The necessity and benefits of multiple feedback for robust biological development

Robust development of biological organisms is known to involve a variety of inhibitors whose specific roles in downregulating the undesirably excessive signaling activities are reasonably well understood. Empirical evidence points to existence of feedback mechanisms for upregulating inhibitory agents. At least two conventional feedback models have been found by model analysis to be ineffective or biologically inappropriate. In this paper, we explore more fully the recently formulated new type of regulatory feedback for robustness to examine all such feedback processes possible in a three-component basic extracellular model for ligand signaling. Acting alone, all processes will again be shown to be ineffective for promoting robustness. The principal finding of the present theoretical analysis is that a concurrent implementation of some combinations of two of these feedback processes actually renders the signaling gradient robust with respect to genetic and epi-genetic perturbations. Moreover, different multifeedback combinations achieve robustness in different ways. These findings provide a possible explanation for the concurrent presence of several such individually ineffective feedback processes in robust signaling gradients.