Mathematical model for animal stripes
Summary:
The back of a tiger could have been a blank canvas. Instead,
nature painted the big cat with parallel stripes, evenly spaced and
perpendicular to the spine. Scientists don't know exactly how stripes develop,
but since the 1950s, mathematicians have been modeling possible scenarios. Now
researchers assemble a range of these models into a single equation to identify
what variables control stripe formation in living things.
This image shows simulations of
Turing stripes. On the left, stripes are evenly spaced, but their direction is
variable. On the right, a signaling gradient has made the stripes align in the
same direction.
Credit: Tom Hiscock
The back of a tiger could have been
a blank canvas. Instead, nature painted the big cat with parallel stripes,
evenly spaced and perpendicular to the spine. Scientists don't know exactly how
stripes develop, but since the 1950s, mathematicians have been modeling
possible scenarios. In Cell Systems on December 23, Harvard researchers
assemble a range of these models into a single equation to identify what
variables control stripe formation in living things.
"We wanted a very simple model
in hopes that it would be big picture enough to include all of these different
explanations," says 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 are surprisingly simple to
model mathematically (and much of the early work on the subject was by Alan
Turing of "The Imitation Game" fame). These patterns emerge when
interacting substances create waves of high and low concentrations of, for
example, a pigment, chemical, or type of cell. What Turing's model doesn't
explain is how stripes orient themselves in one particular direction.
Hiscock's investigation focused on
orientation--e.g., why tiger stripes are perpendicular to its body while
zebrafish stripes are horizontal. One surprise from his integrated model is
that it takes only a small change to the model to switch whether the stripes
are vertical or horizontal. What we don't know is how this translates to living
things--so, for a tiger, what is the variable that pushes the development of
perpendicular stripes?
"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 says. 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," he adds.
His master model predicts three main
perturbations that can affect how stripes orient: one is a change in
"production gradient," which would be a substance that amplifies
stripe pattern density; second is a change in "parameter gradient," a
substance that changes one of the parameters involved in forming the stripe;
and the last is a physical change in the direction of the molecular, cellular,
or mechanical origin of the stripe.
Although this paper is based in
theory, Hiscock believes that we are close to having the experimental tools
that can decipher whether the math holds true in living systems.
Story Source:
The above post is reprinted from materials provided by Cell
Press. Note: Materials may be edited for content and length.
