Simulation of genetic interaction for Drosophila leg formation

The formation of Drosophila wings and legs are major research topics in Drosophila development, and several hypotheses, such as the polar-coordinate model and the boundary model, has been proposed to explain mechanisms behind these phenomena. A series of recent studies have revealed complex interaction among genes involved in establishing three principal axes (A-P, D-V, and P-D) of leg formation. In this paper, we present a simulation system for leg formation, simulating the genes interactions involved. We use this simulator to investigate a mathematical framework of leg formation which is otherwise well-founded from a molecular perspective. Particularly, we focus on the formation of the expression patterns of dpp, wg, dll, dac, al, en, hh and ci genes, which are involved in the development of the third instar Drosophila leg disc. The most interesting part of this research is showing how the coaxial gene expression patterns behind the P-D axis can be formed, and how positional information, as postulated in the polar-coordinate model, can be conveyed to each cell. Our results suggest that P-D axis can be formed by a set of genes with different activation thresholds; the process involves different chemical gradients of dpp and wg products, forming a bi-polar contour. Interestingly, this combination of chemical gradients can specify unique positions of cells for the hemisphere, leaving the A-P axis determiner to decide only whether the cells are anterior or posterior. All in all, our so-called Bi-Polar Model describes axial formation of the leg disc well.