The Art of Genes How Organisms Make Themselves

preserved under this same set of transformations will by definition have full radial symmetry. Many things have this type of symmetry, such as bottles, pawns in a chess game and baseball bats. All of them have a single axis of rotational symmetry about which the object can be turned by any angle, and they also have an infinite number of planes of reflection symmetry.

We can impose yet more asymmetry by taking our object with full radial symmetry and deforming it in other directions, at right angles to its main axis. For example, at each vertical level we might deform the periphery of the object, by pulling it out or pushing it in to some extent, making the outline wavy rather than circular. To keep things as regular as possible in the first instance, the same deformations could be carried out symmetrically about several minor axes around the object, say five minor axes as shown in Fig. 13.5. As with the previous object, there is a single vertical axis of rotational symmetry but instead of being able to rotate the object by any amount, there are now only five angles of rotation that bring it back into itself: turns of 1/5, 2/5, 3/5, 4/5 or 5/5. Similarly, there are now only five planes of reflection symmetry rather than the infinite number of vertical planes in the previous case. In other words, we have reduced the number of ways of transforming the object into itself even more. This sort of symmetry is sometimes called five-fold radial symmetry because of the five-fold nature of the rotation and reflection symmetries. Any other object whose appearance is preserved under this same set of transformations will by definition have five-fold radial symmetry. All such objects will have asymmetry along a single major axis in one direction (e.g. vertical in the case illustrated) as well as a repeating pattern of asymmetry along five minor axes coming off it at right angles (e.g. horizontally in Fig. 13.5).

Fig. 13.5 Deformations along five minor horizontal axes produce an object with five-fold radial symmetry.

We can vary the degree of radial symmetry by changing the number of minor axes. If we had deformed our object at four regular intervals instead of five, giving it four minor axes, it would display a different degree of symmetry, fourfold radial symmetry. If we had deformed it along only two minor axes it would have ended up with two-fold radial symmetry. Many objects can be

classified under these types of heading. If you look at chess pieces, you will see that the king commonly has two-fold radial symmetry, the rook (castle) four-fold radial symmetry, and the queen anywhere from fiveto ten-fold radial symmetry, depending on the chess set. In furniture, oblong tables have two-fold radial symmetry whereas square tables or square stools have four-fold radial symmetry.

There is a particularly important symmetry class that corresponds to deforming our object along only one horizontal axis rather than several. If we carry out such deformations across the whole object, we end up with something like the head shown in Fig. 13.6, with a distinct front and back. The head has been produced by starting at one end of the object and, at each vertical level, deforming it to the same extent on each side while moving along the horizontal axis towards the other end. In the example shown, the front midline of the face has been left unchanged by the deformations: if you look at the head from the side, the frontal outline is the same as that of the fully radially symmetrical object it was derived from. Our new object now has asymmetries along two major axes: one horizontal and one vertical. In terms of geometrical transformations, there is now only one type of rotational symmetry: the trivial one involving a complete turn of 360°. There is also only one plane of reflection symmetry remaining: the one that runs vertically through the midline and divides the object in two. Although it would be reasonable to call this one-fold radial symmetry, I shall use the more common name of bilateral symmetry to refer to this arrangement. Bilateral symmetry, then, is characterised by a single plane of reflection symmetry, and it arises when asymmetries are elaborated along two major axes, in this case a vertical (top-bottom) and horizontal (front-back) axis. There are numerous objects with bilateral symmetry, including chairs, teacups, airplanes or knights in a chess game.

Fig. 13.6 Deformation along a second major axis generates an object with bilateral symmetry.

To summarise, the symmetry of an object can be defined by the number of ways it can be transformed into itself. The most symmetrical objects, such as spheres, have the highest number of these transformations. If we impose a single major axis of asymmetry on a sphere, we reduce the number of possible transformations to those of full radial symmetry, such as bottles. The extent of symmetry can be further reduced by imposing asymmetry along several minor axes at right angles to the first, giving lower degrees of radial symmetry (five-fold, four-fold, etc.). In the case of one-fold radial symmetry, more commonly termed bilateral symmetry, we end up with an object

having asymmetry along two major axes.

