Euclidean random matrix theory: low-frequency non-analyticities and Rayleigh scattering

By calculating all terms of the high-density expansion of the euclidean random matrix theory (up to second-order in the inverse density) for the vibrational spectrum of a topologically disordered system we show that the low-frequency behavior of the self energy is given by $\Sigma(k,z)\propto k^2z^{d/2}$ and not $\Sigma(k,z)\propto k^2z^{(d-2)/2}$, as claimed previously. This implies the presence of Rayleigh scattering and long-time tails of the velocity autocorrelation function of the analogous diffusion problem of the form $Z(t)\propto t^{(d+2)/2}$.Comment: 27 page

A Dual Function for Prickle in Regulating Frizzled Stability during Feedback-Dependent Amplification of Planar Polarity

The core planar polarity pathway coordinates epithelial cell polarity during animal development, and loss of its activity gives rise to a range of defects, from aberrant morphogenetic cell movements to failure to correctly orient structures, such as hairs and cilia. The core pathway functions via a mechanism involving segregation of its protein components to opposite cells ends, where they form asymmetric intracellular complexes that couple cell-cell polarity. This segregation is a self-organizing process driven by feedback interactions between the core proteins themselves. Despite intense efforts, the molecular pathways underlying feedback have proven difficult to elucidate using conventional genetic approaches. Here we investigate core protein function during planar polarization of the Drosophila wing by combining quantitative measurements of protein dynamics with loss-of-function genetics, mosaic analysis, and temporal control of gene expression. Focusing on the key core protein Frizzled, we show that its stable junctional localization is promoted by the core proteins Strabismus, Dishevelled, Prickle, and Diego. In particular, we show that the stabilizing function of Prickle on Frizzled requires Prickle activity in neighboring cells. Conversely, Prickle in the same cell has a destabilizing effect on Frizzled. This destabilizing activity is dependent on the presence of Dishevelled and blocked in the absence of Dynamin and Rab5 activity, suggesting an endocytic mechanism. Overall, our approach reveals for the first time essential in vivo stabilizing and destabilizing interactions of the core proteins required for self-organization of planar polarity

The distribution of polycomb-group proteins during cell division and development in Drosophila embryos: Impact on models for silencing

The subcellular three-dimensional distribution of three polycomb-group (PcG) proteins—polycomb, polyhomeotic and posterior sex combs—in fixed whole-mount Drosophila embryos was analyzed by multicolor confocal fluorescence microscopy. All three proteins are localized in complex patterns of 100 or more loci throughout most of the interphase nuclear volume. The rather narrow distribution of the protein intensities in the vast majority of loci argues against a PcG-mediated sequestration of repressed target genes by aggregation into subnuclear domains. In contrast to the case for PEV repression (Csink, A.K., and S. Henikoff. 1996. Nature. 381:529–531), there is a lack of correlation between the occurrence of PcG proteins and high concentrations of DNA, demonstrating that the silenced genes are not targeted to heterochromatic regions within the nucleus. There is a clear distinction between sites of transcription in the nucleus and sites of PcG binding, supporting the assumption that most PcG binding loci are sites of repressive complexes. Although the PcG proteins maintain tissue-specific repression for up to 14 cell generations, the proteins studied here visibly dissociate from the chromatin during mitosis, and disperse into the cytoplasm in a differential manner. Quantitation of the fluorescence intensities in the whole mount embryos demonstrate that the dissociated proteins are present in the cytoplasm. We determined that <2% of PH remains attached to late metaphase and anaphase chromosomes. Each of the three proteins that were studied has a different rate and extent of dissociation at prophase and reassociation at telophase. These observations have important implications for models of the mechanism and maintenance of PcG- mediated gene repression

DAnkrd49 and Bdbt act via casein kinase Iε to regulate planar polarity in Drosophila

