Algorithmic Reduction of Biological Networks With Multiple Time Scales

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...

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Bibliographic Details
Published inarXiv.org
Main Authors Kruff, Niclas, Lüders, Christoph, Radulescu, Ovidiu, Sturm, Thomas, Walcher, Sebastian
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 02.03.2021
Subjects
Algorithms
Biological models (mathematics)
Cellular communication
Chemical reactions
Differential equations
Epidemiology
Invariants
Networks
Pharmacology
Reduction
Singular perturbation
Solvers
Time
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Summary: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-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.
ISSN:2331-8422