Lie group study of Raman spectra of the Gurken gradient in Drosophila oogenesis.

We carried out a Lie group study of the micro-Raman tissue spectra of the Gurken gradients of Drosophila oogenesis. Matrix representations (2 × 2) resulting from the polarized Raman scattering were employed to assess the roles of the ligand-receptor complexes in follicle cell. It was found that the Gurken expansion caused by overexpressing Dally-like protein (Dlp) revealed an X(1) Lie point symmetry, while the Gurken distribution in the wild-type egg showed an X(23) 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. 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.