High-gain nonlinear observer for simple genetic regulation process

Details High-gain nonlinear observer for simple genetic regulation process High-gain nonlinear observer for simple genetic regulation process

2004-09-29

arxiv.org/abs/q-bio/0409036v2

Physica A 380 (2007) 235-240

Biology

Quantitative Biology

Quantitative Methods

9 pages, one figure

Scientific paper

10.1016/j.physa.2007.02.105

High-gain nonlinear observers occur in the nonlinear automatic control theory and are in standard usage in chemical engineering processes. We apply such a type of analysis in the context of a very simple one-gene regulation circuit. In general, an observer combines an analytical differential-equation-based model with partial measurement of the system in order to estimate the non-measured state variables. We use one of the simplest observers, that of Gauthier et al., which is a copy of the original system plus a correction term which is easy to calculate. For the illustration of this procedure, we employ a biological model, recently adapted from Goodwin's old book by De Jong, in which one plays with the dynamics of the concentrations of the messenger RNA coding for a given protein, the protein itself, and a single metabolite. Using the observer instead of the metabolite, it is possible to rebuild the non-measured concentrations of the mRNA and the protein

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