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Professor Peter Drummond & Dr Xia-Ji Li

Photo: Paul JonesIi

Infectious-disease specialists call it the ‘Red Queen strategy’ and viruses are particularly good at it. By constantly changing their molecular identity through genetic trickery, viruses keep the immune system perpetually running after an ever-elusive opponent … much like the Red Queen’s race in Lewis Carroll’s Through the Looking-Glass, where the Red Queen and Alice run faster and faster just to remain in the same place.

The human immunodeficiency virus, HIV, which is responsible for AIDS, is a master practitioner of the strategy. So is influenza.

Molecular biology has developed the means to even the odds against the viruses, but to make the most of these biotechnologies there is a need to understand how infections unfold in human patients. At stake are the principles that determine how individual viruses infect, reproduce, mutate, spread – or better yet, become extinct – within diverse and unique human hosts.

But while an infection’s predator/prey-like dynamics matter when designing therapeutic counter-strategies to the Red Queen, explaining these dynamics presents enormous problems to mathematicians.

At Swinburne University of Technology, Professor Peter Drummond and Dr Tim Vaughan from the Centre for Atom Optics and Ultrafast Spectroscopy (CAOUS) know first-hand what biomedicine researchers are up against. There are so many interacting health, lifestyle and genetic variables affecting immune systems and viruses across the human population, creating so many infection scenarios, that tracking them all is extraordinarily complex. Professor Drummond says the timeframes needed to run calculations could potentially exceed the lifespan of the universe. In other words, the calculations are solvable, but not in a realistic timeframe.

The complexity is not just due to the evolving, self-organising nature of living organisms. There are also reasons that relate to millennia-old mathematical conundrums posed by dynamic systems that change seemingly chaotically or unpredictably.

“In natural populations humans respond to infection differently, the viral population can mutate as it increases, and this results in an astronomical number of possibilities,” Professor Drummond says. “That’s what we mean by ‘computational complexity’ – situations where the number of states that a calculation needs to track is astronomically high.”

While statistics has solved some issues – notably in the case of thermodynamics and quantum mechanics – Dr Vaughan wants to use new techniques never before applied to biology to efficiently solve population/infection.

“Currently researchers are using supercomputers to run simulations that track every cell death and birth, in a brute force calculation,” Dr Vaughan says. “These computations are driven by the ‘master equation’ – a raw mathematical description of how a probability distribution changes over time. So our goal is to find more efficient ways of solving the master equation, borrowing from techniques used in statistical physics.”

To make the leap to a biological system, however, the project needs data representative of a virus infection. So the Swinburne team is collaborating with bioinformatics expert, Associate Professor Alexei Drummond at the University of Auckland in New Zealand. The analysis is based on blood sample data from real infections with the immunodeficiency virus in humans and cats.

Efforts are also underway to develop a way to model much larger virus numbers than currently possible. Extra mathematical wizardry is also needed to accommodate the mutating nature of real-world viruses.

While the Swinburne campaign to conquer computational complexity is just getting underway, cracks are already appearing in the Red Queen’s defence.

Recently, some early theoretical work done with Swinburne’s Dr Hui Hu (an Australian Research Council QEII Fellow) and Dr Xia-Ji Liu was confirmed experimentally by the prestigious French laboratory, the École Normale Supérieure in Paris. That work involved solving complex computational problems dealing with interacting ultra-cold atoms.

Publishing in the journals Nature and Science, the French team compared their results with Swinburne’s predictions and calculations that relied on huge supercomputers in the United States. The Australian theoretical work came through with flying colours: the French experiments were found to agree with Swinburne’s predictions to the last measured decimal place. The supercomputers were not as accurate.

And there is also progress on the flip side of the same problem. Dr Vaughan explains that while the viral project involves tracking infection scenarios into the future, once the new techniques are in place, it should be possible to run simulations into the past and do so over evolutionary amounts of time.

That strategy could, for example, see the Swinburne mathematicians use contemporary genome sequence data to learn more about humanity’s ancestry, and the ancestry of human disease.

“We are making early first steps,” Dr Vaughan says. “What we are aiming to do is take the master equation description of the forward dynamics, fold in current data – such as DNA sequence – and infer earlier states. We have algorithms that in principle can do this. And we have tried it for simple problems. But there is a long way to go.”

Despite the gargantuan scale of the computations they are facing, Professor Drummond and Dr Vaughan think the problem of computational complexity is well worth their concerted attention. For the work stands to have applications wherever a system – be it chemical, physical or biological – is changing interactively in ways that produce remarkable behaviours.

But rather than chase after the solution with ever-faster computers, these scientists are learning to stop running after more powerful processors and instead solve the problem mathematically. With pencil and paper, in the first instance.