José E. R. Cury, Patrícia Tenera Roxo, Vasco Manquinho, Claudine Chaouiya, Pedro T. Monteiro
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Immediate Neighbours of Monotone Boolean Functions
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.