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A General Formalism for Tissue Morphogenesis Based on Cellular Dynamics and Control System Interactions

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Abstract

Morphogenesis is a key process in developmental biology. An important issue is the understanding of the generation of shape and cellular organisation in tissues. Despite of their great diversity, morphogenetic processes share common features. This work is an attempt to describe this diversity using the same formalism based on a cellular description. Tissue is seen as a multi-cellular system whose behaviour is the result of all constitutive cells dynamics. Morphogenesis is then considered as a spatiotemporal organization of cells activities. We show how this formalism relies on Reaction–Diffusion/Positional Information approach and how it permits to generalize its modelling possibilities. Three quite different applications for concrete morphogenetic processes are presented. The first one is a model for epithelial invagination, the second is a model of cellular differentiation by local cell–cell signalling. The last example is the secondary radial growth of conifer trees. From the mathematical point of view, different modelling tools are used according to the specificity of each process.

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References

  • Aracena J, González M, Zuñiga A, Mendez MA, Cambiazo V (2006) Regulatory network for cell shape changes during Drosophila ventral furrow formation. J Theor Biol 239:49–62

    Article  Google Scholar 

  • Forest L, San Martín J, Padilla J, Chassat F, Giroud F, Demongeot J (2004) Morphogenetic processes: application to cambial growth dynamics. Acta Biotheor 52:415–438

    Article  Google Scholar 

  • Forest L (2005) Modèles de morphogenèse tissulaire à partir de dynamiques cellulaires intégrées. PhD Thesis. Université Joseph Fourier, Grenoble

  • Forest L, Demongeot J (2006) Cellular modelling of secondary radial growth in conifer trees: application to Pinus radiata (D. Don). Bull Math Biol 68:753–784

    Article  Google Scholar 

  • Forest L, Padilla F, Martínez S, Demongeot J, San Martín J (2006) Modelling of auxin transport affected by gravity and differential radial growth. J Theor Biol 241:241–251

    Article  Google Scholar 

  • Forest L, Glade N, Demongeot J (2007) Liénard systems and potential-Hamiltonian decomposition – biological applications. C R Acad Sci Biologies 330:97–106

    Article  Google Scholar 

  • Funada R, Mizukami E, Kubo T, Fushitani M, Sigiyama T (1990) Distribution of Indole-3-acetic acid and compression wood formation in stems of inclined Cryptomeria japonica. Holzforschung 44:331–334

    Article  Google Scholar 

  • Gierer A, Meinhardt H (1972) A theory of biological pattern formation. Kybernetic 12:30–39

    Article  Google Scholar 

  • Kramer EM (2001) A mathematical model of auxin-mediated radial growth in trees. J Theor Biol 208:387–397

    Article  Google Scholar 

  • Kramer EM (2002) A mathematical model of pattern formation in the vascular cambium of trees. J Theor Biol 216:147–158

    Article  Google Scholar 

  • Larson PR (1994) The vascular cambium. Development and structure. Springer-Verlag, Berlin, 725 pp

    Google Scholar 

  • Leptin M, Grunewald B, (1990) Cell shape changes during gastrulation in Drosophila. Development 110:73–84

    Google Scholar 

  • Meinhardt H (1982) Models of biological pattern formation. Academic Press, London, 211 pp

    Google Scholar 

  • Murray JD (2002) Mathematical biology I: an introdution, 3rd edn. Springer-Verlag. New York, 551 pp

    Google Scholar 

  • Murray JD (2003) Mathematical biology II: spatial models and biomedical application, 3rd edn. New York, 811 pp

  • Painter KJ, Maini PK, Othmer HG (1999) Stripe formation in juvenile Pomacanthus explained by generalized Turing mechanism with chemotaxis. Dev Biol 96:5549–5554

    Google Scholar 

  • Painter KJ, Maini PK, Othmer HG (2000) A chemotactic model for the advance and retreat of primitive streak in avian development. Bull Math Biol 62:501–552

    Article  Google Scholar 

  • Peyret F, Prochiantz A (2002) La génisse et le pythagoricien. Traité des formes I, Paris, Odile Jacob

  • Sanchez L, van Helden J, Thieffry D (1997) Establishement of the dorso-ventral pattern during embryonic development of drosophila melanogasater: a logical analysis. J Theor Biol 189:377–389

    Article  Google Scholar 

  • Shen WM, Will P, Galstyan A, Chuong CM (2004) Hormone-inspired self-organization and distributed control of robotic swarms. Auton Robots 17:93–105

    Article  Google Scholar 

  • Turing AM (1952) The chemical basis of morphogenesis. Phil Trans Roy Soc Lond B 237:37–72

    Article  Google Scholar 

  • Uggla C, Magel E, Moritz T, Sunderg B (2001) Function and dynamics of auxin and carbohydrates during earlywood/latewood transition in Scots Pine. Plant Physiol 125:2029–2039

    Article  Google Scholar 

  • Waddington CH (1940) Organisers and genes. Cambridge University Press, UK, 160 pp

  • Wolpert L (1968) The French flag problem: a contribution to the discussion on pattern development and regulation. In: Waddington CH (ed), Towards a theoretical biology, vol 1. Edinburgh University Press, Edinburgh, pp 125–133

  • Wolpert L (1969) Positional information and the spatial pattern of cellular differentiation. J Theor Biol 25:1–47

    Article  Google Scholar 

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Authors and Affiliations

  1. Laboratoire de Mathématiques, INSA de Rouen, B.P. 8, 76131, Mont-Saint-Aignan cedex, France

    Loïc Forest

  2. Laboratoire Techniques de l’Ingénierie Médicale et de la Complexité – Informatique, Mathématiques et Applications de Grenoble (TIMC-IMAG UMR CNRS Université Joseph Fourier 5525), Institut d’Ingénierie de l’Information de Santé, Pavillon Taillefer, Faculté de Médecine, 38706, La Tronche cedex, France

    Jacques Demongeot

  3. Institut Universitaire de France, Paris, France

    Jacques Demongeot

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  1. Loïc Forest
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  2. Jacques Demongeot
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Correspondence to Loïc Forest.

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Forest, L., Demongeot, J. A General Formalism for Tissue Morphogenesis Based on Cellular Dynamics and Control System Interactions. Acta Biotheor 56, 51–74 (2008). https://doi.org/10.1007/s10441-008-9030-4

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  • DOI: https://doi.org/10.1007/s10441-008-9030-4

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