From differential equations to Boolean networks: A Case Study in modeling regulatory networks

TL;DR

This paper establishes a mathematical connection between differential equations and Boolean networks in modeling cellular regulatory networks, demonstrating how Boolean models can be derived as coarse-grained limits of differential models.

Contribution

It provides a formal framework linking differential equations and Boolean networks, enabling controlled application of Boolean models to biological systems.

Findings

Boolean networks can be derived as coarse-grained limits of differential equation models

The approach offers a mathematical foundation for applying Boolean models to biological networks

Demonstrates the relation using the fission yeast cell cycle control network

Abstract

Methods of modeling cellular regulatory networks as diverse as differential equations and Boolean networks co-exist, however, without any closer correspondence to each other. With the example system of the fission yeast cell cycle control network, we here set the two approaches in relation to each other. We find that the Boolean network can be formulated as a specific coarse-grained limit of the more detailed differential network model for this system. This lays the mathematical foundation on which Boolean networks can be applied to biological regulatory networks in a controlled way.