Sunday, 3 November 2013

How the Leopard Got Its Mathematical Spots

According to Rudyard Kipling the leopard got it’s spots because an Ethiopian pressed his finger tips all over the cat’s fur. But for zoologists the biological origin of leopard spots, or even zebra stripes, has been a much more difficult question to answer. Heredity, genetics and evolution play roles in how these features are passed from one generation to the next, but no-one knew how they were created in the first place. I mean, one cell is much like any other in an embryo. So how, when and why does a cell decide it is going to form part of a leopard’s spot? Part of the answer came from another scientific direction – mathematics.

Alan Turing’s last major project, after being a war-time code-breaker and formulator of the theories of modern computer science, was on the matter of morphogenesis, the term used for the way in which both animals and plants develop their different parts.

As a child Alan stared at daisies and wondered how they knew when and where to grow a petal or a leaf. Later in life he began to wonder how a leopard’s spots formed, or patterns on a bird’s feather. Alan believed that chemicals must be the answer, but to explain how these chemical created patterns was another puzzle. Alan tackled it with maths.

Today we know that these patterns (sports, stripes and swirls) and shaped (ears, leaves, antlers) are determined in DNA. Alan used mathematical models to show that hormones were also responsible. Some chemical and hormones inhibit the production of certain cells, while others promote them. In this way one cell affected by a colour-producing hormone would divide and multiply quicker than the other cells around it, producing a patch. Using mathematical models to simulate the creation of these hormones and the division of cells Alan showed how numbers could help explain how animal spots are formed.

During his work Alan would show colleagues and friends papers covered with hundreds of chemical notations and mathematical formulae, some of them connected in shaded areas, and he’d say to them, “Don’t you think that looks like patches on a cow?” They must have looked back and thought “What planet are you living on, Alan?”

Since his day morphogenesis and the understanding of animal markings has progressed, all of it built on Alan’s maths and theories. He realised that his models of the process were simplifications of nature and hoped that it would be useful for future research.

Alan published his theory in 1952. Sadly he didn’t expand on his research. His house was burgled the same year. After admitting that the culprit was a former gay partner he was arrested and later convicted of gross indecency. In one of the tragic ironies of history, Alan chose to undergo treatments with hormones as his sentence rather than have time in prison. He was regulated injected with oestrogen. This hormone was known to cause men to grow breasts and inhibit sexual drive. For Alan it was living, physical evidence of the way hormones change cells, a process happening to his own body which he would have now been able to calculate mathematically.

Oestrogen also leads to anxiety and depression when injected into men, and this could have been the major factor in Alan’s decision to commit suicide in 1954, just a few weeks short of his 42nd birthday.

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