Nav: Home

How to color a lizard: From biology to mathematics

April 12, 2017

From the clown fish to leopards, skin colour patterns in animals arise from microscopic interactions among coloured cells that obey equations discovered by the mathematician Alan Turing. Today, researchers at the University of Geneva (UNIGE), Switzerland, and SIB Swiss Institute of Bioinformatics report in the journal Nature that a southwestern European lizard slowly acquires its intricate adult skin colour by changing the colour of individual skin scales using an esoteric computational system invented in 1948 by another mathematician: John von Neumann. The Swiss team shows that the 3D geometry of the lizard's skin scales causes the Turing mechanism to transform into the von Neumann computing system, allowing biology-driven research to link, for the first time, the work of these two mathematical giants.

A multidisciplinary team of biologists, physicists and computer scientists lead by Michel Milinkovitch, professor at the Department of Genetics and Evolution of the UNIGE Faculty of Science, Switzerland and Group Leader at the SIB Swiss Institute of Bioinformatics, realised that the brown juvenile ocellated lizard (Timon lepidus) gradually transforms its skin colour as it ages to reach an intricate adult labyrinthine pattern where each scale is either green or black. This observation is at odd with the mechanism, discovered in 1952 by the mathematician Alan Turing, that involves microscopic interactions among coloured cells. To understand why the pattern is forming at the level of scales, rather than at the level of biological cells, two PhD students, Liana Manukyan and Sophie Montandon, followed individual lizards during 4 years of their development from hatchlings crawling out of the egg to fully mature animals. For multiple time points, they reconstructed the geometry and colour of the network of scales by using a very high resolution robotic system developed previously in the Milinkovitch laboratory.

Flipping from green to black

The researchers were then surprised to see the brown juvenile scales change to green or black, then continue flipping colour (between green and black) during the life of the animal. This very strange observation prompted Milinkovitch to suggest that the skin scale network forms a so-called 'cellular automaton'. This esoteric computing system was invented in 1948 by the mathematician John von Neumann. Cellular automata are lattices of elements in which each element changes its state (here, its colour, green or black) depending on the states of neighbouring elements. The elements are called cells but are not meant to represent biological cells; in the case of the lizards, they correspond to individual skin scales. These abstract automata were extensively used to model natural phenomena, but the UNIGE team discovered what seems to be the first case of a genuine 2D automaton appearing in a living organism. Analyses of the four years of colour change allowed the Swiss researchers to confirm Milinkovitch's hypothesis: the scales were indeed flipping colour depending of the colours of their neighbour scales. Computer simulations implementing the discovered mathematical rule generated colour patterns that could not be distinguished from the patterns of real lizards.

How could the interactions among pigment cells, described by Turing equations, generate a von Neumann automaton exactly superposed to the skin scales? The skin of a lizard is not flat: it is very thin between scales and much thicker at the center of them. Given that Turing's mechanism involves movements of cells, or the diffusion of signals produced by cells, Milinkovitch understood that this variation of skin thickness could impact on the Turing's mechanism. The researchers then performed computer simulations including skin thickness and saw a cellular automaton behaviour emerge, demonstrating that a Cellular Automaton as a computational system is not just an abstract concept developed by John von Neumann, but also corresponds to a natural process generated by biological evolution.

The need for a formal mathematical analysis

However, the automaton behaviour was imperfect as the mathematics behind Turing's mechanism and von Neumann automaton are very different. Milinkovitch called in the mathematician Stanislav Smirnov, Professor at the UNIGE, who was awarded the Fields Medal in 2010. Before long, Smirnov derived a so-called discretisation of Turing's equations that would constitute a formal link with von Neumann's automaton. Anamarija Fofonjka, a third PhD student in Milinkovitch's team implemented Smirnov new equations in computer simulations, obtaining a system that had become un-differentiable from a von Neumann automaton. The highly multidisciplinary team of researchers had closed the loop in this amazing journey, from biology to physics to mathematics ... and back to biology.


Université de Genève

Related Biology Articles:

A new tool to decipher evolutionary biology
A new bioinformatics tool to compare genome data has been developed by teams from the Max F.
Biology's need for speed tolerates a few mistakes
In balancing speed and accuracy to duplicate DNA and produce proteins, Rice University researchers find evolution determined that speed is favored much more.
How to color a lizard: From biology to mathematics
Skin color patterns in animals arise from microscopic interactions among colored cells that obey equations discovered by Alan Turing.
Behavioral biology: Ripeness is all
In contrast to other members of the Drosophila family, the spotted-wing fly D. suzukii deposits its eggs in ripe fruits.
A systems biology perspective on molecular cytogenetics
Professor Henry Heng's team, from the medical school at Wayne State University, has published a perspective article titled A Systems Biology Perspective on Molecular Cytogenetics to address the issue.
Cell biology: Take the mRNA train
Messenger RNAs bearing the genetic information for the synthesis of proteins are delivered to defined sites in the cell cytoplasm by molecular motors.
Gravitational biology
Akira Kudo at Tokyo Institute of Technology(Tokyo Tech) and colleagues report in Scientific Reports, December 2016, that live-imaging and transcriptome analysis of medaka fish transgenic lines lead to immediate alteration of cells responsible for bone structure formation.
Biology's 'breadboard'
Understanding how the nervous system of the roundworm C. elegans works will give insights into how our vastly more complex brains function and is the subject of a paper in Nature Methods.
The use of Camelid antibodies for structural biology
The use of Camelid antibodies has important implications for future development of reagents for diagnosis and therapeutics in diseases involving a group of enzymes called serine proteases.
Misleading images in cell biology
Virtually all membrane proteins have been reported to be organized as clusters on cell surfaces, when in fact many of them are just single proteins which have been counted multiple times.

Best Science Podcasts 2017

We have hand picked the best science podcasts for 2017. Sit back and enjoy new science podcasts updated daily from your favorite science news services and scientists.
Now Playing: Radiolab

Oliver Sipple
One morning, Oliver Sipple went out for a walk. A couple hours later, to his own surprise, he saved the life of the President of the United States. But in the days that followed, Sipple's split-second act of heroism turned into a rationale for making his personal life into political opportunity. What happens next makes us wonder what a moment, or a movement, or a whole society can demand of one person. And how much is too much?  Through newly unearthed archival tape, we hear Sipple himself grapple with some of the most vexing topics of his day and ours - privacy, identity, the freedom of the press - not to mention the bonds of family and friendship.  Reported by Latif Nasser and Tracie Hunte. Produced by Matt Kielty, Annie McEwen, Latif Nasser and Tracie Hunte. Special thanks to Jerry Pritikin, Michael Yamashita, Stan Smith, Duffy Jennings; Ann Dolan, Megan Filly and Ginale Harris at the Superior Court of San Francisco; Leah Gracik, Karyn Hunt, Jesse Hamlin, The San Francisco Bay Area Television Archive, Mike Amico, Jennifer Vanasco and Joey Plaster. Support Radiolab today at
Now Playing: TED Radio Hour

Future Consequences
From data collection to gene editing to AI, what we once considered science fiction is now becoming reality. This hour, TED speakers explore the future consequences of our present actions. Guests include designer Anab Jain, futurist Juan Enriquez, biologist Paul Knoepfler, and neuroscientist and philosopher Sam Harris.