On the Fourier coefficients of linear fractional stable motion

Inspired by a theorem of Marcinkiewicz [J. Marcinkiewicz, On a class of functions and their Fourier series, C. R. Soc. Sci. Varsovie, 26:71–77, 1934. Reprinted in: J. Marcinkiewicz, Collected Papers (A. Zygmund (Ed.)), PaństwoweWydawnictwo Naukowe,Warsaw, 1964] stating that the maximum of the absolute values of real Fourier coefficients a _n and b _n of a function of bounded p-variation ( p \geqslant 1 ) \left( {p \geqslant 1} \right) on an interval [0, 1] is of order O(n ^−1/p ) as n → ∞, we compute the Fourier coefficients of the linear fractional stable motion (LFSM) and of the closely related Riemann–Liouville (RL) process and investigate the rate of their decay.     

The Impact of an Anchoring Layer on the Formation of Tethered Bilayer Lipid Membranes on Silver Substrates

Tethered bilayer lipid membranes (tBLMs) have been known as stable and versatile experimental platforms for protein–membrane interaction studies. In this work, the assembly of functional tBLMs on silver substrates and the effect of the molecular chain-length of backfiller molecules on their properties were investigated. The following backfillers 3-mercapto-1-propanol (3M1P), 4-mercapto-1-butanol (4M1B), 6-mercapto-1-hexanol (6M1H), and 9-mercapto-1-nonanol (9M1N) mixed with the molecular anchor WC14 (20-tetradecyloxy-3,6,9,12,15,18,22 heptaoxahexatricontane-1-thiol) were used to form self-assembled monolayers (SAMs) on silver, which influenced a fusion of multilamellar vesicles and the formation of tBLMs. Spectroscopic analysis by SERS and RAIRS has shown that by using different-length backfiller molecules, it is possible to control WC14 anchor molecules orientation on the surface. An introduction of increasingly longer surface backfillers in the mixed SAM may be related to the increasing SAMs molecular order and more vertical orientation of WC14 at both the hydrophilic ethylenoxide segment and the hydrophobic lipid bilayer anchoring alkane chains. Since no clustering of WC14 alkane chains, which is deleterious for tBLM integrity, was observed on dry samples, the suitability of mixed-component SAMs for subsequent tBLM formation was further interrogated by electrochemical impedance spectroscopy (EIS). EIS showed the arrangement of well-insulating tBLMs if 3M1P was used as a backfiller. An increase in the length of the backfiller led to increased defectiveness of tBLMs. Despite variable defectiveness, all tBLMs responded to the pore-forming cholesterol-dependent cytolysin, vaginolysin in a manner consistent with the functional reconstitution of the toxin into phospholipid bilayer. This experiment demonstrates the biological relevance of tBLMs assembled on silver surfaces and indicates their utility as biosensing elements for the detection of pore-forming toxins in liquid samples.     

Monitoring the dynamics of ligand-receptor complexes on model membranes

Ligand-induced cross-linking of cell surface receptors is a basic paradigm of signal activation by many transmembrane receptors. After ligand binding, the receptor complexes formed on the membrane are dynamically maintained by two-dimensional protein-protein interactions on the membrane. The biophysical principles governing the dynamics of such interactions have not been understood, mainly because the measurement of lateral interactions on membranes so far has not been experimentally addressed. Here, we describe a generic approach for measuring two-dimensional dissociation rate constants in vitro using a novel high-affinity chelator lipid for reconstituting a ternary cytokine-receptor complex on solid-supported membranes. While monitoring the interaction between the ligand and one of the receptor subunits on the membrane by fluorescence resonance energy transfer, the equilibrium on the surface was perturbed by rapidly tethering a large excess of the unlabeled receptor subunit. Displacement of labeled by unlabeled protein in the ternary complex was detected as a recovery of the donor quenching. Since the dissociation of the ligand-receptor complex in plane of the membrane was the rate-limiting step under these conditions, the two-dimensional rate constant of this process was determined. Strikingly, the two-dimensional dissociation was much slower than ligand dissociation into solution, suggesting that membrane tethering significantly affects the dissociation process. This result highlights the importance of studying ligand-receptor complexes tethered to membranes for understanding the principles governing signal activation by ligand-induced receptor assembling.     

