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But, as we saw in the previous chapter, sonic hedgehog does not just determine how many fingers and toes we have. It also divides our brains, decides how widely spaced our eyes will be, and regulates much else besides. It is an incorrigibly promiscuous molecule. Could we see the pattern of the sonic hedgehog gene’s activity over time, as in time-lapse photography, we would see it flashing on and off throughout the developing embryo and foetus, now in this incipient organ, now in that one.

The devices responsible for all this have a formidable task, and nowhere, given sonic’s power to direct the destiny of cells, do they have much room for error. These devices are transcription factors or ‘molecular switches’. Some of them keep sonic in check. Should they be disabled by mutation, sonic turns on in parts of the limb-bud that it otherwise would not – and the result is extra fingers and toes. Other mutations do not disable the transcription factors themselves, but rather delete the regulatory elements to which they bind. The result, however, is the same: a confusion of morphogen gradients and an embarrassment of digits.

Polydactyly mutations relax control of sonic hedgehog altering the balance of power in favour of ubiquity. But other mutations have exactly the opposite effect and prevent sonic from appearing in the limb-bud at all. The most blatant example of such a mutation is, of course, one that disables the sonic gene itself. Sonic-less mice have, in addition to their many other defects, no paws. This is strikingly reminiscent of a disorder that we have already come across: acheiropody, the disorder of the aleijadinhos. Indeed, there is some (disputed) evidence that the acheiropody mutation disables a regulatory element essential to sonic’s presence in the limb.

This catalogue of mutations only hints at the complexities of gene regulation in the embryo. Whether or not a gene is turned on in a given cell depends on what transcription factors are found in that cell’s nucleus, and their presence depends on the presence of yet other transcription factors, and so on. At first glance hierarchies of this sort seem to involve us in an infinite regression in which the burden of producing order is merely placed upon a previous set of entities which must, themselves, be ordered. But this dilemma is more apparent than real. The embryo’s order is created iteratively. Sonic’s precise presence in the ZPA is defined in part by the activity of Hox genes in the trunk mesoderm from which limbs grow. But the geometrical order that these genes give to the limb is crude; sonic’s task is to refine it further. Beyond sonic there are, of course, yet further levels of refinement in which order is created on ever smaller scales, and each of them requires subtle and interminable negotiations, the nature of which we scarcely understand.

This vision of successive layers of negotiation and control may seem unimaginably complex. But in truth it is not complex enough, for it fails to capture one of the most pervasive properties of the embryo’s programme: its non-linearities. I argued that the acheiropody mutation causes a failure of sonic to appear in the limb. And yet I began this chapter by arguing that infants with amputations in the womb, of whatever severity, were due to failures of the apical ectodermal ridge and the fibroblast growth factors they produce. This may seem like a contradiction, but it is only one if we think of the various limbs’ signals as being independent of each other, when in fact they are not. For one of the most vital roles of sonic hedgehog is to maintain and shape the apical ectodermal ridge and its fibroblast growth factors; and one of the most vital roles of the apical ectodermal ridge is to maintain and shape the production of sonic hedgehog in the zone of polarising activity. There is a reciprocal flow of information as precarious as the flow of batons between two jugglers standing at opposite ends of a stage. Reciprocity of this sort is ubiquitous in the embryo and it alters the way we think about its growth and development. We begin with notions of linear pathways of command and control and simple geometries – and then watch as they unravel. For when, as in the limb, we actually begin to see the outlines of the embryo’s programme, it invariably turns out to resemble a tangle of circuits that loop vertiginously across time and space. Circuits which, in this case, ensure that when we count our fingers and toes we usually come up with twenty.

HANDS, FEET AND ANCESTORS

Around day 32 after conception, when the human limb-bud is already well grown, its amorphous tissue begins to resolve into patterns. Ghostly precursors of bones appear: conglomerations of cells that have migrated together. The technical word for this process is ‘condensation’. It hints at the way in which bones just quietly appear, rather like dew.

The first condensations to form become the bones closest to the body: the humerus in the arm, the femur in the leg. With time, conglomeration sweeps slowly down the limb-bud. The humerus divides into two new long, thin condensations, each of which will bud off by itself: the radius and the ulna. These condensations, in turn, divide and bud to form an arc of cells from which the twenty-seven bones of the wrist and palm are made. By day 38 after conception, the end of each limb-bud has become flat and broad, rather like a paddle. The paddle then folds into parallel valleys – four on each tip – leaving five islands of condensed cells: the future bones of the fingers and toes.

The shapes of the condensations depend, ultimately, on the reference grid laid down by the signalling systems of the limb. But, as elsewhere in the embryo, this information must be translated into cellular action. Hox genes do this for the head-to-tail axis of the embryo, and they also do it for the limb. As the limb-bud grows, some of the thirty-nine Hox genes appear in intricate overlapping patterns. They seem to be engaged in some combinatorial business analogous to the vertebral Hox code. Infants born with a single defective copy of the Hoxa 13 gene have short big toes and bent little fingers. Another human Hox mutation causes synpolydactyly: extra fingers and toes fused together. A particularly devastating mutation that deletes no fewer than nine Hox genes in one go causes infants to be born with missing bones in the forearm, missing fingers and missing toes.

Limbs are not the only appendages in which Hox genes work. Infants born with Hox mutations that affect limbs tend to have malformed genitalia as well; in the worst cases male infants have just the vestiges of a scrotum and penis. Many of the molecules that make limbs also make genitals, and it should be no surprise that some mutations afflict both. The widely rumoured positive correlation between foot and penis size also, surprisingly, turns out to be at least partly true. No man should be judged by the size of his feet, however, for the correlation, though statistically significant, is weak. And then, such data as there are concern ‘stretched’ rather than erect penis length, surely the variable of interest. Still, when the French refer to the penis as le troisième jambe, pied de roi or petit-doigt; and the English to the best-leg-of-three, down-leg or middle-leg, not forgetting the optimistic yard which elsewhere means three feet, they speak truer than they know.

The Hox genes have also begun to tell us about origins. Where do fingers come from? It may seem that this question has a straightforward answer. Our limbs, flexible in so many dimensions, are the cognates of the structures that propel fish through the sea: their fins. But fish don’t have fingers. One might suppose that the rays, those fine, bony projections that spread a fin like a fan, are their piscine equivalents. But fish rays and tetrapod digits are made of quite different kinds of bone – reason enough, anatomists say, to conclude that they have nothing to do with each other.