This article is cited in 4 papers

Mathematical Modeling of Interaction of Two Cells in the Proneural Cluster of the Wing Imaginal Disk of D. Melanogaster

A. A. Akinshin^a, T. A. Bukharina^b, V. P. Golubyatnikov^cd, D. P. Furman<sup>db

a</sup> Altai State Technical University
^b Institute of Cytology and Genetics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^c Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^d Novosibirsk State University

Abstract: 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.

UDC: 573.2:57.017.64

Received: 12.12.2013