From cracking the Enigma to decoding living systems: Turing's gifts

Enigma should have been unbreakable, given the sheer number of permutations enabled by regularly changing the settings.

But the linguists who cracked Enigma were able to spot certain characteristic phrases, or names, used at the start of a transmission. One was “Rosa”, the girlfriend of an Enigma operator. Other common phrases used were ‘nothing to report’ or ‘to the group’. From those small hints, and the knowledge that the Enigma machine would never code a letter as itself, it was possible to work out the rest of a message.

ATGC - the four bases that are the letters of DNA. Only four letters but they combine to produce a language that can describe much of what we see in the natural world. We can rightly analogise that those letters spell words and that those words combine to produce sentences, which we now know of as genes.

In DNA, we find the same complexity and sheer scale of numbers as in Enigma. We also see the same patterns of regularity. In DNA, our ‘Rosa’ is made of three bases with the specific order ATG. Each set of three bases is known as a codon, which codes for a specific amino acid. ATG tells us that we want the amino acid methionine, and this is the first word in almost every sentence of the DNA code. An uncanny parallel.

We use this code to understand life’s very essence, from its beginnings long ago in the primordial broth of a youthful Earth, tracing mutations, evolution and speciation throughout four billion or so years to give us the complex web of living wonders that we thrive amongst today.

We can compare the code of humans with that of algae and find similarities shared with lifeforms that look strange and yet are, in many ways, intimately related to us. We can find differences between more closely-related species that offer tantalising hints to how we can treat diseases. We can even begin to search the DNA of all of life to unlock secrets to making better medicines, or healthier and more sustainable food.

None of this, however, would be possible at scale without another gift of Turing and Bletchley Park.

Alan Turing was primarily a mathematician and it was his statistical insights based on probability theory that helped really ramp up the Bletchley code-breaking operation.

Without statistics, we’d also be hard pressed to deliver the significant results of modern bioscience. One of the tenets of science these days is the importance of showing your results aren’t due to chance, or placebo. Statistics are also crucial for fine tuning and improving how we assemble genomes, as scientists in EI’s Clavijo Group are intimately aware.

Take the K-mer Analysis Tool, or KAT for short, a quality control tool which helps scientists understand the flaws in their DNA sequence data. Through applying mathematics, it’s possible to discern the quality of the information we glean from our DNA sequencing machines, and therefore help the computer algorithms down the pipeline to assemble something as close as possible to the likely truth. Good data in, good data out.

One particularly useful feature of the KAT tool strikes another parallel for the use of statistics in decoding messages.

Rather than try every single iteration of the wheat genome - an enormously complex amount of DNA totalling around 17 billion letters - KAT was able to narrow down how to assemble the genome in one run on the computer, rather than twenty or more, which saved a lot of time and money (and provided the most complete and highly accurate version at the time).

As with KAT and genomes, Turing’s Banburismus technique - now known as sequential analysis - did a similar job, ruling out certain parameters of the Enigma codes and freeing up lots of time for the computers to crunch the more likely combinations. Statistics helped speed up the Bletchley decrypting operation much like they speed up the Earlham Institute DNA decoding operation.