I've been reading Seed to Seed by Nicholas Harberd, a plant-science populariser in the form of a diary. He studies the fruit fly of the plant world, Arabidopsis Thaliana (common name: Thale-cress), the same plant my girlfriend Sue spent her PhD examining. In it, he introduces the reader to plant biology and genetics in a way that conveys not only the mechanisms, but the wonder he finds in telling others about it. He also takes you through his day to day life as a scientist, and his struggle to get past a rut in the work:

Science is always like this. There are peaks and troughs. I've experienced both. But the problem with being in a trough is that it is a place from which the view is limited. There is the feeling of being trapped with no way out. And always the question of how long the entrapment will last. A self-sustaining state: at the time when new vision is most needed, it is most unlikely to come.

A quick aside: these past couple of weeks, I've been helping Sue in the lab, here at UNSW, to extract Gouldian Finch DNA. I've actually got to see the stuff, with the protein-casing of the nucleus stripped away - a hardly visible gossamer, each strand of DNA containing about a billion base pairs coding 20 to 30,000 genes. (Though note this recent story that suggests even this already complex picture may underestimate by orders of magnitude what mind-numbing work a DNA strand does.) A billion base-pairs would stretch out to about a foot in length, if stretching it out were possible. (There's about a metre's worth in every cell of your body.) So its been a good time to read about this stuff. Somehow, interacting with it a little has given me a sense of the basic insaneness of the whole process, and of the impossible-to-grasp microscopic scale of it.

In Seed to Seed, Halberd finds a kind of redemption by getting out of the lab and seeking out a Thale-cress plant growing in the wild. But its the story of the meristem that will concern us here, as it leads on my favourite vegetable in all the world...

The centre of the thale-cress's rosette of leaves is the source of all the rest of it. Each of the thousands of cells from which the rosette is built can be traced back through a line of descent to a founding cell in the centre. To a unique cluster of special cells, a structure known as the meristem, at the very centre of the centre of the disk. Everything seen as the rosette-leaf disk originates from that unseen meristem.

The meristem is usually at the tip of the plant as it grows; in the case of Arabidopsis, it remains at the base for a while, pushing a rosette of leaves out, before it starts to grow the stem.

He attempts to guide the reader in 'seeing the structure of the meristem of the thale-cress in the mind's eye':

The vision is an abstract one. It focuses on central things, omits the peripheral. It sees the meristem as a tiny ball of several hundred cells, a sphere of about 150 micrometres in diameter. The cells in the meristem are smaller than many of the cells in the rest of the plant, because meristematic cells divide after only a relatively short phase of expansion. The meristematic ball of cells is at the apex of a dome, and that dome forms the tip of the plant's stem. And although I envisage it as a sphere within a dome, and have drawn it in this way there is in reality no sharp line that divides the cells of the sphere from the cells of the dome.

The meristem is dynamic: cells constantly flow out from it, becoming the rest of the plant as they do. Right at its centre, cells divide very slowly. Daughter cells are pushed further out - and the further out they get, the faster they divide. This process is regulated by a homeostatic loop embodied in a protein feedback. In the case of the meristem, a protein called WUSCHEL (which means 'disorganised' in German) is regulated by another protein called, er, 'regulator of WUSCHEL', which inhibits WUSCHEL - which then activates the regulator in a negative feedback loop.

(Protein naming convention - for thale-cress at least - often sees proteins named for what happens in their absence, since they're usually discovered when the gene that expresses the protein isn't functioning. Hence WUSCHEL - 'disorganised' - actually regulates the organisation of the meristem.)

Harberd puts WUSCHEL into the context of all the various protein-jobs going on to maintain the meristem:

The WUSCHEL loop is a small part of the mechanism that ensures that the meristem maintains a constant structure despite the fact that the cells from which it is built are flowing through it. One can picture how some of the genes of the cells of the meristem make a pattern - a map - of signals. Other genes control the activity of the cells of the meristem with respect to that map. It is a map that is being made at the same time it is being read, and the reading affects the making and the making effects the reading in loops of subtle complexity that we are only just beginning to understand.

This is a big theme of Fritjof Capra's Web of Life, the first book that turned me on to systems thinking: that anaylsis of the persisting, dynamic patterns of life are at least as important as the study of the material that flow through those patterns.

The simplest computational version of a pattern that both makes itself and reads itself is probably cellular automata: something like the game of life. That link has a drop down menu that shows some nice homeostatic-like patterns. I'm not sure they're actually negative feedback loops, but they maintain a dynamic structure through simple neigbour rule interaction. I can imagine the maintenance of the Arabidopsis meristem being a similar dynamic, but vastly more intricate and at least one layer more complex (since the substrate itself is developing in space, which would in turn effect the signals.)

Leaf and stem are created in the meristem; in the first stages of Arabidopsis growth, each leaf is produced at an angle of 137 degrees: 'exactly how the 137 degree angle is determined remains one of the most tantalising unsolved problems in plant biology.' (137.5 degrees is the golden angle - I'd be curious to know if it is actually 137, or closer to 137.5. this site says its 'approximately' 137.)

Its easy enough to imagine how hugely complex the task of investigating still unsolved problem might be. It would have to start with identifying the key bio-chemical signals, and this task in itself is enormous. In many disciplines a lot of discoveries stem directly from observing the effects of damage: plant science is no different. In the case of one growth-inhibiting gene Harberd describes, the existence of the gene was pursued by zapping 60,000 seedlings with gamma rays and growing the lot, hoping that the appropriate gene's action would have been stopped. They succeeded - but this would be only the first stage in isolating the location of the gene and attempting to identify its actions.

