A dynamical system for biological development: the case of Caenorhabditis elegans

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 Caenrhabditis 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 teh control parameters with time.