On the regime of localized excitations for disordered oscillator systems

Letters in Mathematical Physics - We study quantum oscillator lattice systems with disorder, in arbitrary dimension, requiring only partial localization of the associated effective one-particle...     

Homology for higher-rank graphs and twisted C⁎-algebras

We introduce a homology theory for k-graphs and explore its fundamental properties. We establish connections with algebraic topology by showing that the homology of a k-graph coincides with the homology of its topological realisation as described by Kaliszewski et al. We exhibit combinatorial versions of a number of standard topological constructions, and show that they are compatible, from a homological point of view, with their topological counterparts. We show how to twist the $C^{?}$-algebra of a k-graph by a $\mathbb{T}$-valued 2-cocycle and demonstrate that examples include all noncommutative tori. In the appendices, we construct a cubical set $\stackrel{?}{Q}(\Lambda )$ from a k-graph Λ and demonstrate that the homology and topological realisation of Λ coincide with those of $\stackrel{?}{Q}(\Lambda )$ as defined by Grandis.     

Dissolution-guided wetting for microarray and microfluidic devices

The trapping of air bubbles presents a substantial impediment for the user in the increasingly widespread use of lab-on-a-chip products having microcavities in the forms of microwells, traps, dead ends and corners. Here we demonstrate a simple, effective, and passive method to eliminate air bubbles by coating hydrophilized microarray and microfluidic devices with a monosaccharide such as d-glucose or D-sorbitol, where the microcavities are filled with a conformal, elliptical, cone-shaped monosaccharide solid. These devices were stored in air for up to 6 months with a complete rewetting of the microcavities by dissolution of the monosaccharide with an aqueous solution.     

Polystyrene-coated micropallets for culture and separation of primary muscle cells

Despite identification of a large number of adult stem cell types, current primary cell isolation and identification techniques yield heterogeneous samples, making detailed biological studies challenging. To identify subsets of isolated cells, technologies capable of simultaneous cell culture and cloning are necessary. Micropallet arrays, a new cloning platform for adherent cell types, hold great potential. However, the microstructures composing these arrays are fabricated from an epoxy photoresist 1002F, a growth surface unsuitable for many cell types. Optimization of the microstructures’ surface properties was conducted for the culture of satellite cells, primary muscle cells for which improved cell isolation techniques are desired. A variety of surface materials were screened for satellite cell adhesion and proliferation and compared to their optimal substrate, gelatin-coated Petri dishes. A 1-μm thick, polystyrene copolymer was applied to the microstructures by contact printing. A negatively charged copolymer of 5% acrylic acid in 95% styrene was found to be equivalent to the control Petri dishes for cell adhesion and proliferation. Cells cultured on control dishes and optimal copolymer-coated surfaces maintained an undifferentiated state and showed similar mRNA expression for two genes indicative of cell differentiation during a standard differentiation protocol. Experiments using additional contact-printed layers of extracellular matrix proteins collagen and gelatin showed no further improvements. This micropallet coating strategy is readily adaptable to optimize the array surface for other types of primary cells.     

Kinetic analysis of PI3K reactions with fluorescent PIP<Subscript>2</Subscript> derivatives

Phosphatidylinositol 3-kinase (PI3K) signaling plays important roles in cell differentiation, proliferation, and migration. Increased mutations and expression levels of PI3K are hallmarks for the development of certain cancers. Pharmacological targeting of PI3K activity has also been actively pursued as a novel cancer therapeutic. Consequently, measurement of PI3K activity in different cell types or patient samples holds the promise as being a novel diagnostic tool. However, the direct measurement of cellular PI3K activity has been a challenging task. We report here the characterization of two fluorescent PIP₂ derivatives as reporters for PI3K enzymatic activity. The reporters are efficiently separated from their corresponding PI3K enzymatic products through either thin layer chromatography (TLC) or capillary electrophoresis (CE), and can be detected with high sensitivity by fluorescence. The biophysical and kinetic properties of the two probes are measured, and their suitability to characterize PI3K inhibitors is explored. Both probes show similar capacity as PI3K substrates for inhibitor characterization, yet also possess distinct properties that may suggest their different applications. These characterizations have laid the groundwork to systematically measure cellular PI3K activity, and have the potential to generate molecular fingerprints for diagnostic and therapeutic applications.     

