Researchers at the Okinawa Institute of Science and Technology (OIST) in Japan have identified the first known example of hyperdisorder occurring in a biological system. This phenomenon combines order at the microscopic scale with disorder at the macro level, and it is often present in systems studied in statistical physics. However, the researchers were surprised to observe it while monitoring the development of pigment cells in squid skin. As the hyperdisorder is directly linked to the squid’s growth, the researchers say the discovery could shed light on the physics of growing structures.
In inanimate objects, the emergence of disordered patterns is relatively well understood in physical terms. Living creatures are different, however, as they can display unexpected phenomena as they grow and develop.
To better understand how growth impacts the formation of patterns, a team led by Robert Ross, Simone Pigolotti and Sam Reiter at OIST studied how pigment cells known as chromatophores arrange themselves on the skin of squid as the animal grows and its skin expands. “These pigment cells are important because they play an essential role in camouflage and communication for these animals,” Reiter explains.
Highly unusual statistical patterns
The researchers took a series of 3D optical images of the squid over a period of three months. These observations revealed that the chromatophores behave very differently from other disordered structures. “The chromatophores appear at fixed positions in relation to one another, in a specific pattern,” Reiter explains.
It is this pattern that met the technical criteria for hyperdisorder, which is defined as occurring when the variation in the number of points within a particular measured space increases more rapidly than the volume of that space.
In the squid he and his colleagues studied, Ross explains that new chromatophores appear only at a minimum exclusion distance from pre-existing ones as the animal grows. “We found that this rule coupled with tissue growth leads to the highly unusual statistical patterns we observe,” he says. “Simply put, when you observe a tiny area in a system, it may appear quite ordered, but when viewed at larger scales, it becomes more disordered.”
To explain this finding, the researchers modelled squid development as static circle packing on a growing surface and showed how the hyperdisordered behaviour emerges. “The result is exciting because it highlights the importance of growth on physical properties,” Ross says.
A general feature of many biological structures?
The researchers note that other growing systems, such as the cells in chicken retinas, often display the exact opposite property, which is known as hyperuniformity. In these systems, there is long-range order and patterning despite randomness at a close scale, Ross explains. Such behaviour is thought to provide optimal retinal coverage properties for vision. “This is what we thought we would see in the squid, but what we actually observed was quite different and we have not yet seen any other instances of this packing behaviour in biology,” he says.
The mechanisms described in this work, which is detailed in Physical Review X, may be common in growing, dense natural systems, says Ross: “Indeed, this simple type of growth combined with distance-limited cell insertion might be a general feature of many biological structures.”
Spurred on by their findings, the researchers plan to continue working on a variety of theoretical and experimental systems related to the physics of growing structures. “These include both growing brains and pattern formation in fish,” says Ross. “We hope these systems will provide further examples of the novel physics of growing systems,” he tells Physics World.
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