Complex patterns in frustrated synchronization

Although best known for his roles in founding the field of computer science and in cracking the German Enigma cipher, Alan Turing also made a profound impact on developmental biology. In a 1952 paper, he proposed that a system of chemical substances that react together and diffuse through a tissue could account for morphogenesis—the differentiation of identical cells to form patterns and structures, such as our off-center hearts, zebra stripes, and the formation of fingers and toes. In 2014 Seth Fraden and colleagues at Brandeis University experimentally tested Turing’s model in rings of coupled microdroplets undergoing the famous oscillating Belousov–Zhabotinsky chemical reaction. Brandeis’s Bulbul Chakraborty and her colleagues have now traced the roots of the observed complex spatiotemporal patterns. The theorists worked with a well-studied oscillating reaction model that incorporates an activator and an inhibitor, and they applied it to “cells” arranged in a ring. They found that in the strongly coupled regime, fast inhibitor dynamics endow the cells with a robust preference to be 180° out of phase with their neighbors. But that phase configuration couldn’t be satisfied for rings containing an odd number of cells. Such geometric frustration arose first in a system of three cells, which either had all cells in phase or had one cell out of phase. A ring of five cells was even more interesting; it exhibited an explosion of complex synchronization patterns with overlapping regions of stability. One mode even featured cells oscillating at different frequencies. (D. Goldstein, M. Giver, B. Chakraborty, Chaos 25, 123109, 2015, doi:10.1063/1.4936246 .)