title: A Geometric Method for Model Reduction of Biochemical Networks with Polynomial Rate Functions.
abstract: Model reduction of biochemical networks relies on the knowledge of slow and fast variables. We provide a geometric method, based on the Newton polytope, to identify slow variables of a biochemical network with polynomial rate functions. The gist of the method is the notion of tropical equilibration that provides approximate descriptions of slow invariant manifolds. Compared to extant numerical algorithms such as the intrinsic low-dimensional manifold method, our approach is symbolic and utilizes orders of magnitude instead of precise values of the model parameters. Application of this method to a large collection of biochemical network models supports the idea that the number of dynamical variables in minimal models of cell physiology can be small, in spite of the large number of molecular regulatory actors.
authors.affiliation: Algorithmic Bioinformatics, Bonn-Aachen International Center for IT, Dahlmannstraße 2, 53113, Bonn, Germany. samal@cs.uni-bonn.de.
authors.forename: Satya Swarup
authors.initials: SS
authors.lastname: Samal
authors.affiliation: CNRS, Mathématiques, Université de Lille, 59655, Villeneuve d'Ascq, France. dmitry.grigoryev@math.univ-lille1.fr.
authors.forename: Dima
authors.initials: D
authors.lastname: Grigoriev
authors.affiliation: Algorithmic Bioinformatics, Bonn-Aachen International Center for IT, Dahlmannstraße 2, 53113, Bonn, Germany. frohlich@bit.uni-bonn.de.
authors.forename: Holger
authors.initials: H
authors.lastname: Fröhlich
authors.affiliation: Institut für Informatik II, University of Bonn, Friedrich-Ebert-Allee 144, 53113, Bonn, Germany. weber@cs.uni-bonn.de.
authors.forename: Andreas
authors.initials: A
authors.lastname: Weber
authors.affiliation: DIMNP UMR CNRS 5235, University of Montpellier, Montpellier, France. ovidiu.radulescu@univ-montp2.fr.
authors.forename: Ovidiu
authors.initials: O
authors.lastname: Radulescu
mesh_terms: D000465:Algorithms; D001669:Biochemical Phenomena; D002453:Cell Cycle; D007700:Kinetics; D055641:Mathematical Concepts; D053858:Metabolic Networks and Pathways; D008954:Models, Biological; D049490:Systems Biology
keywords: Algebraic systems biology; Complexity; Model reduction