However, they also have a ventral nerve cord and a dorsal contractile vessel similar to protostomes.

Furthermore, the relative positions other "intermediate" structures in hemichordates, such as the hepatic organs and ventral pygochord, which has been proposed to be homologous to the chordate-defining notochord, are retained but inverted.

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Nübler-Jung and Arendt argue that the principal innovation in the chordate lineage was the obliteration of the mouth on the neural side (as in hemichordates, arthropods, and annelids) and the development of a new mouth on the non-neural ventral side.

One assumption of the inversion hypothesis is that the common ancestor of protostomes and chordates already possessed an organized central nervous system located at one pole of the dorsoventral axis.

In the fruit fly Drosophila melanogaster, as well as in other protostomes, the β-type transforming growth factor (TGF-β) family member decapentaplegic (dpp) is expressed dorsally and is thought to suppress neural fate.

On the ventral side of the embryo, a dpp inhibitor, short gastrulation (sog), is expressed, thus allowing nervous tissue to form ventrally.

suggesting an axial inversion during evolution from basal deuterostome to chordate such like amphioxus.

Because in amphioxus, Nodal signaling pathway is on the left side of the embryo, which is the same situation as vertebrates.

Lacalli (1996) suggested a scenario in which the ancestor had a single opening to the digestive system, and that the neural and non-neural mouths arose independently in protostomes and chordates, respectively.

By this hypothesis, there is no need for inversion.

Sea urchins, like other echinoderms, have radially-symmetric adults, but bilaterally-symmetric larvae.