Spatial Filters on Demand Based on Aperiodic Photonic Crystals

Photonic Crystal spatial filters, apart from stand‐alone spatial filtering function, can also suppress multi‐transverse‐mode operation in laser resonators. Here it is shown that such photonic crystals can be designed by solving the inverse problem: for a given spatial filtering profile. Optimized Photonic Crystal filters were fabricated in photosensitive glass. Experiments have shown that such filters provide a more pronounced filtering effect for total and partial transmissivity conditions.     

Numerical simulation of resonance structures with FDTD algorithms based on GPU B-CALM and CPU Meep

Simulation time is one of the bottlenecks of finite-difference-time-domain (FDTD) method. There are several ways of reducing the simulation time, one of which is the usage of graphical processing unit (GPU). Thus in this paper we present comparison between two free FDTD software packages. One is based on central processing unit and other is based on GPU. The 3D test structures we analyzed were metallic rectangular cavity resonator and microring resonator based refractive index sensor. The comparison between two FDTD software packages is made with regard to simulation time and numerical accuracy. It is shown that both packages agree in numerical results and that GPU based FDTD implementation performs same simulation up to 18 times faster.     

Dielectric response of water confined in metal–organic frameworks

Dielectric response of water confined in metal–organic frameworks was investigated in broad temperature range from 140 to 410 K and from 20 Hz to 1 MHz using a capacitance bridge. Several dispersion regions of characteristic shape were found, caused by freezing–melting of adsorbed water molecules, which disappear after a prolonged heating at 410 K. Temperature dependencies of relaxation time of confined water molecules were obtained and are compared to those of water confined in MCM-41 mesoporous molecular sieves.     

Stripe patterns in degenerate optical parametric oscillators

We experimentally demonstrate the stripe (or roll) patterns in a broad-aperture degenerate optical parametric oscillator in a plane-mirror minicavity. The stabilization of stripes is achieved by seed injection at a subharmonic frequency. We measure the temporal spectra of the stripe pattern and obtain the 1/f-like noise spectra.     

Screen printing for producing ferroelectret systems with polymer-electret films and well-defined cavities

We report a process for preparing polymer ferroelectrets by means of screen printing—a technology that is widely used for the two-dimensional patterning of printed layers. In order to produce polymer-film systems with cavities that are suitable for bipolar electric charging, a screen-printing paste is deposited through a screen with a pre-designed pattern onto the surface of a polymer electret film. Another such polymer film is placed on top of the printed pattern, and well-defined cavities are formed in-between. During heating and curing, the polymer films are tightly bonded to the patterned paste layer so that a stable three-layer system is obtained. In the present work, polycarbonate (PC) films have been employed as electret layers. Screen printing, curing and charging led to PC ferroelectret systems with a piezoelectric d ₃₃ coefficient of about 28 pC/N that is stable up to 100 ^°C. Due to the rather soft patterned layer, d ₃₃ strongly decreases already for static pressures of tens of kPa. The results demonstrate the suitability of screen printing for the preparation of ferroelectret systems.     

Specific and stable fluorescence labeling of histidine-tagged proteins for dissecting multi-protein complex formation

Labeling of proteins with fluorescent dyes offers powerful means for monitoring protein interactions in vitro and in live cells. Only a few techniques for noncovalent fluorescence labeling with well-defined localization of the attached dye are currently available. Here, we present an efficient method for site-specific and stable noncovalent fluorescence labeling of histidine-tagged proteins. Different fluorophores were conjugated to a chemical recognition unit bearing three NTA moieties (tris-NTA). In contrast to the transient binding of conventional mono-NTA, the multivalent interaction of tris-NTA conjugated fluorophores with oligohistidine-tagged proteins resulted in complex lifetimes of more than an hour. The high selectivity of tris-NTA toward cumulated histidines enabled selective labeling of proteins in cell lysates and on the surface of live cells. Fluorescence labeling by tris-NTA conjugates was applied for the analysis of a ternary protein complex in solution and on surfaces. Formation of the complex and its stoichiometry was studied by analytical size exclusion chromatography and fluorescence quenching. The individual interactions were dissected on solid supports by using simultaneous mass-sensitive and multicolor fluorescence detection. Using these techniques, formation of a 1:1:1 stoichiometry by independent interactions of the receptor subunits with the ligand was shown. The incorporation of transition metal ions into the labeled proteins upon labeling with tris-NTA fluorophore conjugates provided an additional sensitive spectroscopic reporter for detecting and monitoring protein-protein interactions in real time. A broad application of these fluorescence conjugates for protein interaction analysis can be envisaged.