Symmetry and function

In practice, the symmetry class of an object is often related to the way it is used. Spherical symmetry, for example, predominates in objects that are used with little or no constraint from any specific direction, as with soccer balls that roll around in any way we choose. Radial symmetry, on the other hand, is common in cases where constraints operate along one major axis. Bottles and stools, for instance, are designed to withstand the effects of gravity: bottles prevent liquids being spilt everywhere, and stools stop you from falling to the floor when you sit down. Both of these types of object have radial symmetry, with a single major axis running vertically, parallel to the gravitational force they are designed to oppose. By contrast, pouring jugs and chairs have bilateral symmetry, because they are designed to accommodate a second directional constraint in addition to gravity, the shape of a hand that comes from one side to lift them or the shape of a person who wishes his back to be supported while he is seated. One consequence of their matching the shape of the user in this way is that they can be approached from only one direction. Compare, for example, the stool of fourfold radial symmetry with the bilaterally symmetrical chair shown in Fig. 13.7. The stool can be sat upon from at least four directions whereas the chair can be comfortably occupied from only one.

Fig. 13.7 Comparison of a chair with bilateral symmetry and a stool with four-fold radial symmetry.

Just as the symmetry of artifacts is related to their use, so the symmetry of organisms is related to the way they are adapted to their environment. Humans, for example, are to a large extent bilaterally symmetrical in terms of their external appearance. We have a single plane of reflection symmetry running down our midline, as a result of asymmetry along two major axes: the asymmetry from head to foot and front to back. The asymmetries along these axes reflect two important directional constraints on us: gravity and movement. If we lived in a free-floating world without gravity, standing would become meaningless and we would have lost much of the rationale behind asymmetry along the head-foot axis. Our second asymmetry, front-back, has more to do with movement. To generate a force that moves us in one direction, it helps to be

asymmetrical along the direction of movement (i.e. the horizontal axis). Many other distinctions between front and back follow on from this. For example, the position of our eyes at the front of our head allows us to see where we are going. Most importantly, these two major aspects of our lifestyle, movement and gravity, are oriented at right angles to each other. If we normally moved parallel to gravity, only moving up or down like springs, we would have only one major direction to deal with and would no longer need to distinguish between, say, front and back. Our asymmetries are related to our lifestyle and environment: we move at right angles to the force of gravity.

For similar reasons, many other animals display bilateral symmetry. When comparing ourselves with them, however, there can be some confusion because of our upright posture. Most animals move along the direction of their head-tail axis whereas we walk at right angles to ours. The 'back' of a horse might mean its tail end (referring to the way it moves) or the part we ride on (corresponding to our back). To avoid confusion, biologists use dorsal to refer to our back and the upper part of most animals, and ventral (belly) to mean our front and the corresponding lower part of most other animals. From now on I shall refer to two major axes in animals as the head-tail axis and the dorsal-ventral axis. Humans move parallel to their dorsal-ventral axis whereas most other animals move parallel to their head-tail axis.

It is because of our familiarity with bilateral symmetry in the living world that we tend to underestimate the asymmetry that lies behind it. When you take an irregular ink blot and fold the paper in half, you end up with an ordered symmetrical pattern that looks harmonious. Yet the original irregularity of the blot has not disappeared, it has simply been balanced by a duplicate image. The single mirror plane relieves tension by giving the blot a symmetry that we are much more familiar with.

Not all animals have bilateral symmetry. A large group of soft-bodied aquatic animals, including jellyfish, sea anemones and Hydra (the polyp mentioned in the previous chapter), have various degrees of radial symmetry. Their lifestyle is correspondingly quite different from ours. They either drift with the water currents most of the time or stay stuck to a surface, like a rock or the sea floor. If they do move around, it is usually parallel to their major axis, as with jellyfish slowly swimming by rhythmic contractions of their bells. Hydra has a different solution: it can somersault its way along by bending its main axis round so that its tentacles touch the ground, and then straightening up again. It is perhaps not too surprising that these radially symmetrical animals are found in aquatic habitats, where the reduced effects of gravity are more conducive to these styles of locomotion.

Plant symmetries are also related to their lifestyle and environment. Plants explore their surroundings by growing; growth often plays a role in the lives of plants similar to movement in animals. But unlike animal movement, which is mainly horizontal, a large part of plant growth is oriented vertically, parallel to many of the environmental factors that dominate their lives, such as gravity and light. Many of their asymmetries are therefore elaborated along a single major axis. This is reflected in the typical radial symmetry of the main stems and roots. Leaves, however, usually grow out more horizontally, roughly at right angles to the direction of the light they harvest. Consequently, leaves tend to be bilaterally symmetrical: their upper surface is usually quite different from the lower and their tip is different from their base.

