A general formalism for tissue morphogenesis based on cellular dynamics and control system interactions

Acta Biotheoretica

Volumn 56, Issue 1-2, 2008, Pages 51-74

  Forest, Loïc ^a   Demongeot, Jacques ^b,c  

^a UNIVERSITÉ ET INSA DE ROUEN   (France)

^b UNIV GRENOBLE ALPES   (France)

^c INSTITUT UNIVERSITAIRE DE FRANCE   (France)

Author keywords

Complex systems; Morphogenesis; Multi agents system; Partial differential equation; Positional information; Reaction diffusion; Weak morphogen

Indexed keywords

CONIFEROUS TREE; CYTOLOGY; MODELING; MORPHOGENESIS; MUSCLE;

ARTICLE; BIOLOGICAL MODEL; CELL; MORPHOGENESIS;

CELLS; MODELS, BIOLOGICAL; MORPHOGENESIS;

CONIFEROPHYTA;

EID: 44949258153     PISSN: 00015342     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10441-008-9030-4     Document Type: Article

References (25)

1. 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
2. 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
3. Forest L (2005) Modèles de morphogenèse tissulaire à partir de dynamiques cellulaires intégrées. PhD Thesis. Université Joseph Fourier, Grenoble
4. 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
5. 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
6. Forest L, Glade N, Demongeot J (2007) Liénard systems and potential-Hamiltonian decomposition - biological applications. C R Acad Sci Biologies 330:97-106
7. 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
8. Gierer A, Meinhardt H (1972) A theory of biological pattern formation. Kybernetic 12:30-39
9. Kramer EM (2001) A mathematical model of auxin-mediated radial growth in trees. J Theor Biol 208:387-397
10. Kramer EM (2002) A mathematical model of pattern formation in the vascular cambium of trees. J Theor Biol 216:147-158
11. Larson PR (1994) The vascular cambium. Development and structure. Springer-Verlag, Berlin, 725 pp
12. Leptin M, Grunewald B, (1990) Cell shape changes during gastrulation in Drosophila. Development 110:73-84
13. Meinhardt H (1982) Models of biological pattern formation. Academic Press, London, 211 pp
14. Murray JD (2002) Mathematical biology I: an introdution, 3rd edn. Springer-Verlag. New York, 551 pp
15. Murray JD (2003) Mathematical biology II: spatial models and biomedical application, 3rd edn. New York, 811 pp
16. Painter KJ, Maini PK, Othmer HG (1999) Stripe formation in juvenile Pomacanthus explained by generalized Turing mechanism with chemotaxis. Dev Biol 96:5549-5554
17. 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
18. Peyret F, Prochiantz A (2002) La génisse et le pythagoricien. Traité des formes I, Paris, Odile Jacob
19. 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
20. Shen WM, Will P, Galstyan A, Chuong CM (2004) Hormone-inspired self-organization and distributed control of robotic swarms. Auton Robots 17:93-105
21. Turing AM (1952) The chemical basis of morphogenesis. Phil Trans Roy Soc Lond B 237:37-72
22. 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
23. Waddington CH (1940) Organisers and genes. Cambridge University Press, UK, 160 pp
24. 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
25. Wolpert L (1969) Positional information and the spatial pattern of cellular differentiation. J Theor Biol 25:1-47