Physical models of plant development.

The definition of shape in multicellular organisms is a major issue of developmental biology. It is well established that morphogenesis relies on genetic regulation. However, cells, tissues, and organism behaviors are also bound by the laws of physics, which limit the range of possible deformations organisms can undergo but also define what organisms must do to achieve specific shapes. Besides experiments, theoretical models and numerical simulations of growing tissues are powerful tools to investigate the link between genetic regulation and mechanics. Here, we provide an overview of the main mechanical models of plant morphogenesis developed so far, from subcellular scales to whole tissues. The common concepts and discrepancies between the various models are discussed.

[1]  Roeland M. H. Merks,et al.  Breakthrough Technologies VirtualLeaf : An Open-Source Framework for Cell-Based Modeling of Plant Tissue Growth and Development 1 , 2010 .

[2]  Jérôme Chopard,et al.  The role of mechanics in morphogenesis , 2010 .

[3]  J. Lockhart Physical nature of irreversible deformation of plant cells. , 1967, Plant physiology.

[4]  J. Lockhart An analysis of irreversible plant cell elongation. , 1965, Journal of theoretical biology.

[5]  Oliver E. Jensen,et al.  A fibre-reinforced fluid model of anisotropic plant cell growth , 2010, Journal of Fluid Mechanics.

[6]  S. McQueen-Mason,et al.  Two endogenous proteins that induce cell wall extension in plants. , 1992, The Plant cell.

[7]  G. S. Avery, STRUCTURE AND DEVELOPMENT OF THE TOBACCO LEAF , 1933 .

[8]  G. Malandain,et al.  Imaging plant growth in 4D: robust tissue reconstruction and lineaging at cell resolution , 2010, Nature Methods.

[9]  Olivier Hamant,et al.  The mechanics behind plant development. , 2010, The New phytologist.

[10]  Patrick Laufs,et al.  In Vivo Analysis of Cell Division, Cell Growth, and Differentiation at the Shoot Apical Meristem in Arabidopsis Article, publication date, and citation information can be found at www.plantcell.org/cgi/doi/10.1105/tpc.017962. , 2004, The Plant Cell Online.

[11]  G. Gierz,et al.  A three-dimensional model of fungal morphogenesis based on the vesicle supply center concept. , 2001, Journal of theoretical biology.

[12]  Andrew J. Fleming,et al.  Induction of Leaf Primordia by the Cell Wall Protein Expansin , 1997 .

[13]  Richard Kennaway,et al.  Generation of Diverse Biological Forms through Combinatorial Interactions between Tissue Polarity and Growth , 2011, PLoS Comput. Biol..

[14]  O. Jensen,et al.  A model of crosslink kinetics in the expanding plant cell wall: yield stress and enzyme action , 2012, Journal of theoretical biology.

[15]  O. Hamant,et al.  Regulatory Role of Cell Division Rules on Tissue Growth Heterogeneity , 2012, Front. Plant Sci..

[16]  D. Cosgrove,et al.  Altered expression of expansin modulates leaf growth and pedicel abscission in Arabidopsis thaliana. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[17]  E. Meyerowitz,et al.  Real-time lineage analysis reveals oriented cell divisions associated with morphogenesis at the shoot apex of Arabidopsis thaliana , 2004, Development.

[18]  D. Ehrhardt,et al.  Visualization of Cellulose Synthase Demonstrates Functional Association with Microtubules , 2006, Science.

[19]  J. C. Ambrose,et al.  Spatial organization of plant cortical microtubules: close encounters of the 2D kind. , 2009, Trends in cell biology.

[20]  Alain Goriely,et al.  Biomechanical models of hyphal growth in actinomycetes. , 2003, Journal of theoretical biology.

[21]  Stephen C. Fry,et al.  Turgor and Cell Expansion: Beyond the Lockhart Equation , 1992 .

[22]  Y. Couder,et al.  Turning a plant tissue into a living cell froth through isotropic growth , 2009, Proceedings of the National Academy of Sciences.

[23]  J. R. Kennaway,et al.  Genetic Control of Organ Shape and Tissue Polarity , 2010, PLoS biology.

[24]  Henrik Jönsson,et al.  Modelling meristem development in plants. , 2007, Current opinion in plant biology.

[25]  Julius Sachs,et al.  Über die Anordnung der Zellen in jüngsten Pflanzentheilen , 2022 .

[26]  Jim Haseloff,et al.  A system for modelling cell-cell interactions during plant morphogenesis. , 2008, Annals of botany.

[27]  T. Lecuit,et al.  Cell surface mechanics and the control of cell shape, tissue patterns and morphogenesis , 2007, Nature Reviews Molecular Cell Biology.

[28]  Benoit Landrein,et al.  Mechanical Stress Acts via Katanin to Amplify Differences in Growth Rate between Adjacent Cells in Arabidopsis , 2012, Cell.

[29]  M. Lahaye,et al.  Another Brick in the Cell Wall: Biosynthesis Dependent Growth Model , 2013, PloS one.

[30]  T. Baskin Anisotropic expansion of the plant cell wall. , 2005, Annual review of cell and developmental biology.

[31]  A. Geitmann,et al.  Mechanics and modeling of plant cell growth. , 2009, Trends in plant science.