Flowers display a variety of symmetries, depending on how they are pollinated. Buttercups, for example, have five-fold radial symmetry, displaying five identical petals spaced out equally

around the flower axis. Like stools, these flowers can be approached from several directions by their visitors. Other flowers, such as those of Antirrhinum or orchids, are more discriminating, accommodating selected guests more precisely through bilateral symmetry. The upper and lower petals of an Antirrhinum flower have quite a different shape and are united for part of their length to form a tube. The lower petals provide a sort of platform for bees to land on, prise open the flower and enter the tube where the nectar is stored (Fig. 13.8). This ensures that the flowers are only visited by certain types of insect: a bumble-bee is large enough to prise open and enter an Antirrhinum flower but a smaller insect would fail. The sex organs of the flower, the stamens and carpels, are carefully positioned within the tube to give and receive pollen from the bee's back. The bilateral symmetry of the flowers therefore allows their pollen to be targeted very effectively to a specific insect carrier. As with chairs, asymmetry along the second major axis of these flowers has to do with accommodating a particular type of animal.

Fig. 13.8 Antirrhinum flower shown in side and face view

For convenience, I shall refer to the uppermost petals of a bilaterally symmetrical flower as dorsal, and the lowermost petals as ventral, using a comparable nomenclature to that in animals. Thus the flowers of Antirrhinum are asymmetrical along a dorsal-ventral axis that runs from top to bottom (Fig. 13.8). Because bees enter Antirrhinum flowers by standing on the lower petals, the bee's dorsal-ventral axis runs in precisely the same direction as that of the flower (this is not true in all cases: for some plant species the animal pollinator enters the flower upside down, with its dorsal-ventral axis inverted relative to that of the flower).

Developing asymmetries

So far I have dealt with the symmetry of mature organisms in terms of geometry and the way they are adapted to their environment. I now want to look at how these manifest aspects of symmetry themselves arise; how the external geometries in the natural world arise from hidden processes.

Organisms usually display a much greater degree of symmetry early in development than later on. The embryos of many plants and animals, including humans, start off as balls of cells with a more or less spherical symmetry. It is only at later stages of development that they come to exhibit asymmetries that give them their characteristic shape and form. From a developmental

perspective, then, the question is not why we are so symmetrical, but why we are not more symmetrical. Why are we not spherical blobs with the same symmetry as early embryos?

As we have seen, to generate something with bilateral symmetry, such as ourselves, we need to elaborate differences along two major axes. However, unlike our earlier exercise with deformations, in the case of development there can be no help from an external guiding hand: the whole process needs to be understood in terms of internal events. To some extent, we have paved the way to understanding how this might be achieved in previous chapters. We have seen how the distinctive features along the head-tail axis of fruit flies depend on the elaboration of hidden colours, eventually resulting in a set of territories from one end to the other. A comparable underlying map is also present along the head-tail axis of vertebrates. In the case of flowers, we have come across a map of concentric territories that vary from the centre outwards, along the radial axis of the flower. For each of these systems, however, we have only considered the elaboration of patterns along a single axis. I now want to bring in a second axis, the dorsal-ventral axis, to show how hidden colours can be combined to account for bilateral symmetry. As with many other developmental problems, we shall begin by turning to mutants for inspiration.

A regular monster

In 1742, a student at the Uppsala Academy in Sweden, Magnus Zioberg, was roaming over an island of the Stockholm archipelago collecting plant specimens, when he came across a strange plant he had never seen before. He dutifully pressed it and took it back to Uppsala. The specimen eventually ended up on the desk of the great taxonomist, Carolus Linnaeus, for identification. Linnaeus was the foremost expert in botany at the time, and his system of classification was destined to become the foundation of plant and animal taxonomy. In spite of Linnaeus's extensive knowledge of plants, he had never seen anything quite like this specimen before. At first he thought it was a species of common toadflax, Linaria vulgaris, with some strange flowers artificially stuck on to it so as to trick the specialist. On looking closer, however, Linnaeus saw that it was genuine enough. He became very excited and asked Zioberg to go back to the island and collect a living specimen so that he could study it in more detail. Linnaeus was so enthralled by the plant that he wrote a small dissertation on it in 1744.

It became clear to Linnaeus that this plant was identical to common Linaria in every way except for the symmetry of the flowers. Like its close relative Antirrhinum, the flowers of Linaria have five petals which are joined together for part of their length to form a tube (Fig. 13.9, left). Linaria flowers normally have bilateral symmetry, with distinctions between petals along the dorsal-ventral axis. This is particularly striking in Linaria because the ventral (lowest) petal has a distinctive outgrowth at its base, called a spur, where the nectar collects. By contrast, the plant that so interested Linnaeus had flowers with five-fold radial symmetry: all five petals were identical (Fig. 13.9, right). Instead of varying along the dorsal-ventral axis, each of the five petals closely resembled the ventral petal of the normal form, giving a flower with five symmetrically arranged spurs. It was as if the ventral petal had become repeated all the way round. We might compare this to deriving a stool from a chair by repeating only the front of a chair all the way round, as shown in Fig. 13.7. The stool can be thought of as a chair that has lost its front-back asymmetry.

