Nested canalizing functions minimize sensitivity and simultaneously promote criticality

Abstract

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.