Positive and negative cycles in Boolean networks

TL;DR

This paper reviews how positive and negative feedback cycles influence the dynamics of asynchronous Boolean networks, which are models used to understand gene regulatory networks, emphasizing the importance of feedback loops in biological systems.

Contribution

It synthesizes existing results on feedback cycles in asynchronous Boolean networks, connecting Thomas' rules with gene network modeling.

Findings

Positive and negative feedback cycles significantly affect network dynamics.

Feedback cycles are central to understanding gene regulation.

The review highlights the relevance of Thomas' ideas in modern systems biology.

Abstract

We review and discuss some results about the influence of positive and negative feedback cycles in asynchronous Boolean networks. These results merge several ideas of Thomas: positive and negative feedback cycles have been largely emphasized by Thomas, through the so called Thomas' rules, and asynchronous Boolean networks have been introduced by Thomas as a model for the dynamics of gene networks, which is nowadays very popular.