Abstract
In the face of incomplete data on a system of interest, constraint-based Boolean modeling still allows for elucidating system characteristics by analyzing sets of models consistent with the available information. In this setting, methods not depending on consideration of every single model in the set are necessary for efficient analysis. Drawing from ideas developed in qualitative differential equation theory, we present an approach to analyze sets of monotonic Boolean models consistent with given signed interactions between systems components. We show that for each such model constraints on its behavior can be derived from a universally constructed state transition graph essentially capturing possible sign changes of the derivative. Reachability results of the modeled system, e.g., concerning trap or no-return sets, can then be derived without enumerating and analyzing all models in the set. The close correspondence of the graph to similar objects for differential equations furthermore opens up ways to relate Boolean and continuous models.
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Notes
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More specifically speaking, we use a multivariate interpolation and a subsequent concatenation with Hill Cubes to obtain an ODE-System, which is guaranteed to have a Jacobi matrix, whose abstraction coincides with the matrix \(\varSigma \) on the off diagonals. Then we choose arbitrarily Hill coefficients and thresholds.
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Schwieger, R., Siebert, H. (2017). Graph Representations of Monotonic Boolean Model Pools. In: Feret, J., Koeppl, H. (eds) Computational Methods in Systems Biology. CMSB 2017. Lecture Notes in Computer Science(), vol 10545. Springer, Cham. https://doi.org/10.1007/978-3-319-67471-1_14
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DOI: https://doi.org/10.1007/978-3-319-67471-1_14
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