553 research outputs found
Selective function of the PDZ domain of Dishevelled in noncanonical Wnt signalling
Dishevelled is a cytoplasmic hub that transduces Wnt signals to cytoplasmic effectors, which can be broadly characterised as canonical (β-catenin dependent) and noncanonical, to specify cell fates and behaviours during development. To transduce canonical Wnt signals, Dishevelled binds to the intracellular face of Frizzled through its DEP domain and polymerises through its DIX domain to assemble dynamic signalosomes. Dishevelled also contains a PDZ domain, whose function remains controversial. Here, we use genome editing to delete the PDZ domain-encoding region from Drosophila dishevelled. Canonical Wingless signalling is entirely normal in these deletion mutants; however, they show defects in multiple contexts controlled by noncanonical Wnt signalling, such as planar polarity. We use nuclear magnetic resonance spectroscopy to identify bona fide PDZ-binding motifs at the C termini of different polarity proteins. Although deletions of these motifs proved aphenotypic in adults, we detected changes in the proximodistal distribution of the polarity protein Flamingo (also known as Starry night) in pupal wings that suggest a modulatory role of these motifs in polarity signalling. We also provide new genetic evidence that planar polarity relies on the DEP-dependent recruitment of Dishevelled to the plasma membrane by Frizzled
A new class of semiclassical wave function uniformizations
We present a new semiclassical technique which relies on replacing
complicated classical manifold structure with simpler manifolds, which are then
evaluated by the usual semiclassical rules. Under circumstances where the
original manifold structure gives poor or useless results semiclassically the
replacement manifolds can yield remarkable accuracy. We give several working
examples to illustrate the theory presented here.Comment: 12 pages (incl. 12 figures
Occurrence of periodic Lam\'e functions at bifurcations in chaotic Hamiltonian systems
We investigate cascades of isochronous pitchfork bifurcations of
straight-line librating orbits in some two-dimensional Hamiltonian systems with
mixed phase space. We show that the new bifurcated orbits, which are
responsible for the onset of chaos, are given analytically by the periodic
solutions of the Lam\'e equation as classified in 1940 by Ince. In Hamiltonians
with C_ symmetry, they occur alternatingly as Lam\'e functions of period
2K and 4K, respectively, where 4K is the period of the Jacobi elliptic function
appearing in the Lam\'e equation. We also show that the two pairs of orbits
created at period-doubling bifurcations of touch-and-go type are given by two
different linear combinations of algebraic Lam\'e functions with period 8K.Comment: LaTeX2e, 22 pages, 14 figures. Version 3: final form of paper,
accepted by J. Phys. A. Changes in Table 2; new reference [25]; name of
bifurcations "touch-and-go" replaced by "island-chain
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
The bends on a quantum waveguide and cross-products of Bessel functions
A detailed analysis of the wave-mode structure in a bend and its
incorporation into a stable algorithm for calculation of the scattering matrix
of the bend is presented. The calculations are based on the modal approach. The
stability and precision of the algorithm is numerically and analytically
analysed. The algorithm enables precise numerical calculations of scattering
across the bend. The reflection is a purely quantum phenomenon and is discussed
in more detail over a larger energy interval. The behaviour of the reflection
is explained partially by a one-dimensional scattering model and heuristic
calculations of the scattering matrix for narrow bends. In the same spirit we
explain the numerical results for the Wigner-Smith delay time in the bend.Comment: 34 pages, 21 figure
Van Gogh and Frizzled Act Redundantly in the Drosophila Sensory Organ Precursor Cell to Orient Its Asymmetric Division
Drosophila sensory organ precursor cells (SOPs) divide asymmetrically along the anterior-posterior (a-p) body axis to generate two different daughter cells. Planar Cell Polarity (PCP) regulates the a-p orientation of the SOP division. The localization of the PCP proteins Van Gogh (Vang) and Frizzled (Fz) define anterior and posterior apical membrane domains prior to SOP division. Here, we investigate the relative contributions of Vang, Fz and Dishevelled (Dsh), a membrane-associated protein acting downstream of Fz, in orienting SOP polarity. Genetic and live imaging analyses suggest that Dsh restricts the localization of a centrosome-attracting activity to the anterior cortex and that Vang is a target of Dsh in this process. Using a clone border assay, we provide evidence that the Vang and fz genes act redundantly in SOPs to orient its polarity axis in response to extrinsic local PCP cues. Additionally, we find that the activity of Vang is dispensable for the non-autonomous polarizing activity of fz. These observations indicate that both Vang and Fz act as cues for downstream effectors orienting the planar polarity axis of dividing SOPs
A role for core planar polarity proteins in cell contact-mediated orientation of planar cell division across the mammalian embryonic skin
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. © The Author(s) 2017. Supplementary information accompanies this paper at doi:10.1038/s41598-017-01971-2.The question of how cell division orientation is determined is fundamentally important for understanding tissue and organ shape in both healthy or disease conditions. Here we provide evidence for cell contact-dependent orientation of planar cell division in the mammalian embryonic skin. We propose a model where the core planar polarity proteins Celsr1 and Frizzled-6 (Fz6) communicate the long axis orientation of interphase basal cells to neighbouring basal mitoses so that they align their horizontal division plane along the same axis. The underlying mechanism requires a direct, cell surface, planar polarised cue, which we posit depends upon variant post-translational forms of Celsr1 protein coupled to Fz6. Our hypothesis has parallels with contact-mediated division orientation in early C. elegans embryos suggesting functional conservation between the adhesion-GPCRs Celsr1 and Latrophilin-1. We propose that linking planar cell division plane with interphase neighbour long axis geometry reinforces axial bias in skin spreading around the mouse embryo body.Peer reviewe
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