A mathematical technique used to study the birth of the universe is helping clinicians in their fight against cancer. Geoff Watts reports

Stephen Smith was drowning in data. The obstetrician and his staff in the reproductive molecular research group at Addenbrooke's Hospital, Cambridge, were trying to find out how the genes that control the reproductive system affect its various tissues in health and disease. Their immediate goal was a way to make fast and accurate diagnoses of ovarian cancer from its distinctive genetic signature. But the confusing surfeit of experimental information was proving very hard to interpret.

One of Smith's researchers, Ann-Marie Martoglio, explained the dilemma to David MacKay, reader in physics and Gatsby senior research fellow at the Cavendish Laboratory, Cambridge. Martoglio knew of MacKay's expertise with statistics through her time as a member of Darwin College, Cambridge, where the physicist was a fellow, and she hoped he might know how to rescue useful meaning from the morass of data. "Ann-Marie was aware I knew a lot about statistics, so we had a chat about her data-modelling problems over a college lunch," MacKay recalls. He thought he might have a solution. That the answer to the clinician's problem might lie in a way of gaining a better understanding of the birth of the universe did not put anyone off.

There was a time when biology was a descriptive science: you looked, then you reported what you had seen. As biologists got to grips with the physiology of organs and cells, they turned to chemistry - and, when they began exploring the molecular basis of life, to physics. Now it's genomics, the study of genes, that is pushing biology into the arms of another branch of science. The partner in this latest embrace is mathematics.

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Smith's group was investigating the genes that play a role in the development of disease in the reproductive system, from the growth of new blood vessels to the emergence of cancer. We know there are upwards of 30,000 genes in every cell. At any one time in any one cell, many of these genes are not active; indeed, ovaries behave like ovaries and not like wombs because only a particular subset of genes is running the show. These combinations of active genes are referred to as "genetic signatures". And the signature of cancerous tissue is different from that of healthy tissue.

Sounds like a heaven-sent opportunity for making diagnoses - and it is, but not easily.

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If all tumours of, say, the ovary were associated with the abnormal activity of just one gene, a test for ovarian cancer would be simple. In reality, the genetic signatures of normal and cancerous tissues show many differences. Moreover, ovarian tumours themselves are not all of a piece.

Slice them up, peer at them through a microscope, and you can spot a number of sub-types. Each of these has a slightly different genetic signature. And there is worse; a study of these signatures reveals still more subtypes invisible to the eye.

The full complexity of the situation becomes clear when you toss three more facts into the pot. First, any one gene is likely to feature in several or even many genetic signatures. Second, the activity of individual genes is not an all-or-none affair but graded: they may be slightly active or very active. Third, there is genetic variation between individuals that adds more "noise" to the signal being sought.

The actual business of testing the activity of large numbers of genes has been reduced to a fine art. Microarray analysis, as it is called, uses robots to stick thousands of chunks of specially prepared DNA on to a surface. When genetic material from a test sample is washed over this surface, particular sequences of its DNA will attach themselves to particular spots. A system of radioactive or fluorescent tags is used to show which DNA sequences have stuck, and in what quantity. From this, it is possible to tell which genes are active in the sample. Studies that would have taken weeks or months can be done thousands of times in a few hours - but analysing the results is tricky.

The way to extract meaning in all of this was, in MacKay's opinion, found in a method known as independent component analysis, or ICA. As impenetrable to the non-specialist as most of the labours of statisticians, it was devised in the mid-1990s by researchers at California's Salk Institute.

ICA is a sort of mathematical equivalent of the familiar cocktail party effect. We can stand in a room with a dozen people talking at once yet still sort out the competing patterns of sound in a way that allows us to understand what one speaker is saying. "Independent component analysis takes information that has got mixed up and separates it out," MacKay says.

"This is not a trivial problem. It's remarkable that it can be done at all.

But we know it can from our own experience of going to cocktail parties."

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Having immediately appreciated ICA's potential for their own work at Cavendish, MacKay and his student James Miskin began applying it. They looked at ways to interpret imaging data of teeth to pinpoint normally invisible patches of decay. They also applied it to studying the sea of microwave radiation in which the entire universe is bathed. Miskin showed how ICA could be used to remove extraneous signals from data of the kind collected in sky searches.

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MacKay was able to guide Smith in the application of ICA to genetics. The technique seemed ideal. "This system doesn't make any prior assumptions about which genes are involved, or in what combinations," Smith says.

Instead it reveals these things. And the more precisely doctors can characterise tumour subtypes, the more accurate will be their prognoses.

Eventually this approach should allow new treatments to be tailored to particular tumours.

MacKay had worked on other biomedical information problems, but this was his first experience of collaborating with clinically oriented researchers.

Not that he sees much distinction. "We're all academics," he says. Smith appears to be more conscious of the difference, particularly when it comes to a sense of urgency. "If you come from a clinical background and you're working on cancer, you want things done as quickly as possible because you have patients. The problems are not just academic."

When I phone to speak to MacKay, on a Friday afternoon, he is in his office at Cavendish. After we talk about ICA, he tells me that much of the coming bank holiday weekend will be taken up with visitors drawn to Cambridge for the European ultimate Frisbee tournament. Ultimate Frisbee, it seems, is a seven-a-side team sport with no referees. The players referee themselves.

Very 1960s, he adds.

The same day, I sit talking with Smith in the formal, very un-1960s ethos of the Royal College of Obstetricians and Gynaecologists. Although just across the road from London's Regents Park, I doubt too many of the fellows pop out to play ultimate Frisbee in their lunch breaks.

I suspect Smith is thinking, however obliquely, about the differences between organisations when he says that new groupings force the creation of new working styles. Sitting with me in the college he talks of archetypes: the arrogant consultant and the idiosyncratic scientist. Unbridled, he suggests, neither persona works well in the more even relationship required when people in dissimilar groups with different expertise get together.

The collaboration between these two groups, with their separate interests and outlooks, has proved fruitful. And there is a kind of inevitability about it. As Smith reflects, our 30,000 genes determine the production of maybe 100,000 proteins. Many of these are continuously interacting with each other in an unimaginably complex soup of chemical feedback loops that control the micro-machinery of the cell. To grasp it all, he says, is mind-numbing.

"As a non-mathematician, I find it almost as difficult to comprehend as the idea of infinity, because the permutations are so large," Smith says. "But if you can succeed in thinking of natural science in the language of mathematics, you may be in a better position to take things forward."

MacKay has found this latest partnership particularly stimulating. That it was born of a lunch with a colleague whose research apparently lay so far from his own highlighted its idiosyncratic nature. "One great thing about Cambridge is that we have the colleges and we get to eat with people from different disciplines," he reflects. Many people, not least those with ovarian cancer, could ultimately benefit as a result.

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