Cell Differentiation Processes as Spatial Networks: identifyingfour-dimensional structure in embryogenesis

There are two basic forms of animal development: mosaic (as found in roundworms and sea squirts) and regulative (as found in amphibians and mammals). How might one distinguish between each type of development? Using a four-dimensional spatial representation (<i>x,y,z,t</i>), major features of the developmental process are revealed. To establish the role of mosaic mechanisms, we can map the cell division process to a computational representation of <i>C. elegans</i> embryogenesis using a directed, acyclic graph (DAG) and a differentiation code. Mosaic development is identifiable by observing spatial localization of progenitor and descendent cells. This three-dimensional compartmentalization should be consistent with nesting in the cell lineage tree. Regulative development should demonstrate spatial “smearing”, or deviations from the compartmentalization of the mosaic process. In a complementary manner, complex network statistics should confirm this by providing an approximation of embryo geometry. Characterizing the spatial organization and geometry of embryos in this way allows for heuristic indicators of developmental patterns both within and between organisms.