Noise-stabilized Turing Patterns in a Synthetic Biofilm*

Deterministic Turing instabilities have been proposed to be a major source of pattern formation in biology, but have been hard to document rigorously, in part because of the requirement for a large ratio of the inhibitor to activator diffusion coefficient. A recently developed theory of stochastic Turing patterns predicts that stochastic or noise-stabilized Turing patterns occur over a larger region of parameter space and do not require as large a separation of diffusion rates. We apply this theory to a biofilm whose signaling molecules have been forward-engineered to exhibit activation and inhibition. Outside of the range of deterministic Turing patterns, we observe noise-stabilized patterns that exhibit a power spectrum power law tail with exponent $-2.3\pm.4$ consistent with theory. Our results are the first report of a spatial pattern in gene expression stabilized by copy number fluctuations.