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Developmental biology - Physiology

Turing patterns in biology

New theory deepens our understanding of Alan Turing's patterns as they determine our physiology....

A team of researchers at the European Molecular Biology Laboratory (EMBL) have expanded Alan Turing's groundbreaking theory on how patterns are created in biological systems. Their work, partly done at the Centre for Genomic Regulation (CRG), may answer whether nature's patterns are governed by Alan Turing's 1952 mathematical model with application to modern tissue engineering. Their results are published in the June 20th issue of Physical Review X.
"From a contradiction, you can deduce everything."

Alan Turing, June 23, 1912 – June 7, 1954) English computer scientist, mathematician, logician, cryptanalyst, philosopher, and theoretical biologist.

Alan Turing was hired by the British government to help break German code during WWII. He did that and much more, laying the foundation for the development of modern computers. His mathmatical interests eventually led to the biology of morphogenesis - or what causes an organism to develop its physical shape, and in animals their patterns of coat color. Among other things, he wanted to know why Fibonacci numbers appeared in the arrangement of leaves on an axis (stem) of plants. The Fibonacci sequence of numbers is characterized by the fact that every number after the first two reflects the sum of the two preceding numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and do forth. Turing proposed that all of biological life is determined through a unique interaction between molecules as they spread into space and chemically interact with each other. His theory can be applied to biology as well as to astrophysics.

Many biological patterns emerge according to Turing's rules, but not with definitive proof they are governed by his theorem. Theoretical analysis also seemed to predict that Turing systems are essentially fragile, and therefore unlikely to co-exist within the rigorous laws of nature.

Going beyond Turing's theory

However, Xavier Diego, James Sharpe and colleagues from EMBL's new site in Barcelona, Spain analysed computational evidence and determined that Turing systems are much more flexible than previously thought. They expanded Turing's original theory using graph theory: a branch of mathematics which studies networks, making it easier to relate complex, realistic systems.
Using network topology - the structure of feedback between network components - they determined many fundamental properties within Turing's topological theory to unify many which had not been well understood. They explicitly defined what is required to make a successful Turing system.

A Turing system consist of an activator - that must diffuse at a much slower rate than an inhibitor - in order to produce a pattern. The majority of Turing models require a level of parameter fine-tuning that prevents them from being a robust mechanism for any real patterning process. "We learned that studying a Turing system through the topological lens really simplifies the analysis. For example, understanding the source of the diffusion restrictions becomes straightforward, and more importantly, we can easily see what modifications are needed to relax these restrictions," explains Xavier Diego, first author of the paper.

"Our approach can be applied to general Turing systems, and the properties will be true for networks with any number of components. We can now predict if the activity in two nodes in the network is in or out of phase, and we also found out which changes are necessary to switch this around. This allows us to build networks that make any desired pair of substances overlap in space, which could have interesting applications in tissue engineering."

Turing hieroglyphs for experimental groups

The researchers also provide a pictorial method that enables researchers to easily analyse existing networks or to come up with new network designs. "We call them 'Turing hieroglyphs' in the lab," says EMBL Barcelona group leader James Sharpe, who led the work. "By using these hieroglyphs, we hope that our methods will be adopted by both theoreticians and by experimental groups that are trying to implement Turing networks in biological cells."

This expanded theory provides experimental research groups with a new approach to making biological cells develop in patterns in the lab. If experimental groups are successful in this, the questions over whether Turing's theory of morphogenesis applies to biological systems will finally be answered.

Turing’s theory of pattern formation is a universal model for self-organization, applicable to many systems in physics, chemistry, and biology. Essential properties of a Turing system, such as the conditions for the existence of patterns and the mechanisms of pattern selection, are well understood in small networks. However, a general set of rules explaining how network topology determines fundamental system properties and constraints has not been found. Here we provide a first general theory of Turing network topology, which proves three key features of a Turing system are directly determined by its topology: (1) the type of restrictions that apply to the diffusion rates, (2) the robustness of the system, and (3) the phase relations of the molecular species.

Authors: Xavier Diego, Luciano Marcon, Patrick Müller, and James Sharpe.

About EMBL
EMBL is Europe's flagship laboratory for the life sciences. We are an intergovernmental organisation established in 1974 and are supported by over 20 member states.

EMBL performs fundamental research in molecular biology, studying the story of life. We offer services to the scientific community; train the next generation of scientists and strive to integrate the life sciences across Europe.

About the Centre for Genomic Regulation (CRG)
The Centre for Genomic Regulation (CRG) is an international biomedical research institute of excellence whose mission is to discover and advance knowledge for the benefit of society, public health and economic prosperity.

The CRG believes that the medicine of the future depends on the groundbreaking science of today. This requires an interdisciplinary scientific team focused on understanding the complexity of life from the genome to the cell to a whole organism and its interaction with the environment, offering an integrated view of genetic diseases.

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Jul 3, 2018   Fetal Timeline   Maternal Timeline   News   News Archive

EMBL scientists extend Turing's theory to help understand how biological patterns are created.
Image credit: Xavier Diego, EMBL.

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