On the Observability and State Estimation in a Class of Gene-Expression System

Abstract

The failure of available physical sensors for the online measurement of protein concentration in cells is a key problem to understanding the transition in bio-systems. In this paper, a new state observer has been designed to estimate three protein concentrations by using a gene-expression mathematical model. Interestingly, its only input is the concentration of one messenger RNA (mRNA). Similarly by differential-algebraic observability analysis is showed that the gene-expression model is indeed observable. The observer convergence was demonstrated by analysing the estimation error dynamics. In silico experiments confirm the satisfactory performance of this new observer.

Using sliding mode observers to estimate BtuB concentration from measured vitamin B 12 concentration

“…Azam et al [14 ] developed a reduced‐order sliding mode observer to estimate the unknown state of the MDM2–p53 protein complex by enforcing a sliding mode on the error in the concentration of p53 protein. Aguilar‐Lopez and Mata‐Machuca [15 ] developed a state observer to estimate the time evolutions of three protein concentrations in a gene expression model by measuring one mRNA concentration using the RT–PCR method. Cacace et al [16 ] developed a Luenberger observer which estimated the concentration of mRNA and the concentration of protein with minor parameter uncertainties.…”