Mapping the attractor landscape of Boolean networks

Boolean networks are popular dynamical models of cellular processes in systems biology. Their attractors model phenotypes that arise from the interplay of key regulatory subcircuits. A succession diagram describes this interplay in a discrete analog of Waddington’s epigenetic attractor landscape that allows for fast identification of attractors and attractor control strategies. We present a new approach to succession diagram construction for asynchronously updated Boolean networks, implemented in the biologist’s Boolean attractor landscape mapper, biobalm, a Python 3 library. We compare the performance of biobalm to similar tools and find a substantial performance increase in succession diagram construction, attractor identification, and attractor control. To illustrate the utility of biobalm, we perform the most comprehensive comparative analysis to date of the succession diagram structure in experimentally-validated Boolean network models of cell processes and random ensembles. We find that random models (including critical Kauffman networks) have relatively small succession diagrams, indicating simple decision structures. In contrast, non-random models from the literature are enriched in extremely large succession diagrams, indicating an abundance of decision points in their dynamics and suggesting the presence of complex Waddington landscapes in nature.