Summarizing complex asynchronous Boolean attractors, application to the analysis of a mammalian cell cycle model

Biological regulatory networks can be efficiently modeled by asynchronous Boolean networks. In such networks, asymptotic dynamical behaviors are captured by asynchronous attractors, which are strongly connected graphs that may include multiple intertwined cycles. If it can be easily computed, comparing such a complex graph with a biological phenomenon may become rapidly cumbersome. In this paper, we propose to use the concept of summary graph to help the analysis of asynchronous attractors, by projecting them on partitions of the state space. The method is applied to a Boolean model of the mammalian cell cycle, for which we propose a suitable partition based on the cycle's phases. Thanks to our approach, we were able to isolate the expected succession of the phases.