The core planar polarity proteins are essential mediators of tissue morphogenesis, controlling both the polarised production of cellular structures and polarised tissue movements. During development the core proteins promote planar polarisation by becoming asymmetrically localised to opposite cell edges within epithelial tissues, forming intercellular protein complexes that coordinate polarity between adjacent cells. Here we describe a novel protein complex that regulates the asymmetric localisation of the core proteins in the Drosophila pupal wing. DAnkrd49 (an ankyrin repeat protein) and Bride of Doubletime (Bdbt, a non-canonical FK506 binding protein family member) physically interact, and regulate each other's levels in vivo. Loss of either protein results in a reduction in core protein asymmetry and disruption of the placement of trichomes at the distal edge of pupal wing cells. Post-translational modifications are thought to be important for the regulation of core protein behaviour and their sorting to opposite cell edges. Consistent with this, we find that loss of DAnkrd49 or Bdbt leads to reduced phosphorylation of the core protein Dishevelled and to decreased Dishevelled levels both at cell junctions and in the cytoplasm. Bdbt has previously been shown to regulate activity of the kinase Discs Overgrown (Dco, also known as Doubletime or Casein Kinase Iε), and Dco itself has been implicated in regulating planar polarity by phosphorylating Dsh as well as the core protein Strabismus. We demonstrate that DAnkrd49 and Bdbt act as dominant suppressors of Dco activity. These findings support a model whereby Bdbt and DAnkrd49 act together to modulate the activity of Dco during planar polarity establishment

Electromagnetic Momentum in Dispersive Dielectric Media

When the effects of dispersion are included, neither the Abraham nor the Minkowski expression for electromagnetic momentum in a dielectric medium gives the correct recoil momentum for absorbers or emitters of radiation. The total momentum density associated with a field in a dielectric medium has three contributions: (i) the Abraham momentum density of the field, (ii) the momentum density associated with the Abraham force, and (iii) a momentum density arising from the dispersive part of the response of the medium to the field, the latter having a form evidently first derived by D.F. Nelson [Phys. Rev. A 44, 3985 (1991)]. All three contributions are required for momentum conservation in the recoil of an absorber or emitter in a dielectric medium. We consider the momentum exchanged and the force on a polarizable particle (e.g., an atom or a small dielectric sphere) in a host dielectric when a pulse of light is incident upon it, including the dispersion of the dielectric medium as well as a dispersive component in the response of the particle to the field. The force can be greatly increased in slow-light dielectric media.Comment: 9 pages. To be published by Optics Communication

Fractional Klein-Kramers equation for superdiffusive transport: normal versus anomalous time evolution in a differential L{\'e}vy walk model

We introduce a fractional Klein-Kramers equation which describes sub-ballistic superdiffusion in phase space in the presence of a space-dependent external force field. This equation defines the differential L{\'e}vy walk model whose solution is shown to be non-negative. In the velocity coordinate, the probability density relaxes in Mittag-Leffler fashion towards the Maxwell distribution whereas in the space coordinate, no stationary solution exists and the temporal evolution of moments exhibits a competition between Brownian and anomalous contributions.Comment: 4 pages, REVTe

Gaussian random waves in elastic media

Similar to the Berry conjecture of quantum chaos we consider elastic analogue which incorporates longitudinal and transverse elastic displacements with corresponding wave vectors. Based on that we derive the correlation functions for amplitudes and intensities of elastic displacements. Comparison to numerics in a quarter Bunimovich stadium demonstrates excellent agreement.Comment: 4 pages, 4 figure

Calculation of atomic spontaneous emission rate in 1D finite photonic crystal with defects

We derive the expression for spontaneous emission rate in finite one-dimensional photonic crystal with arbitrary defects using the effective resonator model to describe electromagnetic field distributions in the structure. We obtain explicit formulas for contributions of different types of modes, i.e. radiation, substrate and guided modes. Formal calculations are illustrated with a few numerical examples, which demonstrate that the application of effective resonator model simplifies interpretation of results.Comment: Cent. Eur. J. Phys, in pres