Spatially varying multifeedback for robust signaling

Abstract

Elaborate regulatory feedback processes are thought to make biological development robust, that is, resistant to changes induced by sustained genetic or environmental perturbations. How this might be accomplished is still not completely understood, especially when models of some known feedback processes have been shown, some analytically and others by numerical simulations, to be ineffective in promoting robust signaling. By working with nonlocal feedback processes, combinations of two of these ineffective feedback processes were found to ensure robustness as measured by a well‐defined robustness index for the Dpp–Tkv (decapentaplegic–thickvein) signaling in the wing imaginal disc of Drosophila fruit flies. In this paper, we show that there are also spatially varying multifeedback combinations of individually ineffective components that are similarly successful. The analysis of these Hill function type multifeedback models are found to be much more challenging mathematically as the relevant boundary‐value problem remains nonlinear even for systems in a steady state of low receptor occupancy.