Computation of Immediate Neighbours of Monotone Boolean Functions

TL;DR

This paper explores the set of monotone Boolean functions relevant to genetic network models, providing rules to efficiently identify neighboring functions to aid in network synthesis and revision.

Contribution

It introduces original rules for computing immediate neighbors of monotone Boolean functions, enhancing methods for Boolean network parametrization and refinement.

Findings

Derived rules for neighbors of monotone Boolean functions

Facilitated exploration of regulatory function space

Supported improved Boolean network synthesis methods

Abstract

Boolean networks constitute relevant mathematical models to study the behaviours of genetic and signalling networks. These networks define regulatory influences between molecular nodes, each being associated to a Boolean variable and a regulatory (local) function specifying its dynamical behaviour depending on its regulators. However, existing data is mostly insufficient to adequately parametrise a model, that is to uniquely define a regulatory function for each node. With the intend to support model parametrisation, this paper presents results on the set of Boolean functions compatible with a given regulatory structure, i.e. the partially ordered set of monotone non-degenerate Boolean functions. More precisely, we present original rules to obtain the direct neighbours of any function of this set. Besides a theoretical interest, presented results will enable the development of more efficient methods for Boolean network synthesis and revision, benefiting from the progressive exploration of the vicinity of regulatory functions.