Abstract
BackgroundThe boundary formation in the Drosophila large intestine is widely studied as an important biological problem. It has been shown that the Delta-Notch signaling pathway plays an essential role in the formation of boundary cells.ResultsIn this paper, we propose a mathematical model for the Delta-Notch dependent boundary formation in the Drosophila large intestine in order to better interpret related experimental findings of this biological phenomenon. To achieve this, we not only perform stability analysis on the model from a theoretical point of view, but also perform numerical simulations to analyze the model with and without noises, the phenotype change with the change of Delta or Notch expression, and the perturbation influences of binding and inhibition parameters on the boundary formation.ConclusionsBy doing all these work, we can assure that our model can better interpret the biological findings related to the boundary formation in the Drosophila large intestine.
Highlights
The boundary formation in the Drosophila large intestine is widely studied as an important biological problem
It has been shown that the Delta-Notch signaling pathway plays an essential role in the boundary formation of the Drosophila large intestine [1, 12]
We propose a mathematical model for the Delta-Notch dependent boundary formation in the Drosophila large intestine based on the work of [13], aiming at better interpreting related biological findings and further making predictions
Summary
The boundary formation in the Drosophila large intestine is widely studied as an important biological problem. The large intestine is a multicellular system that involves a number of cells composed of three cell types, dorsal, ventral and boundary cells, organized in a single-layered epithelial tube [5] For such developmental patterning problems, different kinds of computational strategies [6] have been proposed, e.g., signaling gradients [7] and activator-inhibitor systems [8], It has been shown that the Delta-Notch signaling pathway plays an essential role in the boundary formation of the Drosophila large intestine [1, 12]. The DeltaNotch pathway is considered as one of the six major signaling pathways in cells, which is active in developing embryos at different phases [14] Both Notch and Delta proteins are transmembrane proteins, where Notch proteins act as receptors and Delta proteins as ligands. When Delta ligands in a cell bind to Notch receptors in neighboring cells, all the cells in a system may evolve and form different types of patterns [15,16,17,18]
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