How did the Zebra acquire its beautiful stripes? Alan Turing, a mathematician and computer scientist may have the answer. – DNyuz

How did the zebra get its nicely patterned stripes? The answer may come from mathematician Alan Turing.

Patterns on animal skin, such as zebra stripes and poison frog color patches, serve various biological functions, including temperature regulation, camouflage, and warning signals. These patterns are only effective if the colors used in them are distinct and clearly separated. As a warning, for example, the distinct colors will make it clear to animals. And as camouflage, well-separated colors allow animals to better blend into their surroundings.

In our recently published research in Science Advances my student Ben Alessio, and I proposed a potential mechanisms that explain how these distinct patterns form. This could be used for medical diagnostics or synthetic materials.

A thought experiment can help visualize the challenge of achieving distinctive color patterns. Imagine adding blue and red color to water. The drops will slowly disperse throughout the water due to the process of diffusion, where molecules move from an area of higher concentration to lower concentration. The water eventually will be purple and have a uniform concentration of dyes. Thus, diffusion tends to create color uniformity.

A question naturally arises: How can distinct color patterns form in the presence of diffusion?

Movement and boundaries

Mathematician Alan Turing first addressed this question in his seminal 1952 paper, “The Chemical Basis of Morphogenesis.” Turing showed that under appropriate conditions, the chemical reactions involved in producing color can interact with each other in a way that counteracts diffusion. Turing patterns are formed when colors self-organize to create regions of different color that connect together.

However, in mathematical models, the boundaries between color regions are fuzzy due to diffusion. This is unlike in nature, where boundaries are often sharp and colors are well separated.

Our team thought a clue to figuring out how animals create distinctive color patterns could be found in lab experiments on micron-sized particles, such as the cells involved in producing the colors of an animal’s skin. My work and work from other labs found that micron-sized particles form banded structures when placed between a region with a high concentration of other dissolved solutes and a region with a low concentration of other dissolved solutes.

In the context of this thought experiment, changes to the concentrations of red and blue dyes can cause other particles within the liquid’s fluid to move towards certain directions. The red dye will move into an area with a low concentration and carry nearby particles along. Diffusiophoresis is the name of this phenomenon.

You benefit from diffusiophoresis whenever you do your laundry: Dirt particles move away from your clothing as soap molecules diffuse out from your shirt and into the water.

Drawing sharp boundaries

We wondered whether Turing patterns composed of regions of concentration differences could also move micron-sized particles. Would the patterns that result from particles of this size be clear and not fuzzy if so?

To address this question we ran computer simulations using Turing patterns, including hexagons and stripes. We also tested double spots and even double spots. The diffusiophoresis models were able replicate intricate patterns found on boxfish skin and the jewel moray-eel’s. This is not possible with Turing’s theory.

Further supporting our hypothesis, our model was able to reproduce the findings of a lab study on how the bacterium E. coli moves molecular cargo within themselves. Diffusiophoresis resulted in sharper movement patterns, confirming its role as a physical mechanism behind biological pattern formation.

Because the cells that produce the pigments that make up the colors of an animal’s skin are also micron-sized, our findings suggest that diffusiophoresis may play a key role in creating distinctive color patterns more broadly in nature.

Learning nature’s trick

Understanding how nature programs specific functions can help researchers design synthetic systems that perform similar tasks.

Lab experiments have shown that scientists can use diffusiophoresis to create membrane-less water filters and low-cost drug development tools.

Our work suggests that combining the conditions that form Turing patterns with diffusiophoresis could also form the basis of artificial skin patches. When Turing patterns, such as hexagons or stripes, change they indicate underlying chemical differences inside and outside of the body.

Skin patches that can sense these changes could diagnose medical conditions and monitor a patient’s health by detecting changes in biochemical markers. The skin patches can also detect changes in concentrations of toxic chemicals.

The work ahead

Our simulations exclusively focused on spherical particles, while the cells that create pigments in skin come in varying shapes. The effect of shape on the formation of intricate patterns remains unclear.

Furthermore, pigment cells move in a complicated biological environment. More research is needed to understand how that environment inhibits motion and potentially freezes patterns in place.

Besides animal skin patterns, Turing patterns are also crucial to other processes such as embryonic development and tumor formation. Diffusiophoresis could play a crucial but under-appreciated role in the natural process of tumor formation and embryonic development.

Studying how biological patterns form will help researchers move one step closer to mimicking their functions in the lab — an age-old endeavor that could benefit society.

Ankur Gupta is an assistant professor of chemical and biological engineering at the University of Colorado Boulder.

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