The Art of Genes How Organisms Make Themselves

Although Wittgenstein was concerned with the nature of the word 'leaf' in the mental rather than biological sense, we can get a general insight into the problem he raised based on what we have learned in this chapter. We have seen that in the case of plants, the common unity of plant organs is not a visible leaf at all, but something that can only be described in other terms, such as an underlying pattern of hidden colours. By analogy, we might expect that common mental themes, our general notion of what 'leaf' or 'chair' means, could not be pictured in our mind's eye, but would lie hidden from us. In this case, the theme might reflect a common pattern of brain activity, rather than hidden colours. For example, every time we think of or use the term 'chair', a common set of brain connections could be triggered, irrespective of the individual type of chair involved. This common pattern would itself have been established and elaborated upon during previous responses of our brain to the various situations in which the word 'chair' was used, during which we eventually learned the meaning of the word. The important point is that we would be oblivious to this underlying pattern and would only be conscious of it indirectly, through its manifestation in particular cases, such as when we try to imagine what a chair looks like. The particular type of chair a person imagines may vary according to his or her state of mind, but all such chairs may nevertheless share some underlying patterns of activity in the person's brain. So although we have an implicit notion of a common meaning of the word 'chair', we cannot access the underlying unity directly by introspection. As soon as we try to analyse it, by, say, visualising something, we are stuck with a particular case rather than the underlying theme— much as when we look at a mature plant organ we see one particular manifestation rather than the common theme. It seems to me, then, that by getting a dear understanding of how repeated themes are elaborated during biological development, we can get a useful intuition into how analogous processes might operate in other cases, including the workings of our mind.

We have seen how both the idiosyncrasies and repetitions evident in the anatomy of organisms depend on hidden processes. Development involves the continual interpretation and elaboration of hidden colours, scents and sensitivities, giving an internal patchwork that underlies the final geometry we see. If one or more of these hidden components is lost through mutation, there is a corresponding change in the geometry of the organism that develops. But there is still the issue of how this process of internal painting eventually becomes manifest in the visible structure of each plant or animal. How does a pattern of regional distinctions actually influence the shape and form of the organism as it grows? This is the problem I wish to explore in the next chapter.

Chapter 16 Shifting forms

A striking feature of paintings of the Byzantine period is their curious sense of proportion. Look, for example, at the Madonna and Child of Fig. 16.1. The head of a child is normally bigger in relation to its body than that of an adult; yet in the painting the child is shown with adult proportions, making its head seem unnaturally small. The reason for the difference in proportions between child and adult has to do with the way humans grow. A child's head grows much more slowly that the rest of its body, so that by the time adulthood is reached, relative head size is greatly diminished. The Byzantine artist seems to have taken little account of this, so that the child looks strangely mature for its age.

Fig. 16.1 Enthroned Madonna and Child (detail). Probably painted in Constantinople about AD 1200. National Gallery of Art, Washington, DC.

Not only does relative head size change during growth, but so do facial proportions. Eyes, for example, hardly enlarge at all as a child grows, so they become progressively smaller in relation to the rest of the face. This change in relative size is emphasised by Magritte's painting, The Spirit of Geometry (Fig. 16.2) in which he swaps around the head of a baby with that of its mother, keeping overall head size to scale. The head on the mother now seems to have a disconcertingly large pair of eyes, highlighting the distinctive facial proportions of a baby.

Fig. 16.2The Spirit of Geometry (c. 1936), RenéMagritte. Tate Gallery, London.

These differences in proportion between baby and adult illustrate how the regions of an organism grow to different extents as it develops. Were it not for this, the adult would end up looking just like an enlarged version of the embryo, or going even further back, like an inflated fertilised egg. If we compare the growth of a developing organism to an expanding three-dimensional canvas, we therefore need to imagine that some regions of the canvas grow more quickly than others. It is a dynamic canvas of continually changing size and proportion. But I have also been saying throughout this book that the shape of an organism depends on the interpretation of hidden colours on the canvas. There seems to be a contradiction here. On the one hand, I am saying that an organisms shape reflects the growth of the canvas; on the other, that it depends on the hidden colours on the canvas. How can both of these views be correct?

This brings us to an important distinction between human and internal painting. For an artist, the canvas provides an independent support to which colours are applied. However, for internal painting, the canvas is not an independent support but something that continually changes and interacts with the hidden colours. We shall see in this chapter how this interaction provides the fundamental link between hidden colours and the manifest anatomy of multi-cellular organisms. I should say in advance that this is perhaps the hardest aspect of development to think about and one that is still poorly understood. This chapter will therefore tend to be more speculative than the others. Nevertheless, we shall be able to look at some of the key issues involved.

