Boolean networks model finite discrete dynamical systems with complex behaviours. The state of each component is determined by a Boolean function of the state of (a subset of) the components of the network.This paper addresses the synthesis of these Boolean functions from constraints on their domain and emerging dynamical properties of the resulting network. The dynamical properties relate to the existence and absence of trajectories between partially observed configurations, and to the stable behaviours (fixpoints and cyclic attractors). The synthesis is expressed as a Boolean satisfiability problem relying on Answer-Set Programming with a parametrized complexity, and leads to a complete non-redundant characterization of the set of solutions.Considered constraints are particularly suited to address the synthesis of models of cellular differentiation processes, as illustrated on a case study. The scalability of the approach is demonstrated on random networks with scale-free structures up to 100 to 1,000 nodes depending on the type of constraints.

The construction of models of biological networks from prior knowledge and experimental data often leads to a multitude of candidate models. Devising a single model from them can require arbitrary choices, which may lead to strong biases in subsequent predictions. We introduce here a methodology for a) synthesizing Boolean model ensembles satisfying a set of biologically relevant constraints and b) reasoning on the dynamics of the ensembles of models. The synthesis is performed using Answer-Set Programming, extending prior work to account for solution diversity and universal constraints on reachable fixed points, enabling an accurate specification of desired dynamics. The sampled models are then simulated and the results are aggregated through averaging or can be analyzed as a multi-dimensional distribution. We illustrate our approach on a previously published Boolean model of a molecular network regulating the cell fate decisions in cancer progression. It appears that the ensemble-based approach to Boolean modelling brings new insights on the variability of synergistic interacting mutations effect concerning propensity of a cancer cell to metastasize.