A Logical Constraint-based Approach to Infer and Explore Diversity and Composition in Thresholded Boolean Automaton Networks

Gene regulatory networks (GRN) are often modeled by Boolean networks to describe their structures and properties. Constraint logic programming (CPL) can be used to infer networks that satisfy constraints applied on their structure and their dynamics. Such approach yield complete satisfiable network sets that can be large. Having such complete sets allows to compare networks between each other and to understand how they can be constructed from other networks. In the present paper, we describe this inference approach applied to a particular class of thresholded Boolean automaton networks, a variation of Boolean neural networks, focusing on a necessary step to reduce the size of satisfiable sets to sets of non-redundant networks. For that purpose, we use a recent non-monotonic logic programming technology, namely Answer Set Programming (ASP). Our approach managed to yield complete network sets satisfying a given behavior, namely having a specific dynamics – a binary motif fixed in advance – on at least one node of networks of a given size. This allows us to illustrate how general rules could explain some relations of composition between these networks.