Topological determination of early morphogenesis in Metazoa

This paper presents a topological interpretation of some developmental events through the use of well-known concepts and theorems of combinatorial geometry. The organization of early embryo using a simulation of cleavage considering only blastomere contacts is examined. Each blastomere is modeled as a topological cell and whole embryo--as cell packing. The egg cleavage results in a pattern of cellular contacts on the surface of each blastomere and whole embryo, a discrete morphogenetic field. We find topological distinctions between different types of early egg cleavage and suggest a topological classification of cleavage. Blastulation and gastrulation may be related to an inevitable emergence of discrete curvature that directs development in three-dimensional space. The relationship between local and global orders in metazoan development, i.e., between local morphogenetic processes and integral developmental patterns, is established. Thus, this methodology reveals a topological imperative: a certain set of topological rules that constrains and directs biological morphogenesis.