Design and performance of in vitro transcription rate regulatory circuit

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Elisa Franco, Richard M Murray
Conference on Decision and Control (CDC)

This paper proposes a new synthetic in vitro circuit that aims at regulating the rate of RNA transcription through positive feedback interactions. This design is dual to a previously synthesized transcriptional rate regulator based on self-repression. Two DNA templates are designed to interact through their transcripts, creating cross activating feedback loops that will equate their transcription rates at steady state. A mathematical model is developed for this circuit, consisting of a set of ODEs derived from the mass action laws and Michaelis--Menten kinetics involving all the present chemical species. This circuit is then compared to its regulatory counterpart based on negative feedback. A global sensitivity analysis reveals the fundamental features of the two designs, by evaluating their equilibrium response to changes in the most crucial parameters of the system.