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.

The observed pattern depicts the evolution of morphogen concentrations over time, as illustrated in Plate 5.

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.

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.

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.