Preprint Article Version 1 This version is not peer-reviewed

Theoretical Study of the 1 Self-Regulating Gene in the Modified Wagner Model

Version 1 : Received: 31 January 2018 / Approved: 5 February 2018 / Online: 5 February 2018 (10:54:21 CET)

A peer-reviewed article of this Preprint also exists.

Guyeux, C.; Couchot, J.-F.; Rouzic, A.L.; Bahi, J.M.; Marangio, L. Theoretical Study of the One Self-Regulating Gene in the Modified Wagner Model. Mathematics 2018, 6, 58. Guyeux, C.; Couchot, J.-F.; Rouzic, A.L.; Bahi, J.M.; Marangio, L. Theoretical Study of the One Self-Regulating Gene in the Modified Wagner Model. Mathematics 2018, 6, 58.

Journal reference: Mathematics 2018, 6, 58
DOI: 10.3390/math6040058

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 on how to apply such investigations in the case of the dynamical system representing the one self-regulating gene.

Subject Areas

Sigmoid functions; dynamical systems; gene networks

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