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  I don’t want to get into the details of either gastrulation or neurulation, except to say that they are wonderful, and that the metaphor of origami holds up pretty well for both of them. I am concerned with the general principles by which embryos become more complicated through inflating origami. Below is one of the things that sheets of cells are observed to do during the course of embryonic development, for example during gastrulation. You can easily see how this invagination could be a useful move in inflating origami, and it does indeed play a major role in both gastrulation and neurulation.

  Invagination in a sheet of cells

  Gastrulation and neurulation are accomplished early in development and they affect the whole shape of the embryo. Invagination and other ‘inflating origami’ manœuvres achieve these stages of early embryology, and they and similar tricks are involved later in development, when specialized organs like eyes and the heart are made. But, given that there are no hands to do the folding, by what mechanical process are these dynamic movements achieved? Partly, as I have already said, by simple expansion itself. Cells multiply all through a sheet of tissue. Its area therefore increases and, having nowhere else to go, it has little choice but to buckle or invaginate. But the process is more controlled than that, and it has been deciphered by a group of scientists associated with the brilliant mathematical biologist George Oster, of the University of California at Berkeley.

  MODELLING CELLS LIKE STARLINGS

  Oster and his colleagues followed the same strategy we considered earlier in this chapter for a computer simulation of starlings flocking. Instead of programming the behaviour of a whole blastula, they programmed a single cell. Then they ‘cloned up’ lots of cells, all the same, and watched to see what happened when those cells got together in the computer. When I say they programmed the behaviour of a single cell, it would be better to say they programmed a mathematical model of a single cell, building into the model certain known facts about a single cell, but in simplified form. Specifically, it is known that the interiors of cells are criss-crossed by microfilaments: sort of miniature elastic bands, but with the additional property that they are capable of active contraction, like twitching muscle fibres. Indeed, the microfilaments use the same principle of contraction as muscle fibres.* The Oster model simplified the cell down to two dimensions for drawing on a computer screen, and with only half a dozen filaments, strategically placed in the cell, as you see in the diagram above. In the computer model, all the microfilaments were given certain quantitative properties with names that mean something to physicists: a ‘viscous damping coefficient’ and an ‘elastic spring constant’. Never mind exactly what these mean: they are the kinds of things physicists like to measure in a spring. Although it is probable that in a real cell many filaments would be capable of contraction, Oster and his colleagues simplified matters by endowing only one of their six filaments with this capacity. If they could get realistic results even after throwing away some of the known properties of a cell, it would presumably be possible to get at least as good results with a more complicated model that kept those properties in. Rather than allowing the one contractile filament in their model to contract at will, they built into it a property which is common in certain kinds of muscle fibre: when stretched beyond a certain critical length, the fibre would respond by contracting to a much shorter length than the normal equilibrium length.

  Microfilaments inside Oster’s model cell

  So, we have our model of a single cell: a greatly simplified model consisting of a two-dimensional outline in which are strung six elastic springs, one of which has the special property of responding to an externally imposed stretch by actively contracting. That is stage one of the modelling process. In stage two, Oster and his colleagues cloned up a few dozen of their model cells and arranged them in a circle, like a (two-dimensional) blastula. Then they took one cell and tweaked its contractile filament to provoke it into contracting. What happened next is almost too wonderful to bear. The model blastula gastrulated! Here are six screenshots showing what happened (a to f below). A wave of contraction spread sideways from the cell that was provoked, and the ball of cells spontaneously invaginated.

  Oster’s model blastula gastrulating

  It gets even better. Oster and his colleagues tried the experiment, on their computer model, of lowering the ‘firing threshold’ of the contractile filaments. The result was a wave of invagination that went further, and actually pinched off a ‘neural tube’ (screenshots a to h, overleaf). It is important to understand what a model such as this really is. It is not an accurate representation of neurulation. Quite apart from the fact that it is two-dimensional and simplified in many other ways, the ball of cells that ‘neurulated’ (screenshot a) was not a two-layered ‘gastrula’ as it should have been. It was the same blastula-like starting point as we had for the model of gastrulation above. It doesn’t matter: models are not supposed to be totally accurate in every detail. The model still shows how easy it is to mimic various aspects of the behaviour of cells in an early embryo. The fact that the two-dimensional ‘ball’ of cells responded spontaneously to the stimulus even though the model is simpler than the real situation makes this a more powerful piece of evidence. It reassures us that the evolution of the various procedures of early embryonic development need not have been all that difficult. Note that it is the model that is simple, not the phenomenon that it demonstrates. That is the hallmark of a good scientific model.

