The Drosophila Wnt Protein DWnt-3 Is a Secreted Glycoprotein Localized on the Axon Tracts of the Embryonic CNS

AbstractThe Wnt gene family encodes highly conserved cysteine-rich proteins which appear to act as secreted developmental signals. Both the mouse Wnt-1 gene and the Drosophila wingless (wg) gene play important roles in central nervous system (CNS) development. wg is also required earlier, in the development of the embryonic metameric body pattern. We have begun to characterize the developmental expression and role of another member of the Drosophila Wnt gene family, DWnt-3. Using antisera raised to the DWnt-3 protein, we show that the protein is secreted in vivo. The early protein expression domains include the limb and appendage primordia. Late expression domains comprise the ventral cord and supraesophageal ganglia of the CNS. Notably, DWnt-3 protein accumulates on the commissural and longitudinal axon tracts of the CNS. Ectopic expression of DWnt-3 in transgenic embryos bearing a HS-DWnt-3 construct leads to specific disruption of the commissural axon tracts of the CNS. We also show that DWnt-3 does not functionally replace wg in an in vivo assay. Experiments with a tissue culture cell line transfected with a construct encoding the DWnt-3 gene show that DWnt-3 protein is efficiently synthesized, glycosylated, proteolytically processed, and transported to the extracellular matrix and medium. DWnt-3, therefore, encodes a secreted protein, which is likely to play a role in development of the Drosophila CNS

Vacuum properties of a Non-Local Thirring-Like Model

We use path-integral methods to analyze the vacuum properties of a recently proposed extension of the Thirring model in which the interaction between fermionic currents is non-local. We calculate the exact ground state wave functional of the model for any bilocal potential, and also study its long-distance behavior. We show that the ground state wave functional has a general factored Jastrow form. We also find that it posess an interesting symmetry involving the interchange of density-density and current-current interactions.Comment: 25 pages, latex, no figure

Interplay between axonal Wnt5-Vang and dendritic Wnt5-Drl/Ryk signaling controls glomerular patterning in the Drosophila antennal lobe [preprint]

Despite the importance of dendritic targeting in neural circuit assembly, the mechanisms by which it is controlled still remain incompletely understood. We previously showed that in the developing Drosophila antennal lobe, the Wnt5 protein forms a gradient that directs the ~45° rotation of a cluster of projection neuron (PN) dendrites, including the adjacent DA1 and VA1d dendrites. We report here that the Van Gogh (Vang) transmembrane planar cell polarity (PCP) protein is required for the rotation of the DA1/VA1d dendritic pair. Cell type-specific rescue and mosaic analyses showed that Vang functions in the olfactory receptor neurons (ORNs), suggesting a codependence of ORN axonal and PN dendritic targeting. Loss of Vang suppressed the repulsion of the VA1d dendrites by Wnt5, indicating that Wnt5 signals through Vang to direct the rotation of the DA1 and VA1d glomeruli. We observed that the Derailed (Drl)/Ryk atypical receptor tyrosine kinase is also required for the rotation of the DA1/VA1d dendritic pair. Antibody staining showed that Drl/Ryk is much more highly expressed by the DA1 dendrites than the adjacent VA1d dendrites. Mosaic and epistatic analyses showed that Drl/Ryk specifically functions in the DA1 dendrites in which it antagonizes the Wnt5-Vang repulsion and mediates the migration of the DA1 glomerulus towards Wnt5. Thus, the nascent DA1 and VA1d glomeruli appear to exhibit Drl/Ryk-dependent biphasic responses to Wnt5. Our work shows that the final patterning of the fly olfactory map is the result of an interplay between ORN axons and PN dendrites, wherein converging pre- and postsynaptic processes contribute key Wnt5 signaling components, allowing Wnt5 to orient the rotation of nascent synapses through a PCP mechanism

Non-commutative Chern-Simons for the Quantum Hall System and Duality

The quantum Hall system is known to have two mutually dual Chern-Simons descriptions, one associated with the hydrodynamics of the electron fluid, and another associated with the statistics. Recently, Susskind has made the claim that the hydrodynamic Chern-Simons theory should be considered to have a non-commutative gauge symmetry. The statistical Chern-Simons theory has a perturbative momentum expansion. In this paper, we study this perturbation theory and show that the effective action, although commutative at leading order, is non-commutative. This conclusion is arrived at through a careful study of the three-point function of Chern-Simons gauge fields. The non-commutative gauge symmetry of this system is thus a quantum symmetry, which we show can only be fully realized only through the inclusion of all orders in perturbation theory. We discuss the duality between the two non-commutative descriptions.Comment: 21 pages (preprint), 3 figure

Strongly correlated fermions with nonlinear energy dispersion and spontaneous generation of anisotropic phases

Using the bosonization approach we study fermionic systems with a nonlinear dispersion relation in dimension d>2. We explicitly show how the band curvature gives rise to interaction terms in the bosonic version of the model. Although these terms are perturbatively irrelevant in relation to the Landau Fermi liquid fixed point, they become relevant perturbations when instabilities take place. Using a coherent state path integral technique we built up the effective action that governs the dynamics of the Fermi surface fluctuations. We consider the combined effect of fermionic interactions and band curvature on possible anisotropic phases triggered by negative Landau parameters. In particular we study in some detail the phase diagram for the isotropic/nematic/hexatic quantum phase transition.Comment: RevTeX4, 9 pages, 2 eps figures, Final version as appeared in Phys.Rev.

