On polynomial symbols for subdivision schemes

Given a dilation matrix A :ℤ^d→ℤ^d, and G a complete set of coset representatives of 2π(A ^−Tℤ^d/ℤ^d), we consider polynomial solutions M to the equation ∑ _g∈G M(ξ+g)=1 with the constraints that M≥0 and M(0)=1. We prove that the full class of such functions can be generated using polynomial convolution kernels. Trigonometric polynomials of this type play an important role as symbols for interpolatory subdivision schemes. For isotropic dilation matrices, we use the method introduced to construct symbols for interpolatory subdivision schemes satisfying Strang–Fix conditions of arbitrary order. Research partially supported by the Danish Technical Science Foundation, Grant No. 9701481, and by the Danish SNF-PDE network.     

Asymptotic densities of Maass newforms

We define the counting function for Maass newforms of Hecke congruence groups and calculate the three main terms of this counting function. We then give necessary and sufficient conditions for this expansion to have the same shape as if it were counting eigenvalues related to cocompact surfaces. We relate the result to classical instances of the Jacquet-Langlands correspondence.     

Multi-Wavelength Optical Packet Routing Technologies Based on Superstructured Fiber Bragg Gratings

A WDM compatible Edge-to-Edge Self-Routed optical packet switched network that simplifies the optical processing is proposed. The system employs all-optical packet label generation and recognition using coded superstructured Fiber Bragg gratings.     

1H detection in MAS solid-state NMR spectroscopy of biomacromolecules employing pulsed field gradients for residual solvent suppression

In this communication, we demonstrate the feasibility of 1H detection in MAS solid-state NMR for a microcrystalline, uniformly 2H,15N-labeled sample of a SH3 domain of chicken alpha-spectrin, using pulsed field gradients for suppression of water magnetization. Today, B0 gradients are employed routinely in solution-state NMR for coherence order selection and solvent suppression. We suggest to use gradients to purge water magnetization which cannot be suppressed using conventional water suppression schemes. The achievable gain in sensitivity for 1H detection is in the order of 5 compared to the 15N detected version of the experiment (at a MAS rotation frequency of 13.5 kHz). We expect that this labeling concept which achieves high sensitivity due to 1H detection, in combination with the possibility to measure long range 1H-1H distances as we have shown previously, to be a useful tool for the determination of protein structures in the solid state.     

SPOCC-194, a new high functional group density PEG-based resin for solid-phase organic synthesis

A novel polymer matrix for solid-phase synthesis, SPOCC(194) resin (1), was designed featuring a backbone of homogeneous tetraethylene glycol (TEG(194)) macromonomer linked by quaternary carbon junctions and terminating in primary alcohol functionality. Beaded SPOCC(194) resin was effectively prepared by suspension polymerization of oxetanylated TEG macromonomer 5 in stirred silicon oil. Mechanically stable and inert to a diverse range of reaction conditions, SPOCC(194) possessed a high hydroxyl group loading (0.9-1.2 mmol/g) for substrate attachment and swelled effectively ( approximately 2-4 mL/g) in a variety of organic and aqueous solvents. Developed for solid-phase synthesis at high reactant concentrations for driving organic and aqueous reactions to completion, SPOCC(194) exhibited high functional group density (mmol/mL) similar to that of low-loaded aminomethylated polystyrene-divinylbenzene copolymer (PS-1%DVB) yet significantly higher than that of PEGA(1900), SPOCC(1500), and TentaGel S. High-resolution MAS NMR spectra of Fmoc-derivatized SPOCC(194) indicate that monitoring of functional group transformation is possible. Moreover, by employment of a nonaromatic resin-linker combination, electrophilic chemistry, such as Lewis acid catalyzed glycosylation and Friedel-Crafts acylation, was selectively performed on substrate bound to SPOCC(194) resin. Such properties make SPOCC(194) resin a promising new polymer matrix for the support-bound construction of small organic molecules by parallel and combinatorial synthesis and the scavenging of solution-phase reactants or byproducts.     

