  We prove that nested canalizing functions are the minimum-sensitivity Boolean
functions for any given activity ratio and we characterize the sensitivity
boundary which has a nontrivial fractal structure. We further observe, on an
extensive database of regulatory functions curated from the literature, that
this bound severely constrains the robustness of biological networks. Our
findings suggest that the accumulation near the "edge of chaos" in these
systems is a natural consequence of a drive towards maximum stability while
maintaining plasticity in transcriptional activity.