Deformations

In order to understand how an organism grows, we need to be able to relate the successive shapes it goes through as it develops. One of the best ways of conveying the relationship between two shapes is to imagine ways of deforming one of them, by say stretching or compressing it in

various directions, so that it comes to resemble the other. To give a very simple example, a square may be transformed into a rectangle by stretching it out in one direction. The relationship between these two shapes, square and rectangle, can therefore be summarised by this basic deformation, a linear stretch.

An early illustration of how this approach can be applied to more complex shapes, of the sort encountered in biology, is found in Albrecht Dürer's Four Books of Human Proportion, published in 1528. In this work, Darer describes how the human body should be depicted. He first gives the detailed proportions of what may be considered to be a standard human being. Having established this canonical form, he goes on to give a general method for producing deviations:

Herein will I show how the proportions given above may be altered and changed according to each man's will, the parts being lengthened or shortened so that the figure can no longer be recognised and becometh quite different from its original form.

The key to his method was to alter human proportions by stretching or compressing particular regions. Dürer illustrated his method by showing how a normal head inscribed in a grid could be deformed in various ways by changing its relative proportions, as if the picture were on a piece of deformable rubber (Fig. 16.3). By following his approach, he believed artists might be able to explore a whole new repertoire of facial types and expressions, ranging from the beautiful to the ugly or monstrous. We can recognise a less formal version of this method in many caricatures in which certain facial features, such as a nose or mouth, seem to have been greatly stretched out or magnified.

Fig. 16.3 Standard head (left) compared to three different deformations (after Dürer

The use of deformations for relating shapes was applied more generally in the early twentieth century by the biologist D'Arcy Thompson, in his monumental book On Growth and Form. Look at the top left of Fig. 16.4, which shows a species of fish inscribed within a rectangular grid. By deforming the grid in different ways, Thompson could obtain shapes that came pretty close to other fish species that existed in nature, such as those shown in the rest of the figure. The importance of this method was its simplicity and economy. Without the grid, all the fish species in Fig. 16.4 would look very different on several counts, such as the shape of the different body parts and the various types of fin; but with the benefit of a deformable grid, all of these aspects are seen to flow from much simpler overall deformations. The method allows seemingly unrelated and complex differences between two species to be brought under the umbrella of a single geometrical operation. Thompson applied the same method to illustrate the relationships between many other forms, such as the shapes of different crab shells, or the skulls of related crocodiles. In each case, he inscribed one shape on a regular grid and obtained related forms by simply deforming the grid, bringing apparently complex differences under a unified scheme.

Fig. 16.4 Various types of fish related by deformations (from Thompson 1942).

Thompson realised that his method worked best when comparing closely related forms, where the correspondences between different animals could be easily identified. He therefore applied it to cases where it was possible to make easy and meaningful comparisons, like closely related fish species, or the skulls of various crocodiles. The method could not be used in a convincing way to compare more remote shapes, like those of fishes with birds, where there were too many differences to be accounted for by a simple deformation. He pointed out, though, that even with these more distantly related forms, a certain type of correspondence could still be achieved by an extension of his method:

In these transformations of ours every point may change its place, every line its curvature, every area its magnitude; but on the other hand every point and every line continues to exist, and keeps its relative order and position throughout all distortions and transformations. A series of points, a, b, c, along a certain line persist as corresponding points a ', b', c', however the line connecting them may lengthen or bend; and as with points, so with lines, and so also with areas. Ear, eye and nostril, and all the other great landmarks of cranial anatomy, not only continue to exist but retain their relative order and position throughout all our transformations.

He was saying that an essential feature of his method of deformations was that the relative order of parts remained the same. A simple stretch or compression does not change the order of landmarks on a skull, even though it may alter the distances that separate them. So when you come to compare more distantly related forms, you may still be able to discern the constant relations of their landmarks, even though you cannot draw a simple diagram to relate them. There is no simple way of deforming the skull of a mammal into that of a fish, bird or frog, but there is still something that links them: the relative order or arrangement of their landmarks, like ears, eyes and nose. We have come across this idea before: it is a restatement of Geoffroy's Principle of

Connections (Chapter 7). Geoffroy's principle stated that the relative order of bones — the way they were connected to each other—was preserved in different skeletons, as in a human arm, horse's leg or bird's wing. This is precisely what Thompson was saying, except that he was using the more general term of landmarks rather than bones.

Now although Thompson's approach provides a very useful and immediate way of appreciating relationships, it has an important limitation. Because he is comparing different adult forms, the deformations he shows are indirect. The various fish species in Fig. 16.4 were not actually derived by physically stretching or compressing one form into the other. They are different adults that developed independently. As the biologist J. H. Woodger pointed out:

For no one supposes that an adult crocodile's skull has ever been transformed into another adult crocodile's skull, or that an adult fish of a certain shape has ever been transformed into another adult fish of a different shape, even though the two shapes can be shown to be related in a particular way with the help of some mathematical transformation.

