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Tiger Stripes: Mathematical Models Explain Pattern, Orientation

Dec 27, 2015 09:45 PM EST
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New mathematical models help explain animal stripe orientation. For example, why a tiger's stripes are perpendicular to its body while zebrafish stripes are horizontal.
(Photo : Flickr: Tambako The Jaguar)

How did tigers and zebras get their stripes? Scientists have rattled their brains for years trying to provide an answer to this question. In a new study, however, Harvard researchers assembled a range of mathematical models into a single equation to determine what variables ultimately control these natural patterns. 

"We wanted a very simple model in hopes that it would be big picture enough to include all of these different explanations," Tom Hiscock, lead author and Ph.D. student in Sean Megason's systems biology lab at Harvard Medical School, explained in a news release. "We now get to ask what is common among molecular, cellular, and mechanical hypotheses for how living things orient the directions of stripes, which can then tell you what kinds of experiments will (or won't) distinguish between them."

Stripes are surprisingly simple to model mathematically, researchers say. Tigers, for example, have parallel stripes, evenly spaced and perpendicular to the spine. These natural patterns essentially emerge when interacting substances create waves of high and low concentrations of a pigment, chemical, or type of cell, for example. However this does not explain how stripes orient themselves in one particular direction. That's why Hiscock and his team investigated stripe orientation. 

Interestingly, researchers found only a small change to the model triggers whether stripes are vertical or horizontal, but they are unsure how it translates to all living things. 

"We can describe what happens in stripe formation using this simple mathematical equation, but I don't think we know the nitty-gritty details of exactly what molecules or cells are mapping the formation of stripes," Hiscock said, adding that genetic mutants exist that can't form stripes or make spots instead, such as in zebrafish, but "the problem is you have a big network of interactions, and so any number of parameters can change the pattern." 

To resolve this, researchers created a master model that predicts three main perturbations that can impact stripe orientation. The first is a change in "production gradient," which means a substance basically amplifies stripe pattern density. The second is a change in "parameter gradient," in which a substance changes one of the parameters involved in forming the stripe. The last is a physical change in the direction of the molecular, cellular, or mechanical origin of the stripe, researchers explained. 

While their findings, recently published in the journal Cell Systemsis based in theory, they can be used to verify whether the math holds true in living systems.

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