The team's results could help biologists to better understand the origins of many ordered structures in nature, from spots and stripes on animal coats, to clusters of vegetation in arid environments. In Turing's original model, he introduced two diffusing chemical species to different points on a closed ring of cells. As they diffused across adjacent cells, these species 'competed' with each other as they interacted; eventually organising to form patterns. This pattern formation depended on the fact that the symmetry during this process could be broken to different degrees, depending on the ratio between the diffusion speeds of each species; a mechanism now named the 'Turing instability.' However, a significant drawback of Turing's mechanism was that it relied on the unrealistic assumption that many chemicals diffuse at different paces.

Through their calculations, Asllani's team showed that in sufficiently large rings of cells, where diffusion asymmetry causes both species to travel in the same direction, the instabilities which generate ordered patterns will always arise -- even when competing chemicals diffuse at the same rate. Once formed, the patterns will either remain stationary, or propagate steadily around the ring as waves. The team's result addresses one of Turing's key concerns about his own theory, and is an important step forward in our understanding of the innate drive for living systems to organise themselves.

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Journal Reference:

1. Malbor Asllani, Timoteo Carletti, Duccio Fanelli, Philip K. Maini. A universal route to pattern formation in multicellular systems. The European Physical Journal B, 2020; 93 (7) DOI: 10.1140/epjb/e2020-10206-3