This article is cited in 6 papers

Study of a one-dimensional model, accounting for cell division, of regulation of the renewing zone size in a biological tissue

S. N. Nikolaev^a, U. S. Zubairova^a, S. I. Fadeev^b, E. Mjolsness^c, N. A. Kolchanov<sup>a

a</sup> Institute of Cytology and Genetics, SB RAS, Novosibirsk
^b Institute of Mathematics, SB RAS, Novosibirsk
^c Department of Computer Science, University of California, Irvine, CA, USA

Abstract: We describe the modeling of the dynamics of renewing zone structure in biological tissues in the formalism of parameterized $L$-systems on an example of the shoot apical meristem. Under study is the influence of the ratio of the characteristic times of the cell cycle and diffusion of morphogens on the stability of some spatially distributed molecular-genetic control system. We show that cell division is a perturbing factor for the system regulating the renewing zone structure. Some conditions are found for the loss of stability of the regulation.

Keywords: mathematical modeling, dynamical systems with dynamical structure, parameterized $L$-systems, shoot apical meristem, cell division, molecular-genetic control system.

UDC: 519.61+577.21

Received: 26.02.2010

 English version: Journal of Applied and Industrial Mathematics, 2011, 5:4, 601–611

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