Continuous analysis of dye-loaded, single cells on a microfluidic chip

Continuous analysis of two dyes loaded into single mammalian cells using laser-based lysis combined with electrophoretic separation was developed and characterized on microfluidic chips. The devices employed hydrodynamic flow to transport cells to a junction where they were mechanically lysed by a laser-generated cavitation bubble. An electric field then attracted the analyte into a separation channel while the membranous remnants passed through the intersection towards a waste reservoir. Phosphatidylcholine (PC)-supported bilayer membrane coatings (SBMs) provided a weakly negatively charged surface and prevented cell fouling from interfering with device performance. Cell lysis using a picosecond-pulsed laser on-chip did not interfere with concurrent electrophoretic separations. The effect of device parameters on performance was evaluated. A ratio of 2 : 1 was found to be optimal for the focusing-channel : flow-channel width and 3 : 1 for the flow-channel : separation-channel width. Migration times decreased with increased electric field strengths up to 333 V cm(-1), at which point the field strength was sufficient to move unlysed cells and cellular debris into the electrophoretic channel. The migration time and full width half-maximum (FWHM) of the peaks were independent of cell velocity for velocities between 0.03 and 0.3 mm s(-1). Separation performance was independent of the exact lysis location when lysis was performed near the outlet of the focusing channel. The migration time for cell-derived fluorescein and fluorescein carboxylate was reproducible with <10% RSD. Automated cell detection and lysis were required to reduce peak FWHM variability to 30% RSD. A maximum throughput of 30 cells min(-1) was achieved. Device stability was demonstrated by analyzing 600 single cells over a 2 h time span.     

Norm convergence of realistic projection and reflection methods

We provide sufficient conditions for norm convergence of various projection and reflection methods, as well as giving limiting examples regarding convergence rates.     

Spectral narrowing and stabilization of thulium fiber lasers using guided-mode resonance filters

We used guided-mode resonance filters (GMRFs), fabricated using thin-film deposition and chemical etching, as intracavity feedback elements to stabilize and narrow the output spectrum in thulium-doped fiber oscillators operating in the 2?μm wavelength regime, producing linewidths of <700?pm up to 10?W power levels. A Tm fiber-based amplified spontaneous emission source was used to characterize the reflective properties of the GMRFs. Linewidths of 500?pm and a 7.3?dB reduction in transmission were measured on resonances.     

Synthesis and characterisation of immunogens for the production of antibodies against small hydrophobic molecules with biosignature properties

In the present study, five different classes of small hydrophobic molecular targets, atypical for antibody generation, were structurally modified in order to introduce suitable reactive functionalities and/or spacers which allow covalent coupling to a carrier protein resulting in a stable carrier-hapten complex. These targets were chosen to serve as markers of extant and/or extinct life in the context of the development of the Life Marker Chip (LMC), an antibody-based instrument, which is being developed by a UK-led international consortium for flight to Mars on board the joint ESA/NASA Mars exploration ExoMars mission. The hapten-protein conjugates were designed to be used as immunogens for antibody generation and immunoassay reagents in subsequent stages of the LMC development. The extent of protein modification due to covalent attachment of hapten was determined by two independent methods, i.e. trinitrobenzenesulfonic acid (TNBSA) titrations of remaining protein reactive groups and matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS) of the resultant hapten-protein conjugates. In a further quality validation step, the conjugates were presented to an animal's immune system and polyclonal antibody titres with moderate specificity were obtained. These results suggest that conjugates synthesized as described herein can successfully be used in the generation of antibodies targeting small hydrophobic molecules.