Vertex-element models for anisotropic growth of elongated plant organs

Frontiers in Plant Science

Volumn 4, Issue JUL, 2013, Pages

  Fozard, John A ^a   Lucas, Mikaël ^b   King, John R ^a   Jensen, Oliver E ^a,c  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

^b INSTITUT DE RECHERCHE POUR LE DÉVELOPPEMENT   (France)

^c UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Anisotropy; Microfibrils; Multiscale; Simulation; Viscosity

Indexed keywords

EID: 84899794558     PISSN: None     EISSN: 1664462X     Source Type: Journal    
DOI: 10.3389/fpls.2013.00233     Document Type: Article

References (79)

1. Abera, M. K., Fanta, S. W., Verboven, P., Ho, Q. T., Carmeliet, J., and Nicolai, B. M. (2013). Virtual fruit tissue generation based on cell growth modelling. Food Bioprocess Technol. 6, 859-869. doi: 10.1007/s11947-011-0775-4
2. Alim, K., Hamant, O., and Boudaoud, A. (2012). Regulatory role of cell division rules on tissue growth heterogeneity. Front. Plant Sci 3:174. doi: 10.3389/fpls.2012.00174
3. Anderson, C. T., Carroll, A., Akhmetova, L., and Somerville, C. (2010). Real-time imaging of cellulose reorientation during cell wall expansion in Arabidopsis roots. Plant Physiol. 152, 787-796. doi: 10.1104/pp.109.150128
4. Band, L. R., Fozard, J. A., Godin, C., Jensen, O. E., Pridmore, T., Bennett, M. J., et al. (2012a). Multiscale systems analysis of root growth and development: modeling beyond the network and cellular scales. Plant Cell 24, 3892-3906. doi: 10.1105/tpc.112.101550
5. Band, L. R., Wells, D. M., Larrieu, A., Sun, J., Middleton, A., French, A., et al. (2012b). Root gravitropism is regulated by a transient lateral auxin gradient controlled by a tipping-point mechanism. Proc. Natl. Acad. Sci. U.S.A. 109, 4668-4673. doi: 10.1073/pnas.1201498109
6. Barlow, P. W., Brain, P., and Adam, J. S. (1989). Differential growth and plant tropisms: a study assisted by computer simulation. Environ. Exp. Bot. 29, 71-83. doi: 10.1016/0098-8472(89)90040-3
7. Baskin, T. I. (2005). Anisotropic expansion of the plant cell wall. Annu. Rev. Cell Dev. Biol. 21, 203-222. doi: 10.1146/annurev.cellbio.20.082503.103053
8. Basu, P., Pal, A., Lynch, J. P., and Brown, K. M. (2007). A novel image-analysis technique for kinematic study of growth and curvature. Plant Physiol. 145, 305-316. doi: 10.1104/pp.107.103226
9. Beemster, G. T., and Baskin, T. I. (1998). Analysis of cell division and elongation underlying the developmental acceleration of root growth in Arabidopsis thaliana. Plant Physiol. 116, 1515-1526. doi: 10.1104/pp.116.4.1515
10. Besson, S., and Dumais, J. (2011). Universal rule for the symmetric division of plant cells. Proc. Natl. Acad. Sci. U.S.A. 108, 6294-6299. doi: 10.1073/pnas.1011866108
11. Bonet, J., and Wood, R. (2008). Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge: CUP. doi: 10.1017/CBO9780511755446
12. Brodland, G., Viens, D., and Veldhuis, J. (2007). A new cell-based FE model for the mechanics of embryonic epithelia. Comp. Meth. Biomech. Biomed. Eng. 10, 121-128. doi: 10.1080/10255840601124704
13. Brunoud, G., Wells, D. M., Oliva, M., Larrieu, A., Mirabet, V., Burrow, A. H., et al. (2012). A novel sensor to map auxin response and distribution at high spatio-temporal resolution. Nature 482, 103-106. doi: 10.1038/nature10791
14. Chavarría-Krauser, A. (2006). Quantification of curvature production in cylindrical organs, such as roots and hypocotyls. New Phytol. 171, 633-641. doi: 10.1111/j.1469-8137.2006.01770.x
