Computation of Immediate Neighbours of Monotone Boolean Functions

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.