Generation of Diverse Biological Forms through Combinatorial Interactions between Tissue Polarity and Growth

A major problem in biology is to understand how complex tissue shapes may arise through growth. In many cases this process involves preferential growth along particular orientations raising the question of how these orientations are specified. One view is that orientations are specified through stresses in the tissue (axiality-based system). Another possibility is that orientations can be specified independently of stresses through molecular signalling (polarity-based system). The axiality-based system has recently been explored through computational modelling. Here we develop and apply a polarity-based system which we call the Growing Polarised Tissue (GPT) framework. Tissue is treated as a continuous material within which regionally expressed factors under genetic control may interact and propagate. Polarity is established by signals that propagate through the tissue and is anchored in regions termed tissue polarity organisers that are also under genetic control. Rates of growth parallel or perpendicular to the local polarity may then be specified through a regulatory network. The resulting growth depends on how specified growth patterns interact within the constraints of mechanically connected tissue. This constraint leads to the emergence of features such as curvature that were not directly specified by the regulatory networks. Resultant growth feeds back to influence spatial arrangements and local orientations of tissue, allowing complex shapes to emerge from simple rules. Moreover, asymmetries may emerge through interactions between polarity fields. We illustrate the value of the GPT-framework for understanding morphogenesis by applying it to a growing Snapdragon flower and indicate how the underlying hypotheses may be tested by computational simulation. We propose that combinatorial intractions between orientations and rates of growth, which are a key feature of polarity-based systems, have been exploited during evolution to generate a range of observed biological shapes.

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

[2]  Jennifer A Zallen,et al.  Planar Polarity and Tissue Morphogenesis , 2007, Cell.

[3]  James Sharpe,et al.  The Role of Spatially Controlled Cell Proliferation in Limb Bud Morphogenesis , 2010, PLoS biology.

[4]  L. V. Belousov,et al.  Scott F. Gilbert—Developmental Biology, 2010, Sinauer Associates, Inc., Sunderland, MA Ninth Edition , 2011, Russian Journal of Developmental Biology.

[5]  N. Dyn,et al.  A butterfly subdivision scheme for surface interpolation with tension control , 1990, TOGS.

[6]  Arezki Boudaoud,et al.  Regulation of shape and patterning in plant development. , 2010, Current opinion in genetics & development.

[7]  P. Lintilhac,et al.  An insight into cell elasticity and load-bearing ability. Measurement and theory. , 2001, Plant physiology.

[8]  Z. Hejnowicz.  Autonomous changes in the orientation of cortical microtubules underlying the helicoidal cell wall of the sunflower hypocotyl epidermis: spatial variation translated into temporal changes , 2005, Protoplasma.

[9]  Magalie Uyttewaal,et al.  Integrating physical stress, growth, and development. , 2010, Current opinion in plant biology.

[10]  Jerzy Nakielski,et al.  The tensor-based model for growth and cell divisions of the root apex. I. The significance of principal directions , 2008, Planta.

[11]  Przemyslaw Prusinkiewicz,et al.  The Algorithmic Beauty of Plants , 1990, The Virtual Laboratory.

[12]  Antonio Baonza,et al.  The Orientation of Cell Divisions Determines the Shape of Drosophila Organs , 2005, Current Biology.

[13]  Bart Nicolai,et al.  Micromechanical behaviour of onion epidermal tissue , 2005 .

[14]  O. C. Zienkiewicz,et al.  The Finite Element Method: Its Basis and Fundamentals , 2005 .

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

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

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

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

[19]  T. Lecuit,et al.  Planar polarity and short-range polarization in Drosophila embryos. , 2009, Seminars in cell & developmental biology.

[20]  B. Shraiman,et al.  Mechanical feedback as a possible regulator of tissue growth. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Ottoline Leyser,et al.  An Auxin-Dependent Distal Organizer of Pattern and Polarity in the Arabidopsis Root , 1999, Cell.

[22]  Alain Goriely,et al.  On the definition and modeling of incremental, cumulative, and continuous growth laws in morphoelasticity , 2007, Biomechanics and modeling in mechanobiology.

[23]  Ray Keller,et al.  Shaping the Vertebrate Body Plan by Polarized Embryonic Cell Movements , 2002, Science.

[24]  D. M. Bruce,et al.  RELATIONSHIPS BETWEEN PRIMARY PLANT CELL WALL ARCHITECTURE AND MECHANICAL PROPERTIES FOR ONION BULB SCALE EPIDERMAL CELLS , 2004 .

[25]  Ari Pekka Mähönen,et al.  Generation of cell polarity in plants links endocytosis, auxin distribution and cell fate decisions , 2008, Nature.

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

[27]  P B Green.  Transductions to generate plant form and pattern: an essay on cause and effect. , 1997, Gravitational and space biology bulletin : publication of the American Society for Gravitational and Space Biology.

