  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
