Autonomous Boolean networks (ABNs) are commonly used to model the dynamics of gene regulatory networks. Often, however, most models do not account for time delays along the network links and noise, which are crucial features of real biological systems. Concentrating on the repressilator, we develop an experimental testbed that explicitly includes both inter-node time delays and stochastic noise using digital logic elements on field-programmable gate arrays. We observe transients that last billions of characteristic time scales and scale exponentially with the amount of time delays between nodes, a phenomenon known as supertransient scaling. To counteract these long transients, we show that small, occasional perturbations applied to the time delays can force the transient trajectories to rapidly approach the asymptotic attractors.
This work is in collaboration with Otti Dâ€™Huys, Johannes Lohmann, Nicholas D. Haynes, and Eckehard SchÃ¶ll, and is supported financially by the US Army Research Office Grant # W911NF12-1-0099.