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High-gain nonlinear observer for simple genetic regulation process

Author

Listed:
  • Torres, L.A.
  • Ibarra-Junquera, V.
  • Escalante-Minakata, P.
  • Rosu, H.C.

Abstract

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.

Suggested Citation

  • Torres, L.A. & Ibarra-Junquera, V. & Escalante-Minakata, P. & Rosu, H.C., 2007. "High-gain nonlinear observer for simple genetic regulation process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 235-240.
    • Handle: RePEc:eee:phsmap:v:380:y:2007:i:c:p:235-240
    DOI: 10.1016/j.physa.2007.02.105
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