Abstract
In this chapter, we provide an overview of some of the computational models used to understand morphogenesis in plants. In particular, we focus on models of growth and patterning processes in primary tissues, prior to the onset of lignification. We explain the assumptions behind these models and how they relate to biological evidence. Our aim is to provide some basic intuitions regarding the construction, operation, and interpretation of such models.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abley K, De Reuille PB, Strutt D et al (2013) An intracellular partitioning-based framework for tissue cell polarity in plants and animals. Development 140:2061–2074. https://doi.org/10.1242/dev.062984
Ali O, Mirabet V, Godin C, Traas J (2014) Physical models of plant development. Annu Rev Cell Dev Biol 30:59–78. https://doi.org/10.1146/annurev-cellbio-101512-122410
Alvarez JP, Furumizu C, Efroni I et al (2016) Active suppression of a leaf meristem orchestrates determinate leaf growth. Elife 5:1–17. https://doi.org/10.7554/elife.15023
Barbier de Reuille P, Routier-Kierzkowska A-L, Kierzkowski D et al (2015) MorphoGraphX: a platform for quantifying morphogenesis in 4D. Elife 4:1–20. https://doi.org/10.7554/elife.05864
Barkoulas M, Hay A, Kougioumoutzi E, Tsiantis M (2008) A developmental framework for dissected leaf formation in the Arabidopsis relative Cardamine hirsuta. Nat Genet 40:1136–41. https://doi.org/10.1038/ng.189
Baskin TI (2005) Anisotropic expansion of the plant cell wall. Annu Rev Cell Dev Biol 21:203–222. https://doi.org/10.1146/annurev.cellbio.20.082503.103053
Baskin TI, Jensen OE (2013) On the role of stress anisotropy in the growth of stems. J Exp Bot. https://doi.org/10.1093/jxb/ert176
Bassel GW, Stamm P, Mosca G et al (2014) Mechanical constraints imposed by 3D cellular geometry and arrangement modulate growth patterns in the Arabidopsis embryo. Proc Natl Acad Sci USA 111:8685–8690. https://doi.org/10.1073/pnas.1404616111
Bayer EM, Smith RS, Mandel T et al (2009) Integration of transport-based models for phyllotaxis and midvein formation. Genes Dev 5:373–384. https://doi.org/10.1101/gad.497009.5
Bharathan G, Goliber TE, Moore C et al (2002) Homologies in leaf form inferred from KNOXI gene expression during development. Science 296:1858–1860. https://doi.org/10.1126/science.1070343
Bidhendi AJ, Geitmann A (2016) Relating the mechanics of the primary plant cell wall to morphogenesis. J Exp Bot 67:449–461. https://doi.org/10.1093/jxb/erv535
Bilsborough GD, Runions A, Barkoulas M et al (2011) Model for the regulation of Arabidopsis thaliana leaf margin development. Proc Natl Acad Sci 108:3424–3429. https://doi.org/10.1073/pnas.1015162108
Bolouri H (2008) Computational modeling of gene regulatory networks: a primer. World Scientific Publishing Co Inc
Boudon F, Chopard J, Ali O et al (2015) A computational framework for 3D mechanical modeling of plant morphogenesis with cellular resolution. PLoS Comput Biol 11:e1003950. https://doi.org/10.1371/journal.pcbi.1003950
Bouyer D, Geier F, Kragler F et al (2008) Two-dimensional patterning by a trapping/depletion mechanism: The role of TTG1 and GL3 in Arabidopsis trichome formation. PLoS Biol 6:1166–1177. https://doi.org/10.1371/journal.pbio.0060141
Bozorg B, Krupinski P, Jönsson H (2014) Stress and strain provide positional and directional cues in development. PLoS Comput Biol. https://doi.org/10.1371/journal.pcbi.1003410
Burian A, Raczyńska-Szajgin M, Borowska-Wykręt D et al (2015) The CUP-SHAPED COTYLEDON2 and 3 genes have a post-meristematic effect on Arabidopsis thaliana phyllotaxis. Ann Bot 115:807–820. https://doi.org/10.1093/aob/mcv013