A Signaling Network for Patterning of Neuronal Connectivity in the Drosophila Brain

The precise number and pattern of axonal connections generated during brain development regulates animal behavior. Therefore, understanding how developmental signals interact to regulate axonal extension and retraction to achieve precise neuronal connectivity is a fundamental goal of neurobiology. We investigated this question in the developing adult brain of Drosophila and find that it is regulated by crosstalk between Wnt, fibroblast growth factor (FGF) receptor, and Jun N-terminal kinase (JNK) signaling, but independent of neuronal activity. The Rac1 GTPase integrates a Wnt-Frizzled-Disheveled axon-stabilizing signal and a Branchless (FGF)-Breathless (FGF receptor) axon-retracting signal to modulate JNK activity. JNK activity is necessary and sufficient for axon extension, whereas the antagonistic Wnt and FGF signals act to balance the extension and retraction required for the generation of the precise wiring pattern

A Review of Symmetry Algebras of Quantum Matrix Models in the Large-N Limit

This is a review article in which we will introduce, in a unifying fashion and with more intermediate steps in some difficult calculations, two infinite-dimensional Lie algebras of quantum matrix models, one for the open string sector and one for the closed string sector. Physical observables of quantum matrix models in the large-N limit can be expressed as elements of these Lie algebras. We will see that both algebras arise as quotient algebras of a larger Lie algebra. We will also discuss some properties of these Lie algebras not published elsewhere yet, and briefly review their relationship with well-known algebras like the Cuntz algebra, the Witt algebra and the Virasoro algebra. We will also review how Yang--Mills theory, various low energy effective models of string theory, quantum gravity, string-bit models, and quantum spin chain models can be formulated as quantum matrix models. Studying these algebras thus help us understand the common symmetry of these physical systems.Comment: 77 pages, 21 eps figures, 1 table, LaTeX2.09; an invited review articl

Fermionic Chern-Simons theory for the Fractional Quantum Hall Effect in Bilayers

We generalize the fermion Chern-Simons theory for the Fractional Hall Effect (FQHE) which we developed before, to the case of bilayer systems. We study the complete dynamic response of these systems and predict the experimentally accessible optical properties. In general, for the so called $(m, m, n)$ states, we find that the spectrum of collective excitations has a gap, and the wave function has the Jastrow-Slater form, with the exponents determined by the coefficients $m$, and $n$. We also find that the $(m,m,m)$ states, {\it i.~e.~}, those states whose filling fraction is $1\over m$, have a gapless mode which may be related with the spontaneous appearance of the interlayer coherence. Our results also indicate that the gapless mode makes a contribution to the wave function of the $(m,m,m)$ states analogous to the phonon contribution to the wave function of superfluid $\rm{He}_4$. We calculate the Hall conductance, and the charge and statistics of the quasiparticles. We also present an $SU(2)$ generalization of this theory relevant to spin unpolarized or partially polarized single layers.Comment: 55 pages, Urbana Prepin

Segregation in diffusion-limited multispecies pair annihilation

The kinetics of the q species pair annihilation reaction (A_i + A_j -> 0 for 1 <= i < j <= q) in d dimensions is studied by means of analytical considerations and Monte Carlo simulations. In the long-time regime the total particle density decays as rho(t) ~ t^{- alpha}. For d = 1 the system segregates into single species domains, yielding a different value of alpha for each q; for a simplified version of the model in one dimension we derive alpha(q) = (q-1) / (2q). Within mean-field theory, applicable in d >= 2, segregation occurs only for q < 1 + (4/d). The only physical realisation of this scenario is the two-species process (q = 2) in d = 2 and d = 3, governed by an extra local conservation law. For d >= 2 and q >= 1 + (4/d) the system remains disordered and its density is shown to decay universally with the mean-field power law (alpha = 1) that also characterises the single-species annihilation process A + A -> 0.Comment: 35 pages (IOP style files included), 10 figures included (as eps files

Open Inflation With Scalar-tensor Gravity

The open inflation model recently proposed by Hawking and Turok is investigated in scalar-tensor gravity context. If the dilaton-like field has no potential, the instanton of our model is singular but has a finite action. The Gibbons-Hawking surface term vanishes and hence, can not be used to make $\Omega_0$ nonzero. To obtain a successful open inflation one should introduce other matter fields or a potential for the dilaton-like fields.Comment: 10 pages.1 figure. Some comments and references are improved. to be published in PR