Comptes Rendus
Morphogenesis, elasticity
From growing bubbles and dendrites to biological forms
Comptes Rendus. Mécanique, Volume 348 (2020) no. 6-7, pp. 627-636.

We first describe how some ingenious experiments performed by Yves Couder illuminated the physics of viscous fingering and dendritic growth in solidification. We then recall the analogy he stressed between leaf venation and fractures in drying gels and how this and other results obtained by Yves, greatly contributed to highlight the role of mechanical forces in biological development. Finally, we briefly describe the recently appreciated role of phase separation, a topic with many important contributions of Yves, for the description of membraneless intracellular organelles.

Ce court texte est dédié à la mémoire d’Yves Couder. Nous commençons par décrire brièvement comment quelques expériences qu’il a menées ont mis en évidence des mécanismes fondamentaux à l’oeuvre dans la croissance de digitations visqueuses en mécanique des fluides et, de dendrites cristallines en solidification. Nous rappelons ensuite l’analogie qu’il a soulignée entre les formes des veines sur les feuilles végétales et celles des fractures apparaissant à la surface de gels se desséchant, et comment ces expériences, et d’autres qu’il a conduites, ont souligné le rôle important des forces mécaniques dans le développement biologique. Nous concluons sur l’importance, récemment appréciée, du phénomène de séparation de phase, que les contributions d’Yves ont permis de mieux comprendre, pour l’existence d’organelles intracellulaires sans membrane.

Published online:
DOI: 10.5802/crmeca.23
Keywords: Diffusion-controlled growth, Viscous fingering, Solidification, Phase condensation, Synapses

Vincent Hakim 1

1 Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Vincent Hakim. From growing bubbles and dendrites to biological forms. Comptes Rendus. Mécanique, Volume 348 (2020) no. 6-7, pp. 627-636. doi : 10.5802/crmeca.23. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.23/

[1] G. I. Taylor The Scientific Papers of Sir Geoffrey Ingram Taylor, Cambridge University Press, 1958

[2] K. G. Wilson; J. Kogut The renormalization group and the ϵ expansion, Phys. Rep., Volume 12 (1974) no. 2, pp. 75-199 | DOI

[3] D. Ruelle; F. Takens On the nature of turbulence, Commun. Math. Phys., Volume 20 (1971), p. 167 | DOI | MR | Zbl

[4] M. J. Feigenbaum Quantitative universality for a class of nonlinear transformations, J. Stat. Phys., Volume 19 (1978) no. 1, pp. 25-52 | DOI | MR | Zbl

[5] Y. Pomeau; P. Manneville Intermittent transition to turbulence in dissipative dynamical systems, Commun. Math. Phys., Volume 74 (1980) no. 2, pp. 189-197 | DOI | MR

[6] J.-P. Eckmann Roads to turbulence in dissipative dynamical systems, Rev. Mod. Phys., Volume 53 (1981) no. 4, p. 643 | DOI | MR | Zbl

[7] A. Libchaber; J. Maurer Une expérience de Rayleigh–Bénard de géométrie réduite; multiplication, accrochage et démultiplication de fréquences, Le Journal de Physique Colloques, Volume 41 (1980) no. C3 (C3–51) | DOI

[8] H. Thomé; Y. Couder; A. Libchaber Riedel anomaly and nonlinear effects in Josephson point contacts, J. Appl. Phys., Volume 49 (1978) no. 3, pp. 1200-1207 | DOI

[9] S. Douady; Y. Couder; M. E. Brachet Direct observation of the intermittency of intense vorticity filaments in turbulence, Phys. Rev. Lett., Volume 67 (1991) no. 8, p. 983 | DOI

[10] O. Cadot; Y. Couder; A. Daerr; S. Douady; A. Tsinober Energy injection in closed turbulent flows: stirring through boundary layers versus inertial stirring, Phys. Rev. E, Volume 56 (1997) no. 1, p. 427 | DOI

[11] Y. Couder The observation of a shear flow instability in a rotating system with a soap membrane, J. Phys. Lett., Volume 42 (1981) no. 19, pp. 429-431 | DOI

[12] M. Rabaud; Y. Couder A shear-flow instability in a circular geometry, J. Fluid Mech., Volume 136 (1983), pp. 291-319 | DOI

[13] Y. Couder; C. Basdevant Experimental and numerical study of vortex couples in two-dimensional flows, J. Fluid Mech., Volume 173 (1986), pp. 225-251 | DOI

[14] Y. Couder; J. M. Chomaz; M. Rabaud On the hydrodynamics of soap films, Physica D, Volume 37 (1989) no. 1–3, pp. 384-405 | DOI

[15] Y. Couder Two-dimensional grid turbulence in a thin liquid film, J. Phys. Lett., Volume 45 (1984) no. 8, pp. 353-360 | DOI

