  Reconstruction of biochemical reaction networks is a central topic in systems
biology which raises crucial theoretical challenges in system identification.
Nonlinear Ordinary Differential Equations (ODEs) that involve polynomial and
rational functions are typically used to model biochemical reaction networks.
Such nonlinear models make the problem of determining the connectivity of
biochemical networks from time-series experimental data quite difficult. In
this paper, we present a network reconstruction algorithm that can deal with
model descriptions under the form of polynomial and rational functions. Rather
than identifying the parameters of linear or nonlinear ODEs characterised by
pre-defined equation structures, our methodology allows us to determine the
nonlinear ODEs structure together with their associated reaction constants. To
solve the network reconstruction problem, we cast it as a Compressive Sensing
(CS) problem and use Bayesian Sparse Learning (BSL) algorithms as an efficient
way to obtain its solution.
