Graph Representations of Monotonic Boolean Model Pools

In the face of incomplete data on a system of interest, constraint-based Boolean modeling still allows for elucidating system characteristics by analyzing sets of models consistent with the available information. In this setting, methods not depending on consideration of every single model in the set are necessary for efficient analysis. Drawing from ideas developed in qualitative differential equation theory, we present an approach to analyze sets of monotonic Boolean models consistent with given signed interactions between systems components. We show that for each such model constraints on its behavior can be derived from a universally constructed state transition graph essentially capturing possible sign changes of the derivative. Reachability results of the modeled system, e.g., concerning trap or no-return sets, can then be derived without enumerating and analyzing all models in the set. The close correspondence of the graph to similar objects for differential equations furthermore opens up ways to relate Boolean and continuous models.