Today is the centenary of Alan Turing‘s birth. He was born in London on 23rd June 1912. If you look at the Google homepage, the doodle is a Turing machine. Turing was one of the most brilliant people the Britain produced in the last century. He is one of the fathers of the computer you are using right now, hence the Turing machine doodle by Google. He also made a huge contribution to the Allies winning the Second World War.
Turing took time out from inventing computers to work on the spontaneous formation of patterns. His 1952 paper is here. The basic question he asked is this: start from an initially uniform system, say a system that is grey everywhere, and understand what it would take for the system, without any outside help, to form black and white stripes.
This question was motivated by biology. By scientists asking how, for example, a zebra’s stripes form, and when they do, what determines how wide they are?
Chemists have long studied systems of molecules in testtubes that can do this, can spontaneously form stripes. But seeing in detail and quantitatively how patterns can form spontaneously in a living organism such as a developing embryo is very hard. The embryo may have 1023 molecules, of which maybe only a million are the ones driving the formation of the stripes.
Seeing what these million molecules are doing is like tracking the positions of needles in haystacks, only the needles are only a few nanometres across. Fortunately, the embryos of some species are mostly transparent, for example those of the zebrafish – named because it is striped like a zebra. But even so, looking for molecules in only mostly transparent embryos is really hard.
So perhaps only now, almost 60 years after he died do we have strong quantitative evidence that his model is right for a pattern in a living organism. A few weeks Müller et al published a paper in Science. They studied a pair of proteins with the rather odd names Nodal and Lefty. Nodal’s role in the pattern formation is basically that of an accelerator, while Lefty is the brake. Pattern formation requires both the accelerator and the brake.
A key prediction of Turing’s model is that for the pattern to form, the brake molecule has to move faster than the accelerator molecule. Only if brake moves faster will the peaks and troughs form that are needed to make patterns like stripes.
So, Muller et al. did the very hard job of carefully measuring the speed of diffusion in a zebrafish of the brake Lefty and the accelerator Nodal. Lefty moves faster. Turing was right. So happy birthday Alan Turing!