[16] T. A. Witten Jr; L. M. Sander Diffusion-limited aggregation, a kinetic critical phenomenon, Phys. Rev. Lett., Volume 47 (1981) no. 19, p. 1400 | DOI

[17] J. S. Langer Instabilities and pattern formation in crystal growth, Rev. Mod. Phys., Volume 52 (1980) no. 1, p. 1 | DOI

[18] L. Paterson Diffusion-limited aggregation and two-fluid displacements in porous media, Phys. Rev. Lett., Volume 52 (1984) no. 18, p. 1621 | DOI

[19] P. G. Saffman; G. I. Taylor The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid, Proc. R. Soc. Lond. A, Volume 245 (1958) no. 1242, pp. 312-329 | MR | Zbl

[20] G. P. Ivantsov Temperature field around a spherical, cylindrical and needle-shaped crystal, growing in a pre-cooled melt, Dokl. Akad. Nauk SSSR, Volume 58 (1947), p. 567

[21] P Tabeling; G Zocchi; A Libchaber An experimental study of the Saffman–Taylor instability, J. Fluid Mech., Volume 177 (1987), pp. 67-82 | DOI

[22] Y. Couder; O. Cardoso; D. Dupuy; P. Tavernier; W. Thom Dendritic growth in the Saffman–Taylor experiment, Europhys. Lett., Volume 2 (1986) no. 6, p. 437 | DOI

[23] Y. Couder; N. Gérard; M. Rabaud Narrow fingers in the Saffman–Taylor instability, Phys. Rev. A, Volume 34 (1986) no. 6, p. 5175 | DOI

[24] M. Rabaud; Y. Couder; N. Gérard Dynamics and stability of anomalous Saffman–Taylor fingers, Phys. Rev. A, Volume 37 (1988) no. 3, p. 935 | DOI

[25] P. Pelcé Dynamics of Curved Fronts, Elsevier, San Diego, 1988 | MR | Zbl

[26] J. W. McLean; P. G. Saffman The effect of surface tension on the shape of fingers in a Hele-Shaw cell, J. Fluid Mech., Volume 102 (1981), pp. 455-469 | DOI | Zbl

[27] J.-M. Vanden-Broeck Fingers in a Hele-Shaw cell with surface tension, Phys. Fluids, Volume 26 (1983) no. 8, pp. 2033-2034 | DOI | MR

[28] D. A. Kessler; J. Koplik; H. Levine Pattern selection in fingered growth phenomena, Adv. Phys., Volume 37 (1988) no. 3, pp. 255-339 | DOI

[29] H. Thomé; R. Combescot; Y. Couder Controlling singularities in the complex plane: experiments in real space, Phys. Rev. A, Volume 41 (1990) no. 10, p. 5739 | DOI

[30] H. Thomé; M. Rabaud; V. Hakim; Y. Couder The Saffman–Taylor instability: from the linear to the circular geometry, Phys. Fluids A, Volume 1 (1989) no. 2, pp. 224-240 | DOI

[31] M. Ben Amar; V. Hakim; M. Mashaal; Y. Couder Self-dilating viscous fingers in wedge-shaped Hele-Shaw cells, Phys. Fluids A, Volume 3 (1991) no. 7, pp. 1687-1690 | DOI | Zbl

[32] M. Ben Amar Viscous fingering in a wedge, Phys. Rev. A, Volume 44 (1991) no. 6, p. 3673 | DOI

[33] V. Hakim; M. Rabaud; H. Thomé; Y. Couder Directional growth in viscous fingering, New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena, Springer, New York, 1990, pp. 327-337 | DOI

[34] K. J. Ruschak Coating flows, Annu. Rev. Fluid Mech., Volume 17 (1985) no. 1, pp. 65-89 | DOI

[35] M. Rabaud; S. Michalland; Y. Couder Dynamical regimes of directional viscous fingering: spatiotemporal chaos and wave propagation, Phys. Rev. Lett., Volume 64 (1990) no. 2, p. 184 | DOI

[36] M. Asta; C. Beckermann; A. Karma; W. Kurz; R. Napolitano; M. Plapp; G. Purdy; M. Rappaz; R. Trivedi Solidification microstructures and solid-state parallels: recent developments, future directions, Acta Mater., Volume 57 (2009) no. 4, pp. 941-971 | DOI

[37] S. Douady; Y. Couder Phyllotaxis as a physical self-organized growth process, Phys. Rev. Lett., Volume 68 (1992) no. 13, p. 2098 | DOI

[38] L. Pauchard; F. Parisse; C. Allain Influence of salt content on crack patterns formed through colloidal suspension desiccation, Phys. Rev. E, Volume 59 (1999) no. 3, p. 3737 | DOI

