The eye of Drosophila as a model system for studying intracellular signaling in ontogenesis and pathogenesis

Many human diseases are caused by malfunction of basic types of cellular activity such as proliferation, differentiation, apoptosis, cell polarization, and migration. In turn, these processes are associated with different routes of intracellular signal transduction. A number of model systems have been designed to study normal and abnormal cellular and molecular processes associated with pathogenesis. The developing eye of the fruit fly Drosophila melanogaster is one of these systems. The sequential development of compound eyes of this insect makes it possible to model human neurodegenerative diseases and mechanisms of carcinogenesis. In this paper we overview the program of the eye development in Drosophila, with emphasis on intracellular signaling pathways that regulate this complex process. We discuss in detail the roles of the Notch, Hedgehog, TGFβ, Wnt, and receptor tyrosine kinase signaling pathways in Drosophila eye development and human pathology. We also briefly describe the modern methods of experimentation with this model organism to analyze the function of human pathogenic protein

Trajectories in a space with a spherically symmetric dislocation

We consider a new type of defect in the scope of linear elasticity theory, using geometrical methods. This defect is produced by a spherically symmetric dislocation, or ball dislocation. We derive the induced metric as well as the affine connections and curvature tensors. Since the induced metric is discontinuous, one can expect ambiguity coming from these quantities, due to products between delta functions or its derivatives, plaguing a description of ball dislocations based on the Geometric Theory of Defects. However, exactly as in the previous case of cylindric defect, one can obtain some well-defined physical predictions of the induced geometry. In particular, we explore some properties of test particle trajectories around the defect and show that these trajectories are curved but can not be circular orbits.Comment: 11 pages, 3 figure

Mode of interaction of the Gαo subunit of heterotrimeric G proteins with the GoLoco1 motif of Drosophila Pins is determined by guanine nucleotides.

Drosophila GoLoco motif-containing protein Pins is unusual in its highly efficient interaction with both GDP- and the GTP-loaded forms of the α-subunit of the heterotrimeric Go protein. We analysed the interactions of Gαo in its two nucleotide forms with GoLoco1-the first of the three GoLoco domains of Pins-and the possible structures of the resulting complexes, through combination of conventional fluorescence and FRET measurements as well as through molecular modelling. Our data suggest that the orientation of the GoLoco1 motif on Gαo significantly differs between the two nucleotide states of the latter. In other words, a rotation of the GoLoco1 peptide in respect with Gαo must accompany the nucleotide exchange in Gαo. The sterical hindrance requiring such a rotation probably contributes to the guanine nucleotide exchange inhibitor activity of GoLoco1 and Pins as a whole. Our data have important implications for the mechanisms of Pins regulation in the process of asymmetric cell divisions

Universal conservation law and modified Noether symmetry in 2d models of gravity with matter

It is well-known that all 2d models of gravity---including theories with nonvanishing torsion and dilaton theories---can be solved exactly, if matter interactions are absent. An absolutely (in space and time) conserved quantity determines the global classification of all (classical) solutions. For the special case of spherically reduced Einstein gravity it coincides with the mass in the Schwarzschild solution. The corresponding Noether symmetry has been derived previously by P. Widerin and one of the authors (W.K.) for a specific 2d model with nonvanishing torsion. In the present paper this is generalized to all covariant 2d theories, including interactions with matter. The related Noether-like symmetry differs from the usual one. The parameters for the symmetry transformation of the geometric part and those of the matterfields are distinct. The total conservation law (a zero-form current) results from a two stage argument which also involves a consistency condition expressed by the conservation of a one-form matter ``current''. The black hole is treated as a special case.Comment: 3

Absolute conservation law for black holes

In all 2d theories of gravity a conservation law connects the (space-time dependent) mass aspect function at all times and all radii with an integral of the matter fields. It depends on an arbitrary constant which may be interpreted as determining the initial value together with the initial values for the matter field. We discuss this for spherically reduced Einstein-gravity in a diagonal metric and in a Bondi-Sachs metric using the first order formulation of spherically reduced gravity, which allows easy and direct fixations of any type of gauge. The relation of our conserved quantity to the ADM and Bondi mass is investigated. Further possible applications (ideal fluid, black holes in higher dimensions or AdS spacetimes etc.) are straightforward generalizations.Comment: LaTex, 17 pages, final version, to appear in Phys. Rev.

Comment on: ``Trace anomaly of dilaton coupled scalars in two dimensions''

The trace anomaly for nonminimally coupled scalars in spherically reduced gravity obtained by Bousso and Hawking (hep-th/9705236) is incorrect. We explain the reasons for the deviations from our correct (published) result which is supported by several other recent papers.Comment: 2 page

Geometric Interpretation and Classification of Global Solutions in Generalized Dilaton Gravity

Two dimensional gravity with torsion is proved to be equivalent to special types of generalized 2d dilaton gravity. E.g. in one version, the dilaton field is shown to be expressible by the extra scalar curvature, constructed for an independent Lorentz connection corresponding to a nontrivial torsion. Elimination of that dilaton field yields an equivalent torsionless theory, nonpolynomial in curvature. These theories, although locally equivalent exhibit quite different global properties of the general solution. We discuss the example of a (torsionless) dilaton theory equivalent to the $R^2 + T^2$--model. Each global solution of this model is shown to split into a set of global solutions of generalized dilaton gravity. In contrast to the theory with torsion the equivalent dilaton one exhibits solutions which are asymptotically flat in special ranges of the parameters. In the simplest case of ordinary dilaton gravity we clarify the well known problem of removing the Schwarzschild singularity by a field redefinition.Comment: 21 pages, 6 Postscript figure

Conserved Quasilocal Quantities and General Covariant Theories in Two Dimensions

General matterless--theories in 1+1 dimensions include dilaton gravity, Yang--Mills theory as well as non--Einsteinian gravity with dynamical torsion and higher power gravity, and even models of spherically symmetric d = 4 General Relativity. Their recent identification as special cases of 'Poisson--sigma--models' with simple general solution in an arbitrary gauge, allows a comprehensive discussion of the relation between the known absolutely conserved quantities in all those cases and Noether charges, resp. notions of quasilocal 'energy--momentum'. In contrast to Noether like quantities, quasilocal energy definitions require some sort of 'asymptotics' to allow an interpretation as a (gauge--independent) observable. Dilaton gravitation, although a little different in detail, shares this property with the other cases. We also present a simple generalization of the absolute conservation law for the case of interactions with matter of any type.Comment: 21 pages, LaTeX-fil

Aharonov-Bohm Effect and Disclinations in an Elastic Medium

In this work we investigate quasiparticles in the background of defects in solids using the geometric theory of defects. We use the parallel transport matrix to study the Aharonov-Bohm effect in this background. For quasiparticles moving in this effective medium we demonstrate an effect similar to the gravitational Aharonov- Bohm effect. We analyze this effect in an elastic medium with one and $N$ defects.Comment: 6 pages, Revtex