxylase

Aromatic aldehydes are converted into benzoins by benzoylformate decarboxylase catalyzed C–C bond formation. The reaction affords (R)-benzoins with high enantiomeric excess and in good chemical yields. A broad range of aromatic aldehydes can be used as substrates in aqueous buffer or buffer/DMSO-solutions.     

Hyperbranched polymers as scaffolds for multifunctional reversible addition–fragmentation chain‐transfer agents: A route to polystyrene‐core‐polyesters and polystyrene‐block‐poly(butyl acrylate)‐core‐polyesters

Polydisperse hyperbranched polyesters were modified for use as novel multifunctional reversible addition–fragmentation chain‐transfer (RAFT) agents. The polyester‐core‐based RAFT agents were subsequently employed to synthesize star polymers of n‐butyl acrylate and styrene with low polydispersity (polydispersity index < 1.3) in a living free‐radical process. Although the polyester‐core‐based RAFT agent mediated polymerization of n‐butyl acrylate displayed a linear evolution of the number‐average molecular weight (M_n) up to high monomer conversions (>70%) and molecular weights [M_n > 140,000 g mol^?1, linear poly(methyl methacrylate) equivalents)], the corresponding styrene‐based system reached a maximum molecular weight at low conversions (≈30%, M_n = 45,500 g mol^?1, linear polystyrene equivalents). The resulting star polymers were subsequently used as platforms for the preparation of star block copolymers of styrene and n‐butyl acrylate with a polyester core with low polydispersities (polydispersity index < 1.25). The generated polystyrene‐based star polymers were successfully cast into highly regular honeycomb‐structured microarrays. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3847–3861, 2003