On top of this, something like the 137 degree angle comes into the pattern-map category. Certain proteins may be directly involved, or may be transcription factors leading to the production of others, or may inhibit yet others, or may trigger specific behaviour in cells or inhibit specific hormone actions... and all this interacts in a way that can lead to geometrically precise emergent patterns. Harberd's line again: 'it is a map that is being made at the same time it is being read.'

So, here's my favourite bit. The meristem that produces the leaves and stem is a vegetative meristem. This becomes an inflorescence meristem at a certain point in the plant's development - and this gives birth to floral meristems that produce the flowers. Each of these has the same kind of properties: its a dynamic well-source of new cells. The genes that direct the floral meristem to become distinct entities are called APETALLA1 and CAULIFLOWER. (Note: the gene is in italics; the protein it encodes is plain text. Nice, simple system!) Following the naming convention, if these genes are not active, the new meristems do not become floral: they remain inflorescence. And because inflorescence meristems make new meristems, the process can carry on and on.

In fact, Harberd points out, its exactly this process that occurs in cauliflower - 'because a real cauliflower plant contains a mutant form of the cauliflower version of the thale-cress APETALLA1 and CAULIFLOWER genes' that means a cauliflower is all inflorescence.

Which brings me on to my favourite vegetable: the Romanesque. As this site says:

This is so visually stunning an object that on first encounter it's hard to imagine you're looking at a garden vegetable rather than an alien artefact created with molecular nanotechnology. But of course, then you realise that vegetables are created with molecular nanotechnology, albeit the product of earthly evolution, not extraterrestrial engineering.

It is certainly the vegetable most likely to hang around psychedelic stalls at Glastonbury festival. It is fractal food par excellence. Folk like Strogatz have used it as an example of fractal geometry, to suggest nature and networks are suffuse with it.

But now we have an inkling as to where the Romanesque's profoundly striking vegetablely structure might come from: the whole thing is inflorescence meristem. Every part of it has the potential to become a perfect replica of its parent, as well as create an infinite number of geometrically spaced babies. As with the precise angle of Arabidopsis leaf production, the exact position of each bud appears to be the golden angle, so that all the available space is filled:

In order to optimize the filling, it is necessary to choose the most irrational number there is, that is to say, the one the least well approximated by a fraction [so the plant doesn't get stacking of fractions e.g. once every eight turns if the angle was 45 degrees]. This number is exactly the golden mean. The corresponding angle, the golden angle, is 137.5 degrees.

As John Walker at the above site says, 'this tempts one to speculate that nature generates these patterns through a process akin to computation'... but:

Of course, there's a tendency for thinkers in every age to model the universe in terms of the predominant technology of the day. To the Pythagoreans, all was number and geometry. In Newton's time, the universe seemed an intricate clockwork mechanism. Later, in the age of steam, thermodynamics and heat death dominated models of the universe. Today, surrounded by computers evolving more rapidly than anything in natural history, what could be more natural than regarding the universe as a great automaton performing some kind of cosmic computation?

Indeed, there's really no need for a computational answer for the Romanesque. Well... its easier to explain why with a sunflower or a Thale-cress: the one with the most seeds is going to produce more offspring; the Thale-cress leaves will get the most sun if they follow the Golden angle (and catch the most rain, channeling it back to the root.) Whosoever genetically stumbles upon the golden ratio as a method of seed or leaf production will likely win out in the end, through sheer force of numbers. Of course, this doesn't answer how it produces that ratio. But it might suggest that there's no easy answer, since it could be the result of a vast evolved dance of interacting proteins and inhibitors: an adapted eco-system of feedbacks and messages.

I can't help but wonder, though, whether it would be possible to re-create romanesque growth in silico. Going back to Halberd's quote above: while abstract, it could focus on the central things, omit the peripheral. It would have to include cell production (a kind of three dimensional, warping, growing cellular automata) but how many virtual proteins would you need? How accurately would you need to mimic the transmission signals? What is central, what is peripheral?

What would be the point? Well, I suppose, initially, just a demonstration that it's possible. A verification of Halberd's 'map that is being made at the same time it is being read'. Also, it would also show that it's worth studying at this level. Which is to say, you could investigate it without having to ask future generations of Super-Playstation users to give up processing time to fold every protein; that it makes sense to think of it as relatively simple cells in space, with signals travelling between them.

It could also, perhaps, be something less complex; something more fundamental at the level of the cell that can produce Fibonacci-producing angles without such protein-interacting complexity. This website seems to suggest that meristems in general tend to push cells out in a Fibonacci-like way. But that would do little to tell us what separates the Romanesque from a rose.

Another way to think about the Romanesque might be this: the fractal geometry we see in it is a lucky fluke - a rare case where the self-similarity inherent in certain kinds of cell reproduction creates something we can see in three dimensions as geometrically perfect. But perhaps a cauliflower or a broccoli or a rose is just as geometrically perfect, from the point of view of the plant, as it were. Indeed, a cauliflower may have something extra at work to change that golden meristem production into something pseudo-random. (The above 'fractal food' webpage has a nice paragraph suggesting such random patterns might be the result of a system sitting in the boundary between linear determinism and chaos.)

Aaanyway... let's end on another bit from Halberd:

I find that there's something comforting about the idea that the rate at which the cells in that thale-cress meristem proliferate is dependent on the angle of tilt of the earth with respect to the sun. Why comforting? What do I mean by this? As soon as I've written it I'm aware that there's more to it. But that more is hard to grasp. It is fleeting, unstable, difficult to express. Fades as soon as its captured, slips through the mind. But the declaration of this sense of comfort is at least an identification that this record of the growth of the Thale-cress plant is, for me at least, more than a simple, detached observation of life-cycle progression.