Plasticity and topological defects in cellular structures: Extra matter, folds and crab moulting

Rivier, N.; Miri, MirFaez; Oguey, Christophe

doi:10.1016/j.colsurfa.2005.01.027

Cited by 14 publications

(53 citation statements)

References 15 publications

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“…The cell flow and reorganisation seem to comprise different components, like passive advection [121], cell shape change and intercalation [122,123], which are ascribed to different genetic pathways [119,124]; but these may as well be different outcomes of the same cell flow, the physical forces acting as epigenetic cues. Indeed, it is well known in foam (say soap bubbles) dynamics that foam walls may be advected or may reorganize, depending on local stress conditions [125]. Intercalation is equivalent to foam wall reorganization under compression, the cell tesselation being akin to a distribution of foam walls.…”

Section: Deformation and Cell Movements During Tetrapod Formationmentioning

confidence: 99%

Clarifying tetrapod embryogenesis, a physicist's point of view

Fleury

2009

Eur. Phys. J. Appl. Phys.

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Abstract. The origin of tetrapods is a complex question that webs together genetic, paleontological, developmental and physical facts. Basically, the development of embryos is described by a complex mix of mechanical movements and biochemical inductions of genetic origin. It is difficult to sort out in this scientific question what are the fundamental features imposed by conservation laws of physics, and by force equilibria, and what can be ascribed to successive, very specific, stop-and-go inductions of genetic nature. A posteriori, evolution selects the parameters of this process as found in the observed species. Whether there is a general law to animal formation seems out of the question. However, several concepts developed in biology, like the concept of "organizer" seem questionable from a physics point of view, since the entire deformation and force field should be the "organizer" of development, and one can hardly ascribe such a role to a single small area of the embryo body. In the same spirit, the concept of "positional information" encapsulated in concentration of chemicals seems questionable since the deformation and force fields in embryonic tissues are tensors. Finally, the concept of a development organized in space along three orthogonal ("Cartesian") axes associated to chemical gradients seems also questionable, since early embryo development is driven by complex vortex fields, with hyperbolic trajectories which span the entire embryo. Such hyperbolic trajectories are best understood by a description in terms of dipolar components of the morphogenetic forces, whose projections along orthogonal axes have no specific meaning except as a mathematical tool. I review here the present state of description of several aspects of tetrapods morphogenesis and evolution, from the point of view of physics. It is getting clear that several basic features of tetrapods body are a direct consequences of fundamental laws of physics. Several lines of work reviewed here show that the topology of the tetrapods may be directly related to the structure of the earliest movements in embryos. The bio-mechanical approach leads to important consequences for the constraints on evolution of the craniates. Such consequences have received a controversial welcome in the last decade, although they may encapsulate the true origin of craniates, esp. simians, and eventually homo.

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Section: Deformation and Cell Movements During Tetrapod Formationmentioning

confidence: 99%

Clarifying tetrapod embryogenesis, a physicist's point of view

Fleury

2009

Eur. Phys. J. Appl. Phys.

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“…Returning to polyhedral surfaces we understand that sometimes it is useful to have a notion of combinatorial curvature, independent of all geometrical information (Sullivan 2008). In hexagonal 2d-cell network, presence of faces with another number of sides can be considered as a topological dislocation of homogeneous graph (Duvdevani- Bar and Segel 1994;Rivier et al 2005). The non-hexagonal faces on the sphere (called defects or disclinations) appear to form 12 ''scars'' (or sometimes ''buttons'') roughly centered at the vertices of an inscribed icosahedron.…”

Section: Combinatorial Classification Of Blastomere Packingmentioning

confidence: 99%

Topological determination of early morphogenesis in Metazoa

2010

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This paper presents a topological interpretation of some developmental events through the use of well-known concepts and theorems of combinatorial geometry. The organization of early embryo using a simulation of cleavage considering only blastomere contacts is examined. Each blastomere is modeled as a topological cell and whole embryo--as cell packing. The egg cleavage results in a pattern of cellular contacts on the surface of each blastomere and whole embryo, a discrete morphogenetic field. We find topological distinctions between different types of early egg cleavage and suggest a topological classification of cleavage. Blastulation and gastrulation may be related to an inevitable emergence of discrete curvature that directs development in three-dimensional space. The relationship between local and global orders in metazoan development, i.e., between local morphogenetic processes and integral developmental patterns, is established. Thus, this methodology reveals a topological imperative: a certain set of topological rules that constrains and directs biological morphogenesis.

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“…In planar and spherical phyllotaxis, the innermost ring of defects contains five more pentagons (of topological charge +1) than heptagons (topological charge −1) [5]. This is because the topological charge of a disk (flattened hemisphere) must be +6, with 5 taken up by the innermost grain boundary (polar circle) and +1 by the pole (s = 1, a pentagonal cell).…”

Section: Grain Boundariesmentioning

confidence: 99%

Phyllotaxis: a framework for foam topological evolution

2016

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Phyllotaxis describes the arrangement of florets, scales or leaves in composite flowers or plants (daisy, aster, sunflower, pinecone, pineapple). As a structure, it is a geometrical foam, the most homogeneous and densest covering of a large disk by Voronoi cells (the florets), constructed by a simple algorithm: Points placed regularly on a generative spiral constitute a spiral lattice, and phyllotaxis is the tiling by the Voronoi cells of the spiral lattice. Locally, neighboring cells are organized as three whorls or parastichies, labelled with successive Fibonacci numbers. The structure is encoded as the sequence of the shapes (number of sides) of the successive Voronoi cells on the generative spiral. We show that sequence and organization are independent of the position of the initial point on the generative spiral, that is invariant under disappearance (T 2) of the first Voronoi cell or, conversely, under creation of a first cell, that is under growth. This independence shows how a foam is able to respond to a shear stress, notably through grain boundaries that are layers of square cells slightly truncated into heptagons, pentagons and hexagons, meeting at four-corner vertices, critical points of T 1 elementary topological transformations. Preprint of a paper published in The European Physical Journal E, 39 (1)

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Plasticity and topological defects in cellular structures: Extra matter, folds and crab moulting

Cited by 14 publications

References 15 publications

Clarifying tetrapod embryogenesis, a physicist's point of view

Clarifying tetrapod embryogenesis, a physicist's point of view

Topological determination of early morphogenesis in Metazoa

Phyllotaxis: a framework for foam topological evolution

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