Physical Models of Plant Morphogenesis

  • Mathilde Dumond
  • Arezki BoudaoudEmail author


Biological form is closely associated with function. Yet, despite much progress in developmental biology, we are still far from understanding how organs grow and reach their final size and shape, through a process known as morphogenesis. Morphogenesis is associated with a variety of cellular scale phenomena such as cell expansion, cell proliferation, and cell differentiation. These processes occur within the thousands to billions of cells that yield a well-defined organ. How these phenomena are coordinated over time and space to shape a consistent and reproducible organ or organism is still an open question. In this chapter, we focus on physical models of morphogenesis. We first introduce quantitative descriptions of growth. We then expand on mechanical models of growth; we review types of models and we discuss case studies where such models were used.


  1. 1.
    Alim K, Armon S, Shraiman BI, Boudaoud A (2016) Leaf growth is conformal. Phys Biol 13(5):05LT01CrossRefGoogle Scholar
  2. 2.
    Audoly B, Boudaoud A (2003) Self-similar structures near boundaries in strained systems. Phys Rev Lett 91(8):86105CrossRefGoogle Scholar
  3. 3.
    Avery GS (1933) Structure and development of the tobacco leaf. Am J Bot 20(9):565–592CrossRefGoogle Scholar
  4. 4.
    Bar-Sinai Y, Julien J-D, Sharon E, Armon S, Nakayama N, Adda-Bedia M, Boudaoud A (2016) Mechanical stress induces remodeling of vascular networks in growing leaves. PLOS Comput Biol 12(4):e1004819CrossRefGoogle Scholar
  5. 5.
    Barbier de Reuille P, Routier-Kierzkowska A-L, Kierzkowski D, Bassel GW, Schüpbach T, Tauriello G, Bajpai N, Strauss S, Weber A, Kiss A, Burian A, Hofhuis H, Sapala A, Lipowczan M, Heimlicher MB, Robinson S, Bayer EM, Basler K, Koumoutsakos P, Roeder AHK, Aegerter-Wilmsen T, Nakayama N, Tsiantis M, Hay A, Kwiatkowska D, Xenarios I, Kuhlemeier C, Smith RS (2015) MorphoGraphX: a platform for quantifying morphogenesis in 4D. eLife 4:1–20CrossRefGoogle Scholar
  6. 6.
    Bastien R, Bohr T, Moulia B, Douady S (2013) Unifying model of shoot gravitropism reveals proprioception as a central feature of posture control in plants. Proc. Natl. Acad. Sci. U. S. A. 110(2):755–760CrossRefGoogle Scholar
  7. 7.
    Bastien R, Douady S, Moulia B (2015) A unified model of shoot tropism in plants: photo-, gravi- and propio-ception. PLoS Comput Biol 11(2):1–30CrossRefGoogle Scholar
  8. 8.
    Beauzamy L, Nakayama N, Boudaoud A (2014) Flowers under pressure: ins and outs of turgor regulation in development. Ann Bot 114(7):1517–1533CrossRefGoogle Scholar
  9. 9.
    Beauzamy L, Louveaux M, Hamant O, Boudaoud A (2015) Mechanically, the shoot apical meristem of arabidopsis behaves like a shell inflated by a pressure of about 1 MPa. Front Plant Sci 6:1038CrossRefGoogle Scholar
  10. 10.
    Berleth T, Scarpella E, Prusinkiewicz P (2007) Towards the systems biology of auxin-transport-mediated patterning. Trends Plant Sci 12(4):151–159CrossRefGoogle Scholar
  11. 11.
    Bonazzi D, Julien JD, Romao M, Seddiki R, Piel M, Boudaoud A, Minc N (2014) Symmetry breaking in spore germination relies on an interplay between polar cap stability and spore wall mechanics. Dev Cell 28(5):534–546CrossRefGoogle Scholar
  12. 12.
    Boudon F, Chopard J, Ali O, Gilles B, Hamant O, Boudaoud A, Traas J, Godin C (2015) A computational framework for 3D mechanical modeling of plant morphogenesis with cellular resolution. PLoS Comput Biol 11(1):e1003950CrossRefGoogle Scholar
  13. 13.
    Bozorg B, Krupinski P, Jönsson H (2014) Stress and strain provide positional and directional cues in development. PLoS Comput Biol 10(1):e1003410CrossRefGoogle Scholar
  14. 14.
    Bozorg B, Krupinski P, Jönsson H (2016) A continuous growth model for plant tissue. Phys Biol 13(6):065002CrossRefGoogle Scholar
  15. 15.
    Bringmann M, Bergmann DC (2017) Tissue-wide mechanical forces influence the polarity of stomatal stem cells in arabidopsis. Curr Biol 27(6):1–7CrossRefGoogle Scholar
  16. 16.
