Partial Order on the set of Boolean Regulatory Functions

TL;DR

This paper characterizes the set of monotone Boolean functions compatible with regulatory networks, introduces rules for local exploration of these functions, and relates them to network dynamics, aiding model analysis.

Contribution

It introduces a novel local exploration method for monotone Boolean functions and links these functions to network dynamics, improving model analysis without full enumeration.

Findings

Defined relationships between regulatory functions and dynamics

Developed rules for local exploration of Boolean functions

Applied approach to T helper cell differentiation model

Abstract

Logical models have been successfully used to describe regulatory and signaling networks without requiring quantitative data. However, existing data is insufficient to adequately define a unique model, rendering the parametrization of a given model a difficult task. Here, we focus on the characterization of the set of Boolean functions compatible with a given regulatory structure, i.e. the set of all monotone nondegenerate Boolean functions. We then propose an original set of rules to locally explore the direct neighboring functions of any function in this set, without explicitly generating the whole set. Also, we provide relationships between the regulatory functions and their corresponding dynamics. Finally, we illustrate the usefulness of this approach by revisiting Probabilistic Boolean Networks with the model of T helper cell differentiation from Mendoza & Xenarios.