Plane talk

Topological patterns in metazoan evolution and development

Topological patterns in the development and evolution of metazoa, from sponges to chordates, are considered by means of previously elaborated methodology, with the genus of the surface used as a topological invariant. By this means metazoan morphogenesis may be represented as topological modification(s) of the epithelial surfaces of an animal body. The animal body surface is an interface between an organism and its environment, and topological transformations of the body surface during metazoan development and evolution results in better distribution of flows to and from the external medium, regarded as the source of nutrients and oxygen and the sink of excreta, so ensuring greater metabolic intensity. In sponges and some Cnidaria, the increase of this genus up to high values and the shaping of topologically complicated fractal-like systems are evident. In most Bilateria, a stable topological pattern with a through digestive tube is formed, and the subsequent topological complications of other systems can also appear. The present paper provides a topological interpretation of some developmental events through the use of well-known mathematical concepts and theorems; 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.

RETRACTED: Cdx2 gene expression and trophectoderm lineage specification in mouse embryos

Controversy exists as to whether individual blastomeres from two-cell-stage mouse embryos have identical developmental properties and fate. We show that the transcription factor Cdx2 is expressed in the nuclei of cells derived from the late-dividing but not the first-dividing blastomere of two-cell embryos and, by lineage tracing and RNA interference knock-down experiments, that this lagging cell is the precursor of trophectoderm. Cdx2 mRNA is localized toward the vegetal pole of oocytes, reorients after fertilization, and becomes concentrated in the late-dividing, two-cell-stage blastomere. The asymmetrical distribution of Cdx2 gene products in the oocyte and embryo defines the lineage to trophectoderm.

Mitotic Spindles and Cleavage Planes Are Oriented Randomly in the Two-Cell Mouse Embryo

Most experimental embryological studies performed on the early mouse embryo have led to the conclusion that there are no mosaically distributed developmental determinants in the zygote and early embryo (for example see [1-6]). It has been suggested recently that "the cleavage pattern of the early mouse embryo is not random and that the three-dimensional body plan is pre-patterned in the egg" (in [7] for review see [8-10]). Two major spatial cues influencing the pattern of cleavage divisions have been proposed: the site of the second meiotic division [11, 12] and the sperm entry point [13-14], although the latter is controversial [15-17]. An implication of this hypothesis is that the orientations of the first few cleavage divisions are stereotyped. Such a define cleavage pattern, leading to the segregation of developmental determinants, is observed in many species [18]. Recently, it was shown that the first cleavage plane is not predetermined but defined by the topology of the two apposing pronuclei [19]. Because the position of the female pronucleus is dependent upon the site of polar body extrusion and the position of the male pronuclei is dependent upon the sperm entry point [19-20], this observation leaves open the possibility that the sperm may provide some kind of directionality [7]. But, even if asymmetries were set up only after fertilization, a stereotyped cleavage pattern should take place during the following cleavage divisions. Thus, we studied the cleavage pattern of two-cell embryos by videomicroscopy to distinguish between the two hypotheses. After the mitotic spindle formed, its orientation did not change until cleavage. During late metaphase and anaphase, the spindle poles appear to be anchored to the cortex through astral microtubules and PARD6a. Only at the time of cleavage, during late anaphase, do the forming daughter cells change their relative positions. These studies show that cleavage planes are oriented randomly in two-cell embryos. This argues against a prepatterning of the mouse embryo before compaction.