Cellular automata with dynamic structure to simulate the growth of biological tissues

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• 作者：A. A. Vitvitsky (1)
  
• 关键词：computer simulation ; cellular automata ; cellular automata with dynamic structure ; morphogenesis ; shoot apical meristem ; Arabidopsis Thaliana
• 刊名：Numerical Analysis and Applications
• 出版年：2014
• 出版时间：October 2014
• 年：2014
• 卷：7
• 期：4
• 页码：263-273
• 全文大小：1,274 KB
• 参考文献：1. Nikolaev, S.V., Zubairova, U.S., Fadeev, S.I., Mjolsness, E., and Kolchanov, N.A., Study of a One-Dimensional Model of Regulation of Regeneration Zone Size in a Biological Tissue with Cell Division, / Sib. Zh. Ind. Mat., 2010, vol. 13, no. 4, pp. 70鈥?2.
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  3. Lazareva, G.G., Mironova, V.V., Omelyanchuk, N.A., Shvab, I.V., Vshivkov, V.A., Gorpinchenko, D.N., Nikolaev, S.V., and Kolchanov, N.A., Mathematical Modeling of Vegetation Morphogenesis, / Sib. Zh. Vych. Mat., 2008, vol. 11, no. 2, pp. 151鈥?66.
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  7. Zubairova, U.S., Penenko, A.V., and Nikolaev, S.V., Modeling of Plant Tissue Growth and Development with L-Systems, / Vavilovski Zh. Gen. Sel., 2012, vol. 16, no. 4/1, pp. 816鈥?24.
  8. Toffolli, T., Computation and Construction Universality of Reversible Automata, / J. Comput. Syst. Sci., 1977, vol. 15,iss. 2, pp. 213鈥?31. CrossRef
  
• 作者单位：A. A. Vitvitsky (1)
  
  1. Institute of Computational Mathematics and Mathematical Geophysics, pr. Akad. Lavrent鈥檈va 6, Novosibirsk, 630090, Russia
  
• ISSN：1995-4247

文摘

A concept of cellular automaton with dynamic structure of the cellular space (DCA) is proposed. The DCA extends the capabilities of classical cellular automata (CA) and allows using a cellular automata approach to the problems of simulating biological tissue growth. A DCA differs from a classical CA in that its cells are not located on a regular lattice, and the intercellular connections are explicitly described by a neighborhood matrix. In addition, insertion and partition operators are introduced in the DCA. These operators allow one to dynamically change the cell space structure. Based on this extension, a DCA-model of growth of a shoot apical meristem of Arabidopsis Thaliana is constructed, being a parallel composition of two DCA: an asynchronous two-dimensional DCA simulating self-regulation of biological cells and a synchronous one-dimensional DCA simulating the growth and division of biological cells. The results of computer simulation have shown that the behavior of the DCA-model is the same as that of an existing model based on a composition of differential equations and L-system (Lindenmayer system) methods. The DCA-model allows one to simulate the growth of individual biological cells and to visualize the dynamics of substances in these cells (decay, synthesis, and diffusion).