Section: New Results

Quantitative Model Reduction: a CLP Solver for Computing Tropical Equilibrations

Participants : François Fages, Sylvain Soliman.

Model reduction is a central topic in computational systems biology and dynamical systems theory, for reducing the complexity of quantitative models, finding important parameters, and developing multi-scale models for instance. While perturbation theory is a standard mathematical tool to analyze the different time scales of a dynamical system, and decompose the system accordingly, tropical methods provide a simple algebraic framework to perform these analyses systematically in polynomial systems. The crux of these tropicalization methods is in the computation of tropical equilibrations. In [13] , we show that constraint-based methods, using reified constraints for expressing the equilibration conditions, make it possible to numerically solve non-linear tropical equilibration problems, out of reach of standard computation methods. We illustrate this approach first with the reduction of simple biochemical mechanisms such as the Michaelis-Menten and Goldbeter-Koshland models, and second, with performance figures obtained on a large scale on the model repository biomodels.net .

This work is done in collaboration with Ovidiu Radulescu, Univ. Montpellier, in the context of a larger project about symbolic methods in systems biology with François Boullier, LIFL and Andras Weber, Univ. Bonn.