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The model by Naama Barkai and Stanislas Leibler distinguishes robustness of adaptation from invariance of baseline activity. Figure 1b and equation 1 explain why output-dependent reverse modification can remove the need for tuning to ligand level.

Researcher in quantitative biology. With Naama Barkai, Leibler studied robustness in simple biochemical networks, connecting a system’s organization with its ability to maintain behavior despite changes in component parameters.^[ref]