Canalization in the Critical States of Highly Connected Networks of Competing Boolean Nodes

TL;DR

This paper investigates how highly connected Boolean networks evolve to critical, canalized states, revealing that similar robustness features emerge beyond K=3 inputs when evolution favors homogeneous Boolean functions.

Contribution

It extends previous findings on canalization in Boolean networks to cases with more than three inputs, highlighting the role of evolutionary bias towards homogeneous functions.

Findings

Canalized critical states occur for K>3 with biased evolution.

Symmetry of evolutionary dynamics is linked to the emergence of canalization.

Homogeneous Boolean functions are key to the development of robustness.

Abstract

Canalization is a classic concept in Developmental Biology that is thought to be an important feature of evolving systems. In a Boolean network it is a form of network robustness in which a subset of the input signals control the behavior of a node regardless of the remaining input. It has been shown that Boolean networks can become canalized if they evolve through a frustrated competition between nodes. This was demonstrated for large networks in which each node had K=3 inputs. Those networks evolve to a critical steady-state at the boarder of two phases of dynamical behavior. Moreover, the evolution of these networks was shown to be associated with the symmetry of the evolutionary dynamics. We extend these results to the more highly connected K>3 cases and show that similar canalized critical steady states emerge with the same associated dynamical symmetry, but only if the evolutionary dynamics is biased toward homogeneous Boolean functions.