Stabilizing and Destabilizing Effects of Embedding 3-node Subgraphs on State Space of Boolean Networks

TL;DR

This study investigates how embedding different 3-node subgraphs, especially feedforward structures, influences the dynamical complexity of Boolean networks modeling gene regulation, revealing that feedforward motifs simplify dynamics and enhance information processing.

Contribution

It provides a comparative analysis of how various 3-node subgraphs affect Boolean network dynamics, highlighting the stabilizing role of feedforward motifs in biological networks.

Findings

Feedforward subgraphs reduce network complexity and attractor number.

Feedforward motifs increase mutual information and lower entropy.

Other subgraphs tend to destabilize or complicate network dynamics.

Abstract

We demonstrate the effects of embedding subgraphs using a Boolean network, which is one of the discrete dynamical models for transcriptional regulatory networks. After comparing the dynamical properties of network embedded seven different subgraphs including feedback and feedforward subgraphs, we found that complexity of the state space that increases with longer length of attractors and greater number of attractors is reduced for networks with more feedforward subgraphs. In addition, feedforward subgraphs can also provide higher mutual information with lower entropy in a temporal program of gene expression. Networks with other six subgraphs show opposite effects on dynamics of the networks, is roughly consistent with Thomas's conjecture. These results suggest that feedforward subgraphs are one of the favorable local structures in biological complex networks.