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A constraint solving approach to model reduction by tropical equilibration.

Sylvain Soliman1, François Fages1, Ovidiu Radulescu2

  • 1Inria, Domaine de Voluceau, Rocquencourt, 78150 France.

Algorithms for Molecular Biology : AMB
|December 11, 2014
PubMed
Summary

This study introduces constraint-based methods to solve complex tropical equilibration problems for model reduction in systems biology. This approach enables numerical solutions for non-linear problems, aiding in the analysis of dynamical systems.

Keywords:
Constraint programmingModel reductionSystems biologyTropical algebraTropical equilibration

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Area of Science:

  • Systems Biology
  • Dynamical Systems Theory
  • Computational Mathematics

Background:

  • Model reduction is crucial for simplifying complex biological models and identifying key parameters.
  • Singular perturbation theory analyzes time scales, while tropical methods offer an algebraic framework for polynomial systems.
  • Tropical equilibrations are central to tropical methods but can be computationally challenging.

Purpose of the Study:

  • To present a novel constraint-based method for numerically solving non-linear tropical equilibration problems.
  • To demonstrate the application of this method for model reduction in systems biology.
  • To validate the approach using a biochemical model and large-scale biological data.

Main Methods:

  • Utilizing reified constraints to express tropical equilibration conditions.
  • Applying constraint-based methods to solve non-linear tropical equilibration problems numerically.
  • Testing the method on the Michaelis-Menten enzymatic reaction model and the BioModels database.

Main Results:

  • Successfully solved non-linear tropical equilibration problems intractable by standard methods.
  • Achieved detailed model reduction for the Michaelis-Menten model.
  • Demonstrated scalability and performance on large datasets from the BioModels repository.

Conclusions:

  • Constraint-based methods offer a powerful numerical approach for tropical equilibration problems.
  • This technique facilitates model reduction in systems biology, particularly for complex dynamical systems.
  • The method shows promise for analyzing and simplifying large biological models efficiently.