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Contributed by Nigel Goldenfeld, May 9, 2018 (sent for review November 29, 2017; reviewed by Raymond E. Goldstein, Eric Klavins, and Ehud Meron)
Significance
In 1952, Alan Turing proposed that biological morphogenesis could arise from a dynamical process in reaction systems with a rapidly diffusing inhibitor and a slowly diffusing activator. Turing’s conditions are disappointingly hard to achieve in nature, but recent stochastic extension of the theory predicts pattern formation without such strong conditions. We have forward-engineered bacterial populations with signaling molecules that form a stochastic activator–inhibitor system that does not satisfy the classic Turing conditions but exhibits disordered patterns with a defined length scale and spatial correlations that agree quantitatively with stochastic Turing theory. Our results suggest that Turing-type mechanisms, driven by gene expression or other source of stochasticity, may underlie a much broader range of patterns in nature than currently thought.
Abstract
The origin of biological morphology and form is one of the deepest problems in science, underlying our understanding of development and the functioning of living systems. In 1952, Alan Turing showed that chemical morphogenesis could arise from a linear instability of a spatially uniform state, giving rise to periodic pattern formation in reaction–diffusion systems but only those with a rapidly diffusing inhibitor and a slowly diffusing activator. These conditions are disappointingly hard to achieve in nature, and the role of Turing instabilities in biological pattern formation has been called into question. Recently, the theory was extended to include noisy activator–inhibitor birth and death processes. Surprisingly, this stochastic Turing theory predicts the existence of patterns over a wide range of parameters, in particular with no severe requirement on the ratio of activator–inhibitor diffusion coefficients. To explore whether this mechanism is viable in practice, we have genetically engineered a synthetic bacterial population in which the signaling molecules form a stochastic activator–inhibitor system. The synthetic pattern-forming gene circuit destabilizes an initially homogenous lawn of genetically engineered bacteria, producing disordered patterns with tunable features on a spatial scale much larger than that of a single cell. Spatial correlations of the experimental patterns agree quantitatively with the signature predicted by theory. These results show that Turing-type pattern-forming mechanisms, if driven by stochasticity, can potentially underlie a broad range of biological patterns. These findings provide the groundwork for a unified picture of biological morphogenesis, arising from a combination of stochastic gene expression and dynamical instabilities.
Footnotes
↵1D.K., K.M.M., and T.L. contributed equally to this work.
- ↵2To whom correspondence may be addressed. Email: nigel{at}illinois.edu or rweiss{at}mit.edu.
Author contributions: D.K., K.M.M., T.L., N.G., and R.W. designed research; D.K., K.M.M., T.L., N.G., and R.W. performed research; D.K., T.L., and R.W. contributed new reagents/analytic tools; D.K., K.M.M., T.L., N.A.D., N.G., and R.W. analyzed data; D.K., K.M.M., T.L., N.A.D., N.G., and R.W. wrote the paper.
Reviewers: R.E.G., University of Cambridge; E.K., University of Washington; and E.M., Ben-Gurion University, Blaustein Institutes for Desert Research.
The authors declare no conflict of interest.
Data deposition: The DNA sequences of plasmids reported in this paper have been deposited in the GenBank database (accession nos. MH300673–MH300677).
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1720770115/-/DCSupplemental.
Published under the PNAS license.
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Stochastic Turing patterns in a synthetic bacterial population
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