Fig. 13.9Common form of Linaria vulgaris, with bilateral symmetry, compared to peloria mutant with f

ive-fold radial sy mmetry.

The reason that Linnaeus found this plant so interesting was that he had based his whole system of plant classification on flower structure. Accordingly, the unusual plant with a fundamentally altered flower symmetry should have belonged to a totally new species, yet the overall appearance of the plant was obviously that of common toadflax. Linnaeus had to conclude that this peculiar plant had arisen by some sort of transformation of common toad flax. This was well before Darwin's time, and the idea that one species might be transformed in some way to resemble another was very radical. Species were thought to be timeless acts of creation, forever occupying a fixed position in nature. Monstrosities of various sorts were well known but they were usually defective in some way that prevented their being taken seriously as new or modified species. What startled Linnaeus was that this plant with symmetrical flowers seemed to be a perfectly acceptable species: the flowers were beautifully formed and regular, and they could produce seed. It overturned the dogma that species could not be transformed or tampered with. Linnaeus wrote:

Nothing can, however, be more fantastic than that which has occurred, namely that a malformed offspring of a plant which has previously always produced irregular flowers now has produced regular ones. As a result of this, it does not only deviate from its mother genus but also completely from the entire class and thus an example of something that is unparalleled in botany so that owing to the difference in the flowers no one can recognise the plant any more ... This is certainly no less remarkable than if a cow were to give birth to a calf with a wolf'ss head.

Linnaeus eventually named the plant Peloria, Greek for monster. Paradoxically, the flowers themselves were quite attractive; it was their disturbing biological implications that made them monstrous. The phenomenon of peloria was noted in many other species following Linnaeus's report, but little progress in understanding was made until 1868, when Charles Darwin published some intriguing observations on Antirrhinum. The observations were perhaps more remarkable for what Darwin missed than for what he saw.

Darwin's theory of evolution by natural selection depended on parents being able to transmit some of their characters to their offspring. It only worked if characters giving an advantage during the struggle for existence could be passed on to later generations. Otherwise, selection would be ephemeral and could not contribute to a lasting and gradual transformation of species over many generations. For years Darwin amassed an enormous amount of information on heredity to try and support his theory of evolution. Amongst his experiments, he described some crosses between tw o

varieties of Antirrhinum. As with Linaria, there are some varieties of Antirrhinum that have radially symmetrical flowers, instead of the normal bilaterally symmetrical flowers. These mutant forms are called peloric (Fig. 13.10).

Fig. 13.10 Normal and peloric flowers of Antirrhinum in face view.

Darwin noted that when he crossed a peloric variety with the common form he obtained hybrids with normal flowers; the peloric trait had disappeared. However, when the seed from these hybrids was sown, the peloric form reappeared in 37 out of the 127 progeny. That is, although the more symmetrical form seemed to vanish in the first generation of the cross, it resurfaced in about one-quarter of the progeny in the following generation. Anyone familiar with Gregor Mendel's work, published a few years earlier in 1865, would have concluded from Darwin's results that the peloric trait was probably determined by a single hereditary factor, what we now call a gene. To see why, recall that every individual carries two copies of each gene, one coming from each parent. Suppose that Darwin's parental plant with peloric flowers carried a mutation in both copies of a particular gene, whereas this gene was unaffected in the normal-flowered plant. When the parents were first crossed, the hybrid would have inherited a normal copy of the gene from one parent and the mutated copy from the other. Having one normal copy of a gene is usually enough to ensure proper development, so the hybrid looked normal. But in the next generation, when the hybrid itself reproduced, these two versions of the gene would be shuffled. Each individual would then have a one-half chance of inheriting the mutated copy from its father and a one-half chance of getting it from its mother. The chance of both copies being mutated would therefore be one-quarter this generation, the same as the chance of getting two tails when a pair of coins are tossed. Mendel's theory of inheritance was based on precisely this sort of result, observing about one-quarter mutant progeny in the second generation of a cross. The observations made by Darwin fit this (within the bounds of statistics), implying that the peloric trait depends on a single gene.* (*The story is more complicated than this because out of his 127 progeny, Darw in also obtained 2 with a condition intermediate between peloric and normal. We now know that additional genes can influence the extent of peloria, although it is difficult to know precisely what was going on in Darwin's case given his limited amount of breeding data.)

