Dynamics of Delay Equations, Theory and Applications - Abstract

D'Huys, Otti

Transient dynamics in autonomous Boolean network motifs: On the role of stochastic time delays

Autonomous Boolean networks are a commonly used model for gene regulatory networks, as they allow for the p rediction of stable dynamical attractors. However, most models do not account for time delays along the links and noise, which are inevitably occur in any real (biological) network. Concentrating on two paradigmatic motifs, the toggle switc h and the repressilator, we develop an experimental testbed that explicitly includes both inter-node time delays and noi se, using digital logic elements. We observe transients that last millions to billions of characteristic time scales and scale exponentially with the amount of time delays between nodes. We develop a hybrid model that that includes time delays along network links and allows for stochastic variation in the delays. Using this model, we explain the observed scaling of the transient lengths of both motifs and recreate the exper imentally measured transient distributions.