Analysis of Space-Temporal Symmetry in the Early Embryogenesis of Calla palustris L., Araceae

I.V. Rudskiy¹ ; G.E. Titova¹ ; T.B. Batygina¹

¹ Komarov’s Botanical Institute RAS, St-Petersburg, Russia

Mathematical modelling of natural phenomena, Tome 6 (2011) no. 2, pp. 82-106.

Résumé

Plants and animals have highly ordered structure both in time and in space, and one of the main questions of modern developmental biology is the transformation of genetic information into the regular structure of organism. Any multicellular plant begins its development from the universal unicellular state and acquire own species-specific structure in the course of cell divisions, cell growth and death, according to own developmental program. However the cellular mechanisms of plant development are still unknown. The aim of this work was to elaborate and verify the formalistic approach, which would allow to describe and analyze the large data of cellular architecture obtained from the real plants and to reveal the cellular mechanisms of their morphogenesis. Two multicellular embryos of Calla palustris L. (Araceae) was used as a model for the verification of our approach. The cellular architecture of the embryos was reconstructed from the stack of optical and serial sections in three dimensions and described as graphs of genealogy and space adjacency of cells. In result of the comparative analysis of these graphs, a set of regular cell types and highly conservative pattern of cell divisions during five cell generations were found. This mechanism of cellular development of the embryos could be considered as a developmental program, set of rules or grammars applied to the zygote. Also during the comparative analysis the finite plasticity in cell adjacency was described. The structural equivalence and the same morphogenetic potencies of some cells of the embryos were considered as the space-temporal symmetries. The symmetries were represented as a set of regular cell type permutations in the program of development of the embryo cellular architecture. Two groups of cell type permutations were revealed, each was composed of two elements and could be interpreted as the mirror and rotational space symmetries. The results obtained as well as the developed approach can be used in plant tissue modelling based on the real, large and complex structural data.

Détail

DOI : 10.1051/mmnp/20116203

Bibliographie

[1] O.E. Akimov. Discretnaya matematika: logika, gruppy, graphy. Laboratorya Basovyh Znaniy, Moskva, 2003.

[2] F. Baluška, D. Volkmann, P.W. Barlow Eukaryotic cells and their cell bodies: cell theory revised Annals of Botany 2004 9 32

[3] P.W. Barlow Structure and function at the root apex – phylogenetic and ontogenetic perspectives on apical cells and quiescent centres Plant and Soil 1994 1 16

[4] P.W. Barlow, H.B. Lück, J. Lück The natural philosophy of plant form: autoreproduction as a component of a structural explanation of plant form Annals of Botany 2001 1141 1152

[5] T.B. Batygina, I.V. Rudskiy Role of Stem Cells in Plant Morphogenesis Doklady Biological Sciences 2006 400 402

[6] I. Blilou, J. Xu, M. Wildwater, V. Willemsen, I. Papanov, J. Friml, R. Heidstra, M. Aida, K. Palme, B. Scheres The PIN auxin efflux facilitator network controls growth and patterning in Arabidopsis roots Nature 2005 39 44

[7] M.J.M. De Boer The relationship between cell division pattern and global shape of young fern gamethophytes. II. Morphologenesis of heart-shaped thalli Botanical Gazette 1990 435 439

[8] M.J.M. De Boer, M. De Does The relationship between cell division pattern and global shape of young fern gamethophytes. I. A model study Botanical Gazette 1990 423 434

[9] G. Bossinger, M. Maddaloni, M. Motto, F. Salamini Formation and cell lineage patterns of the shoot apex of maize The Plant Journal 1992 311 320

[10] T.D. Bunney, A.H. De Boer, M. Levin Fusicoccin signaling reveals 14-3-3 protein function as a novel step in left-right patterning during amphibian embryogenesis Development 1999 4847 4858

[11] E. Coen, A-G. Rolland-Lagan, M. Matthews, J.A. Bangham, P. Prusinkiewicz The genetic of geometry PNAS 2004 4728 4735

[12] K. Ehlers, R. Kollmann Primary and secondary plasmodesmata: structure, origin, and functioning Protoplasma 2001 1 30

[13] A. J. Fleming The integration of cell proliferation and growth in leaf morphogenesis Journal of Plant Research 2006 31 36

[14] D. Frumkin, A. Wasserstorm, S. Kaplan, U. Feige, E. Shapiro Genomic variability within an organism exposes its cell lineage tree PLoS Computational Biology 2005

[15] N. Hara Developmental anatomy of the three-dimentional structure of the vegetative shoot apex Journal of Plant Research 1995 115 125

[16] F. Harary. Graph theory. URSS, Moskva, 2009.

