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Sibirskii Zhurnal Industrial'noi Matematiki, 2010, Volume 13, Number 4, Pages 70–82 (Mi sjim639)  
This article is cited in 6 scientific papers (total 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. Nikolaeva, U. S. Zubairovaa, S. I. Fadeevb, E. Mjolsnessc, N. A. Kolchanova

a 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
Full-text PDF (445 kB) Citations (6)
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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.
Received: 26.02.2010
English version:
Journal of Applied and Industrial Mathematics, 2011, Volume 5, Issue 4, Pages 601–611
DOI: https://doi.org/10.1134/S1990478911040156
Bibliographic databases:
Document Type: Article
UDC: 519.61+577.21
Language: Russian
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
Citation in format AMSBIB
\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:
    1. 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  crossref  mathscinet  isi  scopus
    2. 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  crossref  isi
    3. 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  crossref  isi  elib  scopus
    4. A. A. Vitvitsky, “Cellular automata with a dynamic structure for simulating the biological tissues growth”, Num. Anal. Appl., 7:4 (2014), 263–273  mathnet  crossref  mathscinet
    5. 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  mathnet
    6. 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  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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