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.

中文翻译：

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空间变化的多反馈以实现稳健的信令

精心设计的调节反馈过程被认为可以使生物发育稳健，即对持续的遗传或环境扰动引起的变化具有抵抗力。这可能如何实现仍然没有完全理解，特别是当一些已知的反馈过程的模型已经被证明时，一些是分析的，另一些是通过数值模拟，在促进鲁棒信令方面是无效的。通过使用非局部反馈过程，发现这些无效反馈过程中的两个的组合可以确保鲁棒性，如果蝇果蝇翅膀成虫盘中 Dpp-Tkv（decapentaplegic-thickvein）信号的明确鲁棒性指数所衡量的那样。在本文中，我们展示了同样成功的单个无效组件的空间变化多反馈组合。发现对这些希尔函数类型多反馈模型的分析在数学上更具挑战性，因为即使对于处于低受体占用率的稳定状态的系统，相关的边界值问题仍然是非线性的。