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.
Citation:
S. N. Nikolaev, U. S. Zubairova, S. I. Fadeev, E. Mjolsness, N. A. Kolchanov, “Study of a one-dimensional model, accounting for cell division, of regulation of the renewing zone size in a biological tissue”, Sib. Zh. Ind. Mat., 13:4 (2010), 70–82; J. Appl. Industr. Math., 5:4 (2011), 601–611
\Bibitem{NikZubFad10}
\by S.~N.~Nikolaev, U.~S.~Zubairova, S.~I.~Fadeev, E.~Mjolsness, N.~A.~Kolchanov
\paper Study of a~one-dimensional model, accounting for cell division, of regulation of the renewing zone size in a~biological tissue
\jour Sib. Zh. Ind. Mat.
\yr 2010
\vol 13
\issue 4
\pages 70--82
\mathnet{http://mi.mathnet.ru/sjim639}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2841215}
\transl
\jour J. Appl. Industr. Math.
\yr 2011
\vol 5
\issue 4
\pages 601--611
\crossref{https://doi.org/10.1134/S1990478911040156}
Linking options:
https://www.mathnet.ru/eng/sjim639
https://www.mathnet.ru/eng/sjim/v13/i4/p70
This publication is cited in the following 6 articles:
Penenko A., Zubairova U., Mukatova Zh., Nikolaev S., “Numerical Algorithm For Morphogen Synthesis Region Identi<Overline>Cation With Indirect Image-Type Measurement Data”, J. Bioinform. Comput. Biol., 17:1, SI (2019), 1940002
Zubairova U., Nikolaev S., Penenko A., Podkolodnyy N., Golushko S., Afonnikov D., Kolchanov N., “Mechanical Behavior of Cells Within a Cell-Based Model of Wheat Leaf Growth”, Front. Plant Sci., 7 (2016), 1878
Zubairova U., Golushko S., Penenko A., Nikolaev S., “a Computational Model of the Effect of Symplastic Growth on Cell Mechanics in a Linear Leaf Blade”, J. Bioinform. Comput. Biol., 13:1, SI (2015), 1540005
A. A. Vitvitsky, “Cellular automata with a dynamic structure for simulating the biological tissues growth”, Num. Anal. Appl., 7:4 (2014), 263–273
A. V. Penenko, T. S. Troeglazova, U. S. Zubairova, D. Zh. Baishibaev, S. V. Nikolaev, “Primenenie tekhnologii CUDA dlya modelirovaniya protsessov reaktsii-diffuzii na dvumernom kletochnom ansamble”, Matem. biologiya i bioinform., 9:2 (2014), 491–503
A.V. Penenko, A.V. Penenko, “Usage of Parallel Algorithms Based on CUDA Technology for Realisation of Reaction-Diffusion Models of Two-Dimensional Cellular Ensemble”, Math.Biol.Bioinf., 9:2 (2014), 491