Representing Model Ensembles as Boolean Functions

TL;DR

This paper introduces a method to represent families of models, including differential equations and Boolean networks, as Boolean functions, enabling the use of Boolean network analysis techniques to study model behavior and constraints.

Contribution

It demonstrates that qualitative state transition graphs can be reduced to Boolean functions, bridging differential equations and Boolean network analysis.

Findings

Qualitative state transition graphs can be simplified to Boolean functions.

The Boolean function representation preserves reachability properties.

This approach enables applying Boolean network methods to differential equation models.

Abstract

Families of ODE models characterized by a common sign structure of their Jacobi matrix are investigated within the formalism of qualitative differential equations. In the context of regulatory networks the sign structure of the Jacobi matrix carries the information about which components of the network inhibit or activate each other. Information about constraints on the behavior of models in this family is stored in a so called qualitative state transition graph. We showed previously that a similar approach can be used to analyze a model pool of Boolean functions characterized by a common interaction graph. Here we show that the opposite approach is fruitful as well. We show that the qualitative state transition graph can be reduced to a "skeleton" represented by a Boolean function conserving the reachability properties. This reduction has the advantage that approaches such as model checking and network inference methods can be applied to the "skeleton" within the framework of Boolean networks. Furthermore, our work constitutes an alternative to approach to link Boolean networks and differential equations.