[17] C. Hebant, R. Hebant-Mauri, J. Barthonnet Evidence for division and polarity in apical cells of Bryophytes and Pteridophytes Planta 1978 49 52

[18] A. Hudson Development of symmetry of plants Annu. Rev. Plant Mol. Biol. 2000 349 70

[19] R. Imaichi, R. Hiratsuka Evolution of shoot apical meristem structures in vescular plants with respect to plasmodesmatal network American Journal of Botany 2007 1911 1921

[20] M.C. Jarvis, S.P.H. Briggs, J.P. Knox Intercellular adhesion and cell separation in plants Plant, Cell and Environment 2003 977 989

[21] D.A. Johansen. Plant embryology. Chronica Botanica, Waltham MA, 1950.

[22] G. Jürgens Axis Formation in plant embryogenesis: cues and clues Cell 1995 467 470

[23] J.A. Kaltschmidt, A.H. Brand Asymmetric cell division: microtubule dynamics and spindle asymmetry J. Cell Sci. 2002 2257 2264

[24] R.W. Korn The three-dimensional shape of plant cells and its relationship to pattern of tissue growth New Phytologist 1974 927 935

[25] R.W. Korn Apical cells as meristems Acta Biotheretica 1993 175 189

[26] F. Kragler, W.J. Lucas, J. Monzer Plasmodesmata: dunamics, domains and patterning Annals of Botany 1998 1 10

[27] T. Laux, T. Würschum, H. Breuninger Genetic Regulation of embryonic pattern formation The Plant Cell 2004 S190 S202

[28] H.N. Mozingo Changes in the three dimensional shape during growth and division of living epidermal cells in the apical meristem of Phleum pratense roots American Journal of Botany 1951 495 511

[29] J. Nardmann, W. Werr. Patterning of the maize embryo and the perspective of evolutionary developmental biology. In: J.L. Bennetzen, S.C. Hake (eds.). Handbook of maize: its biology. Springer Science + Business Media, LLC, 2009.

[30] P. Piazza, S. Jasinski, M. Tsiantis Evolution of leaf developmental mechanisms New Phytologist 2005 693 710

[31] R. I. Pennel, C. Lamb Programmed cell death in plants The Plant Cell 1997 1157 1168

[32] J.H. Priestley Cell growth and cell division in the shoot of the flowering plant New Phytologist 1929 54 84

[33] R.M. Ranganath. Asymmetric cell division – how plant cells get their unique identity. In: A. Maceira-Coelho (Ed.) Progress in molecular and subcellular biology: Asymmetric cell division, 45 (2007), 39-60.

[34] D. Reinchardt, T. Mandel, C. Kuhlemeier Auxin regulates the initiation and radial position of plant lateral organs The Plant Cell 2000 507 518

[35] D. Reinchardt, E-R. Pesce, P. Stieger, T. Mandel, K. Baltensperger, M. Bennett, J. Traas, J. Friml, C. Kuhlemeier Regulation of phyllotaxis by polar auxin transport Nature 2003 255 260

[36] P.L.H. Rinne, C. Van De Schoot Symplastic fields in the tunica of shoot apical meristem coordinate morphogenetic events Development 1998 1477 1485

[37] J. A. Roberts, K. A. Elliot, Z. H. Gonzales-Carranza Abscission, dehiscence, and other cell separation processes Annual Review of Plant Biology 2002 131 158

[38] T. Rudge, J. Haselhoff. Computational model of cellular morphogenesis in plants. In: M. Carpcarrere. Advances in artificial life: 8th European conference, ECAL 2005, Canterbury, UK, September 5-9, 2005: proceedings. Springer-Verlag Berlin Heidelberg, 2005.

[39] B. Scheres Plant cell identity. The role of position and lineage Plant Physiology 2001 112 114

[40] M. Sauer, J. Balla, C. Luschnig, J. Wiijnewska, V. Reinöhl, J. Friml, E. Benková Canalisation of auxin flow by Aux/IAA-ARF-dependent feedback regulation of PIN polarity Genes and Development 2006 2902 2911

[41] N. Seigerman Three-dimensional cell shape in coconut endosperm American Journal of Botany 1951 811 822

[42] R. Souèges. Exposés d’embryologie et de morphologie végétales. V. La segmentation. Deuxième fascicule: III. – Les phénomènes externes. IV. – Les blastomères. Hermann et Cie, Paris, 1936.

[43] R. Souèges. Exposés d’embryologie et de morphologie végétales. VIII. Les lois du dévelopment. Hermann et Cie, Paris, 1937.

[44] R. Souèges. Exposés d’embryologie et de morphologie végétales. X. Embryogénie et classification. Deuxième fascicule: Essai d’un système embryogénique (Partie générale). Hermann et Cie, Paris, 1939.

[45] T.H. Speller, D. Whitney, E. Crawley Using shape grammar to derive cellular automata rule patterns Complex Systems 2007 79 102

[46] G. Stent Developmental cell lineage Int. J. Dev. Biol. 1998 237 241

[47] R.N. Stewart, H. Dermen Ontogeny in monocotyledons as revealed by studies of the developmental anatomy of periclinal chloroplast chimeras American Journal of Botany 1979 47 58

[48] A. Weismann. The germ-plasm. A theory of heredity. Charles Scribner’s Sons, New York, 1893.