Transient dynamics and their control in time-delay autonomous Boolean ring networks


Biochemical systems with switch-like interactions, such as gene regulatory networks, are well modeled by autonomous Boolean networks. Specifically, the topology and logic of gene interactions can be described by systems of continuous piecewise-linear differential equations, enabling analytical predictions of the dynamics of specific networks. However, most models do not account for time delays along links associated with spatial transport, mRNA transcription, and translation. To address this issue, we have developed an experimental test bed to realize a time-delay autonomous Boolean network with three inhibitory nodes, known as a repressilator, and use it to study the dynamics that arise as time delays along the links vary. We observe various nearly periodic oscillatory transient patterns with extremely long lifetime, which emerge in small network motifs due to the delay, and which are distinct from the eventual asymptotically stable periodic attractors. For repeated experiments with a given network, we find that stochastic processes give rise to a broad distribution of transient times with an exponential tail. In some cases, the transients are so long that it is doubtful the attractors will ever be approached in a biological system that has a finite lifetime. To counteract the long transients, we show experimentally that small, occasional perturbations applied to the time delays can force the trajectories to rapidly approach the attractors.

Publication DOI:
Divisions: College of Engineering & Physical Sciences
Additional Information: © APS
Uncontrolled Keywords: Statistical and Nonlinear Physics,Statistics and Probability,Condensed Matter Physics
Publication ISSN: 1550-2376
Last Modified: 04 Mar 2024 08:20
Date Deposited: 15 Mar 2017 09:25
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
PURE Output Type: Article
Published Date: 2017-02-17
Accepted Date: 2017-01-23
Submitted Date: 2016-05-31
Authors: Lohmann, Johannes
d'Huys, Otti (ORCID Profile 0000-0001-7498-6771)
Haynes, Nicholas D.
Schöll, Eckehard
Gauthier, Daniel J.



Version: Accepted Version

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