Chickarmane V, Roeder AHK, Tarr PT et al (2010) Computational morphodynamics: a modeling framework to understand plant growth. Annu Rev Plant Biol 61:65–87. https://doi.org/10.1146/annurev-arplant-042809-112213
Cieslak M, Runions A, Prusinkiewicz P (2015) Auxin-driven patterning with unidirectional fluxes. J Exp Bot 66:5083–5102. https://doi.org/10.1093/jxb/erv262
Corson F, Hamant O, Bohn S (2009) Turning a plant tissue into a living cell froth through isotropic growth. Proc Natl Acad Sci 106:8453–8458. https://doi.org/10.1073/pnas.0812493106
Cosgrove D (1986) Biophysical control of plant cell growth. Annu Rev Plant Physiol 37:377–405. https://doi.org/10.1146/annurev.pp.37.060186.002113
Cosgrove DJ (2005) Growth of the plant cell wall. Nat Rev Mol Cell Biol 6:850–861. https://doi.org/10.1038/nrm1746
Cosgrove DJ (2016) Plant cell wall extensibility: connecting plant cell growth with cell wall structure, mechanics, and the action of wall-modifying enzymes. J Exp Bot 67:463–476. https://doi.org/10.1093/jxb/erv511
Couder Y, Pauchard L, Allain C et al (2002) The leaf venation as formed in a tensorial field. Eur Phys J B 28:135–138. https://doi.org/10.1140/epjb/e2002-00211-1
De Rybel B, Adibi M, Breda AS et al (2014) Integration of growth and patterning during vascular tissue formation in Arabidopsis. Science 345(80):1255215–1255215. https://doi.org/10.1126/science.1255215
Dumais J (2007) Can mechanics control pattern formation in plants? Curr Opin Plant Biol 10:58–62. https://doi.org/10.1016/j.pbi.2006.11.014
Dumais J, Steele C (2000) New evidence for the role of mechanical forces in the shoot apical meristem. J Plant Growth Regul 7–18. https://doi.org/10.1007/s003440000003
Dyson RJ, Jensen OE (2010) A fibre-reinforced fluid model of anisotropic plant cell growth. J Fluid Mech 655:472–503. https://doi.org/10.1017/s002211201000100x
Errera L (1886) Sur une condition fondamentale d’équilibre des cellules vivantes. Comptes Rendus Hebdomadaires des Seances de l’Academie des Sciences 103:822–824
Fayant P, Girlanda O, Chebli Y et al (2010) Finite element model of polar growth in pollen tubes. Plant Cell 22:2579–2593. https://doi.org/10.1105/tpc.110.075754
Feugier FG, Mochizuki A, Iwasa Y (2005) Self-organization of the vascular system in plant leaves: inter-dependent dynamics of auxin flux and carrier proteins. J Theor Biol 236:366–375. https://doi.org/10.1016/j.jtbi.2005.03.017
Floyd SK, Bowman JL (2010) Gene expression patterns in seed plant shoot meristems and leaves: homoplasy or homology? J Plant Res 123:43–55. https://doi.org/10.1007/s10265-009-0256-2
Fujita H, Toyokura K, Okada K, Kawaguchi M (2011) Reaction-diffusion pattern in shoot apical meristem of plants. PLoS ONE. https://doi.org/10.1371/journal.pone.0018243
Geitmann A, Ortega JKE (2009) Mechanics and modeling of plant cell growth. Trends Plant Sci 14:467–478. https://doi.org/10.1016/j.tplants.2009.07.006
Goriely A, Robertson-Tessi M, Tabor M, Vandiver R (2008) Elastic growth models. In: Mathematical modelling of biosystems. Applied optimization, vol 102. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76784-8_1
Green P (1962) Mechanism for plant cellular morphogenesis
Green PB, Steele CS, Rennich SC (1996) Phyllotactic patterns: a biophysical mechanism for their origin. Ann Bot 77:515–527. https://doi.org/10.1006/anbo.1996.0062
Grieneisen VA, Xu J, Marée AFM et al (2007) Auxin transport is sufficient to generate a maximum and gradient guiding root growth. Nature 449:1008–1013. https://doi.org/10.1038/nature06215
