Lie Group Analysis of the Photo-Induced Fluorescence of Drosophila Oogenesis with the Asymmetrically Localized Gurken Protein

Abstract

Lie group analysis of the photo-induced fluorescence of Drosophila oogenesis with the asymmetrically localized Gurken protein has been performed systematically to assess the roles of ligand-receptor complexes in follicle cells. The (2×2) matrix representations resulting from the polarized tissue spectra were employed to characterize the asymmetrical Gurken distributions. It was found that the fluorescence of the wild-type egg shows the Lie point symmetry X23 at early stages of oogenesis. However, due to the morphogen regulation by intracellular proteins and extracellular proteins, the fluorescence of the embryogenesis with asymmetrically localized Gurken expansions exhibits specific symmetry features: Lie point symmetry Z1 and Lie point symmetry X1. The novel approach developed herein was successfully used to validate that the invariant-theoretical characterizations are consonant with the observed asymmetric fluctuations during early embryological development. © 2013 Wang et al.