A three-cell model of the initial stage of development of a proneural cluster

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Abstract

We construct a 9-dimensional nonlinear dynamical system that simulates the initial stage of interaction of three adjacent cells in the proneural cluster of Drosophila melanogaster. We describe the conditions of existence of three stable equilibrium points in the phase space of this system, list its other equilibrium points, and provide a biological interpretation.

Original languageEnglish
Pages (from-to)168-173
Number of pages6
JournalJournal of Applied and Industrial Mathematics
Volume11
Issue number2
DOIs
Publication statusPublished - 1 Apr 2017

Keywords

  • equilibrium point
  • gene network
  • negative and positive feedback
  • nonlinear dynamical system
  • phase portrait
  • stability

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