Body Plan in Tetrapods Is It Patterned by a Hyperbolic Tissue Flow?

O lena P. Boryskina,1 Alia Al-Kilani2 and Vincent Fleury2,*

1Laboratoire Matière et Systèmes Complexes; Université Paris Diderot; Paris, France; 2I nstitute of Radiophysics and Electronics NAS of Ukraine; Kharkov, Ukraine

A considerable effort has been devoted to recently introduced air-puff tonometer.9 rotation away from the stagnation point understanding the mechanisms of mor- We have found that at these early stages, creates the umbilical area and four limb phogenesis. It is known that vertebrate the embryonic tissue behaves as a viscous plates with opposite chiralities.5-7 development starts off with a roughly fluid5 and thus is subjected to the laws of As the flow is viscous, the flow map is round mass of cells, which gradually hydrodynamics. A similar conclusion was associated with its specific pattern of stress acquires a bilateral elongated aspect and also made by other authors in reference 10. gradients. In reference 6, we predicted in progressively forms a recognizable ani- To address quantitatively the embry- a numerical model and confirmed in mea- mal by large-scale “convergent extension” onic tissue flows in blastula and early gas- surements that the limb plates (regions movements. During this process, cells trula of the chicken embryos, we recorded with a rotatory flow) are concomitant with perform both collective and individual cell trajectories using particle imaging the stress minima. Via mechanotransduc- movements, such as conformational velocimetry.5 It was found that the vor- tion pathways,11 the stress gradients in the changes, rosette reorganization,1 align- tex flow seen in the epiblast during the embryo can specifically induce/modify ments along the Antero-Posterior axis,2 primitive streak initiation,4 acquires a genetic expression, acting as the “physical intercalation,3 epiboly, etc. However, the clear hyperbolic pattern of streamlines morphogenes,” and thus cooperate with relation between the global changes of that “revolve” toward and away from a biochemical signals to specify the pattern the shape of the developing embryo and neutral point at later stages, with four vor- of development. activities of individual cells remains elu- tices of opposite chiralities in the lateral In this connection, a very important ©2011 Landes Bioscience. sive. What is the causeLandes and what ©2011 is the regions of the embryo.5 The flow is pres- question is that of the symmetry break- effect? Regulation of patterning processes ent until the vertebrate bauplan becomes ing factor that determines the specific is traditionally ascribeddistribute. to genetic not fac- recognizable.Do Assuming that the embryo flow map in a given phylum. In the search tors that create a complex morphogenetic tissue behaves as a viscous fluid, we pro- for this element in vertebrates, we identi- field of diffusible molecules.4 However, it posed, and confirmed this hypothesis in a fied the invagination of cells (through the is unclear how biochemical factors alone numerical model,6 that formation of this primitive streak in chicken), which cre- can orchestrate the individual cell events complex flow pattern does not require an ates a strong pulling action “from under- in such a way that they provide a smooth explicit point-by-point time and space neath.” The duplication and reversal of evolution of the organization plans of the morphogenetic coding. On the contrary, traction forces across the primitive streak embryo on different stages of develop- it can be formed directly by the laws of stabilizes what is called in physics a quad- ment, delivering at each step a function- hydrodynamics due to the strong winding rupolar movement and a hyperbolic char- ing organism. of the lateral tissue sheared by the rapidly acter of the flow.5 In a series of articles,5-8 we engaged the extending medial axis, because a localized Thus, from a physical point of view, laws of hydrodynamics to treat the tis- pull in a continuous viscous medium suf- the crucial steps of morphogenesis of sue movements and deformation on early fices to induce long range effects, such as vertebrates, and probably similarly in stages of embryogenesis. Considering a large scale vortices. other phyla,8 can be described as an ini- chicken embryo as an example (Fig. 1), we The hyperbolic rotatory flow gives tial broken symmetry which is up-scaled managed to web together different aspects straightforwardly the pattern of the animal by a slow, continuous, viscoelastic flow to of tetrapod morphogenesis and give a sci- bauplan (or “archetype” or “prototype” as the body plan of the animal. Because of

