Structure identification for gene regulatory networks via linearization and robust state estimation

Inferring causal relationships among cellular components is one of the fundamental problems in understanding biological behaviours. The well known extended Kalman filter (EKF) has been proved to be a useful tool in simultaneously estimating both structure and actual gene expression levels of a gene regulatory network (GRN). First-order approximations, however, unavoidably result in modelling errors, but the EKF based method does not take either unmodelled dynamics or parametric uncertainties into account, which makes its estimation performances not very satisfactory. To overcome these problems, a sensitivity penalization based robust state estimator is adopted in this paper for revealing the structure of a GRN. Based on the specific structure of the estimation problem, it has been proved that under some weak conditions, both the EKF based method and the method suggested in this paper provide a consistent estimate, but the suggested method has a faster convergence speed. Compared with both the EKF and the unscented Kalman filter (UKF) based methods, simulation results and real data based estimations consistently show that both convergence speed and parametric estimation accuracy can be appreciably improved. These lead to significant reductions in both false positive errors and false negative errors, and may imply helpfulness of the suggested method in better understanding the structure and dynamics of actual GRNs.