elf-Replicating Chemical Spots

Chemical patterns formation

The seminal paper "The chemical basis for morphogenesis" by Alan Turing planted in the imagination of scientists the idea that spontaneous patterns can form in chemical systems. Turing proposed chemical pattern formation as the mechanism by which a fertilized egg organizes into a complex organism. While this idea no longer seems feasible, chemical reaction-diffusion systems still provide a robust testing ground for the study of chemical pattern formation and of other chemical instabilities which may find biological relevance and which deepen our understanding of the laws of nature far from equilibrium, where life occurs. At the CNLD we study chemical pattern formation in a variety of chemical systems. Different chemical reaction kinetics, boundary conditions and diffusion give rise to different patterns of chemical concentration; spirals, stripes, rhombiods, hexagons, dividing spots, and labyrinths are examples of the patterns observed. Current research focuses on oscillatory chemical patterns which resonate with the oscillations of a time-periodic external stimulus. Such studies contribute to our understanding of how the heart and other spatially extended periodic systems respond to periodic forcing.

In his classic 1952 paper, Turing suggested a possible connection between patterns in biological systems and patterns that could form spontaneously n chemical reaction-diffusion systems. Turing's analysis stimulated considerable theoretical research on mathematical models of pattern formation, but Turing-type patterns were not observed in controlled laboratory experiments until 1990. Subsequently there has been a renewed interest in chemical pattern formation and in the relationship of chemical patterns to the remarkably similar patterns observed in diverse physical and biological systems. Numerical simulations of a simple model chemical system have recently revealed spot patterns that undergo a continuous process of `birth' through replication and `death' through overcrowding. Here we report the observation of a similar phenomenon in laboratory experiments on the ferrocyanide-iodate-sulphite reaction. Repeated growth and replication can be observed for a wide range of experimental parameters, and can be reproduced by a simple two-species model, suggesting that replicating spots may occur in many reaction-diffusion systems.

Fig. 1: The upper row of images shows the evolution of a chemical pattern observed in a laboratory experiment, and the lower row shows similar behavior found in a numerical simulation of a reaction-diffusion model. In the experiment, blue (red) represents a state of high (low) pH, and the domain size is 7 mm x 7 mm.

Fig. 2: Sequences showing the transition from a spot to an annulus in the experiments and simulations. The parameter values are the same as in Fig. 1.