Darwin, though, was not familiar with Mendel's theory and was thinking along different lines. Ironically, in the same book in which he described his Antirrhinum crosses, Darwin went on to propose his own theory of inheritance, which turned out to be quite incorrect (we shall return to this theory in a later chapter). He based his theory on an enormous body of data, of which his

results with Antirrhinum formed only a minor part. He therefore missed the vital due they offered. Had Darwin placed more emphasis on his experiments with Antirrhinum and followed them up with further breeding studies, perhaps he would have elucidated the principles of heredity as well as those of evolution.

A celestial colour

We now know that the peloric forms of Antirrhinum carry a mutation in a gene called cycloidea (from the Greek cyclo-, meaning circle, referring to the more circular outline of the peloric flower), or cyc for short. It was most probably this gene that Darwin had unwittingly revealed in his crosses. How does the cyc gene influence the symmetry of a flower?

It will help first to schematise the petals of an Antirrhinum flower. The five petals in a normal flower can be classified into three types, each with a distinctive size and shape: two dorsal petals, two lateral petals and one ventral petal (Fig. 13.11, left). The flower has a single plane of reflection symmetry running down the middle (see dotted line in left diagram of Fig. 13.11). By contrast, in peloric flowers, all the petals look similar to each other, so the flower has five-fold radial symmetry rather than bilateral symmetry (Fig. 13.11, right). The petals of the peloric flowers are not of a completely new type; they closely resemble the ventral petal of a normal flower. That is, instead of having petals with three different identities, dorsal, lateral and ventral, the peloric flowers exhibit a single ventral type all the way round. It is as if whatever normally establishes dorsal and lateral identities has been lost, and ventral identity is reiterated by default.

Fig. 13.11

Schematic diagram of petals of normal and peloric flowers, shaded to indicate the different petal identit ies. In the peloric mutant, all petals resemble the ventral type of normal flowers.

To see how this might be explained, I need to describe where the cyc gene is normally expressed. The cyc gene is first switched on at a very early stage of flower development, at a time when the bud is just a tiny bulge of cells with no obvious dorsal-ventral asymmetry. Most importantly, cyc is only switched on in a very specific part of the flower-bud: the dorsal (upper) region. This is shown shaded in Fig. 13.12, where the floral buds are shown in section as bumps on the periphery of the growing tip. So even though the flower -bud itself looks symmetrical from top to bottom at this stage, a hidden asymmetry is already there in terms of cyc expression. You can think of cyc as providing a distinctive hidden colour to the dorsal region of the bud. I shall name this hidden colour celestial-blue, reflecting its location in the higher regions of the bud. It is the production of celestial-blue in the early flower-bud that leads to the manifest asymmetry of the flower later on along the dorsal-ventral axis. In peloric flowers, this colour is missing because of a

mutation in cyc, and the flower develops with radial symmetry.

Fig. 13.12 Pattern of cyc expres sion in very young Antirrhinum floral buds on the periphery of the main growing tip. Each flower grows in the angle of a small leaf (called a bract). Note that cyc is only switched on in the upper (dorsal) region of the flower-bud, nearer to the growing tip

Many of the details of how this celestial-blue colour can give rise to the different petal types in the flower are still not known, but I will try to sketch a reasonable scenario. To do this, I will need to introduce some more hidden colours. First I want a colour that we associate with the lower depths, say sulphur-yellow. We will start off with the flower-bud, schematised as a disc in face view, having a uniform distribution of sulphur-yellow (Fig. 13.13, left). When the cyc gene gets switched on, celestial-blue will be produced towards the top of the bud, so we end up with two colours: celestial-blue in the dorsal region and sulphur-yellow in the remaining part (Fig. 13.13, middle; for simplicity, I am assuming that the blue colour outcompetes or predominates over yellow). Now recall that a hidden colour can lead to a specific scent (signalling molecule) being produced, and that cells may respond to this scent by changing their hidden colour (Chapter 11). Suppose that celestial-blue cells start to produce a scent, a heavenly perfume, to which neighbouring cells respond by turning from sulphur-yellow to a more earthy colour, like terra-cotta. Cells further away, in the lower parts of the bud, might be too far away to detect the heavenly scent and therefore remain sulphur-yellow (Fig. 13.13 right). In this way, we have elaborated three regions along the dorsal-ventral axis: celestial-blue, terra-cotta and sulphur-yellow. The identity of the petals will depend on the hidden colour of the region they come from: the petals from the celestial-blue region will develop with dorsal identity, those from the terra-cotta region will have lateral identity, and the petal from the sulphur-yellow region will have ventral identity.

Fig. 13.13

Elaboration of h

idden colours in

the flower (face

view).