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Some scientists have tried to repeat this unplanned experiment by bathing animal embryos in retinoic acid and then looking for malformations. Often the outcome is just a miscellany of deformities, rather like those shown by isotretinoin-exposed infants. But sometimes the results can be spectacular. If a tadpole’s tail is amputated, it normally grows another one in short order. But if the tail is amputated and the stump is painted with a solution of retinoic acid, the tadpole grows a bouquet of extra legs. This experiment clearly shows that retinoic acid is powerful stuff. It also suggests that tadpoles may use retinoic acid to regulate their rears. It does not, however, prove it. One could object that retinoic acid is, in effect, an exotic sort of poison, one that interferes in a completely unnatural way with the normal course of the embryo’s progress.

Hence the importance of the mermaid mice. They give, for the first time, some real insight into what embryos use retinoic acid for. It seems it is a morphogen, one of the most important in the embryo. Indeed, one might almost call it an Über-morphogen that acts the length and breadth of the embryo. Being a hydrocarbon ring, however, it works rather differently from most other morphogens. Where protein-signalling molecules are too big to enter cells and so bind to receptors on their surfaces, retinoic acid penetrates the cell membrane and attaches to receptors within the cell that go right to the nucleus where they turn genes on and off.

Where does retinoic acid come from? And what, exactly, does it do? The CYP26A1 gene encodes an enzyme that degrades retinoic acid. Thus CYP26A1-defective mice have too much of it. Their mermaid-like limbs are caused by an anomalous surplus of retinoic acid in the embryo’s rear. The rear of an embryo is not the only place affected by high levels of retinoic acid. Sirenomelic infants and mice also usually have head defects – implying that retinoic acid is normally lacking there too. Indeed, it is currently thought that could the concentration gradient of retinoic acid across an embryo be seen, it would resemble a hill with a peak somewhere near the embryo’s future neck and slopes in all directions: sides, front and back. It would show a carefully constructed topography maintained by a balance of enzymes that make and degrade the morphogen, which in frogs with extra legs, mermaid mice, sirenomelic infants and foetuses exposed to acne-medications has been eroded away leaving only an ill-defined plateau.

THE CALCULATOR OF FATE

The morphogens that traverse the developing embryo – be they protein or hydrocarbon ring – provide cells with a kind of coordinate grid that they use to find out where they are and so what they should do and be. A cell is thus rather like a navigator who, traversing the wastes of the ocean, labours with sextant and chronometer to find his longitude and latitude. But there is one difference between navigator and celclass="underline" while the navigator’s referents, the stars and planets, are always where they should be, the cell’s sometimes are not. Sirenomelia and cyclopia are two instances where mutation has warped the universe that cells refer to or even caused its total collapse.

Yet even bearing this difference (inevitable when comparing the clockwork motions of the physical world with the jerry-built devices of biology) in mind, the analogy still has force. For all the constancy of the heavens, navigators have always lost their way – perhaps because the instruments by which they read the heavens become maladjusted. In the same way, the receptors which allow cells to perceive morphogens and measure their concentrations can also go awry – and any number of congenital disorders are caused by mutations that affect them.

But perhaps the deepest level of the analogy comes when we consider the calculations that navigators must make in order to establish where they are. Cells, too, calculate – and they do so with great precision, absorbing information from their environment, adding it up and arriving at a solution. This calculator – one might call it a calculator of fate – is composed of a vast number of proteins that combine their efforts within each cell to arrive at a solution. Of course, the calculator is not infallible: just as navigators occasionally get their sums wrong, so too, occasionally, do cells.

The consequences of cells making mistakes of this sort are beautifully illustrated by one of the more curious pieces of erotica dug from the ruins of Herculaneum. It is a small marble statue – no larger than a shoebox – that depicts Pan the goat-god, whom the Romans knew as Faunus, raping a nanny goat. Masterfully combining the animal and the human in equal parts, the unknown artist has given his Pan shaggy legs, cloven hooves, thick lips, a flattened snout and an expression of concentrated violence. He has also given the god an unusual anatomical feature. Suspended from his neck, just above the clavicles, are two small pendulous lobes that in life would be no more than a few centimetres long.

SUPERNUMERARY NECK AURICLES ON GOAT AND SATYR. PAN RAPING A GOAT. ROMAN COPY OF HELLENISTIC ORIGINAL, SECOND–THIRD CENTURY BC.

These lobes, which are very distinctive, only appear in Pans of the second or third century bc, or, as in this statue (now in the Secret Cabinet of the Naples Archaeological Museum), in later Roman copies of Greek originals. The innumerable goat-gods who chase across the black- or red-figure vases of the Classical period wooing shepherds or grasping at nymphs do not have them, nor do the allegorical Pans of the Renaissance and Baroque such as those in Sandro Botticelli’s Mars and Venus or Annibale Carracci’s Omnia vincit Amor. Neck lobes would also be quite out of place in the beautiful but vapid Pans of the Pre-Raphaelites.

The origin of the god’s lobes is plain enough: they are echoed by an identical pair of appendages on his victim, the neck lobes frequently found on domesticated goats (German goatherds call them Glocken – bells). The sculptor of the original Pan Raping a Goat was clearly an acute observer of nature, and incorporated the lobes as one more detail to signify the goatishness of the god. Neck lobes, however, occur not only in goats but also, albeit rarely, in humans. In 1858 a British physician by the name of Birkett published a short paper describing a seven-year-old girl who had been brought to him with a pair protruding stiffly from either side of her neck. The girl had had them since birth. Birkett was not sure what they were, but he cut them off anyway and put them under the microscope, where he discovered that they were auricles – an extra pair of external ears.

SUPERNUMERARY AURICLES. EIGHT-YEAR-OLD GIRL, ENGLAND 1858. FROM WILLIAM BATESON 1894 MATERIALS FOR THE STUDY OF VARIATION.

Extra auricles are an instance of a phenomenon called homeosis in which one part of a developing embryo becomes anomalously transformed into another. The particular transformation that causes neck-ears has its origins around five months after conception, when five cartilaginous arches form on either side of the embryo’s head, positioned much where gills would be were the embryo a fish. Indeed, were the embryo a fish, gill arches are what they would become. In humans they form a miscellany of head parts including jaws, the tiny bones of the inner ears, and sundry throat cartilages. The visible, protuberant parts of our ears develop out of the cleft between the first and the second pair of arches. The remaining clefts usually just seal over, leaving our necks smooth, but occasionally in humans and often in goats, one of the lower clefts remains open and develops into something that looks much like an ear. The resemblance, however, is only superficiaclass="underline" the ‘ears’ have none of the internal apparatus that would enable them to hear.