PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Estimation of parametric nonlinear ODEs for biological networks identification
Florence d'Alché-Buc and Nicolas Brunel
In: Learning and Inference in Computational Systems Biology (2008) MIT press .


Ordinary Differential Equations (ODEs) provide a theoretical framework for a mechanistic description of biological networks (\emph{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 identification of parameters from time-series of the state variables in nonlinear ODEs. The first 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 estimates 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 filtering and smoothing (performed by the unscented transform). The two approaches are illustrated on numerical examples and discussed.

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EPrint Type:Book Section
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:5112
Deposited By:Florence d'Alché-Buc
Deposited On:24 March 2009