15. Chavarría-Krauser, A., Jäger, W., and Schurr, U. (2005). Primary root growth: a biophysical model of auxin-related control. Funct. Plant Biol. 32, 849-862. doi: 10.1071/FP05033
16. Chavarría-Krauser, A., Nagel, K. A., Palme, K., Schurr, U., Walter, A., and Scharr, H. (2008). Spatio-temporal quantification of differential growth processes in root growth zones based on a novel combination of image sequence processing and refined concepts describing curvature production. New Phytol. 177, 811-821. doi: 10.1111/j.1469-8137.2007.02299.x
17. Chavarría-Krauser, A., and Schurr, U. (2004). A cellular growth model for root tips. J. Theor. Biol. 230, 21-32. doi: 10.1016/j.jtbi.2004.04.007
18. Chen, H. H., and Brodland, G. W. (2000). Cell-level finite element studies of viscous cells in planar aggregates. J. Biomech. Eng. 122, 394-401. doi: 10.1115/1.1286563
19. Cosgrove, D. J. (1993). Wall extensibility: its nature, measurement and relationship to plant cell growth. New Phytol. 124, 1-23. doi: 10.1111/j.1469-8137.1993.tb03795.x
20. Cosgrove, D. J., and Jarvis, M. C. (2012). Comparative structure and biomechanics of plant primary and secondary cell walls. Front Plant Sci. 3:204. doi: 10.3389/fpls.2012.00204
21. Davis, T. A., and Duff, I. S. (1999). A combined unifrontal/multifrontal method for unsymmetric sparse matrices. ACM T. Math. Software 25, 1-20. doi: 10.1145/305658.287640
22. Dissmeyer, N., Weimer, A. K., Pusch, S., De Schutter, K., Alvim Kamei, C. L., Nowack, M. K., et al. (2009). Control of cell proliferation, organ growth, and DNA damage response operate independently of dephosphorylation of the Arabidopsis Cdk1 homolog CDKA;1. Plant Cell 21, 3641-3654. doi: 10.1105/tpc.109.070417
23. Dolan, L., Janmaat, K., Willemsen, V., Linstead, P., Poethig, S., Roberts, K., et al. (1993). Cellular organisation of the Arabidopsis thaliana root. Development 119, 71-84.
24. Dupeux, F., Santiago, J., Betz, K., Twycross, J., Park, S., Rodriguez, L., et al. (2011). A thermodynamic switch modulates abscisic acid receptor sensitivity. EMBO J. 30, 4171-4184. doi: 10.1038/emboj.2011.294
25. Dupuy, L., Mackenzie, J., and Haseloff, J. (2010). Coordination of plant cell division and expansion in a simple morphogenetic system. Proc. Nat. Acad. Sci. U.S.A. 107, 2711-2716. doi: 10.1073/pnas.0906322107
26. Dupuy, L., Mackenzie, J., Rudge, T., and Haseloff, J. (2008). A system for modelling cell-cell interactions during plant morphogenesis. Ann. Bot. 101, 1255-1265. doi: 10.1093/aob/mcm235
27. Dupuy, L., Mackenzie, J. P., and Haseloff, J. P. (2006). "A biomechanical model for the study of plant morphogenesis: Coleocheate orbicularis, a 2d study species, " in Proceedings of the 5th Plant Biomechanics Conference (Stockholm, Sweden).
28. Dyson, R. J., Band, L. R., and Jensen, O. E. (2012). A model of crosslink kinetics in the expanding plant cell wall: yield stress and enzyme action. J. Theor. Biol. 307, 125-136. doi: 10.1016/j.jtbi.2012.04.035
29. Dyson, R. J., and Jensen, O. E. (2010). A fibre-reinforced fluid model of anisotropic plant cell growth. J. Fluid Mech. 655, 472-503. doi: 10.1017/S002211201000100X
30. Fernandez, R., Das, P., Mirabet, V., Moscardi, E., Traas, J., Verdeil, J., et al. (2010). Imaging plant growth in 4D: robust tissue reconstruction and lineaging at cell resolution. Nat. Methods 7, 547-553. doi: 10.1038/nmeth.1472
31. Geitmann, A. (2010). Mechanical modeling and structural analysis of the primary plant cell wall. Curr. Opin. Plant Biol. 13, 693-699. doi: 10.1016/j.pbi.2010.09.017
