Boolean Networks with Multi-Expressions and Parameters

TL;DR

This paper develops a concise algebraic theory for advanced Boolean network models that include multi-level expressions and parameters, addressing gaps in analytical understanding of these complex biological network models.

Contribution

It introduces algebraic definitions for multi-expression and parameterized Boolean networks and analyzes their attractor structures, advancing the theoretical foundation of these models.

Findings

Algebraic definitions for multi-expression Boolean networks

Analysis of attractor structures in asynchronous models

Theorems characterizing network dynamics

Abstract

To model biological systems using networks, it is desirable to allow more than two levels of expression for the nodes and to allow the introduction of parameters. Various modeling and simulation methods addressing these needs using Boolean models, both synchronous and asynchronous, have been proposed in the literature. However, analytical study of these more general Boolean networks models is lagging. This paper aims to develop a concise theory for these different Boolean logic based modeling methods. Boolean models for networks where each node can have more than two levels of expression and Boolean models with parameters are defined algebraically with examples provided. Certain classes of random asynchronous Boolean networks and deterministic moduli asynchronous Boolean networks are investigated in detail using the setting introduced in this paper. The derived theorems provide a clear picture for the attractor structures of these asynchronous Boolean networks.