Preview

Vavilov Journal of Genetics and Breeding

Advanced search

AN L-SYSTEM FOR MODELING OF UNIDIMENSIONALLY GROWING FLAT PLANT TISSUES

Abstract

In this work, a mathematical model and its implementation are proposed for computational simulation of one-dimensional symplastic growth of tissues. We modified the formal grammar of differential L-systems, and in this grammar, we described a dynamic model of symplastic growth with regard to its biomechanics. The results of the simulation of linear leaf blade growth are compared with those for a free-growing cell population. It is shown that in the model proposed symplastic growth causes a greater deviation of the actual cell length from its isosmotic length than in freely growing cells.

About the Authors

U. S. Zubairova
Institute of Cytology and Genetics SB RAS, Novosibirsk, Russia
Russian Federation


S. K. Golushko
Design and Technology Institute of Digital Techniques SB RAS, Novosibirsk, Russia
Russian Federation


A. V. Penenko
Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk, Russia
Russian Federation


S. V. Nikolaev
Institute of Cytology and Genetics SB RAS, Novosibirsk, Russia
Russian Federation


References

1. Зубаирова У.С., Пененко А.В., Николаев С.В. Моделирование роста и развития растительных тканей в формализме L-систем // Вавиловский журнал генетики и селекции. 2012. Т. 16. № 4/1. С. 816–824.

2. Николаев С.В., Зубаирова У.С., Фадеев С.И., Мйолснесс Э., Колчанов Н.А. Исследование одномерной модели регуляции размеров возобновительной зоны в биологической ткани с учетом деления клеток // СибЖИМ. 2010. Т. 13. Вып. 4 (44). С. 70–82.

3. Bryan A.K., Goranov A., Amon A., Manalisa S.R. Measurement of mass, density, and volume during the cell cycle of yeast // PNAS. 2010. V. 107. P. 999–1004.

4. Chickarmane V.S., Gordon S.P., Tarr P.T. et al. Cytokinin signaling as a positional cue for patterning the apical-basal axis of the growing Arabidopsis shoot meristem // Proc. Natl Acad. Sci. USA. 2012. V. 109 (10). P. 4002–4007.

5. Dolan L. Pattern in the Root Epidermis: An Interplay of Diffusible Signals and Cellular Geometry // Annals Botany 1996. V. 77. P. 547–553.

6. Gibson L.J. The hierarchical structure and mechanics of plant materials // J. Royal Society Interface. 2012. published online.

7. Hamant O., Heisler M., Jönsson H. et al. Developmental paterning by mechanical signals in Arabidopsis // Science. 2008. Dec. 12. V. 322 (5908). P. 1650–1655.

8. Honda H., Tanemura M., Nagai T. A three-dimensional vertex dynamics cell model of space-fi lling polyhedra simulating cell behavior in a cell aggregate // Journal Theoretical Biology. 2004. V. 226 (4). P. 439–453.

9. Jönsson H., Heisler M. G., Shapiro B. E. et al. An auxin-driven polarized transport model for phyllotaxis // PNAS. 2005. V. 103. P. 1633–1638.

10. Lindenmayer A. Mathematical models for cellular interaction in development // J. Theor. Biology. 1968. V. 18. P. 280–315.

11. Merks R., Guravage M., Inze D., Beemster G. Virtual Leaf: An Open-Source Framework for Cell-Based Modeling of Plant Tissue Growth and Development // Plant Physiol. 2011. V. 155 (2). P. 656–666.

12. Nakamura M., Kiefer C.S., Grebe M. Planar polarity, tissue polarity and planar morphogenesis in plants // Curr. Opin Plant Biol. 2012. V. 15 (6). P. 593–600.

13. Nobel P.S. Physicochemical and Environmental Plant Physiology. Amsterdam: Elsevier Academic Press, 2005.

14. Ortega J.K. Plant Cell Growth in Tissue // Plant Physiology. 2010. V. 154. P. 1244–1253.

15. Priestley J. Studies in the physiology of cambial activity // New Physiology. 1930. V. 29. P. 96–140.

16. Prusinkiewicz P., Lindenmayer A. The algorithmic beauty of plants. NewYork: Springer, 1990.

17. Prusinkiewicz P., Hammel M., Mjolsness E. Animation of plant development // Proc. SIGGRAPH 93. Anaheim, California. Ann. Conference Series. 1993. P. 351−360.

18. Ryu K.H., Zheng X., Huang L., Schiefelbein J. Computational modeling of epidermal cell fate determination systems // Current Opinion Plant Biology. 2013. V. 16 (1). P. 5–10.

19. Smith R., Guyomarc’h S. et al. A plausible model of phyllotaxis // Proc. Natl Acad. Sci. 2006. V. 103. P. 1301–1306.

20. Williams R.F. The Shoot Apex and Leaf Growth: A Study in Quantitative Biology. London; New York: Cambridge University Press, 1974.

21. Yadav R.K., Perales M., Gruel J. et al. Plant stem cell maintenance involves direct transcriptional repression of differentiation program // Mol. Syst. Biol. 2013. V. 9. Р. 654.


Review

Views: 470


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 2500-3259 (Online)