    Campàs O, Mahadevan L (2009) Shape and dynamics of tip-growing cells. Curr Biol 19(24):2102–2107CrossRefGoogle Scholar
  17. 17.
    Cieslak M, Cheddadi I, Boudon F, Baldazzi V, Génard M, Godin C, Bertin N (2016) Integrating physiology and architecture in models of fruit expansion. Front Plant Sci 7:1–19CrossRefGoogle Scholar
  18. 18.
    Coen E, Rolland-Lagan A-G, Matthews M, Bangham JA, Prusinkiewicz P (2004) The genetics of geometry. Proc Natl Acad Sci 101(14):4728–4735CrossRefGoogle Scholar
  19. 19.
    Corson F, Adda-Bedia M, Boudaoud A (2009) In silico leaf venation networks: growth and reorganization driven by mechanical forces. J Theor Biol 259(3):440–448CrossRefGoogle Scholar
  20. 20.
    Corson F, Hamant O, Bohn S, Traas J, Boudaoud A, Couder Y (2009) Turning a plant tissue into a living cell froth through isotropic growth. Proc Natl Acad Sci 106(21): 8453–8458CrossRefGoogle Scholar
  21. 21.
    Corson F, Henry H, Adda-Bedia M (2010) A model for hierarchical patterns under mechanical stresses. Phil Mag 90(1–4):357–373CrossRefGoogle Scholar
  22. 22.
    De Vos D, Vissenberg K, Broeckhove J, Beemster Gerrit TS (2014) Putting theory to the test: which regulatory mechanisms can drive realistic growth of a root? PLoS Comput Biol 10(10):e1003910CrossRefGoogle Scholar
  23. 23.
    Dumais J, Steele CR (2000) New evidence for the role of mechanical forces in the shoot apical meristem. J Plant Growth Regul 19:7–18CrossRefGoogle Scholar
  24. 24.
    Dumais J, Shaw SL, Steele CR, Long SR, Ray PM (2006) An anisotropic-viscoplastic model of plant cell morphogenesis by tip growth. Int. J. Dev. Biol. 50:209–222CrossRefGoogle Scholar
  25. 25.
    Dupuy L, MacKenzie J, Rudge T, Haseloff J (2008) A system for modelling cell-cell interactions during plant morphogenesis. Ann Bot 101(8):1255–1265CrossRefGoogle Scholar
  26. 26.
    Engler AJ, Sen S, Sweeney HL, Discher DE (2006) Matrix elasticity directs stem cell lineage specification. Cell 126(4):677–689CrossRefGoogle Scholar
  27. 27.
    Erickson RO (1976) Modeling of plant growth. Annu Rev Plant Physiol 27:407–434CrossRefGoogle Scholar
  28. 28.
    Fayant P, Girlanda O, Chebli Y, Aubin C-E, Villemure I, Geitmann A (2010) Finite element model of polar growth in pollen tubes. Plant Cell 22(8):2579–2593CrossRefGoogle Scholar
  29. 29.
    Fernandez R, Das P, Mirabet V, Moscardi E, Traas J, Verdeil J-L, Malandain G, Godin C (2010) Imaging plant growth in 4D: robust tissue reconstruction and lineaging at cell resolution. Nat Methods 7(7):547–53CrossRefGoogle Scholar
  30. 30.
    Fozard JA, Lucas M, King JR, Jensen OE (2013) Vertex-element models for anisotropic growth of elongated plant organs. Front Plant Sci 4:233CrossRefGoogle Scholar
  31. 31.
    Fozard JA, Bennett MJ, King JR, Jensen OE (2016) Hybrid vertex-midline modelling of elongated plant organs. Interface Focus 6(5):20160043CrossRefGoogle Scholar
  32. 32.
    Goriely A, Tabor M (2003) Self-similar tip growth in filamentary organisms. Phys Rev Lett 90(10):108101 (2003)CrossRefGoogle Scholar
  33. 33.
    Granier C, Tardieu F (1998) Spatial and temporal analyses of expansion and cell cycle in sunflower leaves. A common pattern of development for all zones of a leaf and different leaves of a plant. Plant Physiol 116(3):991–1001CrossRefGoogle Scholar
  34. 34.
    Green AA, Kennaway JR, Hanna AI, Bangham JA, Coen E (2010) Genetic control of organ shape and tissue polarity. PLoS Biol 8(11):e1000537CrossRefGoogle Scholar
  35. 35.
    Grieneisen VA, Xu J, Marée AFM, Hogeweg P, Scheres B (2007) Auxin transport is sufficient to generate a maximum and gradient guiding root growth. Nature 449(7165):1008–1013CrossRefGoogle Scholar
  36. 36.