This manuscript has been published online, prior to printing. Once the issue is complete and page numbers have been assigned, the citation will change accordingly. the issue is complete and page numbers have Once to printing. has been published online, prior This manuscript entific rationale to the early steps of the coined by Darwin). The axial structures this, the animal morphogenesis cannot be body plan establishment. are formed along the midline in the areas understood on the basis of static descrip- Are the slow fluid dynamics appli- with a strong, bidirectional straightfor- tions of morphogenetic fields alone. At the cable to embryonic tissue? We believe ward flow; the smooth continuation of the same time, this work points to important so. To prove this hypothesis, we stud- hyperbolic flow toward the posterior and physical parameters that are controlled ied viscoelastic properties of the chicken anterior areas creates, in a self-consistent by genetic expressions, e.g., viscosity, blastula and early gastrula by means of a manner, head, heart and tail, while the elastic modulus, bending modulus, shear

*Correspondence to: Vincent Fleury; Email: [email protected] Submitted: 08/30/11; Accepted: 08/31/11 http://dx.doi.org/10.4161/cc.10.22.17945 Comment on: Boryskina OP, et al. Eur Phys J Appl Phys 2011; 55:21101.

www.landesbioscience.com Cell Cycle 1 Figure 1. Chicken embryo, HH 6 (A), embryo cell trajectories (B). During the early stages of convergent extension, the embryo undergoes an in-plane, long ranged, hyperbolic tissue flow with four conspicuous windings. This flat flow becomes 3D by a viscoelastic buckling and collapse of the folds against each other as they are themselves transported in the flow.T he flow map is upscaled into the organization plan of the animal. (1) The axial structures are formed along the midline in the areas with a strong, bidirectional straightforward flow. (2) Four extremities with opposite chiralities originate from the regions of vortex-type flow in the lateral areas above and below the fixed point. (3)T he area of the hyperbolic point, from where the tissue expands cranially and caudally, becomes the yolk sac stalk. The flow map of the embryo can be easily traced even in the adult vertebrate, for example, in a cat [dorsal view of a cat (C)].

©2011 Landes Bioscience. Landes ©2011 6. Boryskina OP, et al. Eur Phys J Appl Phys 2011; thresholds, etc. By determining these References 55:21101; DOI:10.1051/epjap/2011100468. characteristics at a quantitativedistribute. level, genesnot 1. Do Blankenship JT, et al. Dev Cell 2006; 11:459- 7. Fleury V. Eur Phys J E Soft Matter 2011; 34:1-13; 70; PMID:17011486; DOI:10.1016/j.dev- DOI:10.1140/epje/i2011-11001-4. guarantee the stability of the flow and thus cel.2006.09.007. 8. Fleury V. C R Biol 2011; 334:91-9; PMID:21333940; successive appearance of the animal plans 2. Martin AC, et al. J Cell Biol 2010; 188:735-49; DOI:10.1016/j.crvi.2010.11.009. inside a given phylum in a non-intuitive, PMID:20194639; DOI:10.1083/jcb.200910099. 9. Fleury V, et al. Phys Rev E Stat Nonlin Soft Matter Phys 3. Keller R, et al. Philos Trans R Soc Lond B Biol Sci 2010; 81:021920; PMID:20365608; DOI:10.1103/ but still physical, order. 2000; 355:897-922; PMID:11128984; DOI:10.1098/ PhysRevE.81.021920. rstb.2000.0626. 10. Rauzy M, et al. Nature 2010; 468:1110-4; 4. Sandersius SA, et al. Phys Biol 2011; 8:45008; PMID:21068726; DOI:10.1038/nature09566. PMID:21750368; DOI:10.1088/1478- 11. Farge E. Curr Top Dev Biol 2011; 95:243-65; 3975/8/4/045008. PMID:21501754; DOI:10.1016/B978-0-12-385065- 5. Fleury V, et al. C R Biol 2011; 334:505-15; 2.00008-6. PMID:21784360; DOI:10.1016/j.crvi.2011.03.010.

2 Cell Cycle Volume 10 Issue 22