Estimation of Parametric Nonlinear ODEs for Biological Networks Identification

Florence d'Alché-Buc (1) , Nicolas Brunel (1)

1 IBISC - Informatique, Biologie Intégrative et Systèmes Complexes

Ordinary Di erential Equations (ODEs) provide a theoretical frame- work for a mechanistic description of biological networks (e.g. signalling pathway, gene regulatory network, metabolic pathway) as continuous time dynamical systems. Relevant ODEs are often nonlinear because they are derived from biochemical kinetics and based on law of mass action and its generalizations or Hill kinetics. We present two approaches devoted to the identi cation of parameters from time-series of the state variables in non- linear ODEs. The rst approach is based on a nonparametric estimation of the trajectory of the variables involved in the ODE. The parameters are learned in a second step by minimizing a distance between two esti- mates of the derivatives. In the second approach, dedicated to Bayesian estimation, we build a nonlinear state-space model from the ODEs and we estimate both parameters and hidden variables by approximate nonlinear ltering and smoothing (performed by the unscented transform).The two approaches are illustrated on numerical examples and discussed.

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Florence d'Alché-Buc, Nicolas Brunel. Estimation of Parametric Nonlinear ODEs for Biological Networks Identification. Neil D. Lawrence; Mark Girolami; Magnus Rattray; Guido Sanguinetti. Learning and Inference in Computational Systems Biology, MIT Press, pp.61--96, 2009. ⟨hal-00647275⟩