32. Green, P. B. (1960). Multinet growth in the cell wall of Nitella. J. Biophys. Biochem. Cytol. 7, 289-296. doi: 10.1083/jcb.7.2.289
33. Hamant, O., Heisler, M. G., Jonsson, H., Krupinski, P., Uyttewaal, M., Bokov, P., et al. (2008). Developmental patterning by mechanical signals in Arabidopsis. Science 322, 1650-1655. doi: 10.1126/science.1165594
34. Hejnowicz, Z. (1989). Differential growth resulting in the specification of different types of cellular architecture in root meristems. Environ. Exp. Bot. 29, 85-93. doi: 10.1016/0098-8472(89)90041-5
35. Hindmarsh, A. C., Brown, P. N., Grant, K. E., Lee, S. L., Serban, R., Shumaker, D. E., et al. (2005). SUNDIALS: suite of nonlinear and differential/algebraic equation solvers. ACM T. Math. Softw. 31, 363-396. doi: 10.1145/1089014.1089020
36. Huang, R., Becker, A. A., and Jones, I. A. (2012). Modelling cell wall growth using a fibre-reinforced hyperelastic-viscoplastic constitutive law. J. Mech. Phys. Solids 60, 750-783. doi: 10.1016/j.jmps.2011.12.003
37. Iserles, A. (2009). A First Course in the Numerical Analysis of Differential Equations. Vol. 44. Cambridge: Cambridge University Press.
38. Javot, H., Lauvergeat, V., Santoni, V., Martin-Laurent, F., Güçlü, J., Vinh, J., et al. (2003). Role of a single aquaporin isoform in root water uptake. Plant Cell 15, 509-522. doi: 10.1105/tpc.008888
39. Jönsson, H., Heisler, M. G., Shapiro, B. E., Meyerowitz, E., and Mjolsness, E. (2006). An auxin-driven polarized transport model for phyllotaxis. Proc. Natl. Acad. Sci. U.S.A. 103, 1633-1638. doi: 10.1073/pnas.0509839103
40. Kha, H., Tuble, S. C., Kalyanasundaram, S., and Williamson, R. E. (2010). WallGen, software to construct layered cellulose-hemicellulose networks and predict their small deformation mechanics. Plant Physiol. 152, 774-786. doi: 10.1104/pp.109.146936
41. Kramer, E. M. (2004). PIN and AUX/LAX proteins: their role in auxin accumulation. Trends Plant Sci. 9, 578-582. doi: 10.1016/j.tplants.2004.10.010
42. Lockhart, J. A. (1965). An analysis of irreversible plant cell elongation. J. Theor. Biol 8, 264-275. doi: 10.1016/0022-5193(65)90077-9
43. Merks, R. M., Guravage, M., Inze, D., and Beemster, G. T. (2011). VirtualLeaf: an open-source framework for cell-based modeling of plant tissue growth and development. Plant Physiol. 155, 656-666. doi: 10.1104/pp.110.167619
44. Middleton, A. M., Farcot, E., Owen, M. R., and Vernoux, T. (2012a). Modeling regulatory networks to understand plant development: small is beautiful. Plant Cell 24, 3876-3891. doi: 10.1105/tpc.112.101840
45. Middleton, A. M., Ubeda-Tomas, S., Griffiths, J., Holman, T., Hedden, P., Thomas, S. G., et al. (2012b). Mathematical modeling elucidates the role of transcriptional feedback in gibberellin signaling. Proc. Natl. Acad. Sci. U.S.A. 109, 7571-7576. doi: 10.1073/pnas.1113666109
46. Middleton, A. M., King, J. R., Bennett, M. J., and Owen, M. R. (2010). Mathematical modelling of the Aux/IAA negative feedback loop. Bull. Math. Biol. 72, 1383-1407. doi: 10.1007/s11538-009-9497-4
47. Moulia, B., and Fournier, M. (2009). The power and control of gravitropic movements in plants: a biomechanical and systems biology view. J. Exp. Bot. 60, 461-486. doi: 10.1093/jxb/ern341
48. Muraro, D., Byrne, H., King, J., and Bennett, M. (2013). The role of auxin and cytokinin signalling in specifying the root architecture of Arabidopsis thaliana. J. Theor. Biol. 317, 71-86. doi: 10.1016/j.jtbi.2012.08.032
