Lie group Analyses to pattern formation of Gurken distribution in Drosophila oogenesis

We carried out a Lie group study of the micro-Raman tissue spectra of the Gurken gradients of Drosophila oogenesis. (2×2) matrix representations resulting from the polarized Raman scattering were employed to assess the roles of the Dally-like protein (Dlp) in follicle cell. It was found that the Gurken expansion caused by over-expressing Dlp revealed a X1 Lie point symmetry, while the Gurken distribution in the wild-type egg showed a X23 Lie point symmetry. The correlation between the corresponding continuous symmetry operations and the observed Gurken localization were a corroboration of the significance of the Lie group analysis by means of the reaction-diffusion equation in a prolate spheroidal coordinate system. 2 These investigations suggested that the group-theoretical approach can be applied to characterize the fluctuating asymmetry and the developmental stability in a wide variety of organisms.