How the Leopard Gets Its Spots
A single pattern-formation mechanism could underlie the wide
variety of animal coat markings found in nature. Results from
the mathematical model open lines of inquiry for the biologist
by James D. Murray
ammals exhibit a remarkable
variety of coat patterns; the
variety has elicited a compa-
rable variety of explanations—many
of them at the level of cogency that
prevails in Rudyard Kipling's delight-
ful "How the Leopard Got Its Spots."
Although genes control the proces-
ses involved in coat pattern forma-
tion, the actual mechanisms that cre-
ate the patterns are still not known. It
would be attractive from the view-
point of both evolutionary and devel-
opmental biology if a single mech-
anism were found to produce the
enormous assortment of coat pat-
terns found in nature.
I should like to suggest that a single
pattern-formation mechanism could
in fact be responsible for most if not
all of the observed coat markings. In
this article I shall briefly describe a
simple mathematical model for how
these patterns may be generated in
the course of embryonic develop-
ment. An important feature of the
model is that the patterns it generates
bear a striking resemblance to the
patterns found on a wide variety of
animals such as the leopard, the
cheetah, the jaguar, the zebra and
the giraffe. The simple model is also
consistent with the observation that
although the distribution of spots on
members of the cat family and of
stripes on zebras varies widely and
is unique to an individual, each kind
of distribution adheres to a general
theme. Moreover, the model also pre-
dicts that the patterns can take only
certain forms, which in turn implies
the existence of developmental con-
straints and begins to suggest how
coat patterns may have evolved.
It is not clear as to precisely what
happens during embryonic develop-
ment to cause the patterns. There are
now several possible mechanisms
that are capable of generating such
patterns. The appeal of the simple
80
model comes from its mathematical
richness and its astonishing ability
to create patterns that correspond to
what is seen. I hope the model will
stimulate experimenters to pose rele-
vant questions that ultimately will
help to unravel the nature of the bio-
logical mechanism itself.
ome facts, of course, are known
about coat patterns. Physically,
spots correspond to regions of differ-
ently colored hair. Hair color is deter-
mined by specialized pigment cells
called melanocytes, which are found
in the basal, or innermost, layer of
the epidermis. The melanocytes gen-
erate a pigment called melanin that
then passes into the hair. In mam-
mals there are essentially only two
kinds of melanin: eumelanin, from
the Greek words eu (good) and
melas (black), which results in black
or brown hairs, and phaeomelanin,
from phaeos (dusty), which makes
hairs yellow or reddish orange.
It is believed that whether or not
melanocytes produce melanin de-
pends on the presence or absence of
chemical activators and inhibitors.
Although it is not yet known what
those chemicals are, each observed
coat pattern is thought to reflect
an underlying chemical prepattern.
The prepattern, if it exists, should re-
side somewhere in or just under the
epidermis. The melanocytes are
thought to have the role of "reading
out" the pattern. The model I shall
describe could generate such a
prepattern.
My work is based on a model de-
veloped by Alan M. Turing (the in-
ventor of the Turing machine and the
founder of modern computing sci-
ence). In 1952, in one of the most im-
portant papers in theoretical biology,
Turing postulated a chemical mecha-
nism for generating coat patterns. He
suggested that biological form fol-
lows a prepattern in the concentra-
tion of chemicals he called
morpho-gens. The existence of
morphogens is still largely
speculative, except for
circumstantial evidence, but Turing's
model remains attractive because it
appears to explain a large number of
experimental results with one or two
simple ideas.
Turing began with the assumption
that morphogens can react with one
another and diffuse through cells. He
then employed a mathematical model
to show that if morphogens react and
diffuse in an appropriate way, spatial
patterns of morphogen con-
centrations can arise from an initial
uniform distribution in an assem-
blage of cells. Turing's model has
spawned an entire class of models
that are now referred to as
reaction-diffusion models. These
models are applicable if the scale of
the pattern is large compared with the
diameter of an individual cell. The
models are applicable to the leopard's
coat, for instance, because the
number of cells in a leopard spot at
the time the pattern is laid down is
probably on the order of 100.
Turing's initial work has been
developed by a number of investi-
gators, including me, into a more
complete mathematical theory. In a
typical reaction-diffusion model one
starts with two morphogens that can
react with each other and diffuse at
varying rates. In the absence of dif-
fusion—in a well-stirred reaction,
for example—the two morphogens
would react and reach a steady uni-
form state. If the morphogens are
now allowed to diffuse at equal rates,
any spatial variation from that steady
state will be smoothed out. If, however,
the diffusion rates are not equal,
LEOPARD reposes. Do mathematical as
well as genetic rules produce its spots?
M
S
