Supporting a 60 year old prediction for pattern formation

Six decades ago Alan Turing, the father of modern computer science, proposed a mathematical model to explain pattern formation during development. In our recently published paper in Science, we find biophysical support for Turing's model - the activator Nodal moves more slowly through the embryo than its inhibitor Lefty.

HFSP Long-Term Fellow Patrick Müller and Program Grant holders Alexander Schier and Sharad Ramanathan and colleagues
authored on Wed, 25 April 2012

In one of the most important papers in theoretical biology, Alan Turing proposed a mathematical model to explain how complex patterns, such as zebra stripes or leopard spots, emerge during development. In Turing’s model, two chemicals diffuse in the embryo and react with each other. Alfred Gierer and Hans Meinhardt later proposed that such a reaction-diffusion system consists of an activator that activates both itself and an inhibitor. The central tenet of the reaction-diffusion model is that the inhibitor must move more quickly through the tissue than the activator. The interactions between the slowly moving activator and the fast moving inhibitor can lead to a wide variety of patterns that re-capitulate those observed in nature (see Figure).

Figure: Some of the beautiful patterns that the reaction-diffusion model can generate.

We now find experimental support for the reaction-diffusion model. We analyzed a system of two proteins, the activator Nodal and the inhibitor Lefty, which regulate the development of organ precursor cells and asymmetry in vertebrates. To measure the biophysical properties of Nodal and Lefty, we made fluorescent versions of these proteins and observed that Lefty moved farther through zebrafish embryos than Nodal. We hypothesized that the difference in the range of Nodal and Lefty could be due to differences in the mobility or in the stability of these two proteins. To explore whether Nodal and Lefty might have different stabilities, we made fluorescent versions of Nodal and Lefty that can change color from green to red when photoconverted with a laser. By measuring how long it took for pulse-labeled red fluorescence to disappear, we were able to determine that Nodal and Lefty are similarly stable. In a separate test, we determined the diffusion coefficients of these proteins by “erasing” an area of fluorescent protein by photobleaching and then monitoring how long it took for the “erased” area to fill up with diffusing molecules. The results revealed that Lefty moves more quickly through the tissue than Nodal.

In summary, our experiments showed that Nodal is less diffusive than Lefty, supporting the central tenet of Turing’s reaction-diffusion model. Our publication coincides with Alan Turing’s 100th birthday and the 60th anniversary of his pioneering paper.


Differential diffusivity of Nodal and Lefty underlies a reaction-diffusion patterning system. Müller P, Rogers KW, Jordan BM, Lee JS, Robson D, Ramanathan S, Schier AF. Science (2012), DOI:10.1126/science.1221920 (2012).

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