Regulatory Feedbacks on Receptor and Non-receptor Synthesis for Robust Signaling

Elaborate feedback regulatory processes are thought to make biological developments robust, i.e., resistant to changes induced by genetic or environmental perturbations. How this might be done is still not completely understood. Previous numerical simulations on reaction-diffusion models of Dpp gradients in Drosophila wing imaginal disc showed that feedback (of the Hills function type) on (signaling) receptors and/or non-(signaling) receptors are of limited effectiveness in promoting robustness. Spatial nonuniformity of the feedback processes is thought to lead to serious shape distortion and a principal cause for ineffectiveness. Through mathematical modeling of a spatially uniform nonlocal feedback mechanism, the present paper provides a theoretical support of these observations. More significantly, the new approach also enables us to uncover in this paper a new, theory-based multi-feedback instrument for broadly effective promotion of robust signaling gradients.