Higher order Boolean networks as models of cell state dynamics

The regulation of the cell state is a complex process involving several components. These complex dynamics can be modeled using Boolean networks, allowing us to explain the existence of different cell states and the transition between them. Boolean models have been introduced both as specific examples and as ensemble or distribution network models. However, current ensemble Boolean network models do not make a systematic distinction between different cell components such as epigenetic factors, gene and transcription factors. Consequently, we still do not understand their relative contributions in controlling the cell fate. In this work we introduce and study higher order Boolean networks, which feature an explicit distinction between the different cell components and the types of interactions between them. We show that the stability of the cell state dynamics can be determined solving the eigenvalue problem of a matrix representing the regulatory interactions and their strengths. The qualitative analysis of this problem indicates that, in addition to the classification into stable and chaotic regimes, the cell state can be simple or complex depending on whether it can be deduced from the independent study of its components or not. Finally, we illustrate how the model can be expanded considering higher levels and higher order dynamics.