Maternal-effect genes as the recording genes of Turing-Child patterns: sequential compartmentalization in Drosophila

The early embryo is often a two-dimensional surface. The fate map is the subdivision of this surface into regions which give rise to parts of the phenotype. It is shown for Drosophila that the fate map is generated by the spontaneous and sequential formation of Turing-Child (TC) eigenfunction patterns. These patterns are recorded by the maternal-effect genes. The addition of the nodal lines of the TC patterns yields the correct number, positions, sequences and symmetries of regional boundaries. A simplest nontrivial 'homeotic transformation' is suggested and explained. A single mutation converts a region in one end of the fate map to a mirror-symmetric image of a nonadjacent region in the other end of the fate map, and this is attributed to the geometry of the TC patterns. This geometry also determines the initial shape of the zygotic gene expression. The vision of William Bateson that biological form is shaped like Chladni's patterns in acoustics and music is justified. A similar sequence of TC patterns occurs in the normal development of all organisms, and it is suggested that artificial intervention which completes the full sequence of TC patterns can be useful in the context of regenerative medicine and this is illustrated with the sea urchin.