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Open AccessArticle

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

1
Femto-ST Institute, UMR 6174 CNRS, University of Bourgogne Franche-Comté, 90000 Belfort, France
2
EGCE, CNRS-IRD-Université Paris-Saclay, 91198 Gif-sur-Yvette, France
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(4), 58; https://doi.org/10.3390/math6040058
Received: 31 January 2018 / Revised: 6 March 2018 / Accepted: 31 March 2018 / Published: 9 April 2018
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. View Full-Text
Keywords: gene-network model; Wagner model; discrete dynamical systems gene-network model; Wagner model; discrete dynamical systems
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Guyeux, C.; Couchot, J.-F.; Le Rouzic, A.; Bahi, J.M.; Marangio, L. Theoretical Study of the One Self-Regulating Gene in the Modified Wagner Model. Mathematics 2018, 6, 58.

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