Structural complexity of early embryos:: A study on the nematode Caenorhabditis elegans

For analytical studies on the dynamics of gene expression, gene expression control and cellular interactions, the nematode Caenorhabditis elegans [C. elegans] is at present one of the best suited models [1-4]. In this organism the genetic map and sequence is known [5], moreover the constancy of its lineage tree allows a complete description of cellular clones giving rise to embryos. These characteristics have fostered detailed studies on several aspects of development for this organism. Quantitative studies of cellular movement, through time lapse cinematography of gastrulation, allows the description of cellular migrations giving rise to the final embryonic structure. In perspective, these studies coupled with: genetic analysis, patterns of gene expression obtained through molecular techniques or other methods, open up the possibility of dynamical studies at the organismic scale. This possibility implies, first of all, a study of partitioning of space, and raise several problems in order to define basic conceptual tools to be used in such studies. One of the main problems to handle in this respect is the definition of embryonic structure in a quantitative way. We will show that this aspect is a more general case of distance geometry approaches, as defined in protein folding studies. In this paper we discuss measures of the complexity for embryonal body plans, at the end of grastrulation. These can be applied to studies on the dynamics of gene expression and phylogenetic studies with further experiments or simulations.