[32]  R. O. Erickson Modeling of Plant Growth , 1976 .

[33]  J. Dumais,et al.  Analysis of surface growth in shoot apices. , 2002, The Plant journal : for cell and molecular biology.

[34]  O. Hamant,et al.  Alignment between PIN1 Polarity and Microtubule Orientation in the Shoot Apical Meristem Reveals a Tight Coupling between Morphogenesis and Auxin Transport , 2010, PLoS biology.

[35]  Jacques Dumais,et al.  The Mechanics of Surface Expansion Anisotropy in Medicago truncatula Root Hairs1 , 2004, Plant Physiology.

[36]  Herman Höfte,et al.  Cell wall mechanics and growth control in plants: the role of pectins revisited , 2012, Front. Plant Sci..

[37]  J. Haseloff,et al.  Coordination of plant cell division and expansion in a simple morphogenetic system , 2010, Proceedings of the National Academy of Sciences.

[38]  E. Coen,et al.  JAGGED Controls Arabidopsis Petal Growth and Shape by Interacting with a Divergent Polarity Field , 2013, PLoS biology.

[39]  J. Mikkelsen,et al.  Pectin: new insights into an old polymer are starting to gel , 2006 .

[40]  E. Bayer,et al.  Elastic Domains Regulate Growth and Organogenesis in the Plant Shoot Apical Meristem , 2012, Science.

[41]  Y. Couder,et al.  Developmental Patterning by Mechanical Signals in Arabidopsis , 2009 .

[42]  P B Green,et al.  Metabolic and physical control of cell elongation rate: in vivo studies in nitella. , 1971, Plant physiology.

[43]  Hojae Yi,et al.  Architecture-Based Multiscale Computational Modeling of Plant Cell Wall Mechanics to Examine the Hydrogen-Bonding Hypothesis of the Cell Wall Network Structure Model1[C][OA] , 2012, Plant Physiology.

[44]  John R. King,et al.  Vertex-element models for anisotropic growth of elongated plant organs , 2013, Front. Plant Sci..

[45]  D. Cosgrove Growth of the plant cell wall , 2005, Nature Reviews Molecular Cell Biology.

[46]  E. Coen,et al.  Generation of Leaf Shape Through Early Patterns of Growth and Tissue Polarity , 2012, Science.

[47]  Adrienne Roeder,et al.  Tessellations and Pattern Formation in Plant Growth and Development , 2012, 1209.2937.

[48]  J. Dumais,et al.  Chemically mediated mechanical expansion of the pollen tube cell wall. , 2011, Biophysical journal.

[49]  J. Ortega Augmented growth equation for cell wall expansion. , 1985, Plant physiology.

[50]  D J Cosgrove,et al.  Wall extensibility: its nature, measurement and relationship to plant cell growth. , 1993, The New phytologist.

[51]  P. Prusinkiewicz,et al.  The genetics of geometry. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[52]  Charles R Steele,et al.  An anisotropic-viscoplastic model of plant cell morphogenesis by tip growth. , 2006, The International journal of developmental biology.

[53]  Lionel Dupuy,et al.  A biomechanical model for the study of plant morphogenesis : Coleocheate orbicularis , a 2 D study species , 2006 .

[54]  J. Dumais,et al.  Universal rule for the symmetric division of plant cells , 2011, Proceedings of the National Academy of Sciences.

[55]  Leo Errera,et al.  Sur une condition fondamentale d'équilibre des cellules vivantes , 1886 .

[56]  A. Fleming,et al.  Local expression of expansin induces the entire process of leaf development and modifies leaf shape , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[57]  E. Mjolsness,et al.  An auxin-driven polarized transport model for phyllotaxis , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[58]  P. Schopfer,et al.  Biomechanics of plant growth. , 2006, American journal of botany.

[59]  D J Cosgrove,et al.  A model of cell wall expansion based on thermodynamics of polymer networks. , 1998, Biophysical journal.

[60]  R. O. Erickson,et al.  Relative Elemental Rates and Anisotropy of Growth in Area: a Computer Programme , 1966 .

[61]  Henrik Jönsson,et al.  Stress and Strain Provide Positional and Directional Cues in Development , 2014, PLoS Comput. Biol..

[62]  P B Green,et al.  Growth Physics in Nitella: a Method for Continuous in Vivo Analysis of Extensibility Based on a Micro-manometer Technique for Turgor Pressure. , 1968, Plant physiology.

[63]  Ingo Burgert,et al.  Exploring the micromechanical design of plant cell walls. , 2006, American journal of botany.

[64]  Arezki Boudaoud,et al.  An introduction to the mechanics of morphogenesis for plant biologists. , 2010, Trends in plant science.

[65]  M. Bennett,et al.  Regulation of phyllotaxis by polar auxin transport , 2003, Nature.

[66]  Shankar Kalyanasundaram,et al.  WallGen, Software to Construct Layered Cellulose-Hemicellulose Networks and Predict Their Small Deformation Mechanics1 , 2009, Plant Physiology.

[67]  Sebastian Wolf,et al.  Growth control and cell wall signaling in plants. , 2012, Annual review of plant biology.