Fuzzy differential subordinations connected with the linear operator

summary:We obtain several fuzzy differential subordinations by using a linear operator $\mathcal {I}_{m,\gamma }^{n,\alpha }f(z)=z+\sum \limits _{k=2}^{\infty }(1+\gamma ( k-1))^{n}m^{\alpha }(m+k)^{-\alpha }a_{k}z^{k}$. Using the linear operator $\mathcal {I}_{m,\gamma }^{n,\alpha },$ we also introduce a class of univalent analytic functions for which we give some properties

Dorsal Eye Selector Pannier (pnr) Suppresses the Eye Fate to Define Dorsal Margin of the Drosophila Eye

Axial patterning is crucial for organogenesis. During Drosophila eye development, dorso-ventral (DV) axis determination is the first lineage restriction event. The eye primordium begins with a default ventral fate, on which the dorsal eye fate is established by expression of the GATA-1 transcription factor pannier (pnr). Earlier, it was suggested that loss of pnr function induces enlargement in the dorsal eye due to ectopic equator formation. Interestingly, we found that in addition to regulating DV patterning, pnr suppresses the eye fate by downregulating the core retinal determination genes eyes absent (eya), sine oculis (so) and dacshund (dac) to define the dorsal eye margin. We found that pnr acts downstream of Ey and affect the retinal determination pathway by suppressing eya. Further analysis of the “eye suppression” function of pnr revealed that this function is likely mediated through suppression of the homeotic gene teashirt (tsh) and is independent of homothorax (hth), a negative regulator of eye. Pnr expression is restricted to the peripodial membrane on the dorsal eye margin, which gives rise to head structures around the eye, and pnr is not expressed in the eye disc proper that forms the retina. Thus, pnr has dual function, during early developmental stages pnr is involved in axial patterning whereas later it promotes the head specific fate. These studies will help in understanding the developmental regulation of boundary formation of the eye field on the dorsal eye margin

Drosophila Adult Eye Model to Teach Scanning Electron Microscopy in an Undergraduate Cell Biology Laboratory

We have devised an undergraduate laboratory exercise to study tissue morphology using fruit fly, Drosophila melanogaster, as the model organism. Drosophila can be reared in a cost effective manner in a short period of time. This experiment was a part of the undergraduate curriculum of the cell biology laboratory course aimed to demonstrate the use of scanning electron microscopy (SEM) technique to study the morphology of adult eye of Drosophila. The adult eye of Drosophila is a compound eye, which comprises of 800 unit eyes, and serves as an excellent model for SEM studies. We used flies that were mutant for lobe (L), eyeless (ey), and pannier (pnr) for our studies. The mutant flies exhibit different morphologies of the adult eye. We employed a modified protocol, which reduces sample preparation steps and makes it practically feasible to complete the protocol in assigned time for the cell biology laboratory. The idea of this laboratory exercise is to: (a) familiarize students with the underlying principles of scanning electron microscopy and its application to diverse areas of research, (b) to enable students to sharpen their observation and quantitative microscopy skills, and (c) minimize the preparation time for the instructor