Mathematical Modeling of Interaction of Two Cells in the Proneural Cluster of the Wing Imaginal Disk of~\emph{D.~Melanogaster}
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 14 (2014) no. 4, pp. 3-10
Voir la notice de l'article provenant de la source Math-Net.Ru
We consider the phase portrait of a 6-dimensional nonlinear dynamical system considered as a model of an early stage of morphogenesis of D. melanogaster, i.e., appearance of its parental cell in the proneural cluster. Sufficient conditions of existence of two stable equilibrium points of this system are described, and biological interpretation is given.
Keywords:
cell complex, nonlinear dynamical systems, negative and positive feedbacks, equilibrium points, the Notch signaling pathway.
@article{VNGU_2014_14_4_a0,
author = {A. A. Akinshin and T. A. Bukharina and V. P. Golubyatnikov and D. P. Furman},
title = {Mathematical {Modeling} of {Interaction} of {Two} {Cells} in the {Proneural} {Cluster} of the {Wing} {Imaginal} {Disk} {of~\emph{D.~Melanogaster}}},
journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
pages = {3--10},
publisher = {mathdoc},
volume = {14},
number = {4},
year = {2014},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VNGU_2014_14_4_a0/}
}
TY - JOUR
AU - A. A. Akinshin
AU - T. A. Bukharina
AU - V. P. Golubyatnikov
AU - D. P. Furman
TI - Mathematical Modeling of Interaction of Two Cells in the Proneural Cluster of the Wing Imaginal Disk of~\emph{D.~Melanogaster}
JO - Sibirskij žurnal čistoj i prikladnoj matematiki
PY - 2014
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PB - mathdoc
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A. A. Akinshin; T. A. Bukharina; V. P. Golubyatnikov; D. P. Furman. Mathematical Modeling of Interaction of Two Cells in the Proneural Cluster of the Wing Imaginal Disk of~\emph{D.~Melanogaster}. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 14 (2014) no. 4, pp. 3-10. http://geodesic.mathdoc.fr/item/VNGU_2014_14_4_a0/