Abstract
We show how a simple nonlinear dynamical system (the discrete quadratic iteration on the unit segment) can be the basis for modelling the embryogenesis process. Such an approach, even though being crude, can nevertheless prove to be useful when looking with the two main involved processes:
-
i)
on one hand the cell proliferation under successive divisions
-
ii)
on the other hand, the differentiation between cell lineages.
We illustrate this new approach in the case of Caenorhabditis elegans by looking at the early stages of embryogenesis, up to several hundreds of cells (“lima bean” larval stage). We show how the many results that have been obtained by several groups can be interpreted in terms of values for the parameters controlling the dynamical system. Furthermore, we can extend the model to the cases of genetic mutations. More precisely the teratogenetic and lethal effects are associated with abnormal variation of the control parameters with time.
Similar content being viewed by others
References
Bailly, F., F. Gaill and R. Mosseri (1988). Rev. Intern. Syst., 2 n°3, p.295.
Bailly, F., F. Gaill and R. Mosseri (1989). Cong. Europ. Syst., Lausanne, AFCET.
Bailly, F., F. Gaill and R. Mosseri (in press,a). Sém. Biol. Théo., Solignac 1987.
Bailly, F., F. Gaill and R. Mosseri (in press,b). Sém. Biol. Théo., Solignac 1988.
Berge, P., Y. Pomeau and Ch. Vidal. (1984). L'Ordre dans le Chaos. Hermann.
Chandebois, R. (1989). Le gène et la forme. Espace 34:
Collet, P. and J. Eckmann (1983). Iterated Maps on the Interval as Dynamical Systems. Birkhäuser.
Ehrenstein, G. von and E. Schierenberg (1980). Cell lineages and development of Caenorhabditis elegans and other nematodes. chap. I In: Nematodes and Biological Models, Vol. 1, Acad.Press.
Feigenbaum, M.J. (1978a). J.Stat.Phys. 19: p.25.
Feigenbaum, M.J. (1978b). J.Stat.Phys. 52: p.527.
Mandelbrot, B. (1982). The Fractal Geometry of Nature. New York, W.H.Freeman.
May, R.M. (1976). Nature 261: p.459.
Schuster, H.G. (1988). Deterministic Chaos. VCH.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bailly, F., Gaill, F. & Mosseri, R. A dynamical system for biological development: The case of Caenorhabditis elegans . Acta Biotheor 39, 167–184 (1991). https://doi.org/10.1007/BF00114173
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00114173