Chemical pattern formation in three dimensions

Chemical pattern formation in three dimensions. Irving Epstein and his coworkers at Brandeis University in Waltham, Massachusetts, have shown that a chemical mechanism for producing patterns in two dimensions also works in three. Proposed in 1952 by Alan Turing, the mechanism relies on the competition between a slow-diffusing chemical that activates a reaction and a fast-diffusing chemical that inhibits the reaction. Nudging the reaction–diffusion system into a metastable state yields stable stripes, spots, and other periodic patterns. Turing’s analysis and its subsequent experimental confirmation was for two-dimensional systems. Although computer simulations suggest the mechanism also operates in 3D, proving it in the lab is challenging: The extra spatial dimension makes it difficult to see patterns inside the medium. To meet that challenge, the Brandeis team used optical tomography to view a medium made up of aqueous droplets embedded in oil. Turing’s model doesn’t ordinarily apply to such an inhomogeneous medium. However, by coating the droplets with a surfactant, the team ensured that the slow-diffusing activator and fast-diffusing inhibitor leaked in and out at rates that sustained pattern formation on scales larger than the droplets themselves. To monitor the system, the team rotated the reaction vessel (a quartz cylinder) in front of a camera that took a sequence of 2D images. Tomographic reconstruction of the system under different initial conditions revealed a gallery of structures, including the labyrinthine worms shown here. Epstein anticipates that the 3D version of Turing’s model may explain the formation of some biological patterns, such as the process by which Hydra regrows its tentacle-tipped head after decapitation. (T. Bánsági Jr, V. K. Vanag, I. R. Epstein, Science 331, 1309, 2011.)