Computing Maximal and Minimal Trap Spaces of Boolean Networks

TL;DR

This paper introduces an optimization-based approach to compute all minimal and maximal trap spaces in Boolean networks, aiding the analysis of biological systems' attractors and model reduction.

Contribution

It presents a novel method for computing trap spaces, including a new lower bound for cyclic attractors, and compares solver performance on random networks.

Findings

The method effectively computes trap spaces in biological models.

A new lower bound for cyclic attractors is established.

Solver performance varies with network complexity.

Abstract

Asymptotic behaviors are often of particular interest when analyzing Boolean networks that represent biological systems such as signal trans- duction or gene regulatory networks. Methods based on a generalization of the steady state notion, the so-called trap spaces, can be exploited to investigate attractor properties as well as for model reduction techniques. In this paper, we propose a novel optimization-based method for com- puting all minimal and maximal trap spaces and motivate their use. In particular, we add a new result yielding a lower bound for the number of cyclic attractors and illustrate the methods with a study of a MAPK pathway model. To test the efficiency and scalability of the method, we compare the performance of the ILP solver gurobi with the ASP solver potassco in a benchmark of random networks.