Hamant O, Heisler MG, Jönsson H et al (2008) Developmental patterning by mechanical signals in Arabidopsis. Science 322:1650–1655. https://doi.org/10.1126/science.1165594
Hay A, Barkoulas M, Tsiantis M (2006) ASYMMETRIC LEAVES1 and auxin activities converge to repress BREVIPEDICELLUS expression and promote leaf development in Arabidopsis. Development 133:3955–3961. https://doi.org/10.1242/dev.02545
Heisler MG, Hamant O, Krupinski P et al (2010) Alignment between PIN1 polarity and microtubule orientation in the shoot apical meristem reveals a tight coupling between morphogenesis and auxin transport. PLoS Biol 8:e1000516. https://doi.org/10.1371/journal.pbio.1000516
Hejnowicz Z, Borowska-Wykrȩt D (2005) Buckling of inner cell wall layers after manipulations to reduce tensile stress: observations and interpretations for stress transmission. Planta 220:465–473. https://doi.org/10.1007/s00425-004-1353-z
Hejnowicz Z, Rusin A, Rusin T (2000) Tensile tissue stress affects the orientation of cortical microtubules in the epidermis of sunflower hypocotyl. J Plant Growth Regul 19:31–44. https://doi.org/10.1007/s003440000005
Hernandez L, Green P (1993) Transductions for the expression of structural pattern: analysis in sunflower. Plant Cell 5:1725–1738. https://doi.org/10.1105/tpc.5.12.1725
Hisanaga T, Kawade K, Tsukaya H (2015) Compensation: a key to clarifying the organ-level regulation of lateral organ size in plants. J Exp Bot 66:1055–1063. https://doi.org/10.1093/jxb/erv028
Hofmeister W (1863) Zusatze und berichtigungen zu den 1851 veröffentlichen untersuchungen der entwicklung höherer kryptogamen. Jahrbucher für Wissenschaft und Botanik 3:259–293
Hofmeister W (1868) Allgemeine Morphologie der Gewächse. W. Engelmann
Hofhuis H, Moulton D, Lessinnes T et al (2016) Morphomechanical innovation drives explosive seed dispersal. Cell 166:222–233. https://doi.org/10.1016/j.cell.2016.05.002
Jönsson H, Heisler MG, Shapiro BE et al (2006) An auxin-driven polarized transport model for phyllotaxis. Proc Natl Acad Sci USA 103:1633–1638. https://doi.org/10.1073/pnas.0509839103
Kazama T, Ichihashi Y, Murata S, Tsukaya H (2010) The mechanism of cell cycle arrest front progression explained by a KLUH/CYP78A5-dependent mobile growth factor in developing leaves of arabidopsis thaliana. Plant Cell Physiol 51:1046–1054. https://doi.org/10.1093/pcp/pcq051
Kennaway R, Coen E, Green A, Bangham A (2011) Generation of diverse biological forms through combinatorial interactions between tissue polarity and growth. PLoS Comput Biol 7:e1002071. https://doi.org/10.1371/journal.pcbi.1002071
Kierzkowski D, Nakayama N, Routier-Kierzkowska A-L et al (2012) Elastic domains regulate growth and organogenesis in the plant shoot apical meristem. Science 335(80):1096. https://doi.org/10.1126/science.1213100
Kicheva A, Pantazis P, Bollenbach T, Kalaidzidis Y, Bittig T, Jülicher F, González-Gaitán M (2007) Kinetics of morphogen gradient formation. Science 315:521–525. https://doi.org/10.1126/science.1135774
Koenig D, Bayer E, Kang J, Kuhlemeier C, Sinha N (2009) Auxin patterns Solanum lycopersicum leaf morphogenesis. Development 136:2997–3006. https://doi.org/10.1242/dev.033811
Kondo S, Miura T (2010) Reaction-diffusion model as a framework for understanding biological pattern formation. Science 329(80):1616–20. https://doi.org/10.1126/science.1179047
Kramer EM (2009) Auxin-regulated cell polarity: an inside job? Trends Plant Sci 14:242–247. https://doi.org/10.1016/j.tplants.2009.02.005
