On the Algebraic Geometry of Polynomial Dynamical Systems

Jarrah, Abdul Salam; Laubenbacher, Reinhard

doi:10.1007/978-0-387-09686-5_5

Cited by 2 publications

(1 citation statement)

References 21 publications

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“…This framework can be generalized to the case when there are more than two states chosen from some alphabet. More generally the states can take different values in algebraic groups or fields Jarrah and Laubenbacher (2008). We have freedom to choose different updating regimes as well.…”

Section: Discussionmentioning

confidence: 99%

Higher order Boolean networks as models of cell state dynamics

Markert

Baas

Levine

et al. 2010

Journal of Theoretical Biology

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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 * Corresponding author Preprint submitted to Journal of Theoretical Biology February 17, 2018 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.

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Section: Discussionmentioning

confidence: 99%