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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
.
Abstract 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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