But a system which has spherical symmetry, and whose state is changing because of chemical reactions and diffusion, will remain spherically symmetrical for ever. It certainly cannot result in an organism such as a horse, which is not spherically symmetrical.
In 1948 a man called Alan Turing went to Manchester to help develop computers at Max Newman's Computing Machine Laboratory. Only a few years before, Turing and Newman had both worked for the Government Code and Cypher School�and had helped to end a war.
Turing became interested in mathematical biology. In particular, he was interested in morphogenesis�or how structure originates and develops in organisms. All the code to create an organism exists in each one of its cells, but why does one cell form a foot and another an eye?
To try and explain this, he invents the concept of a morphogen. He doesn't define what a morphogen is, but it doesn't matter�he only needs to show that the mathematics behind it works. He does, however, give some examples of chemicals in real biological systems that probably have a morphogenic role: hormones, skin pigmentation, genes.
Turing views genes as a special class of morphogen. Most morphogens will need to diffuse between cells in order to differentiate them. Genes cannot diffuse, and so whilst involved, genes cannot be the cause of morphogenesis. He states:
The function of genes is presumed to be purely catalytic. They catalyze the production of other morphogens, which in turn may only be catalysts. Eventually, presumably, the chain leads to some morphogens whose duties are not purely catalytic.
This is still though to be broadly correct, despite many decades of advances in genetics.
So how does an embryo, a spherical structure, become a horse that isn't particularly spherical at all. Turing shows us how, first by arguing that we can consider an embryo as a perfect sphere, and then by showing us the fallacy.
An embryo in its spherical blastula stage has spherical symmetry, or if there are any deviations from perfect symmetry, they cannot be regarded as of any particular importance, for the deviations vary greatly from embryo toembryo within a species, though the organisms developed from them are barely distinguishable.
So embryos are never perfectly spherical, but the imperfections in them are random, and seem not to have much effect on the resulting organism. If the imperfections don't matter, then we can just ignore them; but then we are back to the spherical embryo that cannot possibly become a non-spherical horse.
There is a fallacy in this argument. It was assumed that the deviations from spherical symmetry in the blastula could be ignored because it makes no particular difference what form of asymmetry there is. It is, however, important that there are some deviations, for the system may reach a state of instability in which these irregularities, or certain components of them, tend to grow. If this happens a new and stable equilibrium is usually reached, with the symmetry entirely gone. The variety of such new equilibria will normally not be so great as the variety of irregularities giving rise to them.
Turing draws the following analogy: if you place a marble on the top of a dome, it will fall�provided it is not perfectly balanced. The end result (the marble falling), is similar regardless of the exacting nature of the imbalance. In a similar way, a spherical blastula is in a state of unstable equilibrium, and if anything knocks it out of that state then it will inevitably change until it reaches a stable equilibrium: a non-spherical horse�given the right conditions.
Morphogens turn the simple but chaotic structure of a blastula into a complex and ordered organism, but the chaos is not optional.
Turing's theory explains much of the complexity of nature, but it is of most use when considering the emergence of complex patterns that are not genetic. Tiger stripes are a good example. There is no genetic code that says which stripe goes where, or how thick a given stripe should be. All tigers have different stripes, and none of them are determined by genes. The genes say that a tiger has stripes, but the pattern itself is laid out at random, determined�as Turing showed�by random imperfections.
Turing notes a possible problem with the morphogen theory. Some organisms are not bilaterally symmetrical; for example, the largest part of the human heart is slightly offset to the left side�but not in every case. Similarly, there are many animals that show "left-handed" or "right-handed" traits, where each of the two variants of the trait do not occur with uniform probability.
Turing realises that this is strange given the following assumptions:
(i) The laws of physics are F-symmetrical.
(ii) The initial totality of zygotes for the species is F-symmetrical.
(iii) The statistical distribution of disturbances is F-symmetrical.
So what breaks the symmetry?
The answer, Turing says, lies in the fact that morphogens do not always have the same number of right- or left-handed molecules. Proteins that occur on Earth are almost entirely left-handed, created using the code stored in right-handed DNA molecules. The cause of the prevalence of left-handed proteins is not really known, as right-handed proteins should work just as well. Whilst natural selection would probably favour a dominant chirality, the fact that left-handed won out was probably down to chance.
Turing submitted his paper, The Chemical Basis of Morphogenesis, to the University of Manchester on the 9th November 1951. Less than 3 years later, in 1954, Turing was found dead. A post-mortem examination determined that he had died from cyanide poisoning. An inquest found his death to be suicide.