IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v6y2018i4p58-d140244.html
   My bibliography  Save this article

Theoretical Study of the One Self-Regulating Gene in the Modified Wagner Model

Author

Listed:
  • Christophe Guyeux

    (Femto-ST Institute, UMR 6174 CNRS, University of Bourgogne Franche-Comté, 90000 Belfort, France)

  • Jean-François Couchot

    (Femto-ST Institute, UMR 6174 CNRS, University of Bourgogne Franche-Comté, 90000 Belfort, France)

  • Arnaud Le Rouzic

    (EGCE, CNRS-IRD-Université Paris-Saclay, 91198 Gif-sur-Yvette, France)

  • Jacques M. Bahi

    (Femto-ST Institute, UMR 6174 CNRS, University of Bourgogne Franche-Comté, 90000 Belfort, France)

  • Luigi Marangio

    (Femto-ST Institute, UMR 6174 CNRS, University of Bourgogne Franche-Comté, 90000 Belfort, France)

Abstract

Predicting how a genetic change affects a given character is a major challenge in biology, and being able to tackle this problem relies on our ability to develop realistic models of gene networks. However, such models are rarely tractable mathematically. In this paper, we propose a mathematical analysis of the sigmoid variant of the Wagner gene-network model. By considering the simplest case, that is, one unique self-regulating gene, we show that numerical simulations are not the only tool available to study such models: theoretical studies can be done too, by mathematical analysis of discrete dynamical systems. It is first shown that the particular sigmoid function can be theoretically investigated. Secondly, we provide an illustration of how to apply such investigations in the case of the dynamical system representing the one self-regulating gene. In this context, we focused on the composite function f a ( m . x ) where f a is the parametric sigmoid function and m is a scalar not in { 0 , 1 } and we have proven that the number of fixed-point can be deduced theoretically, according to the values of a and m .

Suggested Citation

  • Christophe Guyeux & Jean-François Couchot & Arnaud Le Rouzic & Jacques M. Bahi & Luigi Marangio, 2018. "Theoretical Study of the One Self-Regulating Gene in the Modified Wagner Model," Mathematics, MDPI, vol. 6(4), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:4:p:58-:d:140244
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/6/4/58/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/6/4/58/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. M. Perc, 2009. "Stochastic resonance on paced genetic regulatory small-world networks: effects of asymmetric potentials," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 69(1), pages 147-153, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhdanov, Vladimir P., 2012. "Periodic perturbation of genetic oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 45(5), pages 577-587.
    2. Zhdanov, Vladimir P., 2011. "Periodic perturbation of the bistable kinetics of gene expression," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(1), pages 57-64.
    3. Hu, Yahong & Zhu, Quanyong, 2017. "New analytic solutions of two-dimensional nonlocal nonlinear media," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 53-61.
    4. Xie, Tianting & Ji, Yuandong & Yang, Zhongshan & Duan, Fabing & Abbott, Derek, 2023. "Optimal added noise for minimizing distortion in quantizer-array linear estimation," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    5. Zeng, Lingzao & Li, Jianlong & Shi, Jiachun, 2012. "M-ary signal detection via a bistable system in the presence of Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 378-382.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:6:y:2018:i:4:p:58-:d:140244. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.