49. Nagai, T., and Honda, H. (2001). A dynamic cell model for the formation of epithelial tissues. Philos. Mag B 81, 699-719. doi: 10.1080/13642810108205772
50. Nakielski, J. (2008). The tensor-based model for growth and cell divisions of the root apex. I. The significance of principal directions. Planta 228, 179-189. doi: 10.1007/s00425-008-0728-y
51. Papanastasiou, T. (1987). Flows of materials with yield. J. Rheol. 31, 385-404. doi: 10.1122/1.549926
52. Passioura, J. B., and Boyer, J. S. (2003). Tissue stresses and resistance to water flow conspire to uncouple the water potential of the epidermis from that of the xylem in elongating plant cells. Funct. Plant Biol. 30, 325-334. doi: 10.1071/FP02202
53. Passioura, J. B., and Fry, S. C. (1992). Turgor and cell expansion: beyond the Lockhart equation. Aust. J. Plant Physiol. 19, 565-576. doi: 10.1071/PP9920565
54. Péret, B., Li, G., Zhao, J., Band, L. R., Voß, U., Postaire, O., et al. (2012). Auxin regulates aquaporin function to facilitate lateral root emergence. Nat. Cell Biol. 14, 991-998. doi: 10.1038/ncb2573
55. Peters, W. S., and Baskin, T. I. (2006). Tailor-made composite functions as tools in model choice: the case of sigmoidal vs bi-linear growth profiles. Plant Methods 2:11. doi: 10.1186/1746-4811-2-11
56. Pound, M., French, A. P., Wells, D. M., Bennett, M. J., and Pridmore, T. P. (2012). CellSeT: novel software to extract and analyze structured networks of plant cells from confocal images. Plant Cell 24, 1353-1361. doi: 10.1105/tpc.112.096289
57. Pradal, C., Dufour-Kowalski, S., Boudon, F., Fournier, C., and Godin, C. (2008). Openalea: a visual programming and component-based software platform for plant modelling. Funct. Plant Biol. 35, 751-760. doi: 10.1071/FP08084
58. Priestley, J. (1930). Studies in the physiology of cambial activity. New Phytol. 29, 96-140. doi: 10.1111/j.1469-8137.1930.tb06983.x
59. Pritchard, J., Hetherington, P. R., Fry, S. C., and Tomos, A. D. (1993). Xyloglucan endotransglycosylase activity, microfibril orientation and the profiles of cell wall properties along growing regions of maize roots. J. Exp. Bot. 44, 1281-1289. doi: 10.1093/jxb/44.8.1281
60. Rudge, T., and Haseloff, J. P. (2005). "A computational model of cellular morphogenesis in plants, " in Advances in Artificial Life, volume 3630 of Lecture Notes in Computer Science, eds M. Capcarrèere, A. Freitas, P. Bentley, C. Johnson, and J. Timmis (Berlin: Springer), 78-87.
61. Sahlin, P., and Jönsson, H. (2010). A modeling study on how cell division affects properties of epithelial tissues under isotropic growth. PLoS ONE 5:e11750. doi: 10.1371/journal.pone.0011750
62. Sanchez-Rodríguez, C., Rubio-Somoza, I., Sibout, R., and Persson, S. (2010). Phytohormones and the cell wall in Arabidopsis during seedling growth. Trends Plant Sci. 15, 291-301. doi: 10.1016/j.tplants.2010.03.002
63. Santner, A., Calderon-Villalobos, L. I., and Estelle, M. (2009). Plant hormones are versatile chemical regulators of plant growth. Nat. Chem. Biol. 5, 301-307. doi: 10.1038/nchembio.165
64. Shewchuk, J. R. (1996). "Triangle: engineering a 2D quality mesh generator and delaunay triangulator, " in Applied Computational Geometry: Towards Geometric Engineering, volume 1148 of Lecture Notes in Computer Science, eds M. C. Lin and D. Manocha (Berlin: Springer-Verlag), 203-222.
