State observers for the estimation of mRNA and protein dynamics

In this paper we study the state estimation problem for a basic model of gene expression. The model describes the interrelation between mRNA and protein within the transcription-translation process. Based on such generic dynamic model, we address the problem of estimating mRNA concentration by only measuring total protein concentration, and we propose a solution to it by means of different state estimation schemes, namely a nonlinear observer, an approximate linear observer and a hybrid extended Kalman filter. Finally, by means of in silico experiments, we compare the proposed structures using a model of the p53 gene network.