Kuchen EE, Fox S, de Reuille PB et al (2012) Generation of leaf shape through early patterns of growth and tissue polarity. Science 335:1092–1096. https://doi.org/10.1126/science.1214678
Kwiatkowska D (2004) Structural integration at the shoot apical meristem: models, measurements, and experiments. Am J Bot 91:1277–1293. https://doi.org/10.3732/ajb.91.9.1277
Laguna MF, Bohn S, Jagla EA (2008) The role of elastic stresses on leaf venation morphogenesis. PLoS Comput Biol. https://doi.org/10.1371/journal.pcbi.1000055
Landrein B, Lathe R, Bringmann M et al (2013) Impaired cellulose synthase guidance leads to stem torsion and twists phyllotactic patterns in arabidopsis. Curr Biol 23:895–900. https://doi.org/10.1016/j.cub.2013.04.013
Laskowski M, Grieneisen VA, Hofhuis H et al (2008) Root system architecture from coupling cell shape to auxin transport. PLoS Biol 6:2721–2735. https://doi.org/10.1371/journal.pbio.0060307
Liang H, Mahadevan L (2009) The shape of a long leaf. Proc Natl Acad Sci USA 106:22049–22054. https://doi.org/10.1073/pnas.0911954106
Liang H, Mahadevan L (2011) Growth, geometry, and mechanics of a blooming lily. Proc Natl Acad Sci USA 108:5516–5521. https://doi.org/10.1073/pnas.1007808108
Lockhart JA (1965) An analysis of irreversible plant cell elongation. J Theor Biol 8:264–275. https://doi.org/10.1016/0022-5193(65)90077-9
Mähönen AP, Ten Tusscher K, Siligato R et al (2014) PLETHORA gradient formation mechanism separates auxin responses. Nature 515:125–129. https://doi.org/10.1038/nature13663
Marcos D, Berleth T (2014) Dynamic auxin transport patterns preceding vein formation revealed by live-imaging of Arabidopsis leaf primordia. Front Plant Sci 5:235. https://doi.org/10.3389/fpls.2014.00235
Meinhardt H (2009) The algorithmic beauty of sea shells. Springer Science & Business Media. https://doi.org/10.1007/978-3-662-03617-4
Meinhardt H, Koch A-J, Bernasconi G (1998) Models of pattern formation applied to plant development. In: Barabe D, Jean RV (eds) Symmetry in plants. World Scientific, Singapore, pp 723–758. https://doi.org/10.1142/9789814261074_0027
Merks RMH, Guravage M, Inze D, Beemster GTS (2011) VirtualLeaf: an open-source framework for cell-based modeling of plant tissue growth and development. Plant Physiol 155:656–666. https://doi.org/10.1104/pp.110.167619
Mitchison GJ (1980) The dynamics of auxin transport. Proc R Soc London Ser B Biol Sci 209:489–511. https://doi.org/10.1098/rspb.1980.0109
Mitchison GJ (1977) Phyllotaxis and the fibonacci series. Science 196:270–275. https://doi.org/10.1126/science.196.4287.270
Mitchison GJ, Hanke DE, Sheldrake AR (1981) The polar transport of auxin and vein patterns in plants [and discussion]. Philos Trans R Soc B Biol Sci 295:461–471. https://doi.org/10.1098/rstb.1981.0154
Mosca G, Sapala A, Strauss S et al (2017) On the micro-indentation of plant cells in a tissue context. Phys Biol 14:15003. https://doi.org/10.1088/1478-3975/aa5698
Nolte T, Schopfer P (1997) Viscoelastic versus plastic cell wall extensibility in growing seedling organs: a contribution to avoid some misconceptions. J Exp Bot 48:2103–2107. https://doi.org/10.1093/jxb/48.12.2103
O’Connor DL, Runions A, Sluis A et al (2014) A division in PIN-Mediated auxin patterning during organ initiation in grasses. PLoS Comput Biol 10:21–24. https://doi.org/10.1371/journal.pcbi.1003447
Owens A, Cieslak M, Hart J et al (2016) Modeling dense inflorescences. ACM Trans Graph 35:1–14. https://doi.org/10.1145/2897824.2925982
Peters WS, Tomos AD (1996) The history of tissue tension. Ann Bot 77:657–65. https://doi.org/10.1006/anbo.1996.0082