    Hamant O, Heisler MG, Jonsson H, Krupinski P, Uyttewaal M, Bokov P, Corson F, Sahlin P, Boudaoud A, Meyerowitz EM, Couder Y, Traas J (2008) Developmental patterning by mechanical signals in arabidopsis. Science 322(5908):1650–1655CrossRefGoogle Scholar
  37. 37.
    Hervieux N, Dumond M, Sapala A, Routier-Kierzkowska A-L, Kierzkowski D, Roeder AHK, Smith RS, Boudaoud A, Hamant O (2016) A mechanical feedback restricts sepal growth and shape in arabidopsis. Curr Biol 26(8):1019–1028CrossRefGoogle Scholar
  38. 38.
    Höhn S, Honerkamp-Smith AR, Haas PA, Trong PK, Goldstein RE (2015) Dynamics of a volvox embryo turning itself inside out. Phys Rev Lett 114(17):1–5CrossRefGoogle Scholar
  39. 39.
    Holloway DM, Harrison LG (2008) Pattern selection in plants: coupling chemical dynamics to surface growth in three dimensions. Ann Bot 101(3):361–374CrossRefGoogle Scholar
  40. 40.
    Hong L, Dumond M, Tsugawa S, Sapala A, Routier-Kierzkowska A-L, Zhou Y, Chen C, Kiss A, Zhu M, Hamant O, Smith RS, Komatsuzaki T, Li C-B, Boudaoud A, Roeder AHK (2016) Variable cell growth yields reproducible organdevelopment through spatiotemporal averaging. Dev Cell 38(1):15–32CrossRefGoogle Scholar
  41. 41.
    Kennaway R, Coen E, Green A, Bangham JA (2011) Generation of diverse biological forms through combinatorial interactions between tissue polarity and growth. PLoS Comput Biol 7(6):e1002071CrossRefGoogle Scholar
  42. 42.
    Kierzkowski D, Nakayama N, Routier-Kierzkowska A-L, Weber A, Bayer EM, Schorderet M, Reinhardt D, Kuhlemeier C, Smith RS (2012) Elastic domains regulate growth and organogenesis in the plant shoot apical meristem. Science 335(6072):1096–1099CrossRefGoogle Scholar
  43. 43.
    Laguna MF, Bohn S, Jagla EA (2008) The role of elastic stresses on leaf venation morphogenesis. PLOS Comput Biol 4(4):e1000055CrossRefGoogle Scholar
  44. 44.
    Liang H, Mahadevan L (2009) The shape of a long leaf. Proc Natl Acad Sci U. S. A. 106(52):22049–54CrossRefGoogle Scholar
  45. 45.
    Liang H, Mahadevan L (2011) Growth, geometry, and mechanics of a blooming lily. Proc Natl Acad Sci U.S.A 108(14):5516–5521CrossRefGoogle Scholar
  46. 46.
    Louveaux M, Julien J-D, Mirabet V, Boudaoud A, Hamant O (2016) Cell division plane orientation based on tensile stress in Arabidopsis thaliana. Proc Natl Acad Sci 113(30):E4294–E4303CrossRefGoogle Scholar
  47. 47.
    Lucas M, Kenobi K, von Wangenheim D, Voss U, Swarup K, De Smet I, Van Damme D, Lawrence T, Peret B, Moscardi E, Barbeau D, Godin C, Salt D, Guyomarc’h S, Stelzer EHK, Maizel A, Laplaze L, Bennett MJ (2013) Lateral root morphogenesis is dependent on the mechanical properties of the overlaying tissues. Proc Natl Acad Sci 110(13):5229–5234CrossRefGoogle Scholar
  48. 48.
    Maksymowych R (1959) Quantitative analysis of leaf development in xanthium pensylvanicum. Am J Bot 46(9):635–644CrossRefGoogle Scholar
  49. 49.
    Merks RM, Guravage M, Inzé D, Beemster GTS (2011) VirtualLeaf: an open source framework for cell-based modeling of plant tissue growth and development. Plant Phys 155(2): 656–666CrossRefGoogle Scholar
  50. 50.
    Meyer HM, Roeder AHK (2014) Stochasticity in plant cellular growth and patterning. Front Plant Sci 5:420PubMedPubMedCentralGoogle Scholar
  51. 51.
    Milani P, Braybrook SA, Boudaoud A (2013) Shrinking the hammer: micromechanical approaches to morphogenesis. J Exp Bot 64(15):4651–4662CrossRefGoogle Scholar
  52. 52.
    Mitchison G (2016) Conformal growth of Arabidopsis leaves. J Theor Biol 408:155–166CrossRefGoogle Scholar
  53. 53.
    Montenegro-Johnson TD, Stamm P, Strauss S, Topham AT, Tsagris M, Wood ATA, Smith RS, Bassel GW (2015) Digital single-cell analysis of plant organ development using 3DCellAtlas. Plant Cell 27(4):1018–1033CrossRefGoogle Scholar
  54. 54.
