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Using the laws of nature to predict tumour growth

In the future, doctors could use mathematical rules to predict how cancers change with time, helping to guide their treatment decisions. Liz Burtally looks at research that could help to make this a reality.

Wilms tumour

How is the flowing of a river and the luminosity of the stars related to cancer? The answer lies in the laws that govern these natural processes, and scientists are becoming increasingly interested in using these laws to predict the evolutionary outcomes of cancer.

We often think of cancers as being the chaotic and uncontrolled growth of cells within the body. But increasing evidence is now pointing to the fact that cancer evolution is often highly ordered and can even be explained by a straightforward mathematical rule. This rule is important because it hugely simplifies our view of how cancers evolve.

Dr Andrea Sottoriva – a Chris Rokos Fellow in the Centre for Evolution and Cancer at The Institute of Cancer Research, London – is using genomics and computational approaches to understand cancer as a complex system through mathematical modelling.

“What happens in the early, undetectable stages of cancer is still unknown because direct observations are pretty much impossible,” explains Dr Sottoriva. “But since tumour growth is an evolutionary process and the tumour’s ancestral history is recorded within its cell genomes, detailed information on the early beginnings may be encoded in the complex patterns of the final tumour’s genetic make-up.”

Decoding tumours

By constructing a quantitative framework, Dr Sottoriva has been able to interpret tumour growth dynamics, and has even decoded the origins of the tumour’s genetic diversity.

His research – recently covered in a news article – shows that the timing of a mutation appears to be more important than the relative evolutionarily fitness advantage it confers, so only those that occur early have enough time to expand to a detectable size through cell division. “This concept shares an interesting analogy with the cosmic microwave background in the earliest phase of our universe, which subsequently streamed through the expanding cosmos,” says Dr Sottoriva. “From this cosmic microwave background signature it is possible to reconstruct the events that occurred right after the birth of our universe.”

More recently, Dr Sottoriva and his team have been collaborating with colleagues from the Queen Mary University of London to elucidate patterns of evolution in cancer, using data from more than 900 tumours of 14 different cancer types.

The model found that in many tumours, all important cancer genes are already present at the beginning of tumour growth, and new mutations inside the tumour are essentially ‘passengers’, with no additional effect. Passenger mutations appear to accumulate following a so-called 1/𝑓 power-law distribution, a pattern influencing many natural processes such as the flow of rivers and the brightness of stars.

Brain and pancreatic tumours were less predictable when using the model, suggesting that in these cases natural selection – driven by pressures on resources and space – might play a greater role in the spread of mutations.

“This predictability means that we can harness the vast amount of genetic data that are generated from tumour biopsies to predict the cancer’s behaviour,” says Dr Sottoriva. “The information can tell us how a given cancer will develop over time – which mutations will drive the tumour into a more aggressive disease versus ‘passenger mutations’ that may have no effect on cancer growth.

"We can also predict when targetable mutations emerge, and choose which drugs would best to target them. Like in a game of chess, the aim is anticipating the next move of the adversary, to ultimately win the game.”

Precision medicine

Since every tumour may follow a different set of rules to grow, metastasise and develop resistance to therapy, Dr Sottoriva’s aim is to identify those rules in each patient. Although finding those specific rulesets in the vast range of possibilities may sound unfeasible, an approach based on the integration of genomic data and mathematical modelling allows researchers to measure the dynamics directly from human samples in a quantitative manner.

One thing is for certain: our research in cancer evolution is helping to fine-tune our delivery of precision medicine to patients. Much like predicting where a river flows, or how bright a star will shine, doctors could in the future use mathematical rules to reliably forecast how cancers change with time, helping them to choose the most effective treatments for each patient.

Dr Sottoriva’s work was funded by a donation to The Institute of Cancer Research by Chris Rokos and by other organisations including the Wellcome Trust, Cancer Research UK and the Medical Research Council.

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