Nested canalizing functions minimize sensitivity and simultaneously promote criticality

TL;DR

This paper proves that nested canalizing functions have minimal sensitivity for any activity ratio, influencing biological network robustness and the balance between stability and plasticity.

Contribution

It characterizes the sensitivity boundary of nested canalizing functions and links this to biological network robustness and criticality.

Findings

Nested canalizing functions minimize sensitivity for given activity ratios.

The sensitivity boundary has a fractal structure.

Biological networks tend to operate near the edge of chaos due to these properties.

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.