МОДЕЛИРОВАНИЕ БИОМЕХАНИКИ И МОРФОДИНАМИКИ РАСТЕНИЙ В ПАКЕТЕ COMSOL
Аннотация
В статье дан краткий обзор пакета COMSOL Multiphysics; показаны способы построения модели и спецификации задачи в пакете COMSOL; продемонстрированы возможности пакета при изучении нескольких конкретных проблем биомеханики и морфодинамики растений.
Ключевые слова
COMSOL Multiphysics,
метод конечных элементов,
математическое моделирование,
биомеханика,
морфодинамика,
атомная силовая микроскопия,
АСМ,
клетки растений,
стенка растительной клетки
При поддержке: Суперкомпьютерный центрй Новосибирского государственного университета; гранты РФФИ-НИСИ № 11-04-91397-а, РФФИ № 11–04–01748-а
Об авторе
С. В. Николаев
Федеральное государственное бюджетное научное учреждение «Федеральный исследовательский центр Институт цитологии и генетики Сибирского отделения Российской академии наук», Новосибирск, Россия
Россия
Россия
Список литературы
1. Бате К., Вилсон Е. Численные методы анализа и метод конечных элементов. M., Стройиздат, 1982. 448 с.
2. Николаев С.В., Колчанов Н.А., Голушко С.К. и др. Моделирование морфодинамики на ранних стадиях эмбриогенеза растения // Вавилов. журн. генет. и селекции. 2012. Т. 16. Вып. 4/1. С. 805–815.
3. Тимошенко С.П. Сопротивление материалов. Т. 1. Элементарная теория и задачи. М.: Наука, 1965.
4. Фейнман Р., Лейтон Р., Сэндс М. Фейнмановские лекции по физике. Т. 7. Физика сплошных сред. М.: Мир, 1967.
5. Atchley W.R., Hall B.K. A model for development and evolution of complex morphological structures // Biol. Rev. 1991. V. 66. P. 101–157.
6. Barreira R., Elliott C., Madzvamuse A. The surface finite element method for pattern formation on evolving biological surfaces // J. Mathemat. Biol. 2011. V. 63. P. 1095–1119.
7. Boudaoud A. An introduction to the mechanics of morphogenesis for plant biologists // Trends Plant Sci. 2010. V. 15. P. 353–360.
8. Braybrook S.A., Hofte H., Peaucelle A. Probing the mechanical contributions of the pectin matrix: insights for cell growth // Plant Signal Behav. 2012. V. 7. P. 1037–1041.
9. Bruce D.M. Mathematical modelling of the cellular mechanics of plants // Philos. Trans. Roy. Soc. Lond. Series B: Biological Sciences. 2003. V. 358. P. 1437–1444.
10. Campbell G.S., Norman J.M. An Introduction to Environmental Biophysics. 2nd ed. Springer, 2000. 286 p.
11. Chatziprodromou I., Tricoli A., Poulikakos D., Ventikos Y. Haemodynamics and wall remodelling of a growing cerebral aneurysm: A computational model // J. Biomech. 2007. V. 40. P. 412–426.
12. Dyson R., Band L., Jensen O. A model of crosslink kinetics in the expanding plant cell wall: Yield stress and enzyme action // J. Theor. Biol. 2012. V. 307. P. 125–136.
13. Fernandes A.N., Chen X., Scotchford C.A. et al. Mechanical properties of epidermal cells of whole living roots of Arabidopsis thaliana: an atomic force microscopy study // Phys. Rev. E. 2012. V. 85. Р. 021916.
14. Geitmann A. Mechanical modeling and structural analysis of the primary plant cell wall // Curr. Opin. Plant Biol. 2010. V. 13. P. 693–699.
15. Hamant O., Traas J. The mechanics behind plant development // New Phytol. 2010. V. 185. P. 369–385.
16. Hansen S.L., Ray P.M., Karlsson A.O. et al. Mechanical properties of plant cell walls probed by relaxation spectra // Plant Physiol. 2011. V. 155. P. 246–258.
17. Heisler M.G., Hamant O., Krupinski P. et al. Alignment between PIN1 polarity and microtubule orientation in the shoot apical meristem reveals a tight coupling between morphogenesis and auxin transport // PLoS Biol. 2010. V. 8. e1000516.
