Phenotype control and elimination of variables in Boolean networks

TL;DR

This paper explores how variable elimination in Boolean networks influences their long-term behavior and control strategies, providing structural conditions for preserving key dynamics across various control methods and update schemes.

Contribution

It introduces a structural condition that guarantees the preservation of minimal trap spaces during variable elimination in Boolean networks.

Findings

Elimination of variables can preserve or alter asymptotic dynamics.

A structural condition ensures minimal trap space preservation.

Different control approaches are affected variably by variable elimination.

Abstract

We investigate how elimination of variables can affect the asymptotic dynamics and phenotype control of Boolean networks. In particular, we look at the impact on minimal trap spaces, and identify a structural condition that guarantees their preservation. We examine the possible effects of variable elimination under three of the most popular approaches to control (attractor-based control, value propagation and control of minimal trap spaces), and under different update schemes (synchronous, asynchronous, generalized asynchronous). We provide some insights on the application of reduction, and an ample inventory of examples and counterexamples.