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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Vydáno v:Mathematics in computer science Ročník 15; číslo 3; s. 499 - 534
Hlavní autoři: Kruff, Niclas, Lüders, Christoph, Radulescu, Ovidiu, Sturm, Thomas, Walcher, Sebastian
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 01.09.2021
Springer Nature B.V
Springer
Témata:
Algebraic Geometry
Algorithms
Biochemistry, Molecular Biology
Biological models (mathematics)
Cellular communication
Chemical reactions
Computer Science
Differential equations
Dynamical Systems
Epidemiology
Invariants
Life Sciences
Logic in Computer Science
Mathematics
Mathematics and Statistics
Molecular Networks
Networks
Pharmacology
Reduction
Singular perturbation
Symbolic Computation
Time
Primary 68W30
Singular perturbation
Tropical geometry
Invariant set
Satisfiability modulo theories
Symbolic computation
34E15
Logic computation
Dimension reduction
92C45
Compartmental model
Multiple time scales
Polynomial differential equations
Secondary 14P10
37D10
Chemical reaction network
Real algebraic computation
Tropical geometry Mathematics Subject Classification Primary 68W30
ISSN:1661-8270, 1661-8289
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Popis
Shrnutí: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.
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ISSN:1661-8270
1661-8289
DOI:10.1007/s11786-021-00515-2