Robert Schwieger ; Elisa Tonello - Reduction for asynchronous Boolean networks: elimination of negatively autoregulated components

dmtcs:10930 - Discrete Mathematics & Theoretical Computer Science, March 22, 2024, vol. 25:2 -
Reduction for asynchronous Boolean networks: elimination of negatively autoregulated componentsArticle

Authors: Robert Schwieger ; Elisa Tonello

    To simplify the analysis of Boolean networks, a reduction in the number of components is often considered. A popular reduction method consists in eliminating components that are not autoregulated, using variable substitution. In this work, we show how this method can be extended, for asynchronous dynamics of Boolean networks, to the elimination of vertices that have a negative autoregulation, and study the effects on the dynamics and interaction structure. For elimination of non-autoregulated variables, the preservation of attractors is in general guaranteed only for fixed points. Here we give sufficient conditions for the preservation of complex attractors. The removal of so called mediator nodes (i.e. vertices with indegree and outdegree one) is often considered, and frequently does not affect the attractor landscape. We clarify that this is not always the case, and in some situations even subtle changes in the interaction structure can lead to a different asymptotic behaviour. Finally, we use properties of the more general elimination method introduced here to give an alternative proof for a bound on the number of attractors of asynchronous Boolean networks in terms of the cardinality of positive feedback vertex sets of the interaction graph.

    Volume: vol. 25:2
    Section: Automata, Logic and Semantics
    Published on: March 22, 2024
    Accepted on: November 28, 2023
    Submitted on: February 8, 2023
    Keywords: Computer Science - Discrete Mathematics

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