  Formation of ‘neural tube’ in Oster’s model

  My purpose in expounding the Oster models has been to show the general kind of principle by which single cells can interact with each other to build a body, without any blueprint representing the whole body. Origami-like folding, Oster-style invagination and pinching off: these are just some of the simplest tricks for building embryos. Other more elaborate ones come into play later in embryonic development. For example, ingenious experiments have shown that nerve cells, when they grow out from the spinal cord, or from the brain, find their way to their end organ not by following any kind of overall plan but by chemical attraction, rather as a dog sniffs around to find a bitch in season. An early classic experiment by the Nobel Prize-winning embryologist Roger Sperry illustrates the principle perfectly. Sperry and a colleague took a tadpole and removed a tiny square of skin from the back. They removed another square, the same size, from the belly. They then regrafted the two squares, but each in the other’s place: the belly skin was grafted on the back, and the back skin on the belly. When the tadpole grew up into a frog, the result was rather pretty, as experiments in embryology often are: there was a neat postage stamp of white belly skin in the middle of the dark, mottled back, and another neat postage stamp of dark mottled skin in the middle of the white belly. And now for the point of the story. Normally, if you tickle a frog on its back with a bristle, the frog will wipe the place with a foot, as if deterring an irritating fly. But when Sperry tickled his experimental frog on the white ‘postage stamp’ on its back, it wiped its belly! And when Sperry tickled it on the dark postage stamp on its belly, the frog wiped its back.

  What happens in normal embryonic development, according to Sperry’s interpretation, is that axons (long ‘wires’, each one a narrow, tubular extension of a single nerve cell) grow questingly out from the spinal cord, sniffing like a dog for belly skin. Other axons grow out from the spinal cord, sniffing out back skin. And normally this gives the right result: tickles on the back feel as though they are on the back, while tickles on the belly feel as though they are on the belly. But in Sperry’s experimental frog, some of the nerve cells sniffing out belly skin found the postage stamp of belly skin grafted on the back, presumably because it smelled right. And vice versa. People who believe in some sort of tabula rasa theory – whereby we are all born with a blank sheet for a mind, and fill it in by experience – must be surprised at Sperry’s result. They would expect that frogs would learn from experience to feel their way around their own skin, associating the rig
ht sensations with the right places on the skin. Instead, it seems that each nerve cell in the spinal cord is labelled, say, a belly nerve cell or a back nerve cell, even before it makes contact with the appropriate skin. It will later find its designated target pixel of skin, wherever it may be. If a fly were to crawl up the length of its back, Sperry’s frog would presumably experience the illusion that the fly suddenly leaped from back to belly, crawled a little further, then instantaneously leaped to the back again.

  Experiments like this led Sperry to formulate his ‘chemo-affinity’ hypothesis, according to which the nervous system wires itself up not by following an overall blueprint but by each individual axon seeking out end organs with which it has a particular chemical affinity. Once again, we have small, local units following local rules. Cells in general bristle with ‘labels’, chemical badges that enable them to find their ‘partners’. And we can go back to the origami analogy to find another place where the labelling principle comes in useful. Human paper origami doesn’t use glue, but it could. And the origami of the embryo, whereby animal bodies put themselves together, does indeed use something equivalent to glue. Glue s, rather, because there are lots of them, and this is where labelling comes triumphantly into its own. Cells have a complicated repertoire of ‘adhesion molecules’ on their surfaces, whereby they stick to other cells. This cellular glueing plays an important role in embryonic development in all parts of the body. There is a significant difference from the glues that we are familiar with, however. For us, glue is glue is glue. Some glues are stronger than others, and some glues set faster than others, and some glues are more suitable for wood, say, while others work better for metals or plastics. But that’s about it for variety among glues.

  Cell adhesion molecules are much more ingenious than that. More fussy, you could say. Unlike our artificial glues, which will stick to most surfaces, cell adhesion molecules bind only to particular other cell adhesion molecules of exactly the right kind. One class of adhesion molecules in vertebrates, the cadherins, come in about eighty currently known flavours. With some exceptions, each of these eighty or so cadherins will bind only to its own kind. Forget glue for a minute: a better analogy might be the children’s party game where each child is assigned an animal, and they all have to mill about the room making noises like their own allotted animals. Each child knows that only one other child has been assigned the same animal as herself, and she has to find her partner by listening through the cacophony of farmyard imitations. Cadherins work like that. Perhaps, like me, you can dimly imagine how the judicious doping of cell surfaces with particular cadherins at strategic spots might refine and complicate the self-assembly principles of embryo origami. Note, once again, that this doesn’t imply any kind of overall plan, but rather a piecemeal collection of local rules.

  ENZYMES

  Having seen how whole sheets of cells play the origami game in shaping the embryo, let’s now dive inside a single cell, where we’ll find the same principle of self-folding and self-crumpling, but on a much smaller scale, the scale of the single protein molecule. Proteins are immensely important, for reasons that I must take time to explain, beginning with a teasing speculation to celebrate the unique importance of proteins. I love speculating on how weirdly different we should expect life to be elsewhere in the universe, but one or two things I suspect are universal, wherever life might be found. All life will turn out to have evolved by a process related to Darwinian natural selection of genes. And it will rely heavily on proteins – or molecules which, like proteins, are capable of folding themselves up into a huge variety of shapes. Protein molecules are virtuosos of the auto-origamic arts, on a scale much smaller than that of the sheets of cells we have so far dealt with. Protein molecules are dazzling showcases of what can be achieved when local rules are obeyed on a local scale.

