  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.
