The state observer as a tool for the estimation of gene expression

In this paper a mathematical tool is presented, to estimate unknown variables of transcription networks, according to a set of measurements of the transcriptional activity of promoters. The approach is based on the use of the mathematical model of the network under investigation and on the state-reconstruction technique known as ‘state observer’, borrowed from the control theory. To this aim, besides the general case, the network motif of the Multi-Output Feed-Forward Loop (MO-FFL) will be investigated in details. Simulations show the effectiveness of the proposed approach in a wide range of possible critical frameworks, such as only one target gene measurements, non-smooth input perturbations, noisy measurements and model parameter uncertainties.