[39] Y. Couder; L. Pauchard; C. Allain; M. Adda-Bedia; S. Douady The leaf venation as formed in a tensorial field, Eur. Phys. J. B-Condensed Matter Complex Systems, Volume 28 (2002) no. 2, pp. 135-138 | DOI

[40] D. E. Ingber Tensegrity: the architectural basis of cellular mechanotransduction, Annu. Rev. Physiol., Volume 59 (1997) no. 1, pp. 575-599 | DOI

[41] E. Farge Mechanical induction of twist in the drosophila foregut/stomodeal primordium, Curr. Biol., Volume 13 (2003), pp. 1365-1377 | DOI

[42] O. Hamant; M. G. Heisler; H. Jönsson; P. Krupinski; M. Uyttewaal; P. Bokov; F. Corson; P. Sahlin; A. Boudaoud; E. M. Meyerowitz et al. Developmental patterning by mechanical signals in arabidopsis, Science, Volume 322 (2008) no. 5908, pp. 1650-1655 | DOI

[43] C.-P. Heisenberg; Y. Bellaïche Forces in tissue morphogenesis and patterning, Cell, Volume 153 (2013) no. 5, pp. 948-962 | DOI

[44] L. LeGoff; T. Lecuit Mechanical forces and growth in animal tissues, Cold Spring Harb. Perspect. Biol., Volume 8 (2016) no. 3 (a019232) | DOI

[45] Y. Couder; J. Maurer; R. González-Cinca; A. Hernández-Machado Side-branch growth in two-dimensional dendrites. I. Experiments, Phys. Rev. E, Volume 71 (2005) no. 3 (031602) | DOI

[46] A. A. Hyman; C. A. Weber; F. Jülicher Liquid–liquid phase separation in biology, Annu. Rev. Cell Dev. Biol., Volume 30 (2014), pp. 39-58 | DOI

[47] S. F. Banani; H. O. Lee; A. A. Hyman; M. K. Rosen Biomolecular condensates: organizers of cellular biochemistry, Nat. Rev. Mol. Cell Biol., Volume 18 (2017) no. 5, pp. 285-298 | DOI

[48] Y. Shin; C. P. Brangwynne Liquid phase condensation in cell physiology and disease, Science, Volume 357 (2017) no. 6357 (eaaf4382) | DOI

[49] M. S. Turner; P. Sens; N. D. Socci Nonequilibrium raftlike membrane domains under continuous recycling, Phys. Rev. Lett., Volume 95 (2005) no. 16 (168301)

[50] B.-A. T. Quang; M. Mani; O. Markova; T. Lecuit; P.-F. Lenne Principles of e-cadherin supramolecular organization in vivo, Curr. Biol., Volume 23 (2013) no. 22, pp. 2197-2207

[51] C. A. Haselwandter; M. Calamai; M. Kardar; A. Triller; R. A. da Silveira Formation and stability of synaptic receptor domains, Phys. Rev. Lett., Volume 106 (2011) no. 23 (238104)

[52] M. Zeng; Y. Shang; Y. Araki; T. Guo; R. L. Huganir; M. Zhang Phase transition in postsynaptic densities underlies formation of synaptic complexes and synaptic plasticity, Cell, Volume 166 (2016) no. 5, pp. 1163-1175 | DOI

[53] J. Ranft; L. G. Almeida; P. C. Rodriguez; A. Triller; V. Hakim An aggregation-removal model for the formation and size determination of post-synaptic scaffold domains, PLoS Comput. Biol., Volume 13 (2017) no. 4 (e1005516) | DOI

[54] A. Tatarakis; R. Behrouzi; D. Moazed Evolving models of heterochromatin: from foci to liquid droplets, Mol. Cell, Volume 67 (2017) no. 5, pp. 725-727 | DOI

[55] S. Hahn Phase separation, protein disorder, and enhancer function, Cell, Volume 175 (2018) no. 7, pp. 1723-1725 | DOI

[56] E. M. Lifshitz; L. P. Pitaevskii Physical kinetics. Landau and Lifshitz Course of Theoretical Physics, Vol. 10, Pergamon Press, Oxford, 1981

[57] D. Choquet; A. Triller The dynamic synapse, Neuron, Volume 80 (2013) no. 3, pp. 691-703 | DOI

[58] V. Hakim; J. Ranft Lifetime of a structure evolving by cluster aggregation and particle loss, and application to postsynaptic scaffold domains, Phys. Rev. E, Volume 101 (2020) no. 1 (012411) | DOI

[59] D. Zwicker; A. A. Hyman; F. Juelicher Suppression of ostwald ripening in active emulsions, Phys. Rev. E, Volume 92 (2015) no. 1 (012317) | DOI

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