Plants And Animals

# Mathematical Model Shows What Makes Some Animals Have A Certain Pattern Of Stripes

Researchers have assembled a range of mathematical models into a single equation to identify what variables control stripes formation in animals like tiger.

Since the 1950s, scientists have been trying to model possible scenarios why some animals have certain patterns of stripes. For example, instead of having just a black canvas, tigers have parallel stripes that are evenly spaced and perpendicular to the spine. In quest for the answer, researchers from Harvard Medical School have assembled a range of models into a single equation to identify what variables control stripe formation in some animals.

“We wanted a very simple model in hopes that it would be big picture enough to include all of these different explanations,” said lead author Tom Hiscock, a PhD student in Sean Megason’s systems biology lab at Harvard Medical School. “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 in animals emerge when interacting substances create waves of high and low concentrations of a pigment, chemical, or type of cell. While they are easy to model mathematically, the tough part is that Turing’s model doesn’t explain how they orient themselves in one particular direction.

The study, particularly for now, focused on orientation, so the researchers investigated why tiger stripes are perpendicular to its body while zebrafish stripes are horizontal. As one of the integrated model shows, it only takes a small change to the model to switch whether the stripes are vertical or horizontal. However, the answers to – how this translates to living things and the variable that pushes the development of perpendicular stripes in tiger – are not known yet.

“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,” said Hiscock. 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.”

As Hiscock’s master model predicts, three main perturbations can affect how the stripes in animals orient the way they do. They are:

1. A change in “production gradient,” which would be a substance that amplifies stripe pattern density.
2. A change in “parameter gradient,” a substance that changes one of the parameters involved in forming the stripe.
3. A physical change in the direction of the molecular, cellular, or mechanical origin of the stripe.

Tom Hiscock’s findings are published in the journal Cell Systems. Although his paper is based in theory, he believes they are close to having the experimental tools that can decipher whether the math holds true in living systems.

Hat Tip:

• Harvard Medical School – Mathematical Model For Animal Stripes
• Cell Press – Orientation of Turing-like Patterns by Morphogen Gradients and Tissue Anisotropies