###### August 3, 2014

# Turing Theory Explains The Formation Of Stripes, Spots, Fingers And Toes

**Rayshell Clapper for redOrbit.com - Your Universe Online**

Mathematics are a part of everything in life. Algebra explains how we open soda bottles while trigonometry helps us with building things. Even simple arithmetic helps us to balance our budgets. Now, as it turns out, we learn once more just how crucial math is in our lives.

According to a recent Center for Genomic Regulation (CRG) study, math can also explain biology, specifically in how fingers and toes form. The algorithm that explains finger growth is a direct result of the work of Alan Turing - who is most famous for Turing Test for artificial intelligence (AI). In addition to AI, Turing also had quite an impact on other technology such as computers. But AI and computers were not the only areas that Turing impacted; he also studied and proposed theories on biological math.In 1952, Turing wrote a paper that addressed how patterns form mathematically. He found that two molecules could start with no pattern (otherwise known as starting from a uniform condition) and then the two molecules could spontaneously self-organize into repetitive spatial patterns such as are seen in zebra stripes, ridges on sand dunes, or leopard spots. Though his theory could explain these patterns, for decades the theory has been resisted as an explanation for the formation of different structures like fingers. As it turns out, fingers are simply patterns of this nature.

Today, researchers from CRG have found that fingers and toes are patterned by a Turing Mechanism based on new data. The research team combined experimental work with computational modeling, which is collectively called a systems biology approach. "By screening for the expression of many different genes, they found that two signaling pathways stood out as having the required activity patterns: BMPs and WNTs. They gradually constructed the minimal possible mathematical model compatible with all the data, and found that the two signaling pathways were linked through a non-diffusible molecule – the transcription factor Sox9. Finally, they were able to make computational predictions about the effects of inhibiting these 2 pathways – either individually, or in combination – which predicted how the pattern of fingers should change. Strikingly, when the same experiments were done on small pieces of limb bud tissue cultured in a petri dish the same alterations in embryonic finger pattern were observed, confirming the computational prediction."

The Turing systems that explain the math behind the patterns of fingers and toes also allow for explanations of common polydactyl (extra fingers or toes) birth defects because they mathematically have slightly lower precision in regulating patterns than other theories. Furthermore, these findings also add another dimension to how the body's millions of cells arrange themselves. Prior to the CRG study, the primary thought was the "important traditional idea called positional information, proposed by Lewis Wolpert which states that cells know what to do because they all receive information about their "coordinates" in space (a bit like longitude and latitude on a world map)." But the CRG and Turing findings focus instead on how important self-organizing mechanisms are in how the cells know to arrange themselves.

The CRG study is pivotal in furthering the development of effective regenerative medicine as well as for increasing the potential of replacement tissues for organs. However, it also supports Turing's 62-year-old theory.

The researchers have published results of their study in the journal *Science*.

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