Analysis of a Digital Clock for Molecular Computing

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Johan Ugander, Mary J Dunlop, Richard M Murray
American Control Conference, 2007 (submitted)

Gene expression is often controlled by natural genetic regulatory networks that govern the rates at which genes are transcribed. Recent work has shown that synthetic versions of genetic networks can be designed and built in living cells. Applications for these synthetic regulatory networks include intracellular decision-making and computation. In this study, we propose a new synthetic genetic network that behaves as a digital clock, producing square waveform oscillations. We analyze two models of the network, a deterministic model based on Michaelis-Menten kinetics, as well as a stochastic model based on the Gillespie algorithm. Both models predict regions of oscillatory behavior; the deterministic model provides insight into the conditions required to produce the oscillating clock-like behavior, while the stochastic model is truer to natural dynamics. Intracellular stochasticity is seen to contribute phase noise to the oscillator, and we propose improvements for the network and discuss the conceptual foundations of these improvements.