Mathematical methods for inferring regulatory networks interactions: application to genetic regulation

This paper deals with the problem of reconstruction of the intergenic interaction graph from the raw data of genetic co-expression coming with new technologies of bio-arrays (DMA-arrays, protein-arrays, etc.). These new imaging devices in general only give information about the asymptotical part (fixed configurations of co-expression or limit cycles of such configurations) of the dynamical evolution of the regulatory networks (genetic and/or proteic) underlying the functioning of living systems. Extracting the casual structure and interaction coefficients of a gene interaction network from the observed configurations is a complex problem. But if all the fixed configurations are supposedly observed and if they are factorizable into two or more subsets of values, then the interaction graph possesses as many connected components as the number of factors and the solution is obtained in polynomial time. This new result allows us for example to partly solve the topology of the genetic regulatory network ruling the flowering in Arabidopsis thaliana .