Section 2
Table of Contents
Section 4
3. Pigmentation patterns in seashells
A variant of the reaction-diffusion model proposed by Gierer and Meinhardt
[Gie1972] (see also [Mei1982]) was adopted by
Meinhardt [Mei1984] and
Meinhardt and Klinger [Mei1987a, Mei1987b] to capture pigmentation
patterns in seashells. In this case, the reacting substances (called the
activator and substrate or the activator and inhibitor, depending on the
variant of the model) diffuse in one dimension, along the growing edge of
the shell. One possible set of equations describing this process is shown
in Plate 4 (see caption). The observed pattern depicts
the evolution of morphogen concentrations over time, as illustrated in Plate 5 (see caption). The image on the left shows the
distribution of the areas of low and high concentration of the activator in
a plane with time progressing from the top of the image down. After an
initial period, a stable pattern of areas with low and high concentrations
develops, resulting in a series of parallel lines. In a real shell, the
growing edge is curved. A stable distribution of regions with low and high
concentration of the activator along the edge results in a series of
stripes perpendicular to the growing edge, as shown in the hypothetical
shell on the right side of Plate 5 (see caption). Using a different set of
parameters, the model can produce a pattern that is not stable over time,
but oscillates. If all points along the growing edge are in the same state
of activation at the same time, the pattern consists of a sequence of
stripes parallel to the growing edge of the shell, as shown in Plate 6 (see caption). Here the shell on the left side of
the picture is a digitized image, and the one on the right is a model. By
further modifying the values of parameters, the model can enter a mode in
which some points of the growing edge are in a stable state of high
concentration of the activator, producing lines perpendicular to the
growing edge of the shell, while some other points oscillate. This is
illustrated by the model of the Bednall's volute shell shown in Plate 7 (see caption).
Section 2
Table of Contents
Section 4