An Aldehyde Responsive,Cleavable Linker for Glucose Responsive Insulins

A glucose responsive insulin (GRI) that responds to changes in blood glucose concentrations has remained an elusive goal. Here we describe the development of glucose cleavable linkers based on hydrazone and thiazolidine structures. We developed linkers with low levels of spontaneous hydrolysis but increased level of hydrolysis with rising concentrations of glucose, which demonstrated their glucose responsiveness in vitro. Lipidated hydrazones and thiazolidines were conjugated to the LysB29 side-chain of HI by pH-controlled acylations providing GRIs with glucose responsiveness confirmed in vitro for thiazolidines. Clamp studies showed increased glucose infusion at hyperglycemic conditions for one GRI indicative of a true glucose response. The glucose responsive cleavable linker in these GRIs allow changes in glucose levels to drive the release of active insulin from a circulating depot. We have demonstrated an unprecedented, chemically responsive linker concept for biopharmaceuticals.     

Investigating the Disordered and Membrane-Active Peptide A-Cage-C Using Conformational Ensembles

The driving forces and conformational pathways leading to amphitropic protein-membrane binding and in some cases also to protein misfolding and aggregation is the subject of intensive research. In this study, a chimeric polypeptide, A-Cage-C, derived from α-Lactalbumin is investigated with the aim of elucidating conformational changes promoting interaction with bilayers. From previous studies, it is known that A-Cage-C causes membrane leakages associated with the sporadic formation of amorphous aggregates on solid-supported bilayers. Here we express and purify double-labelled A-Cage-C and prepare partially deuterated bicelles as a membrane mimicking system. We investigate A-Cage-C in the presence and absence of these bicelles at non-binding (pH 7.0) and binding (pH 4.5) conditions. Using in silico analyses, NMR, conformational clustering, and Molecular Dynamics, we provide tentative insights into the conformations of bound and unbound A-Cage-C. The conformation of each state is dynamic and samples a large amount of overlapping conformational space. We identify one of the clusters as likely representing the binding conformation and conclude tentatively that the unfolding around the central W23 segment and its reorientation may be necessary for full intercalation at binding conditions (pH 4.5). We also see evidence for an overall elongation of A-Cage-C in the presence of model bilayers.     

Single‐Molecule Fluorescence Detection of a Synthetic Heparan Sulfate Disaccharide

The first single‐molecule fluorescence detection of a structurally‐defined synthetic carbohydrate is reported: a heparan sulfate (HS) disaccharide fragment labeled with Alexa488. Single molecules have been measured whilst freely diffusing in solution and controlled encapsulation in surface‐tethered lipid vesicles has allowed extended observations of carbohydrate molecules down to the single‐molecule level. The diverse and dynamic nature of HS–protein interactions means that new tools to investigate pure HS fragments at the molecular level would significantly enhance our understanding of HS. This work is a proof‐of‐principle demonstration of the feasibility of single‐molecule studies of synthetic carbohydrates which offers a new approach to the study of pure glycosaminoglycan (GAG) fragments.     

Click Chemistry Mediated Functionalization of Vertical Nanowires for Biological Applications

Semiconductor nanowires (NWs) are gaining significant importance in various biological applications, such as biosensing and drug delivery. Efficient and controlled immobilization of biomolecules on the NW surface is crucial for many of these applications. Here, we present for the first time the use of the Cu^I‐catalyzed alkyne–azide cycloaddition and its strain‐promoted variant for the covalent functionalization of vertical NWs with peptides and proteins. The potential of the approach was demonstrated in two complementary applications of measuring enzyme activity and protein binding, which is of general interest for biological studies. The attachment of a peptide substrate provided NW arrays for the detection of protease activity. In addition, green fluorescent protein was immobilized in a site‐specific manner and recognized by antibody binding to demonstrate the proof‐of‐concept for the use of covalently modified NWs for diagnostic purposes using minute amounts of material.