Theoretical study of the one self-regulating gene in the modified Wagner model
type: Item
instance of: scholarly article
title: Theoretical study of the one self-regulating gene in the modified Wagner model
zbMATH Open document ID: 1394.92083
author: Christophe Guyeux
author: Jean-François Couchot
author: Arnaud Le Rouzic
author: Jacques M. Bahi
author: Luigi Marangio
published in: Mathematics
publication date: 2018-07-05T00:00:00Z
review text: Summary: 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 \(m\).
Mathematics Subject Classification ID: 92D10
Mathematics Subject Classification ID: 92C40
zbMATH DE Number: 6898750
zbMATH Keywords: gene-network model
zbMATH Keywords: Wagner model
zbMATH Keywords: discrete dynamical systems
MaRDI profile type: Publication
full work available at URL: math6040058
OpenAlex ID: W2785745014
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cites work: Wagner's canalization model
cites work: Phenotype-genotype relation in Wagner's canalization model
DOI: 10.3390/MATH6040058
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description: scientific article; zbMATH DE number 6898750