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Predictability from Chaos: Understanding the Behaviour of Living Organisms through Mathematics and Modelling

Researchers from the Biological Physics Theory Unit at the Okinawa Institute of Technology Graduate University (OIST) use mathematical modelling to dispel the belief that the behaviour of living organisms cannot be predicted.

Science often tries to predict events and phenomena, based on past trends, calculations, or experimental evidence. This is especially seen in fields like astronomy, where specific events like eclipses can be predicted months, or even years, in advance, based on mathematical computations. However, it is usually believed that the behaviour of living organisms, especially animals, cannot be predicted simply by mathematical means.

This assumption may not be true, according to research by the Biological Physics Theory Unit at the Okinawa Institute of Technology Graduate University (OIST). While the field of studying and modelling the behaviour of living animals is still very new, this research unit has found evidence suggesting that the how animals behave may be governed by mathematical laws, just like physical phenomena.

According to Dr. Tosif Ahamed, a recent OIST PhD graduate and the first author of the study, “neuroscience tends to focus on what goes on inside the brain, but this is often expressed through an animal’s movement and behaviour. Therefore, understanding their behaviour gives us a window into their brains. Recently, there has been an explosion of technology that can record the behaviour of animals in high resolution.”

“Remarkable technological progress has enabled new, precision measurements of living systems on all scales, from molecules of DNA to brain cells, to entire organisms,” elaborates Professor Greg Stephens, the leader of the OIST unit. He further explained that while a large amount of information can be collected, researchers “lack a fundamental framework for understanding the dynamics of these systems and the sequences of measurements over time”, and is hopeful that the work done by the OIST unit could help with this problem.

The team’s research was recently published in Nature Physics this year, and was conducted in collaboration with Dr. Antonio Costa from Vrije Universiteit Amsterdam. They used Caenorhabditis elegans, a common model organism used in biological investigations, and studied its movement by dividing the worm into 100 points before measuring the tangent angles at each of these points. The choice of C. elegans as the organism studied held some advantages, including its simple shape which can be approximated as a curve, and prior research by the team, showing that the animal’s physical structure could be represented by just four stereotyped shapes, known as “eigenworms”, which can be combined differently to provide full details of the worm’s structure at any point in time.

In order to predict the behaviour of the worms, the researchers studied the past shape sequences of the animals and used them to make forecasts of the organisms’ current structures. However, their movements proved to be rather unpredictable, leading the team to explore chaotic dynamics instead. Chaotic dynamics refers to how minute uncertainties in measurements disrupt our abilities to make long-term predictions.

As they investigated this further, the team found that two worms that started out with similar behaviours tend to continue behaving in similar ways for around one second, before their patterns differ. The specific duration before divergence can be determined mathematically and is related to a particular measure of predictability in chaotic systems. Ultimately, the researchers observed that the behaviour of the C. elegans studied was closely tied to a mathematical structure governing energy conservation. This conclusion was surprising to the scientists, since biological systems typically lose energy over time, through metabolic processes or to the environment.

The researchers are optimistic that their findings could be applicable to the study of other biological systems. According to Dr. Ahamed, “people generally don’t think that living organisms can be mathematically modelled, but there’s a finite number movements that any animal can make and there’s a measurable probability that they’ll make certain movements over others. We’re now at the stage where we can find mathematical frameworks. Next, we’ll develop equations and models to explain these frameworks.”  [APBN]