Updating Turing's model of pattern formation

Date:
August 7, 2020
Source:
Springer
Summary:
New research revisits the Turing instability mechanism; proving
mathematically how the instabilities which give rise to patterns can
occur through simple reactions, and in widely varied environmental
conditions.



FULL STORY ==========================================================================
In 1952, Alan Turing published a study which described mathematically
how systems composed of many living organisms can form rich and diverse
arrays of orderly patterns. He proposed that this 'self-organisation'
arises from instabilities in un-patterned systems, which can form as
different species jostle for space and resources. So far, however,
researchers have struggled to reproduce Turing patterns in laboratory conditions, raising serious doubts about its applicability. In a new
study published in EPJ B, researchers led by Malbor Asllani at the
University of Limerick, Ireland, have revisited Turing's theory to prove mathematically how instabilities can occur through simple reactions,
and in widely varied environmental conditions.


==========================================================================
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.


========================================================================== Story Source: Materials provided by Springer. Note: Content may be edited
for style and length.


========================================================================== 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 ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2020/08/200807111942.htm

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