Correspondence of Trap Spaces in Different Models of Bioregulatory Networks

Please always quote using this URN: urn:nbn:de:0297-zib-67121
  • Mathematical models for bioregulatory networks can be based on different formalisms, depending on the quality of available data and the research question to be answered. Discrete boolean models can be constructed based on qualitative data, which are frequently available. On the other hand, continuous models in terms of ordinary differential equations (ODEs) can incorporate time-series data and give more detailed insight into the dynamics of the underlying system. A few years ago, a method based on multivariate polynomial interpolation and Hill functions has been developed for an automatic conversion of boolean models to systems of ordinary differential equations. This method is frequently used by modellers in systems biology today, but there are only a few results available about the conservation of mathematical structures and properties across the formalisms. Here, we consider subsets of the phase space where some components stay fixed, called trap spaces, and demonstrate how boolean trap spaces can be linked to invariant sets in the continuous state space. This knowledge is of practical relevance since finding trap spaces in the boolean setting, which is relatively easy, allows for the construction of reduced ODE models.

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Author:Robert Schwieger, Heike Siebert, Susanna RöblitzORCiD
Document Type:ZIB-Report
Tag:Boolean networks; attractors; dynamical systems; invariant sets; ordinary differential equations; trap spaces
MSC-Classification:37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] / 37Nxx Applications / 37N25 Dynamical systems in biology [See mainly 92-XX, but also 91-XX]
92-XX BIOLOGY AND OTHER NATURAL SCIENCES / 92Bxx Mathematical biology in general / 92B05 General biology and biomathematics
Date of first Publication:2018/02/19
Series (Serial Number):ZIB-Report (18-10)
ISSN:1438-0064
Published in:SIAM J. Appl. Dyn. Syst., 17(2), 1742–1765
DOI:https://doi.org/https://doi.org/10.1137/17M1155302