To get around this problem it is no good simply comparing adults, you need to look at how each adult itself develops. Fish have different shapes because of a difference in the way that each fish species grows from a fertilised egg. Several scientists in the 1930s and 40s who wished to apply Thompson's method concluded that it might be more useful for comparing different developmental stages of the same species rather than adults from different species. Look at Fig. 16.5, for example, which shows various stages of human growth inscribed on a simple grid, taken from a paper by Peter Medawar at that time (1945). By adjusting each stage to the same height, the diagram shows how the upper part of the human body, including the head, grows much more slowly in relation to the lower parts. It is a more formal way of describing the changes in proportion we encountered at the beginning of this chapter. Medawar is using the method of deformations to relate various developmental stages within one species, humans in this case, rather than to compare adults from different species. This means that the deformations he shows are those that actually occur as a human grows up. As far as Thompson's method was concerned, Medawar wrote: 'There can be no doubt ... that its true field of application lies in development, and not in evolution; in the process of transforming, and not in the fait accompli'.

Fig. 16.5 Different stages of human development, adjusted to the same size (from Medawar 1945).

Even when applied to development in this way, however, the method of deformations still has a fundamental limitation. It is relatively easy to follow the growth from foetus to adult, because the essential landmarks, such as ears, eyes and nose, are already present at the foetal stage. All we have to do is measure the relative distance between these pre-existing features as the baby grows.

But what about earlier stages, before the landmarks have appeared? Without ears, eyes or nose, it is obviously not possible to make any measurements on their relative positions: comparisons become meaningless. You cannot extend the human measurements all the way back to the fertilised egg because the landmarks are simply not there. Much of development is about the origin of landmarks, the production of greater complexity as the organism grows. Thompson's method assumes a constant level of complexity and therefore ignores a fundamental aspect of development: the increase in geometrical complexity. As Medawar himself concluded: 'the most important problem of all is so far wholly out of reach'

Growth and hidden colours

It seems to me that many of the problems encountered with the method of deformations stem from the fact that it was applied to visible features rather than to underlying processes; it gives a limited description of the outcome of development, without addressing the mechanisms behind it. It is instructive to look at how D'Arcy Thompson tried to address this issue. He sought analogies between development and the way humans modify or transform shapes, such as a glass-blower gradually working a piece of glass into a particular form. Another example he gave was the way humans could influence biological forms, such as the shape of a gourd (a fruit of the same family as melons and pumpkins):

The little round gourd grows naturally, by its symmetrical forces of expansive growth, into a big, round, or somewhat oval pumpkin or melon. But the Moorish husbandman ties a rag round its middle, and the same forces of growth, unaltered save for the presence of this trammel, now expand the globular structure into two superposed and connected globes. And again, by varying the position of the encircling band, or by applying several such ligatures instead of one, a great variety of artificial forms of 'gourd' may be, and actually are, produced. It is clear, I think, that we may account for many ordinary biological processes of development or transformation of form by the existence of trammels or lines of constraint, which limit and determine the action of the expansive forces of growth that would otherwise be uniform and symmetrical.

By this example, Thompson wanted to show how a simple physical restraint, like tying a rag round the middle of a growing fruit, can result in a transformation in shape: from a sphere to a dumb-bell. The constriction imposes an asymmetry on the growing system which results in a more elaborate form. Now the key asymmetry here is imposed from outside the organism, by a Moorish husbandman who ties the rag and therefore imposes a restriction on the gourd. It seems to me that Thompson chose an external asymmetry because during his time there was no clear understanding of how internal asymmetries could arise or be elaborated. There was no picture of hidden colours, scents or sensitivities that might have helped him to link observable deformations in geometry with internal processes. I now want to try and show how such a link might be made.

We shall begin with a hypothetical layer of cells with a very simple patchwork of hidden colours (Fig. 16.6). Each of the hidden colours will be interpreted by genes, leading to particular genes being switched on or off in the various regions. I want to concentrate on one particular region in the centre of the patchwork, with a hidden colour that I shall call sandy-yellow. Now suppose that the sandy-yellow colour specifically leads to the activation of genes that promote cell growth and division. That is, the proteins produced by these genes modify the chemical reactions in a cell in such a way that it grows and proliferates more quickly. This would mean that the

sandy-yellow patch would start to expand more than the surroundings. To accommodate the expanding island of sandy-yellow, either some of the surrounding regions would have to be compressed or the island might bulge out of the plane. Either way, the patchwork would become deformed, as shown on the right of Fig. 16.6.

Fig. 16.6 Deformation of a patchwork by interpretation of hidden colours.