  Proteins are chains of smaller molecules called amino acids, and these chains, like the sheets of cells we have been considering, also fold themselves, in highly determined ways but on a much smaller scale. In naturally occurring proteins (this is one fact that will presumably be different on alien worlds) there are only twenty kinds of amino acid, and all proteins are chains strung together from just this repertoire of twenty, drawn from a much larger set of possible amino acids. Now for the auto-origami. Protein molecules, simply following the laws of chemistry and thermodynamics, spontaneously and automatically twist themselves into precisely shaped three-dimensional configurations – I almost said ‘knots’ but, unlike hagfish (if I might impart a gratuitously inconsequential but engaging fact), proteins don’t literally tie themselves in knots. The three-dimensional structure into which a protein chain folds and twists itself is the ‘tertiary structure’ that we briefly met when considering the self-assembly of viruses. Any given sequence of amino acids dictates a particular folding pattern. The amino-acid sequence, which itself is determined by the sequence of letters in the genetic code, determines the shape of the tertiary pattern.* The shape of the tertiary structure, in turn, has hugely important chemical consequences.

  The auto-origami by which protein chains fold and coil themselves is ruled by the laws of chemical attraction, and the laws determining the angles at which atoms bind to one another. Imagine a necklace of curiously shaped magnets. The necklace would not hang in a graceful catenary around a graceful neck. It would assume some other shape, becoming tangled up as the magnets latched on to each other and slotted into each other’s nooks and crannies at various points along the length of the chain. Unlike the case of the protein chain, the exact shape of the tangle would not be predictable, because any magnet will attract any other. But it does suggest how chains of amino acids can spontaneously form a complicated knot-like structure, which may not look like a chain or a necklace.

  The details of how the laws of chemistry determine the tertiary structure of a protein are not yet fully understood: chemists can’t yet deduce, in all cases, how a given sequence of amino acids will coil up. Nevertheless, there is good evidence that the tertiary structure is in principle deducible from the sequence of amino acids. There’s nothing mysterious about the phrase ‘in principle’. Nobody can predict how a die will fall, but we all believe it is wholly determined by precise details of how it is thrown, plus some additional facts about wind resistance and so on. It is a demonstrated fact that a particular sequence of amino acids always does coil up into a particular shape, or one of a discrete set of alternative shapes (see the long footnote opposite). And – the important point for evolution – the sequence of amino acids is itself fully determined, through implementation of the rules of the genetic code, by the sequence of (triplets of) ‘letters’ in a gene. Even though it is not easy for human chemists to predict what change in protein shape will result from a particular genetic mutation, it is still a fact that once a mutation has occurred, the resulting change of protein shape will be in principle predictable. The same mutant gene will reliably produce the same altered protein shape (or discrete menu of alternative shapes). And that is all that matters for natural selection. Natural selection doesn’t need to understand why a genetic change has a certain consequence. It is sufficient that it does. If that consequence affects survival, the changed gene itself will stand or fall in the competition to dominate the gene pool, whether or not we understand the exact route by which the gene affects the protein.

  Given that protein shape is immensely versatile, and given that it is determined by genes, why is it so supremely important? Partly because some proteins have a direct structural role to play in the body. Fibrous proteins, such as collagen, join together in stout ropes, which we call ligaments and tendons. But most proteins are not fibrous. Instead, they fold themselves up into their own characteristic globular shape, complete with subtle dents, and this shape determines the protein’s characteristic role as an enzyme, which is a catalyst.

  A catalyst is a chemical substance that speeds up, by as much as a billion or even a trillion times, a chemical reaction between other substances, w
hile the catalyst itself emerges from the process unscathed and free to catalyse again. Enzymes, which are protein catalysts, are champions among catalysts because of their specificity: they are very fussy about precisely which chemical reactions they speed up. Or perhaps we could say: chemical reactions in living cells are very fussy about which enzymes speed them up. Many reactions in cell chemistry are so slow that, without the right enzyme, for practical purposes they don’t occur at all. But with the right enzyme they happen very fast, and can churn out products in bulk.

  Here’s how I like to put it. A chemistry lab has hundreds of bottles and jars on its shelves, each containing a different pure substance: compounds and elements, solutions and powders. A chemist wishing to perform a certain chemical reaction selects two or three bottles, takes a sample from each, mixes them in a test tube or a flask, perhaps applies heat, and the reaction takes place. Other chemical reactions that could take place in the lab don’t, because the glass walls of the bottles and jars prevent the ingredients meeting. If you want a different chemical reaction, you mix different ingredients in a different flask. Everywhere there are glass barriers keeping the pure substances separate from one another in bottles or jars, and keeping the reacting combinations separate from one another in test tubes or flasks or beakers.