Mathematical Study of the Role of Delta/Notch Lateral Inhibition during Primary Branching of Drosophila Trachea Development

A wide range of cellular developmental processes employ intercellular signaling via the Delta/Notch lateral inhibitory pathway to achieve stable spatial patterning. Recent genetic experiments have shown the importance of Delta/Notch lateral inhibition for regulating the number of tip cells in the tracheal primary branching of Drosophila. To examine the role of Delta/Notch regulation in the tip-cell selection, we analyzed a mathematical model of a simple lateral inhibitory system having input signals. Mathematical and numerical analyses revealed that the lateral inhibition did not amplify the signal difference between neighboring cells over the parameter ranges in which the spatial pattern of tip selection was realized. We also show that the number of tip cells becomes less affected by a fluctuation of the input gradient signal as the lateral inhibition becomes stronger. In addition, we demonstrate that the lateral inhibitory regulation enhances the robustness of the tip-cell selection compared with a system regulated by self-inhibition, an alternative means of inhibitory regulation. These results suggest that the lateral inhibition promotes the robustness of tip-cell selection in the tracheal development of Drosophila.