Prusinkiewicz P, Crawford S, Smith RS et al (2009) Control of bud activation by an auxin transport switch. Proc Natl Acad Sci USA 106:17431–17436. https://doi.org/10.1073/pnas.0906696106
Prusinkiewicz P, Runions A (2012) Computational models of plant development and form. New Phytol 193:549–569. https://doi.org/10.1111/j.1469-8137.2011.04009.x
Reinhardt D, Pesce E-R, Stieger P et al (2003) Regulation of phyllotaxis by polar auxin transport. Nature 426:255–260. https://doi.org/10.1038/nature02081
Rodkaew Y, Chongstitvatana P, Siripant S, Lursinsap C (2003) Particle systems for plant modeling. In: B-G Hu, M Jaeger (eds) Plant growth modeling and applications. Proceedings of PMA03, Tsinghua University Press and Springer, Beijing, pp 210–217
Roeder AH (2012) When and where plant cells divide: a perspective from computational modeling. Curr Opin Plant Biol 15:638–644. https://doi.org/10.1016/j.pbi.2012.08.002
Rojas ER, Hotton S, Dumais J (2011) Chemically mediated mechanical expansion of the pollen tube cell wall. Biophys J 101:1844–1853. https://doi.org/10.1016/j.bpj.2011.08.016
Rolland-Lagan A-G, Remmler L, Girard-Bock C (2014) Quantifying shape changes and tissue deformation in leaf development. Plant Physiol 165:496–505. https://doi.org/10.1104/pp.113.231258
Rolland-Lagan AG, Prusinkiewicz P (2005) Reviewing models of auxin canalization in the context of leaf vein pattern formation in Arabidopsis. Plant J 44:854–865. https://doi.org/10.1111/j.1365-313x.2005.02581.x
Roussel MR, Slingerland MJ (2012) A biochemically semi-detailed model of auxin-mediated vein formation in plant leaves. BioSystems 109:475–487. https://doi.org/10.1016/j.biosystems.2012.05.010
Routier-Kierzkowska A-L, Smith RS (2012) Measuring the mechanics of morphogenesis. Curr Op Plant Biol 16:25–32. https://doi.org/10.1016/j.pbi.2012.11.002
Runions A, Fuhrer M, Lane B et al (2005) Modeling and visualization of leaf venation patterns. ACM Trans Graph 24:702. https://doi.org/10.1145/1073204.1073251
Runions A (2014) Computational modeling of leaf development and form (Doctoral dissertation, University of Calgary)
Runions A, Smith RS, Prusinkiewicz P et al (2014) Computational models of auxin-driven development. Auxin Its Role Plant Dev 9783709115:315–357. https://doi.org/10.1007/978-3-7091-1526-8
Runions A, Tsiantis M, Prusinkiewicz P (2017) A common developmental programme can produce diverse leaf shapes. New Phytol. https://doi.org/10.1111/nph.14449
Sachs J (1878) Über die anordnung der zellen in jüngsten pflanzentheilen. Arb bot Inst Wurzburg 2:46
Sachs T (2003) Collective specification of cellular development. BioEssays 25:897–903. https://doi.org/10.1002/bies.10328
Scarpella E, Marcos D, Friml J, Berleth T (2006) Control of leaf vascular patterning by polar auxin transport. Genes Dev 20:1015–1027. https://doi.org/10.1101/gad.1402406
Schopfer P (2006) Biomechanics of plant growth. Am J Bot 93:1415–1425. https://doi.org/10.3732/ajb.93.10.1415
Shapiro BE, Meyerowitz EM, Mjolsness E (2013) Using cellzilla for plant growth simulations at the cellular level. Front Plant Sci 4:408. https://doi.org/10.3389/fpls.2013.00408
Sharon E, Roman B, Swinney HL (2007) Geometrically driven wrinkling observed in free plastic sheets and leaves. Phys Rev E Stat Nonlinear Soft Matter Phys 75:1–7. https://doi.org/10.1103/physreve.75.046211
Smith RS (2007) Simulation models of phyllotaxis and morphogenesis in plants. (Doctoral dissertation, University of Calgary)
Smith RS (2011) Modeling plant morphogenesis and growth. In: New trends in the physics and mechanics of biological systems. Oxford University Press, pp 301–338