18. Kraft R.H., Mckee P.J., Dagro A.M., Grafton S.T. Combining the finite element method with structural connectomebased analysis for modeling neurotrauma: connectome neurotrauma mechanics // PLoS Comput Biol. 2012. V. 8. Р. e1002619.
19. Kwiatkowska D. Structural integration at the shoot apical meristem: models, measurements, and experiments // Amer. J. Bot. 2004. V. 91. P. 1277–1293.
20. Laux T., Jürgens G. Embryogenesis: a new start in life // Plant Cell. 1997. V. 9. P. 989–1000.
21. Milani P., Gholamirad M., Traas J. et al. In vivo analysis of local wall stiffness at the shoot apical meristem in Arabidopsis using atomic force microscopy // Plant J. 2011. V. 67. P. 1116–1123.
22. Mirabet V., Das P., Boudaoud A., Hamant O. The role of mechanical forces in plant morphogenesis // Annu. Rev. Plant Biol. 2011. V. 62. P. 365–385.
23. Missel P. Finite element modeling of diffusion and partitioning in biological systems: the infinite composite medium problem // Ann. Biomed. Eng. 2000. V. 28. P. 1307–1317.
24. Nakielski J. The tensor-based model for growth and cell divisions of the root apex. I. The significance of principal directions // Planta. 2008. V. 228. P. 179–189.
25. Ortega J.K. Augmented growth equation for cell wall expansion // Plant Physiol. 1985. V. 79. P. 318–320.
26. Peaucelle A., Braybrook S.A., Le Guillou L. et al. Pectin-induced changes in cell wall mechanics underlie organ initiation in Arabidopsis // Curr. Biol. 2011. V. 21. P. 1720–1726.
27. Proseus T.E., Ortega J.K., Boyer J.S. Separating growth from elastic deformation during cell enlargement // Plant Physiol. 1999. V. 119. P. 775–784.
28. Rayfield E.J. Using finite-element analysis to investigate suture morphology: A case study using large carnivorous dinosaurs // Anat. Rec. Part A: Discoveries in Molecular, Cellular, and Evolutionary Biology. 2005. V. 283A. P. 349–365.
29. Rayfield E.J. Finite element analysis and understanding the biomechanics and evolution of living and fossil organisms // Annu. Rev. Earth Planet. Sci. 2007. Book Series: Annu. Rev. Earth Planet. Sci. V. 35. P. 541–576.
30. Richmond B.G., Wright B.W., Grosse I. et al. Finite element analysis in functional morphology // Anat. Rec. Part A: Discoveries in Molecular, Cellular, and Evolutionary Biology. 2005. V. 283A. P. 259–274.
31. Routier-Kierzkowska A.-L., Weber A., Kochova P. et al. Cellular force microscopy for in vivo measurements of plant tissue mechanics // Plant Physiol. 2012. V. 158. P. 1514–1522.
32. Schopfer P. Biomechanics of plant growth // Am. J. Bot. 2006. V. 93. P. 1415–1425.
33. Spatz H., Kohler L., Niklas K. Mechanical behaviour of plant tissues: composite materials or structures? // J. Experim. Biol. 1999. V. 202. P. 3269–3272.
34. Suslov D., Verbelen J.-P., Vissenberg K. Onion epidermis as a new model to study the control of growth anisotropy in higher plants // J. Experim. Bot. 2009. V. 60. P. 4175–4187.
35. Tang Y., Cao G., Chen X. et al. A finite element framework for studying the mechanical response of macromolecules: application to the gating of the mechanosensitive channel MscL // Biophys. J. 2006. V. 91. Р. 1248–1263.
36. Thompson D.S. How do cell walls regulate plant growth? // J. Experim. Bot. 2005. V. 56. P. 2275–2285.
37. Thompson D.S. Extensiometric determination of the rheological properties of the epidermis of growing tomato fruit // J. Experim. Bot. 2001. V. 52. P. 1291–1301.
38. Volokh K.Y. A simple phenomenological theory of tissue growth // Mech. Chem. Biosyst. 2004. V. 1. P. 147–160.
39. You T.J., Harvey S.C. Finite element approach to the electrostatics of macromolecules with arbitrary geometries // J. Computat. Chem. 1993. V. 14. P. 484–501.
Рецензия
Просмотров:
656
Послать статью по эл. почте 