The topology of cleavage patterns with examples from embryos ofNereis,StyelaandXenopus

Abstract

A theoretical scheme of cleavage is defined and used to construct topological maps of the cleavage patterns in embryos ofNeris,StyelaandXenopus. The maps are a projection of the surface of the embryo showing every blastomere and every neighbour of each blastomere. They simplify the cleavage pattern. The cellular arrangements observed in blastulae can be reconstructed from the topological maps after specifying the mechanics that shape cellular arrangements. The mechanics of the rotations of blastomeres in the spiral cleavage ofNereisare found by these means. The maps ofNereisandStyelashow the differences between spiral and bilateral cleavage. The map ofXenopushas bilateral symmetry and strongly resembles that ofStyela. The variable cleavage patterns inXenopuswere recorded easily in topological maps. A numbering system for blastomeres ofXenopus, based on Conklin’s scheme forStyela, is described for experimental use. To explain the forms of cleavage patterns, we consider ways of dividing the plane into polygons each with six neighbours by lines drawn sequentially. Some ways have bilateral symmetry. We show how such partitioning of the plane can be transferred to a sphere. This allows cleavage patterns, which are a partitioning of a sphere, to be transferred back to the plane and so be compared with the partitioning that gives six neighbours. We conclude that cleavage patterns have features that bias the number of neighbours of each cell towards six. The forms of cleavage patterns, it is suggested, preserve spatial information in the cytoplasm, such as that set up during oogenesis and during ooplasmic segregation after fertilization, during the partitioning of the zygote into cells. They could be mechanically stable ways of dividing the zygotic cytoplasm that reduce stresses so blastomeres do not shift and disrupt the established spatial values. The apparently conflicting views of Thompson (On growth and form. Cambridge University Press (1917)), who believed /cleavage patterns were determined solely by mechanical forces, and Wilson (The cell in development and heredity. New York: Macmillan (1925)), who argued that cleavage patterns had promorphological significance, may thus be reconciled.