Chaos in the square billiard with a modified reflection law

The purpose of this paper is to study the dynamics of a square billiard with a non-standard reflection law such that the angle of reflection of the particle is a linear contraction of the angle of incidence. We present numerical and analytical arguments that the nonwandering set of this billiard decomposes into three invariant sets, a parabolic attractor, a chaotic attractor, and a set consisting of several horseshoes. This scenario implies the positivity of the topological entropy of the billiard, a property that is in sharp contrast with the integrability of the square billiard with the standard reflection law.     

Search for time dependence of the Cs decay constant

Starting from June 2011, the activity of a ¹³⁷Cs source has been measured by means of a HPGe detector installed deep underground in the Gran Sasso Laboratory. Over 5100 hourly recorded energy spectra have been collected in 217 days. These data allowed the search for time variations of the decay constant with periods from a few hours to 1 year. No signal with amplitude larger than 9.6⋅10⁻⁵$9.6\cdot {10}^{-5}$ at 95% C.L. has been detected. These limits are more than one order of magnitude lower than the values on the oscillation amplitude reported in literature. In particular, for 1 year period an oscillation amplitude larger than 8.5⋅10⁻⁵$8.5\cdot {10}^{-5}$ has been excluded at 95% C.L., independently of the phase. The same data give a value of 29.96±0.08$29.96\pm 0.08$ years for the ¹³⁷Cs half-life, in good agreement with the world mean value of 30.05±0.08$30.05\pm 0.08$ years.     

Efficient synthesis of N-methoxyindoles via alkylative cycloaddition of nitrosoarenes with alkynes

[reaction: see text] N-Methoxyindoles are produced in moderate to excellent yields from the reaction between nitrosoarenes and alkynes in the presence of K2CO3/(CH3)2SO4. Terminal alkynes with conjugating substituents afford 3-substituted N-methoxyindoles exclusively. The analogous reactions with methyl propiolate provide a one-step preparation of phytoalexin analogues from Wasabi.     

Self‐Assembled Functional DNA Superstructures as High‐Density and Versatile Recognition Elements for Printed Paper Sensors

Micrometer‐sized functional nucleic acid (FNA) superstructures (denoted as 3D DNA) were examined as a unique class of biorecognition elements to produce highly functional bioactive paper surfaces. 3D DNA containing repeating sequences of either a DNA aptamer or DNAzyme was created from long‐chain products of rolling circle amplification followed by salt aging. The resulting 3D DNA retained its original spherical shape upon inkjet printing and adhered strongly to the paper surface via physisorption. 3D DNA paper sensors showed resistance to degradation by nucleases, suppressed nonspecific protein adsorption, and provided a much higher surface density of functional DNA relative to monomeric FNAs, making such species ideally suited for development of paper‐based biosensors.     

Surface‐initiated atom transfer radical polymerization grafting of poly(2,2,2‐trifluoroethyl methacrylate) from flat silicon wafer surfaces

Poly(2,2,2‐trifluoroethyl methacrylate) (PTFEMA), a partially fluorinated polymer, was directly grafted from silicon wafer surfaces by a surface‐initiated atom‐transfer radical polymerization (ATRP). The polymer layer thickness increased linearly with monomer conversion and molecular weight of free polymers in solution. The thickness was mainly determined by the experimental conditions such as activator/deactivator ratio, monomer/catalyst ratio, and monomer concentration. PTFEMA layers of more than 100‐nm thick were obtained. The grafted PTFEMA chains were “living” and allowed the extension of a second block of PMMA. X‐ray photoelectron spectroscopy study showed that the chemical compositions at the surfaces agreed well with their theoretical values. A novel surface‐attachable difunctional initiator was also synthesized and applied to the grafting of PTFEMA. The grafting density was doubled using this difunctional initiator, from 0.48 to 0.86 chains/nm². © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1252–1262, 2006     

Automatic transwell assay by an EIS cell chip to monitor cell migration

Here an EIS (electrochemical impedance spectroscopy) biochip to detect cell migration is demonstrated. This biochip has been inspired by a traditional transwell assay/modified Boyden chamber and consists of two compartments separated by a porous membrane. This structure (PDMS-based) is aligned to EIS sensors. Cells are seeded in the upper chamber through microfluidic channels. During migration cells go through the pores of the membrane and get in touch with the electrodes that detect migrated cells. The performance of our cell-chip was tested by investigating the migratory ability of hepatocellular carcinoma (HCC) cells as a function of microenvironment. For this purpose we challenged HCC cells to migrate on different extra-cellular matrix (ECM) components including laminin 1, collagen IV and laminin 5. The results reveal that our cell chip provides reliable results that consistently overlap with those obtained with traditional standardized Boyden chambers. Thus, we demonstrate a new, easy tool to study cell migration and to perform automatic assays. This approach is easier and faster than traditional transwell assays and can be suitable for high-throughput studies in drug discovery applications.     

Paramagnetic-based NMR restraints lift residual dipolar coupling degeneracy in multidomain detergent-solubilized membrane proteins

Residual dipolar couplings (RDCs) are widely used as orientation-dependent NMR restraints to improve the resolution of the NMR conformational ensemble of biomacromolecules and define the relative orientation of multidomain proteins and protein complexes. However, the interpretation of RDCs is complicated by the intrinsic degeneracy of analytical solutions and protein dynamics that lead to ill-defined orientations of the structural domains (ghost orientations). Here, we illustrate how restraints from paramagnetic relaxation enhancement (PRE) experiments lift the orientational ambiguity of multidomain membrane proteins solubilized in detergent micelles. We tested this approach on monomeric phospholamban (PLN), a 52-residue membrane protein, which is composed of two helical domains connected by a flexible loop. We show that the combination of classical solution NMR restraints (NOEs and dihedral angles) with RDC and PRE constraints resolves topological ambiguities, improving the convergence of the PLN structural ensemble and giving the depth of insertion of the protein within the micelle. The combination of RDCs with PREs will be necessary for improving the accuracy and precision of membrane protein conformational ensembles, where three-dimensional structures are dictated by interactions with the membrane-mimicking environment rather than compact tertiary folds common in globular proteins.