Smith RS, Bayer EM (2009) Auxin transport-feedback models of patterning in plants. Plant Cell Environ 32:1258–1271. https://doi.org/10.1111/j.1365-3040.2009.01997.x
Smith RS, Guyomarc’h S, Mandel T et al (2006a) A plausible model of phyllotaxis. Proc Natl Acad Sci USA 103:1301–6. https://doi.org/10.1073/pnas.0510457103
Smith RS, Kuhlemeier C, Prusinkiewicz P (2006b) Inhibition fields for phyllotactic pattern formation: a simulation study. This article is one of a selection of papers published on the Special Theme of Shoot Apical Meristems. Can J Bot 84:1635–1649. https://doi.org/10.1139/b06-133
Stoma S, Lucas M, Chopard J et al (2008) Flux-based transport enhancement as a plausible unifying mechanism for auxin transport in meristem development. PLoS Comput Biol 4:e1000207. https://doi.org/10.1371/journal.pcbi.1000207
Vlad D, Kierzkowski D, Rast MI et al (2014) Leaf shape evolution through duplication, regulatory diversification, and loss of a homeobox gene. Science 343(80):780–3. https://doi.org/10.1126/science.1248384
Vogler H, Draeger C, Weber A, Felekis D et al (2013) The pollen tube: a soft shell with a hard core. Plant J 73:617–627. https://doi.org/10.1111/tpj.12061
Wabnik K, Kleine-Vehn J, Balla J et al (2010) Emergence of tissue polarization from synergy of intracellular and extracellular auxin signaling. Mol Syst Biol 6:447. https://doi.org/10.1038/msb.2010.103
Wartlick O, Kicheva A, González-Gaitán M (2009) Morphogen gradient formation. Cold Spring Harb Perspect Biol 1:1–23. https://doi.org/10.1101/cshperspect.a001255
Weber A, Braybrook S, Huflejt M, Mosca G et al (2015) Measuring the mechanical properties of plant cells by combining micro-indentation with osmotic treatments. J Exp Bot 66:3229–3241. https://doi.org/10.1093/jxb/erv135
Winship LJ, Obermeyer G, Geitmann A, Hepler PK (2010) Under pressure, cell walls set the pace. Trends Plant Sci 15:363–369. https://doi.org/10.1016/j.tplants.2010.04.005
Wolpert L (1969) Positional information and the spatial pattern of cellular differentiation. J Theor Biol 25:1–47. https://doi.org/10.1016/s0022-5193(69)80016-0
Yanagisawa M, Desyatova AS, Belteton SA et al (2015) Patterning mechanisms of cytoskeletal and cell wall systems during leaf trichome morphogenesis. Nat Plants 1:15014. https://doi.org/10.1038/nplants.2015.14
Yoshida S, Barbier de Reuille P, Lane B et al (2014) Genetic control of plant development by overriding a geometric division rule. Dev Cell 29:75–87. https://doi.org/10.1016/j.devcel.2014.02.002
Acknowledgements
We thank Richard Smith for helpful discussions and providing the simulation of auxin patterning in a developing leaf. We also would like the thank Przemyslaw Prusinkiewicz for discussions that helped to formulate some of the ideas appearing in this chapter. Support for this work was provided by the Bundesministerium für Bildung und Forschung grant 031A492, the Human Frontier Science Program grant RGP0008/2013 and the Max Planck Society. Funding from the European Commission from a Marie Skłodowska-Curie individual fellowship (Horizon 2020, 703886) is also gratefully acknowledged by AR.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Routier-Kierzkowska, AL., Runions, A. (2018). Modeling Plant Morphogenesis: An Introduction. In: Geitmann, A., Gril, J. (eds) Plant Biomechanics. Springer, Cham. https://doi.org/10.1007/978-3-319-79099-2_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-79099-2_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-79098-5
Online ISBN: 978-3-319-79099-2
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)