The research could shed important new light on the fundamental biology of how patterns form in nature.

The project is funded by the Swindon-based Engineering and Physical Sciences Research Council. The work is being carried out at the University of Oxford, led by Dr. Andrew Wathen in the Computing Laboratory and Professor Philip Maini in the Centre for Mathematical Biology.

The researchers are developing a model to describe the distribution of “morphogens” in the wing of a butterfly. Morphogens are chemicals which are hypothesized to induce cells to become pigmented, often leading to striking patterns.

To model the distribution and movement of morphogens in a butterfly’s wing, the researchers are using a “moving grid finite element” technique.

Conventional finite element analysis is a widely used method in engineering in which a structure is divided or “discretized” into a grid of interconnected cells or elements. If one cell is subjected to particular conditions, the effect on neighboring cells and on the structure as a whole can be calculated.

However, while effective for structures with a fixed shape, the technique is less well suited to discretization of a growing organism, which is constantly expanding and changing shape.

The use of “moving grids” enables the technique of finite element analysis to be applied to such deforming geometries.

The two dimensional shape of the growing butterfly’s wing can be discretized in this way. Initially, the morphogen is distributed uniformly across the surface of the structure.

“If the distribution of the morphogen remained uniform, no patterning would be seen,” says Dr. Wathen. “The key to forming a pattern is to introduce some form of instability into the system.”

This is achieved by allowing the morphogen to diffuse.

“If one includes the effect of diffusion in a system that has stable morphogen kinetics, then so called “Turing instability” arises, in which any small disturbance to an initial state causes the morphogen to redistribute itself across the wing, forming “contours” of concentration, with ridges and furrows of high and low concentration and thus creating patterns,” says Dr. Wathen.

“What we are finding is that for a given set of initial parameters, crucially the shape of the wing, it does not matter what form the small perturbation takes. You find you end up with a similar pattern.”

Interestingly, by introducing growth and expansion into the models, the final pattern is even less sensitive to other potentially interfering factors.

“We are not entirely sure why this should be the case,” says Dr. Wathen. “The results of the simulation show that with growth in the system we can vary the parameters much more but still end up with a similar final pattern.”

The researchers hope that the work will give developmental biologists a greater insight into the fundamental mechanisms of the formation of patterns in growing organisms, and how this can ultimately be related back to the organism’s genetic code.

04-Sep-2001