65. Smith, C., Prusinkiewiz, P., and Samavati, F. (2003). "Local specification of surface subdivision algorithms, " in Proceedings of AGTIVE 2003, volume 3062 of Lecture Notes in Computer Science (Charlottesville, VA), 313-327.
66. Smith, R. S., Guyomarc'h, S., Mandel, T., Reinhardt, D., Kuhlemeier, C., and Prusinkiewicz, P. (2006). A plausible model of phyllotaxis. Proc. Natl. Acad. Sci. U.S.A. 103, 1301-1306. doi: 10.1073/pnas.0510457103
67. Steudle, E., and Peterson, C. A. (1998). How does water get through roots? J. Exp. Bot. 49, 775-788. doi: 10.1093/jxb/49.322.775
68. Stočkus, A., and Moore, D. (1996). Comparison of plant and fungal gravitropic responses using imitational modelling. Plant Cell Environ. 19, 787-800. doi: 10.1111/j.1365-3040.1996.tb00416.x
69. Ubeda-Tomas, S., Beemster, G. T. S., and Bennett, M. J. (2012). Hormonal regulation of root growth: integrating local activities into global behaviour. Trends Plant Sci. 17, 326-331. doi: 10.1016/j.tplants.2012.02.002
70. Ubeda-Tomas, S., Swarup, R., Coates, J., Swarup, K., Laplaze, L., Beemster, G. T., et al. (2008). Root growth in Arabidopsis requires gibberellin/DELLA signalling in the endodermis. Nat. Cell Biol. 10, 625-628. doi: 10.1038/ncb1726
71. Uyttewaal, M., Burian, A., Alim, K., Landrein, B., Borowska-Wykret, D., Dedieu, A., et al. (2012). Mechanical stress acts via katanin to amplify differences in growth rate between adjacent cells in Arabidopsis. Cell 149, 439-451. doi: 10.1016/j.cell.2012.02.048
72. van der Weele, C. M., Jiang, H. S., Palaniappan, K. K., Ivanov, V. B., Palaniappan, K., and Baskin, T. I. (2003). A new algorithm for computational image analysis of deformable motion at high spatial and temporal resolution applied to root growth. Roughly uniform elongation in the meristem and also, after an abrupt acceleration, in the elongation zone. Plant Physiol. 132, 1138-1148. doi: 10.1104/pp.103.021345
73. Verbelen, J. P., De Cnodder, T., Le, J., Vissenberg, K., and Baluska, F. (2006). The root apex of Arabidopsis thaliana consists of four distinct zones of growth activities: meristematic zone, transition zone, fast elongation zone and growth terminating zone. Plant Signal Behav. 1, 296-304. doi: 10.4161/psb.1.6.3511
74. Walter, A., Feil, R., and Schurr, U. (2003). Expansion dynamics, metabolite composition and substance transfer of the primary root growth zone of zea mays l. grown in different external nutrient availabilities. Plant Cell Environ. 26, 1451-1466. doi: 10.1046/j.0016-8025.2003.01068.x
75. Walter, A., Spies, H., Terjung, S., Kusters, R., Kirchgessner, N., and Schurr, U. (2002). Spatio-temporal dynamics of expansion growth in roots: automatic quantification of diurnal course and temperature response by digital image sequence processing. J. Exp. Bot. 53, 689-698. doi: 10.1093/jexbot/53.369.689
76. Weliky, M., and Oster, G. (1990). The mechanical basis of cell rearrangement. I. Epithelial morphogenesis during Fundulus epiboly. Development 109, 373-386.
77. Wiegers, B. S., Cheer, A. Y., and Silk, W. K. (2009). Modeling the hydraulics of root growth in three dimensions with phloem water sources. Plant Physiol. 150, 2092-2103. doi: 10.1104/pp.109.138198
78. Yi, H., and Puri, V. M. (2012). Architecture-based multiscale computational modeling of plant cell wall mechanics to examine the hydrogen-bonding hypothesis of the cell wall network structure model. Plant Physiol. 160, 1281-1292. doi: 10.1104/pp.112.201228
79. Zienkiewicz,O.C.,andTaylor, R. L.(2000). The Finite Element Method. Oxford: Butterworth-Heinemann