Skip to Main content Skip to Navigation
New interface
Journal articles

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. The existence of invariant manifolds is subject to hyperbolicity conditions, for which we propose an algorithmic test based on 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-theshelf 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.
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-03438176
Contributor : Thomas Sturm Connect in order to contact the contributor
Submitted on : Sunday, November 21, 2021 - 8:08:05 AM
Last modification on : Wednesday, November 23, 2022 - 10:16:08 AM
Long-term archiving on: : Tuesday, February 22, 2022 - 6:56:50 PM

File

Kruff2021_Article_AlgorithmicR...
Files produced by the author(s)

Licence


Distributed under a Creative Commons Attribution 4.0 International License

Identifiers

Citation

Niclas Kruff, Christoph Lüders, Ovidiu Radulescu, Thomas Sturm, Sebastian Walcher. Algorithmic Reduction of Biological Networks with Multiple Time Scales. Mathematics in Computer Science, 2021, 15 (3), pp.499 - 534. ⟨10.1007/s11786-021-00515-2⟩. ⟨hal-03438176⟩

Share

Metrics

Record views

51

Files downloads

18