AND-NOT logic framework for steady state analysis of Boolean network models

TL;DR

This paper introduces AND-NOT networks as a subclass of Boolean models for biological systems, enabling simplified analysis and broad applicability, demonstrated through a Th-cell differentiation case study.

Contribution

It proposes AND-NOT networks for biological modeling, establishing their advantages and equivalence to general finite dynamical systems for steady state analysis.

Findings

Any finite dynamical system can be represented as an AND-NOT network.

There is a one-to-one correspondence between AND-NOT networks, wiring diagrams, and dynamics.

Results can be applied to any Boolean network without loss of information.

Abstract

Finite dynamical systems (e.g. Boolean networks and logical models) have been used in modeling biological systems to focus attention on the qualitative features of the system, such as the wiring diagram. Since the analysis of such systems is hard, it is necessary to focus on subclasses that have the properties of being general enough for modeling and simple enough for theoretical analysis. In this paper we propose the class of AND-NOT networks for modeling biological systems and show that it provides several advantages. Some of the advantages include: Any finite dynamical system can be written as an AND-NOT network with similar dynamical properties. There is a one-to-one correspondence between AND-NOT networks, their wiring diagrams, and their dynamics. Results about AND-NOT networks can be stated at the wiring diagram level without losing any information. Results about AND-NOT networks are applicable to any Boolean network. We apply our results to a Boolean model of Th-cell differentiation.