Algorithmic Reduction of Biological Networks with Multiple Time Scales
Copyright policy )Algorithmic Reduction of Biological Networks with Multiple Time Scales
AbstractWe 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.
- University of Montpellier France
- French National Centre for Scientific Research France
- RWTH Aachen University Germany
- RWTH Aachen University (Medical Faculty) Germany
- University of Bonn Germany
37D10, Computer Science - Symbolic Computation, FOS: Computer and information sciences, Computer Science - Logic in Computer Science, [INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO], multiple time scales, Molecular Networks (q-bio.MN), satisfiability modulo theories, Dynamical Systems (math.DS), 92C45, Real algebraic computation, Secondary 14P10, Symbolic computation, chemical reaction network, Logic computation, Quantitative Biology - Molecular Networks, Mathematics - Dynamical Systems, Singular perturbation, singular perturbation, Invariant set, Multiple time scales, Polynomial differential equations, [INFO.INFO-SC] Computer Science [cs]/Symbolic Computation [cs.SC], [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], 004, Dimension reduction, Tropical geometry Mathematics Subject Classification Primary 68W30, polynomial differential equations, Chemical reaction network, info:eu-repo/classification/ddc/004, dimension reduction, [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], Symbolic Computation (cs.SC), Symbolic computation and algebraic computation, invariant set, Singular perturbations for ordinary differential equations, FOS: Mathematics, Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.), Satisfiability modulo theories, 68W30 (Primary), 14P10, 34E15, 37D10, 92C45 (Secondary), 34E15, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Invariant manifold theory for dynamical systems, Compartmental model, symbolic computation, Logic in Computer Science (cs.LO), [SDV.BBM.MN] Life Sciences [q-bio]/Biochemistry, Molecular Biology/Molecular Networks [q-bio.MN], tropical geometry, FOS: Biological sciences, real algebraic computation, logic computation, compartmental model
37D10, Computer Science - Symbolic Computation, FOS: Computer and information sciences, Computer Science - Logic in Computer Science, [INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO], multiple time scales, Molecular Networks (q-bio.MN), satisfiability modulo theories, Dynamical Systems (math.DS), 92C45, Real algebraic computation, Secondary 14P10, Symbolic computation, chemical reaction network, Logic computation, Quantitative Biology - Molecular Networks, Mathematics - Dynamical Systems, Singular perturbation, singular perturbation, Invariant set, Multiple time scales, Polynomial differential equations, [INFO.INFO-SC] Computer Science [cs]/Symbolic Computation [cs.SC], [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], 004, Dimension reduction, Tropical geometry Mathematics Subject Classification Primary 68W30, polynomial differential equations, Chemical reaction network, info:eu-repo/classification/ddc/004, dimension reduction, [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], Symbolic Computation (cs.SC), Symbolic computation and algebraic computation, invariant set, Singular perturbations for ordinary differential equations, FOS: Mathematics, Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.), Satisfiability modulo theories, 68W30 (Primary), 14P10, 34E15, 37D10, 92C45 (Secondary), 34E15, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Invariant manifold theory for dynamical systems, Compartmental model, symbolic computation, Logic in Computer Science (cs.LO), [SDV.BBM.MN] Life Sciences [q-bio]/Biochemistry, Molecular Biology/Molecular Networks [q-bio.MN], tropical geometry, FOS: Biological sciences, real algebraic computation, logic computation, compartmental model
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