Boolean Threshold Networks: Virtues and Limitations for Biological Modeling

TL;DR

Boolean threshold networks are useful for modeling genetic regulation but have limitations, as their dynamics only align with biological systems under specific parameter conditions, highlighting both their strengths and constraints.

Contribution

This paper analyzes the dynamical properties of Boolean threshold networks, revealing their limited parameter range for biological relevance and contrasting them with Kauffman networks.

Findings

Threshold networks only match biological dynamics in restricted parameter regimes.

The threshold value significantly influences the network's dynamical behavior.

Limitations of threshold networks are discussed in relation to biological modeling.

Abstract

Boolean threshold networks have recently been proposed as useful tools to model the dynamics of genetic regulatory networks, and have been successfully applied to describe the cell cycles of \textit{S. cerevisiae} and \textit{S. pombe}. Threshold networks assume that gene regulation processes are additive. This, however, contrasts with the mechanism proposed by S. Kauffman in which each of the logic functions must be carefully constructed to accurately take into account the combinatorial nature of gene regulation. While Kauffman Boolean networks have been extensively studied and proved to have the necessary properties required for modeling the fundamental characteristics of genetic regulatory networks, not much is known about the essential properties of threshold networks. Here we study the dynamical properties of these networks with different connectivities, activator-repressor proportions, activator-repressor strengths and different thresholds. Special attention is paid to the way in which the threshold value affects the dynamical regime in which the network operates and the structure of the attractor landscape. We find that only for a very restricted set of parameters, these networks show dynamical properties consistent with what is observed in biological systems. The virtues of these properties and the possible problems related with the restrictions are discussed and related to earlier work that uses these kind of models.