Identification of parameters and structure of piecewise affine models of genetic networks

In this paper we consider piecewise affine models of genetic regulatory networks proposed by Glass and Kaufmann in the 70's and discuss a method for their identification. These systems have specific features that must be preserved by the identification procedure in order to obtain biologically meaningful models. Moreover, rather than producing a single hypothesis about the way genes interact, identification should produce alternatives consistent with the available data so as to provide biologists with multiple hypothesis about the network functioning. The input of the identification method consists of time-series measurements of concentrations of gene products. As outputs, estimates of the modes of operation of the GRN as well as all possible minimal combinations of threshold concentrations of the gene products accounting for switches between the modes of operation are provided. Individual steps of the identification method have been been described separately in previous publications and the main aim of this paper is to test the applicability of the whole procedure. To this purpose, we use simulated data obtained from a model of the carbon starvation response in the bacterium E. coli. In particular, performance of the method under different data characteristics, notably variations in the noise level and the sampling density, are discussed.