Estimating parameters and hidden variables in non-linear state-space models based on ODEs for biological networks inference

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

1 IBISC - Informatique, Biologie Intégrative et Systèmes Complexes

Statistical inference of biological networks such as gene regulatory networks, signaling pathways and metabolic networks can contribute to build a picture of complex interactions that take place in the cell. However, biological systems considered as dynamical, nonlinear and generally partially observed processes may be difficult to estimate even if the structure of interactions is given. Using the same approach as Sitz et al. (2002) proposed in another context, we derive nonlinear state-space models from ODEs describing biological networks. In this framework, we apply Unscented Kalman Filtering (UKF) to the estimation of both parameters and hidden variables of nonlinear state-space models. We instantiate the method on a transcriptional regulatory model based on Hill kinetics and a signaling pathway model based on mass action kinetics and successfully use synthetic data and experimental data to test our approach.This approach covers a large set of biological networks models and gives rise to simple and fast estimation algorithms. Moreover, the Bayesian tool used here directly provides uncertainty estimates on parameters and hidden states. Let us also emphasize that it can be coupled with structure inference methods used in Graphical Probabilistic Models.

Domaines: Informatique; Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]; Modélisation et simulation; Apprentissage [cs.LG]; Base de données [cs.DB]

Minh Quach, Nicolas Brunel, Florence d'Alché-Buc. Estimating parameters and hidden variables in non-linear state-space models based on ODEs for biological networks inference. Bioinformatics, 2007, 23, pp.3209--3216. ⟨10.1093/bioinformatics/btm510⟩. ⟨hal-00341950⟩