A dynamic model of gene regulatory networks based on inertia principle Florence d’Alch´ e–Buc 1 , Pierre-Jean Lahaye 1 , Bruno-Edouard Perrin 1,2 , Liva Ralaivola 1 , Todor Vujasinovic 2 , Aur´ elien Mazurie 2 , and Samuele Bottani 2 1 Laboratoire d’Informatique de Paris 6, CNRS UMR 7606, 8 rue du capitaine Scott, 75015 Paris, FRANCE 2 Laboratoire de G´ en´ etique Mol´ eculaire de la Neurotransmission et des Processus D´ eg´ en´ eratifs,CNRS UMR 7091, Hˆopital La Piti´ e-Salpˆ etri` ere, 75013 Paris, FRANCE 1 Introduction In molecular biology, functions are produced by a set of macromolecules that interact at different levels. Genes and their products, proteins, participate to regulatory networks that control the response of the cell to external in- put signals. One of the most important challenge to biologists is undoubtedly to understand the mechanisms that govern this regulation, and to identify among a set of genes which play a regulator role and which are regulated. While the problem used to be approached by a gene to gene approach, this is changed significantly by the development of microarray technology. Expression of thousands of genes of a given organism or a given tissue can now be mea- sured simultaneously on the same chip. This revolution opens a large avenue for research on reconstruction of gene regulatory networks from experimental data. In this chapter, we claim that both machine learning and modeling of dynamical processes offer a formal and methodological framework to tackle this problem. In our approach, gene regulatory networks are considered as complex, distributed and dynamic systems. The first step consists in the def- inition of a model of the underlying dynamics. Then, the availability of gene expression kinetics makes it possible to learn parameters of the model. A ma- jor advantage of considering the dynamics of the system lies in the fact that the identification step yields both the interaction graph between genes and a simulator for the system. We propose here a linear dynamical model which captures complex behaviours of interactions and a machine learning scheme to identify its parameters. The framework of linear Gaussian state-space models provides a way to take into account noise both in the observations and in the