This type of deformation is vividly illustrated by M. C. Escher's lithograph, Balcony (Fig. 16.7, top). Below is shown Escher's original sketch of the scene before he applied the deformation. The central balcony, the fifth one from the bottom, seems tiny in comparison with the deformed version on the right (the final lithograph is a mirror image of the original sketch because of the inversion caused by lithography). The overall visual effect of the deformation is that the centre of the picture seems to bulge out towards you.

Fig. 16.7

Balcony (1945), M. C. Escher, compared to preliminary sketch (below).

The changes in shape of a sheet of cells show how, in principle, a deformation can result from the interpretation of hidden colours. In the example I gave, the deformation only affected the internal regions of the sheet, leaving its perimeter unchanged. But you could equally well imagine a hidden colour influencing the shape of the outline as well. For instance, if one of the squares at the edge of the sheet had a hidden colour leading to rapid growth, this region would grow more than its neighbours, tending to displace one edge outw ards, deforming the outline. The key point is that the sheet of cells, the canvas, both supports and is modified by the colours. It would be as if every time an artist put a colour on a canvas, the newly coloured region might start to grow or shrink relative to the rest of the picture. The final shape of the painting could end up being rather complicated, simply because of the hidden colours that are applied. Of course, you should really imagine all of these deformations affecting a three-dimensional canvas rather than a two-dimensional sheet.

It is important to be clear about what this sort of explanation has achieved. If you were to observe the development of an organism from a purely external point of view, you might try to account for the various deformations in terms of some regions growing more quickly than others. But you would be at a loss to explain why this was so; unable to account for what makes one region behave differently from another. That is why D'Arcy Thompson was driven to use analogies with artificial deformations caused by imposing asymmetries from the outside, like a glass-blower at work, or a man tying a rag around a gourd: there was no notion of how

asymmetries could arise or be interpreted from within. But we have seen in previous chapters how distinctions between regions are generated during development through the elaboration of hidden colours. These colours provide an internal frame of reference that underlies the geometry we see: if one or more of these colours is lost through mutation, the external appearance of the organism undergoes a corresponding change. Furthermore, we have seen how this hidden patchwork can be interpreted by genes through their regulatory regions, allowing each gene to be expressed in a specific regional pattern. Once we have this internal view of the organism in mind, it is no longer difficult to see why one region might grow differently from another: it reflects the way the hidden patchwork is interpreted by genes that influence growth.

As well as accounting for differential growth, the patchwork of hidden colours also provides a set of landmarks: each region of colour can be thought of as a hidden landmark, equivalent to an anatomical feature used by D'Arcy Thompson. The patterns of growth may displace and deform the boundaries between these hidden landmarks, but their relative order remains the same, just as with anatomical landmarks. Unlike anatomical landmarks, however, which can only be traced back to the time when they first become visible, we have seen how the patchwork of hidden landmarks is anchored in earlier events, through the process of internal painting. If we simply observe the development of a fertilised egg from an external point of view, anatomical landmarks such as ears, eyes or nose seem to appear from out of the blue, representing a mysterious increase in complexity. But this is not the case when we look at development from within: the internal landmarks of hidden colour are firmly grounded on earlier processes of interpretation and elaboration. Indeed, the anatomical landmarks are themselves a later manifestation of these internal processes: the emergence of ears, eyes or nose in particular positions depends on the interpretation of the patchwork of hidden colours. This means that the relatively constant pattern of anatomical connections noted by D'Arcy Thompson and Geoffroy Saint-Hilaire is itself a reflection of the preserved order in the underlying pattern of hidden colours.

Nevertheless, in spite of this considerable advance in our understanding of development, there is still an important gap in our knowledge. Although many genes affecting the growth and division of cells have been identified, it is not clear precisely how they respond to or interpret patterns of hidden colour, scents and sensitivities, so as to change the size and shape of particular regions in the developing organism. I believe that one reason for our present ignorance may be that these genes act in a quantitative way, slightly increasing or decreasing the rate of growth here or there; making them more difficult to pin down than the genes that establish the patchwork. One of the major challenges facing biologists is to try and understand precisely how genes influence growth in response to the developing patchwork of hidden colours, scents and sensitivities.

Direction of growth

In my hypothetical example, I assumed that each region of the cell layer grew in a symmetrical fashion, but it is also possible for growth to be oriented in particular directions. A good illustration of this comes from a study on the growth of gourds carried out in the 1930s by Edmund Sinnott at Columbia University. Gourds come in many different shapes and sizes. A commonly grown type, known as the bottle gourd, has a broad base and narrow waist, resembling the shape of a bottle. Sinnott was comparing two different races of bottle gourd: a miniature form that was only about 10 cm long at maturity, and a giant form that was more than twice this length (Fig. 16.8, top).