Theory in Biosciences

, Volume 129, Issue 4, pp 259–270

Topological determination of early morphogenesis in Metazoa

Original Paper

DOI: 10.1007/s12064-010-0103-y

Cite this article as:
Presnov, E., Isaeva, V. & Kasyanov, N. Theory Biosci. (2010) 129: 259. doi:10.1007/s12064-010-0103-y


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.


BlastulationCell packingCombinatorial curvatureConvex polytopeEgg cleavageGastrulationPlanar graphStructural stabilityTopological polyhedraTopological singularity

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Eugene Presnov
    • 1
  • Valeria Isaeva
    • 2
    • 3
  • Nikolay Kasyanov
    • 4
  1. 1.The Volcani CenterGilatIsrael
  2. 2.A.N. Severtsov Institute of Ecology and Evolution of the Russian Academy of ScienceMoscowRussia
  3. 3.A.V. Zhirmunsky Institute of Marine BiologyFar East Branch of Russian Academy of SciencesVladivostokRussia
  4. 4.Institute of Theory of Architecture and Town PlanningMoscowRussia