The Stability of Boolean Networks with Generalized Canalizing Rules

TL;DR

This paper investigates the stability of Boolean networks with generalized canalizing rules, extending previous models to include canalizing behavior and analyzing their order/disorder transitions.

Contribution

It introduces a framework for analyzing Boolean networks with generalized canalizing rules, broadening understanding of their stability properties.

Findings

Derived stability conditions for networks with canalizing rules

Extended previous models to include generalized canalization

Provided insights into order/disorder transitions in these networks

Abstract

Boolean networks are discrete dynamical systems in which the state (zero or one) of each node is updated at each time t to a state determined by the states at time t-1 of those nodes that have links to it. When these systems are used to model genetic control, the case of 'canalizing' update rules is of particular interest. A canalizing rule is one for which a node state at time $t$ is determined by the state at time t-1 of a single one of its inputs when that inputting node is in its canalizing state. Previous work on the order/disorder transition in Boolean networks considered complex, non-random network topology. In the current paper we extend this previous work to account for canalizing behavior.