# Tuning a synthetic in vitro oscillator using control-theoretic tools

### Christopher Sturk, Elisa Franco, Richard M Murray

Conference on Decision and Control (CDC), 2010 (Submitted)

This paper demonstrates the effectiveness of sim- ple control-theoretic tools in generating simulation-guided ex- periments on a synthetic in vitro oscillator. A theoretical analysis of the behavior of such system is motivated by high cost, time consuming experiments, together with the excessive number of tuning parameters. A simplified model of the synthetic oscillator is chosen to capture only its essential features. The model is analyzed using the small gain theorem and the theory of describing functions. Such analysis reveals what are the parameters that primarily determine when the system can admit stable oscillations. Experimental verification of the theoretical and numerical findings is carried out and confirms the predicted results regarding the role of production and degradation rates.

- Preprint: http://www.cds.caltech.edu/~murray/preprints/sfm10-cdc_s.pdf
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