A family of macrocyclic antibiotics with a mixed peptide-peptoid beta-hairpin backbone conformation

Macrocyclic peptidomimetics having a mixed peptide-peptoid backbone have been synthesized and shown to possess antibiotic activity against gram-positive and -negative bacteria with a low hemolytic activity against human erythrocytes; one is shown to adopt a regular beta-hairpin conformation by NMR in aqueous solution.     

Non-covalent stabilization of a beta-hairpin peptide into liposomes

An oligopeptide modified on both the N- and C-termini with hydrophobic moieties was prepared on a solid phase and anchored into a liposome, stabilizing the fold of the peptide into a beta-hairpin, which would otherwise be a random coil.     

Monitoring and fast detection of mycotoxin-producing fungi based on headspace solid-phase microextraction and headspace sorptive extraction of the volatile metabolites

Solid phase microextraction in combination with capillary GC-MS was used as monitoring technique for the collection and detection of the fungal volatile metabolite (+)-aristolochene by sporulated surface cultures of Penicillium roqueforti. A comparison was made between different toxigenic and nontoxigenic strains of P. roqueforti. Different growth conditions and media, such as malt extract agar, potato dextrose agar and sabouraud dextrose agar were compared. Whereas toxigenic strains produced large amounts of (+)-aristolochene, beta-elemene, valencene and germacrene A, nontoxigenic P. roqueforti strains showed a remarkably different headspace profile, in which ethyl-2-hexenoate, E-beta-caryophyllene, aromadendrene and beta-patchoulene were the predominant volatiles, apart from other sesquiterpene hydrocarbons present at lower concentrations. Stir bar sorptive extraction, was also applied in the headspace sampling mode, i.e. headspace sorptive extraction (HSSE) for the enrichment of fungal volatiles from sporulated surface cultures to differentiate between toxigenic and nontoxigenic fungi. Hence, it can be concluded that headspace analysis of volatile fungal metabolites by SPME and HSSE in combination with capillary GC-MS is a suitable monitoring technique for the fast detection of mycotoxin producing fungi.     

A continuous parametric shape model

In this paper we propose a flexible continuous parametric shape model for star-shaped planar objects. The model is based on a polar Fourier expansion of the normalized radius-vector function. The expected phase amplitudes are modelled by a simple regression with parameters having nice geometric interpretations. The suggestedgeneralized p-order model is an extension of first- and second-order Gaussian shape models, and in particular the Gaussian assumption is relaxed. The statistical analysis is straightforward, as demonstrated by an application concerning shape discrimination of two cell nuclei populations.     

Graphs that are not complete pluripolar

Let be domains in . Under very mild conditions on we show that there exist holomorphic functions , defined on with the property that is nowhere extendible across , while the graph of over is not complete pluripolar in . This refutes a conjecture of Levenberg, Martin and Poletsky (1992).

     

Effects of uncertainties in the domain on the solution of Dirichlet boundary value problems

Summary. A domain with possibly non-Lipschitz boundary is defined as a limit of monotonically expanding or shrinking domains with Lipschitz boundary. A uniquely solvable Dirichlet boundary value problem (DBVP) is defined on each of the Lipschitz domains and the limit of these solutions is investigated. The limit function also solves a DBVP on the limit domain but the problem can depend on the sequences of domains if the limit domain is unstable with respect to the DBVP. The core of the paper consists in estimates of the difference between the respective solutions of the DBVP on two close domains, one of which is Lipschitz and the other can be unstable. Estimates for starshaped as well as rather general domains are derived. Their numerical evaluation is possible and can be done in different ways. Received October 16, 2001 / Revised version received January 16, 2002 / Published online: April 17, 2002 RID="*" ID="*" The research was funded partially by the National Science Foundation under the grants NSF–Czech Rep. INT-9724783 and NSF DMS-9802367 RID="**" ID="**" Support for Jan Chleboun coming from the Grant Agency of the Czech Republic through grant 201/98/0528 is appreciated     

Porous sets that are Haar null, and nowhere approximately differentiable functions

We define a new notion of ``HP-small' set which implies that is both -porous and Haar null in the sense of Christensen. We show that the set of all continuous functions on which have finite unilateral approximate derivative at a point is HP-small, as well as its projections onto hyperplanes. As a corollary, the same is true for the set of all Besicovitch functions. Also, the set of continuous functions on which are Hölder at a point is HP-small.