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

[29]  Christophe Godin,et al.  Using mechanics in the modelling of meristem morphogenesis , 2007 .

[30]  L. G. Harrison,et al.  Pattern selection in plants: coupling chemical dynamics to surface growth in three dimensions. , 2007, Annals of botany.

[31]  Philip K. Maini,et al.  Mechanochemical models for generating biological pattern and form in development , 1988 .

[32]  J. Murray.  A Pre-pattern formation mechanism for animal coat markings , 1981 .

[33]  M. Ben Amar,et al.  Morphogenesis of growing soft tissues. , 2007, Physical review letters.

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

[35]  P. Prusinkiewicz,et al.  A model for cellular development in morphogenetic fields , 1992 .

[36]  Anne-Gaëlle Rolland-Lagan,et al.  A computational method for inferring growth parameters and shape changes during development based on clonal analysis. , 2005, Journal of theoretical biology.

[37]  J. Dervaux,et al.  Elastic growth in thin geometries , 2009 .

[38]  L. Wolpert.  Developmental Biology , 1968, Nature.

[39]  T. Steeves,et al.  Patterns in plant development: Subject index , 1972 .

[40]  W. Silk,et al.  Quantitative Descriptions of Development , 1984 .

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

[42]  J. Achenbach.  THE LINEARIZED THEORY OF ELASTICITY , 1973 .

[43]  Cris Kuhlemeier,et al.  How a Plant Builds Leaves , 2010, Plant Cell.

[44]  J. C. Criscione,et al.  Complex distributions of residual stress and strain in the mouse left ventricle: experimental and theoretical models , 2003, Biomechanics and modeling in mechanobiology.

[45]  J. Dumais.  Can mechanics control pattern formation in plants? , 2007, Current opinion in plant biology.

[46]  Frank Jülicher,et al.  Cell Flow Reorients the Axis of Planar Polarity in the Wing Epithelium of Drosophila , 2010, Cell.

[47]  Michael P Marder,et al.  Leaves, flowers and garbage bags: Making waves , 2004 .

[48]  J. Bangham,et al.  Quantitative Control of Organ Shape by Combinatorial Gene Activity , 2010, PLoS biology.

[49]  M. Maurel,et al.  Origins of Life: Self-Organization and/or Biological Evolution? , 2009 .

[50]  E. Coen,et al.  Genetic Control of Surface Curvature , 2003, Science.

[51]  Ottoline Leyser,et al.  Auxin Distribution and Plant Pattern Formation: How Many Angels Can Dance on the Point of PIN? , 2005, Cell.

[52]  J. Dumais,et al.  Growth and morphogenesis at the vegetative shoot apex of Anagallis arvensis L. , 2003, Journal of experimental botany.

[53]  A. M. Turing,et al.  The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

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

[55]  Alain Goriely,et al.  Growth and instability in elastic tissues , 2005 .

[56]  M. Buckingham,et al.  Right Ventricular Myocardium Derives From the Anterior Heart Field , 2004, Circulation research.

[57]  Julian Lewis,et al.  From Signals to Patterns: Space, Time, and Mathematics in Developmental Biology , 2008, Science.

[58]  Pasquale Ciarletta,et al.  Morphogenesis of thin hyperelastic plates: A constitutive theory of biological growth in the Föppl-von Kármán limit , 2009 .

[59]  Paul B. Green.  Expression of form and pattern in plants — a role for biophysical fields , 1996 .

[60]  Lewis Wolpert,et al.  Principles of Development , 1997 .

[61]  Jim Haseloff,et al.  A Computational Model of Cellular Morphogenesis in Plants , 2005, ECAL.

[62]  Mark Miodownik,et al.  A 3D finite element model of ventral furrow invagination in the Drosophila melanogaster embryo. , 2008, Journal of the mechanical behavior of biomedical materials.

[63]  D'arcy W. Thompson,et al.  On Growth and Form , 1917, Nature.

[64]  Michel Kerszberg,et al.  Establishment and maintenance of planar epithelial cell polarity by asymmetric cadherin bridges: A computer model , 2006, Developmental dynamics : an official publication of the American Association of Anatomists.

[65]  E. Sharon,et al.  Shaping of Elastic Sheets by Prescription of Non-Euclidean Metrics , 2007, Science.

[66]  Mark Jeffrey Matthews,et al.  Physically based simulation of growing surfaces , 2002 .

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

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

[69]  R. Kupferman,et al.  Elastic theory of unconstrained non-Euclidean plates , 2008, 0810.2411.

[70]  M. Grebe.  Ups and downs of tissue and planar polarity in plants , 2004, BioEssays : news and reviews in molecular, cellular and developmental biology.