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Algorithmic Reduction of Biological Networks With Multiple Time Scales

Abstract : We present a symbolic algorithmic approach that allows to compute invariant manifolds and corresponding reduced systems for differential equations modeling biological networks which comprise chemical reaction networks for cellular biochemistry, and compartmental models for pharmacology, epidemiology and ecology. Multiple time scales of a given network are obtained by scaling, based on tropical geometry. Our reduction is mathematically justified within a singular perturbation setting using a recent result by Cardin and Teixeira. The existence of invariant manifolds is subject to hyperbolicity conditions, which we test algorithmically using Hurwitz criteria. We finally obtain a sequence of nested invariant manifolds and respective reduced systems on those manifolds. Our theoretical results are generally accompanied by rigorous algorithmic descriptions suitable for direct implementation based on existing off-the-shelf software systems, specifically symbolic computation libraries and Satisfiability Modulo Theories solvers. We present computational examples taken from the well-known BioModels database using our own prototypical implementations.
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https://hal.archives-ouvertes.fr/hal-02977490
Contributor : Thomas Sturm Connect in order to contact the contributor
Submitted on : Sunday, October 25, 2020 - 10:04:47 AM
Last modification on : Saturday, October 16, 2021 - 11:26:06 AM

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  • HAL Id : hal-02977490, version 1
  • ARXIV : 2010.10129

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Niclas Kruff, Christoph Lüders, Ovidiu Radulescu, Thomas Sturm, Sebastian Walcher. Algorithmic Reduction of Biological Networks With Multiple Time Scales. 2020. ⟨hal-02977490⟩

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