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Condition for Periodic Attractor in 4-Dimensional Repressilators

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Computational Methods in Systems Biology (CMSB 2023)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 14137))

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Abstract

One of the key questions about gene regulatory networks is how to predict complex dynamical properties based on the influence graph’s topology. Earlier theoretical studies have identified conditions for complex dynamical properties, like multistability or oscillations, based on topological features, like the presence of a positive (negative) feedback loop. This work follows this path and aims to find a sufficient and necessary condition for the existence of a periodic attractor in 4-dimensional (4 genes) repressilators based on a discrete modeling framework under some dynamical assumptions. These networks are extensions of the widely studied 3-dimensional repressilator, which has been used in synthetic biology to produce synthetic oscillations. While other researchers have explored specific extensions of the 3-dimensional repressilator to improve synthetic oscillation control, our work investigates all 4-dimensional networks with only inhibitions. By uncovering new insights about periodic attractors in these small networks, our findings could aid the design of new synthetic oscillations. We search for condition for period attractor in an exhaustive manner with the guide of a decision tree model. Our major contributions include: 1) discovering that, with one exception, the relations between gene regulation thresholds do not impact the existence of periodic attractors in any of the influence graphs considered in this study; 2) identifying a sufficient and necessary condition of simple form for the existence of a periodic attractor when the exception is ignored; 3) identifying new topological features of influence graphs that are necessary for predicting the existence of periodic attractor in 4-dimensional repressilators.

Supported by China Scholarship Council.

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Acknowledgements

We would like to thank Gilles Bernot and Jean-Paul Comet for their fruitful discussions. We would also like to thank Coraly Soto for her internship report which helped us in the early stage of this work to find features to predict the existence of a periodic attractor.

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Authors and Affiliations

  1. Nantes Université, École Centrale Nantes, CNRS, LS2N, UMR 6004, 44000, Nantes, France

    Honglu Sun & Morgan Magnin

  2. Univ. Lille, CNRS, Centrale Lille, UMR 9189 CRIStAL, 59000, Lille, France

    Maxime Folschette

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  1. Honglu Sun
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Correspondence to Honglu Sun .

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Editors and Affiliations

  1. University of Luxembourg, Esch-sur-Alzette, Luxembourg

    Jun Pang

  2. Inria Lille, Villeneuve d’Ascq, France

    Joachim Niehren

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Sun, H., Folschette, M., Magnin, M. (2023). Condition for Periodic Attractor in 4-Dimensional Repressilators. In: Pang, J., Niehren, J. (eds) Computational Methods in Systems Biology. CMSB 2023. Lecture Notes in Computer Science(), vol 14137. Springer, Cham. https://doi.org/10.1007/978-3-031-42697-1_13

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  • DOI: https://doi.org/10.1007/978-3-031-42697-1_13

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  • Online ISBN: 978-3-031-42697-1

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