    Ortega JK (1985) Augmented growth equation for cell wall expansion. Plant Physiol 79(1):318–320CrossRefGoogle Scholar
  55. 55.
    Poethig RS, Sussex IM (1985) The developmental morphology and growth dynamics of the tobacco leaf. Planta 165(2):158–169CrossRefGoogle Scholar
  56. 56.
    R S L B P B S Record: 2290 Poethig (1987) Clonal analysis of cell lineage patterns in plant development. Am J Bot 74(4):581–594Google Scholar
  57. 57.
    Remmler L, Rolland-Lagan AG (2012) Computational method for quantifying growth patterns at the adaxial leaf surface in three dimensions. Plant Physiol 159:27–39CrossRefGoogle Scholar
  58. 58.
    Rojas ER, Hotton S, Dumais J (2011) Chemically mediated mechanical expansion of the pollen tube cell wall. Biophys J 101(8):1844–1853CrossRefGoogle Scholar
  59. 59.
    Rolland-Lagan A-G, Bangham JA, Coen E (2003) Growth dynamics underlying petal shape and asymmetry. Nature 422(6928):161–163CrossRefGoogle Scholar
  60. 60.
    Rolland-Lagan A-G, Remmler L, Girard-Bock C (2014) Quantifying shape changes and tissue deformation in leaf development. Plant Physiol 165:496–505CrossRefGoogle Scholar
  61. 61.
    Romero-Arias JR, Hernández-Hernández V, Benítez M, Alvarez-Buylla ER, Barrio RA (2017) Model of polar auxin transport coupled to mechanical forces retrieves robust morphogenesis along the < math> < mi mathvariant=”italic”> Arabidopsis< /mi> < /math> root. Phys Rev E 95(3):032410CrossRefGoogle Scholar
  62. 62.
    Routier-Kierzkowska A-L, Smith RS (2013) Measuring the mechanics of morphogenesis. Curr Opin Plant Biol 16(1):25–32CrossRefGoogle Scholar
  63. 63.
    Routier-Kierzkowska A-L, Weber A, Kochova P, Felekis D, Nelson BJ, Kuhlemeier C, Smith RS, Breakthrough Technologies (2012) Cellular force microscopy for in vivo measurements of plant tissue mechanics. Plant Physiol 158:1514–1522CrossRefGoogle Scholar
  64. 64.
    Sampathkumar A, Gutierrez R, McFarlane HE, Bringmann M, Lindeboom J, Emons A-M, Samuels L, Ketelaar T, Ehrhardt DW, Persson S (2013) Patterning and lifetime of plasma membrane-localized cellulose synthase is dependent on actin organization in Arabidopsis interphase cells. Plant Physiol 162(2):675–688CrossRefGoogle Scholar
  65. 65.
    Silk WK, Erickson RO (1979) Kinematics of plant growth. J Theor Biol 76(4):481–501CrossRefGoogle Scholar
  66. 66.
    Tauriello G, Meyer HM, Smith RS, Koumoutsakos P, Roeder AHK (2015) Variability and constancy in cellular growth of Arabidopsis sepals. Plant Physiol 169:2342–2358PubMedPubMedCentralGoogle Scholar
  67. 67.
    Vandiver R, Goriely A (2008) Tissue tension and axial growth of cylindrical structures in plants and elastic tissues. Europhys Lett 84, 58004CrossRefGoogle Scholar
  68. 68.
    Vogler H, Felekis D, Nelson B, Grossniklaus U, Measuring the mechanical properties of plant cell walls. Plants 4(2):167–182CrossRefGoogle Scholar
  69. 69.
    Yang W, Schuster C, Beahan CT, Doblin MS, Wightman R, Meyerowitz EM, Yang W, Schuster C, Beahan CT, Charoensawan V, Peaucelle A, Bacic A (2016) Regulation of meristem morphogenesis by cell wall synthases in arabidopsis article regulation of meristem morphogenesis by cell wall synthases in arabidopsis. Curr Biol 26(11):1404–1415CrossRefGoogle Scholar
  70. 70.
    Žádníková P, Wabnik K, Abuzeineh A, Gallemi M, Van Der Straeten D, Smith RS, Inzé D, Friml J, Prusinkiewicz P, Benková E (2016) A model of differential growth-guided apical hook formation in plants. Plant Cell 28(10):2464–2477CrossRefGoogle Scholar
  71. 71.
    Zubairova U, Nikolaev S, Penenko A, Podkolodnyy N, Golushko S, Afonnikov D, Kolchanov N (2016) Mechanical behavior of cells within a cell-based model of wheat leaf growth. Front Plant Scie 7:1–15Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Laboratoire Reproduction et Développement des PlantesUniv Lyon, ENS de Lyon, UCB Lyon 1, CNRS, INRALyonFrance

Personalised recommendations