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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, while 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.

The living cell, too, is a great chemistry lab, and it has a similarly large store of chemicals. But they aren't kept in separate bottles and jars on shelves. They are all mixed up together. It is as though a vandal, a chemical lord of misrule, entered the lab, seized all the bottles on all the shelves, and tipped them with anarchistic abandon into one great cauldron. Terrible thing to do? Well, it would be if they all reacted together, in all possible combinations. But they don't. Or if they do, the rate at which they react together is so slow that they might as well not be reacting at all. Except - and this is the whole point - if an enzyme is present. There is no need for glass bottles and jars to keep the substances apart because, to all intents and purposes, they are not going to react together anyway - unless the right enzyme is present. The equivalent of keeping the chemicals in stoppered bottles until you want to mix a particular pair, say A and B, is to mix all the hundreds of substances up in a great witch's brew, but supply only the right enzyme to catalyse the reaction between A and B and no other combination. Actually, the metaphor of the anarchically inclined bottle-tipper goes too far. Cells do contain an infrastructure of membranes between which, and within which, chemical reactions go on. To some extent, these membranes play the role of glass partitions between test tubes and flasks.

The point of this section of the chapter is that 'the right enzyme' achieves its 'rightness' largely through its physical shape (and that's important, because the physical shape is determined by genes, and it is genes whose variations are ultimately favoured or disfavoured by natural selection). Molecules aplenty are drifting and twisting and spinning through the soup that bathes the interior of a cell. A molecule of substance A might be happy to react with a molecule of substance B, but only if they happen to collide when facing in exactly the right direction, relative to each other. Crucially, that seldom happens - unless the right enzyme intervenes. The enzyme's precise shape, the shape into which it folded itself like a magnetic necklace, leaves it pitted with cavities and dents, each one of which itself has a precise shape. Each enzyme has a so-called 'active site', which is usually a particular dent or pocket, whose shape and chemical properties confer upon the enzyme its specificity. The word 'dent' doesn't adequately convey the specificity, the precision, of this mechanism. Perhaps a better comparison is with an electric socket. In what my friend the zoologist John Krebs calls 'the great plug conspiracy', different countries around the world have irritatingly adopted different arbitrary conventions for plugs and sockets. British plugs won't fit American sockets, or French sockets, and so on. The active sites on the surface of protein molecules are sockets into which only certain molecules will fit. But whereas the great plug conspiracy runs to only half a dozen separate shapes around the world (quite enough to constitute a continual annoyance to the traveller), the different kinds of sockets sported by enzymes are far more numerous.

Think of a particular enzyme, which catalyses the chemical combination of two molecules, P and Q, to make the compound PQ. One half of the active site 'socket' is just right for a molecule of type P to nestle into, like a jigsaw piece. The other half of the same socket is equally precisely shaped for a Q molecule to slot in - facing exactly the right way to combine chemically with the P molecule that is already there. Sharing a dent, firmly held at just the right angle to each other by the matchmaking enzyme molecule, P and Q unite. The new compound, PQ, now breaks away into the soup, leaving the active dent in the enzyme molecule free to bring together another P and another Q. A cell may be filled with swarms of identical enzyme molecules, all working away like robots in a car factory, churning out PQ in the cellular equivalent of industrial quantities. Put a different enzyme into the same cell, and it will churn out a different product, perhaps PR, or QS or YZ. The end product is different, even though the available raw materials are the same. Other types of enzymes are concerned not with constructing new compounds, but with breaking down old ones. Some of these enzymes are involved in digesting food, and they are exploited, too, in 'biological' washing powders. But, since this chapter is about the construction of embryos, we are here mostly concerned with constructive enzymes, which broker the synthesis of new chemical compounds. One such process is shown in action on colour page 12.

A problem may have occurred to you. It's all very well to talk of jigsaw dents and sockets, highly specific active sites capable of speeding up a particular chemical reaction a trillionfold. But doesn't it sound too good to be true? How do enzyme molecules of exactly the right shape evolve from less perfect beginnings? What is the probability that a socket, shaped at random, will have just the right shape, and just the right chemical properties, to arrange a marriage between two molecules, P and Q, finessing their encounter at exactly the right angle? Not very great if you think 'finished jigsaw' - or, indeed, if you think 'great plug conspiracy'. Instead, you have to think 'smooth gradient of improvement'. As so often when we are faced with the riddle of how complex and improbable things can arise in evolution, it is a fallacy to assume that the final perfection that we see today is the way it always was. Fully fashioned, highly evolved enzyme molecules achieve trillionfold speedups of the reactions they catalyse, and they do so by being beautifully crafted to exactly the right shape. But you don't need a trillionfold speedup in order to be favoured by natural selection. A millionfold will do nicely! So will a thousandfold. And even tenfold or twofold would be enough for natural selection to get an adequate grip. There is a smooth gradient of improvement in an enzyme's performance, all the way from almost no dent at all, through a crudely shaped dent, to a socket of exactly the right shape and chemical signature. 'Gradient' means that each step is a noticeable improvement, however slight, over the one before. And 'noticeable' for natural selection can mean an improvement smaller than the minimum that would be required for us to notice it.

So, you see the way it works. Elegant! A cell is a versatile chemical factory, capable of spewing out massive quantities of a wide variety of different substances, the choice being made by which enzyme is present. And how is that choice made? By which gene is turned on. Just as the cell is a vat filled with lots of chemicals, only a minority of which react with each other, so every cell nucleus contains the entire genome, but with only a minority of genes turned on. When a gene is turned on in, say, a cell of the pancreas, its sequence of code letters directly determines the sequence of amino acids in a protein; and the sequence of amino acids determines (remember the image of the magnetic necklace?) the shape into which the protein folds itself; and the shape into which the protein folds itself determines the precisely shaped sockets that marry up substances drifting around in the cell. Every cell, with very few exceptions such as red blood corpuscles, which lack a nucleus, contains the genes for making all the enzymes. But in any one cell, only a few genes will be turned on at any one time. In, say, thyroid cells, the genes that make the right enzymes for catalysing the manufacture of thyroid hormone are turned on. And correspondingly for all the different kinds of cells. Finally, the chemical reactions that go on in a cell determine the way that cell is shaped and the way it behaves, and the way it participates in origami-style interactions with other cells. So the whole course of embryonic development is controlled, via an intricate sequence of events, by genes. It is genes which determine sequences of amino acids, which determine tertiary structures of proteins, which determine the socket-like shapes of active sites, which determine cell chemistry, which determine 'starling-like' cell behaviour in embryonic development. So, differences in genes can, at the originating end of the complex chain of events, cause differences in the way embryos develop, and hence differences in the form and behaviour of adults. The survival and reproductive success of those adults then feeds back on the survival in the gene pool of the genes that made the difference between success and failure. And that is natural selection.

Cellular family tree of Caenorhabditis elegans

Embryology seems complicated - is complicated - but it is easy to grasp the important point, which is that we are dealing with local self-assembly processes all the way. It's a separate question, given that (almost) all the cells contain all the genes, how it is decided which genes are turned on in each different kind of cell. I must briefly deal with that now.

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